%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWW205+1 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jul 27 13:22:07 EDT 2022 % Result : Unknown 12.99s 12.88s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWW205+1 : TPTP v8.1.0. Released v5.2.0. % 0.00/0.12 % Command : otter-tptp-script %s % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Jul 27 03:03:17 EDT 2022 % 0.12/0.33 % CPUTime : % 12.93/12.80 ----- Otter 3.3f, August 2004 ----- % 12.93/12.80 The process was started by sandbox2 on n006.cluster.edu, % 12.93/12.80 Wed Jul 27 03:03:17 2022 % 12.93/12.80 The command was "./otter". The process ID is 10326. % 12.93/12.80 % 12.93/12.80 set(prolog_style_variables). % 12.93/12.80 set(auto). % 12.93/12.80 dependent: set(auto1). % 12.93/12.80 dependent: set(process_input). % 12.93/12.80 dependent: clear(print_kept). % 12.93/12.80 dependent: clear(print_new_demod). % 12.93/12.80 dependent: clear(print_back_demod). % 12.93/12.80 dependent: clear(print_back_sub). % 12.93/12.80 dependent: set(control_memory). % 12.93/12.80 dependent: assign(max_mem, 12000). % 12.93/12.80 dependent: assign(pick_given_ratio, 4). % 12.93/12.80 dependent: assign(stats_level, 1). % 12.93/12.80 dependent: assign(max_seconds, 10800). % 12.93/12.80 clear(print_given). % 12.93/12.80 % 12.93/12.80 formula_list(usable). % 12.93/12.80 all A (A=A). % 12.93/12.80 all V_gb_2 V_fa_2 ((all B_x (hAPP(V_fa_2,B_x)=hAPP(V_gb_2,B_x)))->V_fa_2=V_gb_2). % 12.93/12.80 c_SEQ_Osubse_q(v_ga____). % 12.93/12.80 c_SEQ_Osubse_q(v_f____). % 12.93/12.80 c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))). % 12.93/12.80 c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))). % 12.93/12.80 -(all B_g (c_SEQ_Osubse_q(B_g)-> -c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))))). % 12.93/12.80 all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n)),v_r). % 12.93/12.80 exists B_f (c_SEQ_Osubse_q(B_f)&c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,v_s),B_f))). % 12.93/12.80 c_Lim_OisUCont(tc_Complex_Ocomplex,tc_RealDef_Oreal,c_Complex_ORe). % 12.93/12.80 all V_k_2 V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)->c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))))). % 12.93/12.80 all V_k_2 V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))->c_SEQ_OBse_q(T_a,V_X_2))). % 12.93/12.80 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2))<->c_SEQ_OBse_q(T_a,V_X_2))). % 12.93/12.80 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)->c_SEQ_OBse_q(T_a,V_X_2))). % 12.93/12.80 exists B_f (c_SEQ_Osubse_q(B_f)&c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,v_s),v_f____),B_f))). % 12.93/12.80 all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,hAPP(v_s,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.80 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),v_r). % 12.93/12.80 c_Lim_OisUCont(tc_Complex_Ocomplex,tc_RealDef_Oreal,c_Complex_OIm). % 12.93/12.80 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.80 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Omonose_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))))| (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))). % 12.93/12.80 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.80 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.80 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.80 all V_x (hAPP(c_Complex_OIm,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x))). % 12.93/12.80 all V_x (hAPP(c_Complex_ORe,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x))). % 12.93/12.80 all V_X_2 (c_SEQ_OCauchy(tc_Complex_Ocomplex,V_X_2)->c_SEQ_OCauchy(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2))). % 12.93/12.80 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_SEQ_Omonose_q(T_a,V_a_2)->c_SEQ_Omonose_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))). % 12.93/12.80 all V_fa_2 V_X_2 T_a (class_RealVector_Ometric__space(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)-> (c_SEQ_Osubse_q(V_fa_2)->c_SEQ_OCauchy(T_a,c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,V_fa_2))))). % 12.93/12.80 all V_X_2 (c_SEQ_OCauchy(tc_Complex_Ocomplex,V_X_2)->c_SEQ_OCauchy(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2))). % 12.93/12.80 all V_y V_x (hAPP(c_Complex_ORe,V_x)=hAPP(c_Complex_ORe,V_y)-> (hAPP(c_Complex_OIm,V_x)=hAPP(c_Complex_OIm,V_y)->V_x=V_y)). % 12.93/12.80 all V_y_2 V_x_2 (V_x_2=V_y_2<->hAPP(c_Complex_ORe,V_x_2)=hAPP(c_Complex_ORe,V_y_2)&hAPP(c_Complex_OIm,V_x_2)=hAPP(c_Complex_OIm,V_y_2)). % 12.93/12.80 all V_y V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))). % 12.93/12.80 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.80 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))). % 12.93/12.80 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r). % 12.93/12.80 all V_m V_l V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_l)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_m)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_l)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_y),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_m))))). % 12.93/12.80 all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.80 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))). % 12.93/12.80 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)&c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2))). % 12.93/12.80 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)))). % 12.93/12.80 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b))). % 12.93/12.80 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.80 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 12.93/12.80 hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.80 hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.80 hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.80 all V_r (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)). % 12.93/12.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.80 all V_a_2 V_x_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=V_a_2). % 12.93/12.80 all V_y_2 V_x_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_y_2=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2)). % 12.93/12.80 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x))). % 12.93/12.80 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2))). % 12.93/12.80 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2),V_y_2)). % 12.93/12.80 all V_n_2 V_fa_2 (c_SEQ_Osubse_q(V_fa_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2))). % 12.93/12.80 all V_y V_x (hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))). % 12.93/12.80 all V_y V_x (hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))). % 12.93/12.80 hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.80 all V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.80 all V_z V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))). % 12.93/12.80 all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)->V_b=V_c)). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)). % 12.93/12.81 all V_c_2 V_a_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)<->V_b_2=V_c_2)). % 12.93/12.81 all V_c_2 V_b_2 V_a_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)<->V_b_2=V_c_2)). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))). % 12.93/12.81 all V_x_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_a))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)<->V_a_2=V_b_2)). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=V_b_2<->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)=V_a_2)). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)<->V_b_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))). % 12.93/12.81 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=V_a). % 12.93/12.81 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)->V_z=V_w)). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k))). % 12.93/12.81 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)). % 12.93/12.81 all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)). % 12.93/12.81 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a). % 12.93/12.81 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))). % 12.93/12.81 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))). % 12.93/12.81 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=V_a_2<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)<->c_Groups_Ozero__class_Ozero(T_a)=V_a_2)). % 12.93/12.81 all T_a (class_Groups_Ogroup__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))). % 12.93/12.81 all V_a_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),V_a_2))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=V_b). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))=V_b). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_RealVector_Onorm__class_Onorm(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=c_RealVector_Onorm__class_Onorm(T_a,V_x)). % 12.93/12.81 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))). % 12.93/12.81 all V_ra_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_ra_2),V_x_2)&c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_ra_2)). % 12.93/12.81 all V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a)). % 12.93/12.81 all V_y V_x (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_y)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_y),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)=V_b)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_y_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))). % 12.93/12.81 all V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 12.93/12.81 all V_X_2 V_fa_2 T_a T_b (class_RealVector_Ometric__space(T_b)&class_RealVector_Ometric__space(T_a)-> (c_Lim_OisUCont(T_a,T_b,V_fa_2)-> (c_SEQ_OCauchy(T_a,V_X_2)->c_SEQ_OCauchy(T_b,c_COMBB(T_a,T_b,tc_Nat_Onat,V_fa_2,V_X_2))))). % 12.93/12.81 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))). % 12.93/12.81 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)). % 12.93/12.81 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)-> -(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))). % 12.93/12.81 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)). % 12.93/12.81 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))). % 12.93/12.81 all V_y V_z V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))). % 12.93/12.81 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,B_x),hAPP(V_gb_2,B_x))))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))). % 12.93/12.81 all V_x_2 V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_gb_2,V_x_2)))). % 12.93/12.81 all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))). % 12.93/12.81 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))). % 12.93/12.81 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))). % 12.93/12.81 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))). % 12.93/12.81 all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))). % 12.93/12.81 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))). % 12.93/12.81 all V_x_2 V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_gb_2,V_x_2)))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))). % 12.93/12.81 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)). % 12.93/12.81 all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))). % 12.93/12.81 all V_k V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2). % 12.93/12.81 all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))). % 12.93/12.81 all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n). % 12.93/12.81 all T_e T_d T_c T_a T_b V_x_H_2 V_g_H_2 V_f_H_2 V_x_2 V_gb_2 V_fa_2 (hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))->hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2)). % 12.93/12.81 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_n (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n). % 12.93/12.81 all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m). % 12.93/12.81 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 12.93/12.81 all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)). % 12.93/12.81 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))). % 12.93/12.81 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))). % 12.93/12.81 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))). % 12.93/12.81 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)<-> (exists B_n (V_l_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n)))). % 12.93/12.81 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))). % 12.93/12.81 all V_y V_x T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)))). % 12.93/12.81 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a). % 12.93/12.81 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a). % 12.93/12.81 all V_a_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)))))). % 12.93/12.81 all V_X_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<->c_SEQ_Oincse_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2)))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))). % 12.93/12.81 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)). % 12.93/12.81 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))). % 12.93/12.81 all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)<->V_x_2=V_y_2)). % 12.93/12.81 all V_x_2 V_A_2 T_b T_a (class_Groups_Ouminus(T_a)->hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2))). % 12.93/12.81 all V_x T_a (class_Lattices_Oboolean__algebra(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=V_x). % 12.93/12.81 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)->c_SEQ_Omonose_q(T_a,V_X_2))). % 12.93/12.81 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)->c_SEQ_Omonose_q(T_a,V_X_2))). % 12.93/12.81 all V_x_2 V_A_2 T_b T_a (class_Groups_Ouminus(T_a)->hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2))). % 12.93/12.81 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). % 12.93/12.81 all V_K_2 V_X_2 V_N_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> ((all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_N_2,B_n)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)))->c_SEQ_OBse_q(T_a,V_X_2))). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_x!=c_Groups_Ozero__class_Ozero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.81 all V_p_2 T_a (class_Groups_Ozero(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_p_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_SEQ_OBse_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)))). % 12.93/12.81 all V_x_2 V_fa_2 V_c_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,c_COMBK(T_a,T_b,V_c_2),V_fa_2),V_x_2)=V_c_2). % 12.93/12.81 all V_x_2 V_gb_2 V_fa_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_SEQ_Omonose_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)))). % 12.93/12.81 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x). % 12.93/12.81 all V_n V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a)). % 12.93/12.81 all V_n V_x T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all T_a (class_Groups_Osgn__if(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x))). % 12.93/12.81 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_h_2 V_gb_2 T_d V_fa_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2))=c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2)). % 12.93/12.81 all V_x_2 V_gb_2 V_fa_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))). % 12.93/12.81 all V_v_2 V_c_2 V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=V_c_2->hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,V_v_2)). % 12.93/12.81 all V_v_2 V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)->hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,hAPP(V_d_2,V_v_2))). % 12.93/12.81 all V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)-> (all B_v (hAPP(V_a_2,hAPP(V_b_2,B_v))=hAPP(V_c_2,hAPP(V_d_2,B_v))))). % 12.93/12.81 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))). % 12.93/12.81 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))). % 12.93/12.81 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n))=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.81 all V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_n_2 V_a_2 T_a (class_Power_Opower(T_a)&class_Rings_Omult__zero(T_a)&class_Rings_Ono__zero__divisors(T_a)&class_Rings_Ozero__ne_q__one(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a). % 12.93/12.81 all V_n V_a T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_n T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)). % 12.93/12.81 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)))). % 12.93/12.81 all V_x (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x)=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)))). % 12.93/12.81 all V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))). % 12.93/12.81 hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)))))). % 12.93/12.81 all V_c_2 T_a (class_RealVector_Ometric__space(T_a)->c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_RealVector_Oreal__algebra__1(T_a)-> (hAPP(c_RealVector_Oof__real(T_a),V_x_2)=hAPP(c_RealVector_Oof__real(T_a),V_y_2)<->V_x_2=V_y_2)). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)->c_SEQ_Oconvergent(T_a,c_COMBB(tc_RealDef_Oreal,T_a,tc_Nat_Onat,c_RealVector_Oof__real(T_a),V_X_2)))). % 12.93/12.81 all V_real2_H_2 V_real1_H_2 V_real2_2 V_real1_2 (c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)<->V_real1_2=V_real1_H_2&V_real2_2=V_real2_H_2). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->c_Lim_OisUCont(tc_RealDef_Oreal,T_a,c_RealVector_Oof__real(T_a))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))). % 12.93/12.81 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))). % 12.93/12.81 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))). % 12.93/12.81 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))). % 12.93/12.81 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))). % 12.93/12.81 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)). % 12.93/12.81 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))). % 12.93/12.81 all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))). % 12.93/12.81 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)). % 12.93/12.81 all V_xa_2 V_y_2 V_x_2 (c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_xa_2)<->V_x_2=V_xa_2&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 all V_r (hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)=c_Complex_Ocomplex_OComplex(V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 12.93/12.81 all V_y_2 V_x_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)))). % 12.93/12.81 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))). % 12.93/12.81 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))). % 12.93/12.81 all V_r V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_x,V_y)),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_r),V_y)). % 12.93/12.81 all V_y V_x V_r (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)),c_Complex_Ocomplex_OComplex(V_x,V_y))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_x),V_y)). % 12.93/12.81 all V_n V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_x)),V_n)=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&V_x_2!=V_y_2)). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2)). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))). % 12.93/12.81 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))). % 12.93/12.81 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))). % 12.93/12.81 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))). % 12.93/12.81 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)). % 12.93/12.81 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))). % 12.93/12.81 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))). % 12.93/12.81 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))). % 12.93/12.81 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))). % 12.93/12.81 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))). % 12.93/12.81 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))). % 12.93/12.81 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))). % 12.93/12.81 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))). % 12.93/12.81 all V_z (hAPP(c_Complex_ORe,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_z))=V_z). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),V_a_2))). % 12.93/12.81 all V_a_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)&V_x_2!=V_y_2). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2). % 12.93/12.81 all V_r T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(c_RealVector_Oof__real(T_a),V_r))=hAPP(c_RealVector_Oof__real(T_a),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r))). % 12.93/12.81 all V_y V_x (hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_x). % 12.93/12.81 all V_y V_x (hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_y). % 12.93/12.81 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))). % 12.93/12.81 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.81 all V_X_2 T_a (class_SEQ_Ocomplete__space(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)<->c_SEQ_Oconvergent(T_a,V_X_2))). % 12.93/12.81 all V_X_2 T_a (class_SEQ_Ocomplete__space(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)->c_SEQ_Oconvergent(T_a,V_X_2))). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Ometric__space(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)->c_SEQ_OCauchy(T_a,V_X_2))). % 12.93/12.81 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))). % 12.93/12.81 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.81 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.81 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))). % 12.93/12.81 all V_X_2 (c_SEQ_OCauchy(tc_RealDef_Oreal,V_X_2)->c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)). % 12.93/12.81 all V_Y_2 V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)-> (c_SEQ_Oconvergent(T_a,V_Y_2)->c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2))))). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)<->c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2)))). % 12.93/12.81 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.81 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_x_2 T_a (class_RealVector_Oreal__algebra__1(T_a)-> (hAPP(c_RealVector_Oof__real(T_a),V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 12.93/12.81 all V_z (hAPP(c_Complex_OIm,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_z))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),hAPP(c_RealVector_Oof__real(T_a),V_y))). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),hAPP(c_RealVector_Oof__real(T_a),V_y))). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(T_a)). % 12.93/12.81 all V_n V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),V_n)). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))). % 12.93/12.81 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x))). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->hAPP(c_RealVector_Oof__real(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x))). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))). % 12.93/12.81 all V_n_2 V_m_2 V_a_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)<->V_m_2=V_n_2))). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))<->V_a_2!=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)). % 12.93/12.81 all V_r T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),V_r))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)&c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2))). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.81 all V_z (c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z))=V_z). % 12.93/12.81 all V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)<->V_a_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_d V_c V_b V_a (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d))). % 12.93/12.81 all V_b V_a (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b))=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_b))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OCauchy(tc_RealDef_Oreal,V_X_2)->c_SEQ_OCauchy(T_a,c_COMBB(tc_RealDef_Oreal,T_a,tc_Nat_Onat,c_RealVector_Oof__real(T_a),V_X_2)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))). % 12.93/12.81 all V_X_2 (c_SEQ_OBse_q(tc_RealDef_Oreal,V_X_2)-> (c_SEQ_Omonose_q(tc_RealDef_Oreal,V_X_2)->c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2))). % 12.93/12.81 all V_a T_a (class_Groups_Oabs__if(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))& (-c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)). % 12.93/12.81 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))). % 12.93/12.81 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Oone__class_Oone(T_a)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a))). % 12.93/12.81 all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))))). % 12.93/12.81 all V_x ((V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). % 12.93/12.81 all V_a ((V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_a!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2))). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2),V_y_2)). % 12.93/12.81 all V_r ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_r))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=V_r)). % 12.93/12.81 all V_a ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=V_a)). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)). % 12.93/12.81 all V_x (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)). % 12.93/12.81 all V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)<->V_a_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 all V_fa_2 V_X_2 T_a (class_SEQ_Ocomplete__space(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)-> (c_SEQ_Osubse_q(V_fa_2)->c_SEQ_Oconvergent(T_a,c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,V_fa_2))))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.81 all V_y_2 V_x_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2)))). % 12.93/12.81 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)))). % 12.93/12.81 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Osgn__class_Osgn(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)))). % 12.93/12.81 all V_x T_a (class_Groups_Osgn__if(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a))& (V_x!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))))). % 12.93/12.81 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))). % 12.93/12.81 all V_real2 V_real1 (c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_real2 V_real1 (c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_k (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)& (exists B_x all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_X_2,B_n)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),B_x))),B_k)))))). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_k (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)& (exists B_N all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_X_2,B_n)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_X_2,B_N)))),B_k)))))). % 12.93/12.81 all V_real2_2 V_real1_2 V_f1_2 T_a (c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)). % 12.93/12.81 all V_real2_2 V_real1_2 V_f1_2 T_a (c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)). % 12.93/12.81 all V_x V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatceiling(V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). % 12.93/12.81 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 12.93/12.81 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)). % 12.93/12.81 all V_P_2 V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))). % 12.93/12.81 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n). % 12.93/12.81 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)). % 12.93/12.81 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))). % 12.93/12.81 all V_n_2 V_m_2 (V_m_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)). % 12.93/12.81 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)). % 12.93/12.81 all V_m_2 V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)<->V_n_2=V_m_2). % 12.93/12.81 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2,V_fa_2))). % 12.93/12.81 all V_n V_m (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))). % 12.93/12.81 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)). % 12.93/12.81 all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))<->V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_x (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x)). % 12.93/12.81 all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))). % 12.93/12.81 all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)). % 12.93/12.81 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)). % 12.93/12.81 all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))). % 12.93/12.81 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))). % 12.93/12.81 all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))). % 12.93/12.81 all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))). % 12.93/12.81 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))). % 12.93/12.81 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_i)). % 12.93/12.81 all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_i)). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)&V_m_2!=V_n_2). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n). % 12.93/12.81 all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n). % 12.93/12.81 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)). % 12.93/12.81 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))). % 12.93/12.81 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))))). % 12.93/12.81 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.81 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n))). % 12.93/12.81 all V_n (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 12.93/12.81 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)). % 12.93/12.81 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 12.93/12.81 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)). % 12.93/12.81 all V_n V_x (V_x=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))->c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)). % 12.93/12.81 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))). % 12.93/12.81 all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)). % 12.93/12.81 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))). % 12.93/12.81 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)). % 12.93/12.81 all V_X_2 (c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)->c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2))). % 12.93/12.81 all V_X_2 (c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)->c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2))). % 12.93/12.81 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). % 12.93/12.81 all V_a_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2))). % 12.93/12.81 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_a=V_b))))). % 12.93/12.81 all V_a_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))). % 12.93/12.81 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.81 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a)). % 12.93/12.81 all V_n V_z (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 12.93/12.81 all V_x V_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=V_n)). % 12.93/12.81 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a)). % 12.93/12.81 all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)). % 12.93/12.81 all V_X_2 V_K_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)-> ((all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2))->c_SEQ_OBse_q(T_a,V_X_2)))). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)))))). % 12.93/12.81 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))). % 12.93/12.81 all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)& (all B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,B_k)-> -hBOOL(hAPP(V_P_2,B_i))))&hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))). % 12.93/12.81 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.81 all V_i ((V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (V_i!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Oone__class_Oone(tc_Int_Oint))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))). % 12.93/12.81 all V_z_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)). % 12.93/12.81 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.81 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 12.93/12.81 all V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))). % 12.93/12.81 all V_z V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)). % 12.93/12.81 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)). % 12.93/12.81 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2). % 12.93/12.81 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2)). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))). % 12.93/12.81 all V_z V_z_H V_w V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)). % 12.93/12.81 all V_w_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)&V_z_2!=V_w_2). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),hAPP(c_RealVector_Oof__real(T_a),V_y))). % 12.93/12.81 all V_i ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=V_i)). % 12.93/12.81 all V_n V_x c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))). % 12.93/12.81 all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))))). % 12.93/12.81 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))). % 12.93/12.81 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_a_2!=V_b_2&V_c_2!=V_d_2<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))). % 12.93/12.81 all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m)). % 12.93/12.81 all V_z_2 V_x_2 V_y_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))<->V_w_2=V_x_2|V_y_2=V_z_2)). % 12.93/12.81 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))). % 12.93/12.81 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))). % 12.93/12.81 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))). % 12.93/12.81 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))). % 12.93/12.81 all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c)). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))). % 12.93/12.81 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a). % 12.93/12.81 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))). % 12.93/12.81 all V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)<->V_a_2=V_b_2|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))). % 12.93/12.81 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.81 all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))). % 12.93/12.81 all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)<->V_a_2=V_b_2)). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)<->V_a_2=V_b_2)). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z). % 12.93/12.81 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))). % 12.93/12.81 c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.81 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))). % 12.93/12.81 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))). % 12.93/12.81 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))). % 12.93/12.81 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)). % 12.93/12.81 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))). % 12.93/12.81 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)). % 12.93/12.81 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))). % 12.93/12.81 all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.81 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)). % 12.93/12.81 all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x). % 12.93/12.81 all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a). % 12.93/12.81 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))). % 12.93/12.81 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))). % 12.93/12.81 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z). % 12.93/12.81 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b))). % 12.93/12.81 all V_Y_2 V_X_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)-> (c_SEQ_Oconvergent(T_a,V_Y_2)->c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2))))). % 12.93/12.81 all V_y_2 V_X_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)->c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)))). % 12.93/12.81 all V_x_2 V_X_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)->c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)))). % 12.93/12.81 all V_x_2 V_X_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)->c_SEQ_OCauchy(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)))). % 12.93/12.81 all V_y_2 V_X_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)->c_SEQ_OCauchy(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)))). % 12.93/12.81 all V_x_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Lim_OisUCont(T_a,T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2))). % 12.93/12.81 all V_y_2 T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Lim_OisUCont(T_a,T_a,c_COMBC(T_a,T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_y_2))). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))). % 12.93/12.81 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))). % 12.93/12.81 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_b_2 V_c_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))). % 12.93/12.81 all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))). % 12.93/12.81 all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))). % 12.93/12.81 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))). % 12.93/12.81 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))). % 12.93/12.81 all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))). % 12.93/12.81 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))). % 12.93/12.81 all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m)). % 12.93/12.81 all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)). % 12.93/12.81 all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)). % 12.93/12.81 all V_x_2 T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)))). % 12.93/12.81 all V_x T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x)). % 12.93/12.81 all V_d V_b V_c V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))))). % 12.93/12.81 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q))). % 12.93/12.81 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.81 all V_y V_x V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)))). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))). % 12.93/12.81 all V_y_2 V_x_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2))). % 12.93/12.81 all V_y_2 V_x_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 all V_x V_u c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)). % 12.93/12.81 all V_x T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x))=V_x). % 12.93/12.81 all V_k T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)))). % 12.93/12.81 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))). % 12.93/12.81 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))). % 12.93/12.81 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x))))). % 12.93/12.81 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x))))). % 12.93/12.81 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x)=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)))). % 12.93/12.81 all V_b V_a T_a (class_Rings_Oordered__ring__abs(T_a)-> ((c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))& (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)))->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Oring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.81 all V_y_2 V_x_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2))). % 12.93/12.81 all V_y_2 V_x_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2))). % 12.93/12.81 all V_y V_x V_c (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 12.93/12.81 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a))))))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))). % 12.93/12.81 all V_y V_x V_c T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))->V_x=c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a))))))). % 12.93/12.81 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))). % 12.93/12.81 all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)). % 12.93/12.81 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))). % 12.93/12.81 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))). % 12.93/12.81 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))). % 12.93/12.81 all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)). % 12.93/12.81 all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))). % 12.93/12.81 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))). % 12.93/12.81 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n). % 12.93/12.81 all V_n_2 V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.81 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n). % 12.93/12.81 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.81 all V_n V_m (c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))=c_Groups_Oone__class_Oone(tc_Int_Oint)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z). % 12.93/12.81 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z). % 12.93/12.81 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))). % 12.93/12.81 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))). % 12.93/12.81 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w))). % 12.93/12.81 all V_w V_z (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))). % 12.93/12.81 all V_z (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))=V_z). % 12.93/12.81 all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w). % 12.93/12.81 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k))). % 12.93/12.81 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)->V_z=V_w)). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))). % 12.93/12.81 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))). % 12.93/12.81 all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))). % 12.93/12.81 all V_w V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))). % 12.93/12.81 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))). % 12.93/12.81 all V_n V_m (V_m=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)->V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 12.93/12.81 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))). % 12.93/12.81 all V_b V_a (c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))). % 12.93/12.81 all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))). % 12.93/12.81 all V_r V_y V_x (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_x,V_y)),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_r))). % 12.93/12.81 all V_y V_x V_r (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)),c_Complex_Ocomplex_OComplex(V_x,V_y))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_y))). % 12.93/12.81 all V_y V_x (hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))). % 12.93/12.81 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))))). % 12.93/12.81 all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)))). % 12.93/12.81 all V_r_H V_q_H V_b_H V_r V_q V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))))). % 12.93/12.81 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))). % 12.93/12.81 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)). % 12.93/12.81 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))). % 12.93/12.81 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)). % 12.93/12.81 all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)))). % 12.93/12.81 all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). % 12.93/12.81 all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))). % 12.93/12.81 all V_r_H V_q_H V_b_H V_r V_q V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))))). % 12.93/12.81 all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))). % 12.93/12.81 all V_n V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (exists B_z c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2). % 12.93/12.81 all V_k V_j V_u V_i (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k)). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2)). % 12.93/12.81 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))). % 12.93/12.81 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.81 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))). % 12.93/12.81 all V_x_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.81 exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))). % 12.93/12.81 exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)))))). % 12.93/12.81 exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))). % 12.93/12.81 exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)))))). % 12.93/12.81 all T_a (class_Power_Opower(T_a)->c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))). % 12.93/12.81 all V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2). % 12.93/12.81 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))). % 12.93/12.81 all T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_a B_b c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))). % 12.93/12.81 exists B_K all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)). % 12.93/12.81 exists B_K all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)). % 12.93/12.81 all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (exists B_K all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)))). % 12.93/12.81 all V_n V_a V_r (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n)=c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))). % 12.93/12.81 all V_y V_x (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b)=V_a). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=V_a). % 12.93/12.81 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2)))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))). % 12.93/12.81 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)). % 12.93/12.81 all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_RealVector_Oof__real(T_a),V_x),hAPP(c_RealVector_Oof__real(T_a),V_y))). % 12.93/12.81 all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_RealVector_Oof__real(T_a),V_x),hAPP(c_RealVector_Oof__real(T_a),V_y))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))). % 12.93/12.81 all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))). % 12.93/12.81 all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))). % 12.93/12.81 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (V_a_2=V_b_2<->V_c_2=V_d_2))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))). % 12.93/12.81 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)))). % 12.93/12.81 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a). % 12.93/12.81 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))). % 12.93/12.81 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=V_b_2)). % 12.93/12.81 all V_y V_x (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_y))). % 12.93/12.81 all V_s V_r (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_s))). % 12.93/12.81 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))). % 12.93/12.81 all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))). % 12.93/12.81 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)=V_d_2)). % 12.93/12.81 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)<->V_c_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))). % 12.93/12.81 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))). % 12.93/12.81 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))). % 12.93/12.81 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))). % 12.93/12.81 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))). % 12.93/12.81 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2),V_d_2))). % 12.93/12.81 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2)))). % 12.93/12.81 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2)))). % 12.93/12.81 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2),V_d_2))). % 12.93/12.81 all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))). % 12.93/12.81 all V_ra_2 V_a_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)&c_Orderings_Oord__class_Oless(T_a,V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2)))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))). % 12.93/12.81 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))). % 12.93/12.81 all V_r (c_Complex_Orcis(V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)). % 12.93/12.81 all V_a V_b c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)). % 12.93/12.81 all V_a V_r (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)). % 12.93/12.81 all V_a (c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). % 12.93/12.81 all V_d V_c V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))). % 12.93/12.81 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))). % 12.93/12.81 all V_d V_c V_b V_a (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c)))). % 12.93/12.81 all V_y V_x (hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))). % 12.93/12.81 all V_b V_r2 V_a V_r1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b))=c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b))). % 12.93/12.81 all V_e_2 V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e_2)-> (exists B_M all B_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_M,B_m)-> (all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_M,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))),V_e_2)))))))). % 12.93/12.81 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)<-> (all B_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)-> (exists B_M all B_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_M,B_m)-> (all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_M,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))),B_e))))))))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)))). % 12.93/12.81 all V_n V_m V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2))). % 12.93/12.81 all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i). % 12.93/12.81 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))). % 12.93/12.81 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))). % 12.93/12.81 all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m). % 12.93/12.81 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n)=V_m). % 12.93/12.81 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n)=V_m). % 12.93/12.81 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))). % 12.93/12.81 all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 12.93/12.81 all V_y V_x (hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y))). % 12.93/12.81 all V_y V_x (hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y))). % 12.93/12.81 all V_d V_c V_b V_a (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d))). % 12.93/12.81 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m). % 12.93/12.81 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)). % 12.93/12.81 all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)). % 12.93/12.81 all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))). % 12.93/12.81 all V_w V_z (c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))). % 12.93/12.81 all V_w V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)). % 12.93/12.81 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j)). % 12.93/12.81 all V_i_2 V_k_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))). % 12.93/12.81 all V_m V_n V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m). % 12.93/12.81 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)). % 12.93/12.81 all V_i_2 V_j_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2))). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n)=V_m). % 12.93/12.81 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2))). % 12.93/12.81 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))). % 12.93/12.81 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)). % 12.93/12.81 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)). % 12.93/12.81 all V_c V_b V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)))). % 12.93/12.81 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m). % 12.93/12.81 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2)). % 12.93/12.81 all V_n_2 V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))). % 12.93/12.81 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))). % 12.93/12.81 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))). % 12.93/12.81 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))). % 12.93/12.81 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))). % 12.93/12.81 all V_y V_x (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_y))). % 12.93/12.81 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)->hBOOL(hAPP(V_P_2,B_d))))). % 12.93/12.81 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)& -hBOOL(hAPP(V_P_2,B_d)))))). % 12.93/12.81 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)). % 12.93/12.81 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)<->V_m_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))). % 12.93/12.81 all V_n V_m V_u V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n))). % 12.93/12.81 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)))). % 12.93/12.81 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)=V_n_2)). % 12.93/12.81 all V_n V_m V_u V_i V_j (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n)). % 12.93/12.81 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2),V_n_2))). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 12.93/12.81 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)))). % 12.93/12.81 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2),V_n_2))). % 12.93/12.81 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))). % 12.93/12.81 all V_p V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). % 12.93/12.81 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)). % 12.93/12.81 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)). % 12.93/12.81 all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))). % 12.93/12.81 all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y))))). % 12.93/12.81 all V_z V_x V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z)). % 12.93/12.81 all V_x V_z V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))). % 12.93/12.81 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)). % 12.93/12.81 all V_m V_n T_a (class_Power_Opower(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). % 12.93/12.81 all V_z (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.81 hAPP(c_Complex_ORe,c_Complex_Oii)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.81 hAPP(c_Complex_OIm,c_Complex_Oii)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.81 c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). % 12.93/12.81 c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). % 12.93/12.81 all V_x (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x)). % 12.93/12.81 all V_y_2 V_x_2 (c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)=c_Complex_Oii<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.81 c_Complex_Oii=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.81 all V_b V_a (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Ocomplex_OComplex(V_a,V_b))=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_b),V_a)). % 12.93/12.81 all V_b V_a (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Oii)=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_b),V_a)). % 12.93/12.81 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). % 12.93/12.81 all V_r (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)),c_Complex_Oii)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)). % 12.93/12.81 all V_r (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r))=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)). % 12.93/12.81 all V_r (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)-> (exists B_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))))). % 12.93/12.81 all V_X_2 V_M_2 T_a T_b (class_RealVector_Oreal__normed__vector(T_b)&class_Orderings_Oord(T_a)-> ((all B_n (c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))-> (all B_n (c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))))))). % 12.93/12.81 all V_x V_y ((c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y))& (-c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 12.93/12.81 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)))). % 12.93/12.81 all V_x V_y (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)). % 12.93/12.81 all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))). % 12.93/12.81 all V_k_2 V_P_2 V_d_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2)))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))))))). % 12.93/12.81 all V_b V_x V_a (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_a,B_y)&c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_y,V_b))))))). % 12.93/12.81 all V_k_2 V_P_2 V_d_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))))))). % 12.93/12.81 all V_a V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n)=V_a& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)=V_a->B_y=B_x)))))). % 12.93/12.81 all V_a V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n)=V_a)))). % 12.93/12.81 all T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_a B_b c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))). % 12.93/12.81 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))). % 12.93/12.81 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))). % 12.93/12.81 all V_X_2 (c_SEQ_OBse_q(tc_RealDef_Oreal,V_X_2)-> ((all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))))->c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2))). % 12.93/12.81 all V_n V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x))). % 12.93/12.81 all V_gb_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_Oconvergent(T_a,V_gb_2)->c_SEQ_Olim(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_gb_2))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_SEQ_Olim(T_a,V_gb_2)))). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)))). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)-> (c_Transcendental_Oln(V_x_2)=c_Transcendental_Oln(V_y_2)<->V_x_2=V_y_2))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),V_x)). % 12.93/12.81 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.81 all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Transcendental_Oln(V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))). % 12.93/12.81 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))). % 12.93/12.81 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)))). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)),V_x)). % 12.93/12.81 all V_k_2 V_fa_2 V_n_2 ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_n_2)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_fa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(V_fa_2,B_i))),c_Groups_Oone__class_Oone(tc_Int_Oint))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))-> (exists B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,V_n_2)&hAPP(V_fa_2,B_i)=V_k_2))))). % 12.93/12.81 all V_k_2 V_fa_2 V_n_2 ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_n_2)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_fa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(V_fa_2,B_i))),c_Groups_Oone__class_Oone(tc_Int_Oint))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))-> (exists B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,V_n_2)&hAPP(V_fa_2,B_i)=V_k_2))))). % 12.93/12.81 all V_b V_x V_a (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b))))))). % 12.93/12.81 all V_X_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> ((exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K))))<-> (exists B_N all B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)). % 12.93/12.81 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)). % 12.93/12.81 all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))). % 12.93/12.81 all V_i V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)). % 12.93/12.81 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)&c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)). % 12.93/12.81 all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))). % 12.93/12.81 all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m))). % 12.93/12.81 all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j))). % 12.93/12.81 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.81 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))). % 12.93/12.81 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n). % 12.93/12.81 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)). % 12.93/12.81 all V_k V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)). % 12.93/12.81 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)). % 12.93/12.81 all V_n V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)). % 12.93/12.81 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))). % 12.93/12.81 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->V_a=V_b)))). % 12.93/12.81 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))))). % 12.93/12.81 all V_y_2 V_x_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_x_2=V_y_2|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))). % 12.93/12.81 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))))). % 12.93/12.81 all V_n_2 V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2))). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)). % 12.93/12.81 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)<->V_m_2=V_n_2). % 12.93/12.81 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))). % 12.93/12.81 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))). % 12.93/12.81 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))). % 12.93/12.81 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))). % 12.93/12.81 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))). % 12.93/12.81 all V_n V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.81 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)). % 12.93/12.81 all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=c_Nat_OSuc(B_j)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))). % 12.93/12.81 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.81 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)<-> (exists B_m (V_n_2=c_Nat_OSuc(B_m)))). % 12.93/12.81 all V_n_2 V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.81 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))). % 12.93/12.81 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))). % 12.93/12.81 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.81 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))). % 12.93/12.81 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))). % 12.93/12.81 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ocomm__ring(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ocomm__ring(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat). % 12.93/12.81 class_Rings_Ocomm__semiring__0(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Ocomm__semiring__0(tc_Int_Oint). % 12.93/12.81 class_Rings_Ocomm__ring(tc_Int_Oint). % 12.93/12.81 all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))). % 12.93/12.81 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))). % 12.93/12.81 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))). % 12.93/12.81 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))). % 12.93/12.81 all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))). % 12.93/12.81 all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))). % 12.93/12.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint). % 12.93/12.81 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint). % 12.93/12.81 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__semiring__strict(tc_Int_Oint). % 12.93/12.81 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint). % 12.93/12.81 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint). % 12.93/12.81 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint). % 12.93/12.81 class_Groups_Olinordered__ab__group__add(tc_Int_Oint). % 12.93/12.81 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint). % 12.93/12.81 class_Rings_Oordered__cancel__semiring(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__ring__strict(tc_Int_Oint). % 12.93/12.81 class_Rings_Oring__no__zero__divisors(tc_Int_Oint). % 12.93/12.81 class_Rings_Oordered__comm__semiring(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__semiring__1(tc_Int_Oint). % 12.93/12.81 class_Groups_Oordered__ab__group__add(tc_Int_Oint). % 12.93/12.81 class_Groups_Ocancel__semigroup__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__semiring(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__semidom(tc_Int_Oint). % 12.93/12.81 class_Groups_Oab__semigroup__mult(tc_Int_Oint). % 12.93/12.81 class_Groups_Ocomm__monoid__mult(tc_Int_Oint). % 12.93/12.81 class_Groups_Oab__semigroup__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Oordered__semiring(tc_Int_Oint). % 12.93/12.81 class_Rings_Oordered__ring__abs(tc_Int_Oint). % 12.93/12.81 class_Rings_Ono__zero__divisors(tc_Int_Oint). % 12.93/12.81 class_Groups_Ocomm__monoid__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__ring(tc_Int_Oint). % 12.93/12.81 class_Rings_Olinordered__idom(tc_Int_Oint). % 12.93/12.81 class_Rings_Ocomm__semiring__1(tc_Int_Oint). % 12.93/12.81 class_Rings_Ocomm__semiring(tc_Int_Oint). % 12.93/12.81 class_Groups_Oab__group__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Ozero__ne_q__one(tc_Int_Oint). % 12.93/12.81 class_Rings_Oordered__ring(tc_Int_Oint). % 12.93/12.81 class_Orderings_Opreorder(tc_Int_Oint). % 12.93/12.81 class_Orderings_Olinorder(tc_Int_Oint). % 12.93/12.81 class_Groups_Omonoid__mult(tc_Int_Oint). % 12.93/12.81 class_Rings_Ocomm__ring__1(tc_Int_Oint). % 12.93/12.81 class_Groups_Omonoid__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Osemiring__0(tc_Int_Oint). % 12.93/12.81 class_Groups_Ogroup__add(tc_Int_Oint). % 12.93/12.81 class_Rings_Omult__zero(tc_Int_Oint). % 12.93/12.81 class_Orderings_Oorder(tc_Int_Oint). % 12.93/12.81 class_Rings_Osemiring(tc_Int_Oint). % 12.93/12.81 class_Orderings_Oord(tc_Int_Oint). % 12.93/12.81 class_Groups_Ouminus(tc_Int_Oint). % 12.93/12.81 class_Groups_Osgn__if(tc_Int_Oint). % 12.93/12.81 class_Groups_Oabs__if(tc_Int_Oint). % 12.93/12.81 class_Rings_Oring__1(tc_Int_Oint). % 12.93/12.81 class_Groups_Ominus(tc_Int_Oint). % 12.93/12.81 class_Power_Opower(tc_Int_Oint). % 12.93/12.81 class_Groups_Ozero(tc_Int_Oint). % 12.93/12.81 class_Rings_Oring(tc_Int_Oint). % 12.93/12.81 class_Rings_Oidom(tc_Int_Oint). % 12.93/12.81 class_Groups_Oone(tc_Int_Oint). % 12.93/12.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat). % 12.93/12.81 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat). % 12.93/12.81 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat). % 12.93/12.81 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat). % 12.93/12.81 class_Rings_Oordered__comm__semiring(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat). % 12.93/12.81 class_Rings_Olinordered__semiring(tc_Nat_Onat). % 12.93/12.81 class_Rings_Olinordered__semidom(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oab__semigroup__mult(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oab__semigroup__add(tc_Nat_Onat). % 12.93/12.81 class_Rings_Oordered__semiring(tc_Nat_Onat). % 12.93/12.81 class_Rings_Ono__zero__divisors(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ocomm__monoid__add(tc_Nat_Onat). % 12.93/12.81 class_Rings_Ocomm__semiring__1(tc_Nat_Onat). % 12.93/12.81 class_Rings_Ocomm__semiring(tc_Nat_Onat). % 12.93/12.81 class_Rings_Ozero__ne_q__one(tc_Nat_Onat). % 12.93/12.81 class_Orderings_Opreorder(tc_Nat_Onat). % 12.93/12.81 class_Orderings_Olinorder(tc_Nat_Onat). % 12.93/12.81 class_Groups_Omonoid__mult(tc_Nat_Onat). % 12.93/12.81 class_Groups_Omonoid__add(tc_Nat_Onat). % 12.93/12.81 class_Rings_Osemiring__0(tc_Nat_Onat). % 12.93/12.81 class_Rings_Omult__zero(tc_Nat_Onat). % 12.93/12.81 class_Orderings_Oorder(tc_Nat_Onat). % 12.93/12.81 class_Rings_Osemiring(tc_Nat_Onat). % 12.93/12.81 class_Orderings_Oord(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ominus(tc_Nat_Onat). % 12.93/12.81 class_Power_Opower(tc_Nat_Onat). % 12.93/12.81 class_Groups_Ozero(tc_Nat_Onat). % 12.93/12.81 class_Groups_Oone(tc_Nat_Onat). % 12.93/12.81 class_Lattices_Oboolean__algebra(tc_HOL_Obool). % 12.93/12.81 class_Orderings_Opreorder(tc_HOL_Obool). % 12.93/12.81 class_Orderings_Oorder(tc_HOL_Obool). % 12.93/12.81 class_Orderings_Oord(tc_HOL_Obool). % 12.93/12.81 class_Groups_Ouminus(tc_HOL_Obool). % 12.93/12.81 class_Groups_Ominus(tc_HOL_Obool). % 12.93/12.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal). % 12.93/12.81 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal). % 12.93/12.81 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal). % 12.93/12.81 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal). % 12.93/12.81 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__semiring(tc_RealDef_Oreal). % 12.93/12.81 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__semidom(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal). % 12.93/12.81 class_RealVector_Ometric__space(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oordered__semiring(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__ring(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Olinordered__idom(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ocomm__semiring(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oab__group__add(tc_RealDef_Oreal). % 12.93/12.81 class_SEQ_Ocomplete__space(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oordered__ring(tc_RealDef_Oreal). % 12.93/12.81 class_Orderings_Opreorder(tc_RealDef_Oreal). % 12.93/12.81 class_Orderings_Olinorder(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Omonoid__mult(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Omonoid__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Osemiring__0(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ogroup__add(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Omult__zero(tc_RealDef_Oreal). % 12.93/12.81 class_Orderings_Oorder(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Osemiring(tc_RealDef_Oreal). % 12.93/12.81 class_Orderings_Oord(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ouminus(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Osgn__if(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oabs__if(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oring__1(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ominus(tc_RealDef_Oreal). % 12.93/12.81 class_Power_Opower(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Ozero(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oring(tc_RealDef_Oreal). % 12.93/12.81 class_Rings_Oidom(tc_RealDef_Oreal). % 12.93/12.81 class_Groups_Oone(tc_RealDef_Oreal). % 12.93/12.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex). % 12.93/12.81 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex). % 12.93/12.81 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex). % 12.93/12.81 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex). % 12.93/12.81 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex). % 12.93/12.81 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex). % 12.93/12.81 class_RealVector_Ometric__space(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Oab__group__add(tc_Complex_Ocomplex). % 12.93/12.81 class_SEQ_Ocomplete__space(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Omonoid__mult(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Omonoid__add(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Osemiring__0(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ogroup__add(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Omult__zero(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Osemiring(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ouminus(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Oring__1(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ominus(tc_Complex_Ocomplex). % 12.93/12.81 class_Power_Opower(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Ozero(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Oring(tc_Complex_Ocomplex). % 12.93/12.81 class_Rings_Oidom(tc_Complex_Ocomplex). % 12.93/12.81 class_Groups_Oone(tc_Complex_Ocomplex). % 12.93/12.81 all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))). % 12.93/12.82 all V_Q V_P T_b T_a (hAPP(c_COMBK(T_a,T_b,V_P),V_Q)=V_P). % 12.93/12.82 all V_R_2 V_Q_2 V_P_2 T_c T_a T_b (hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2))). % 12.93/12.82 all V_R_2 V_Q_2 V_P_2 T_a T_c T_b (hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2)). % 12.93/12.82 all V_R_2 V_Q_2 V_P_2 T_a T_c T_b (hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2))). % 12.93/12.82 -c_SEQ_OBse_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))). % 12.93/12.82 end_of_list. % 12.93/12.82 % 12.93/12.82 -------> usable clausifies to: % 12.93/12.82 % 12.93/12.82 list(usable). % 12.93/12.82 0 [] A=A. % 12.93/12.82 0 [] hAPP(V_fa_2,$f1(V_gb_2,V_fa_2))!=hAPP(V_gb_2,$f1(V_gb_2,V_fa_2))|V_fa_2=V_gb_2. % 12.93/12.82 0 [] c_SEQ_Osubse_q(v_ga____). % 12.93/12.82 0 [] c_SEQ_Osubse_q(v_f____). % 12.93/12.82 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))). % 12.93/12.82 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))). % 12.93/12.82 0 [] c_SEQ_Osubse_q($c1). % 12.93/12.82 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,$c1)))). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n)),v_r). % 12.93/12.82 0 [] c_SEQ_Osubse_q($c2). % 12.93/12.82 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,v_s),$c2)). % 12.93/12.82 0 [] c_Lim_OisUCont(tc_Complex_Ocomplex,tc_RealDef_Oreal,c_Complex_ORe). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))|c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2))|c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2))| -c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.82 0 [] c_SEQ_Osubse_q($c3). % 12.93/12.82 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,v_s),v_f____),$c3)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,hAPP(v_s,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),v_r). % 12.93/12.82 0 [] c_Lim_OisUCont(tc_Complex_Ocomplex,tc_RealDef_Oreal,c_Complex_OIm). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,X2),hAPP(V_X_2,X1)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f3(V_X_2,T_a),$f2(V_X_2,T_a)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f3(V_X_2,T_a)),hAPP(V_X_2,$f2(V_X_2,T_a))). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f5(V_X_2,T_a),$f4(V_X_2,T_a)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f4(V_X_2,T_a)),hAPP(V_X_2,$f5(V_X_2,T_a))). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 12.93/12.82 0 [] hAPP(c_Complex_OIm,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)). % 12.93/12.82 0 [] -c_SEQ_OCauchy(tc_Complex_Ocomplex,V_X_2)|c_SEQ_OCauchy(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_SEQ_Omonose_q(T_a,V_a_2)|c_SEQ_Omonose_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)). % 12.93/12.82 0 [] -class_RealVector_Ometric__space(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)| -c_SEQ_Osubse_q(V_fa_2)|c_SEQ_OCauchy(T_a,c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,V_fa_2)). % 12.93/12.82 0 [] -c_SEQ_OCauchy(tc_Complex_Ocomplex,V_X_2)|c_SEQ_OCauchy(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2)). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,V_x)!=hAPP(c_Complex_ORe,V_y)|hAPP(c_Complex_OIm,V_x)!=hAPP(c_Complex_OIm,V_y)|V_x=V_y. % 12.93/12.82 0 [] V_x_2!=V_y_2|hAPP(c_Complex_ORe,V_x_2)=hAPP(c_Complex_ORe,V_y_2). % 12.93/12.82 0 [] V_x_2!=V_y_2|hAPP(c_Complex_OIm,V_x_2)=hAPP(c_Complex_OIm,V_y_2). % 12.93/12.82 0 [] V_x_2=V_y_2|hAPP(c_Complex_ORe,V_x_2)!=hAPP(c_Complex_ORe,V_y_2)|hAPP(c_Complex_OIm,V_x_2)!=hAPP(c_Complex_OIm,V_y_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_l)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_m)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_l)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_y),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_m))))). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 12.93/12.82 0 [] hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r). % 12.93/12.82 0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=V_a_2. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=V_a_2. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2),V_y_2). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2),V_y_2). % 12.93/12.82 0 [] -c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)). % 12.93/12.82 0 [] hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))). % 12.93/12.82 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c. % 12.93/12.82 0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c. % 12.93/12.82 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c. % 12.93/12.82 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)|V_b_2=V_c_2. % 12.93/12.82 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)|V_b_2!=V_c_2. % 12.93/12.82 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)|V_b_2=V_c_2. % 12.93/12.82 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)|V_b_2!=V_c_2. % 12.93/12.82 0 [] -class_Groups_Oab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)). % 12.93/12.82 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)|V_a_2=V_b_2. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)|V_a_2!=V_b_2. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)!=V_b_2|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)=V_a_2. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=V_b_2|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)!=V_a_2. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)|V_b_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)|V_b_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=V_a. % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)|V_z=V_w. % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a). % 12.93/12.82 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a. % 12.93/12.82 0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a. % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a. % 12.93/12.82 0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a. % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)!=V_a_2|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=V_a_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)|c_Groups_Ozero__class_Ozero(T_a)=V_a_2. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)|c_Groups_Ozero__class_Ozero(T_a)!=V_a_2. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),V_a_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),V_a_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=V_b. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))=V_b. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)). % 12.93/12.82 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=c_RealVector_Onorm__class_Onorm(T_a,V_x). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_ra_2),V_x_2). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_ra_2). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_ra_2),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_ra_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a). % 12.93/12.82 0 [] c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_y)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_y),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x))). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)=V_b. % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2). % 12.93/12.82 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a. % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 12.93/12.82 0 [] -class_RealVector_Ometric__space(T_b)| -class_RealVector_Ometric__space(T_a)| -c_Lim_OisUCont(T_a,T_b,V_fa_2)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_OCauchy(T_b,c_COMBB(T_a,T_b,tc_Nat_Onat,V_fa_2,V_X_2)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)). % 12.93/12.82 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,B_x),hAPP(V_gb_2,B_x)). % 12.93/12.82 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,$f6(V_gb_2,V_fa_2,T_a,T_b)),hAPP(V_gb_2,$f6(V_gb_2,V_fa_2,T_a,T_b))). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y). % 12.93/12.82 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_gb_2,V_x_2)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a). % 12.93/12.82 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y. % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x). % 12.93/12.82 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_gb_2,V_x_2)). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2. % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n. % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k). % 12.93/12.82 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n). % 12.93/12.82 0 [] hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))!=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))|hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2). % 12.93/12.82 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m. % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f7(V_n_2,V_m_2)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),$f8(V_l_2,V_k_2)). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f10(V_X_2,T_a),$f9(V_X_2,T_a)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f9(V_X_2,T_a)),hAPP(V_X_2,$f10(V_X_2,T_a))). % 12.93/12.82 0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a. % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a. % 12.93/12.82 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f12(V_X_2,T_a),$f11(V_X_2,T_a)). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f12(V_X_2,T_a)),hAPP(V_X_2,$f11(V_X_2,T_a))). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)|c_SEQ_Oincse_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -c_SEQ_Oincse_q(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a). % 12.93/12.82 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Groups_Ouminus(T_a)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)). % 12.93/12.82 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=V_x. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_Groups_Ouminus(T_a)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)). % 12.93/12.82 0 [] c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_N_2,$f13(V_K_2,V_X_2,V_N_2,T_a))|c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f13(V_K_2,V_X_2,V_N_2,T_a))),V_K_2)|c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|V_x!=c_Groups_Ozero__class_Ozero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_p_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)). % 12.93/12.82 0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_p_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_SEQ_OBse_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)). % 12.93/12.82 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,c_COMBK(T_a,T_b,V_c_2),V_fa_2),V_x_2)=V_c_2. % 12.93/12.82 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_SEQ_Omonose_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x. % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Osgn__if(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)). % 12.93/12.82 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2))=c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2). % 12.93/12.82 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)). % 12.93/12.82 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=V_c_2|hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,V_v_2). % 12.93/12.82 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)|hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,hAPP(V_d_2,V_v_2)). % 12.93/12.82 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)|hAPP(V_a_2,hAPP(V_b_2,B_v))=hAPP(V_c_2,hAPP(V_d_2,B_v)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)). % 12.93/12.82 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n))=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.82 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a. % 12.93/12.82 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)). % 12.93/12.82 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x)=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x))). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))). % 12.93/12.82 0 [] hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f14(V_X_2,T_a)). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),$f14(V_X_2,T_a)). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f15(V_X_2,T_a,B_K))),B_K). % 12.93/12.82 0 [] -class_RealVector_Ometric__space(T_a)|c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2)). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),V_x_2)!=hAPP(c_RealVector_Oof__real(T_a),V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),V_x_2)=hAPP(c_RealVector_Oof__real(T_a),V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)|c_SEQ_Oconvergent(T_a,c_COMBB(tc_RealDef_Oreal,T_a,tc_Nat_Onat,c_RealVector_Oof__real(T_a),V_X_2)). % 12.93/12.82 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)!=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real1_2=V_real1_H_2. % 12.93/12.82 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)!=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real2_2=V_real2_H_2. % 12.93/12.82 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real1_2!=V_real1_H_2|V_real2_2!=V_real2_H_2. % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Lim_OisUCont(tc_RealDef_Oreal,T_a,c_RealVector_Oof__real(T_a)). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a). % 12.93/12.82 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a). % 12.93/12.82 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y. % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y. % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x). % 12.93/12.82 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)!=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_xa_2)|V_x_2=V_xa_2. % 12.93/12.82 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)!=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_xa_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_xa_2)|V_x_2!=V_xa_2|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)=c_Complex_Ocomplex_OComplex(V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_x,V_y)),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_r),V_y). % 12.93/12.82 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)),c_Complex_Ocomplex_OComplex(V_x,V_y))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_x),V_y). % 12.93/12.82 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_x)),V_n)=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y). % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y. % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x). % 12.93/12.82 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z). % 12.93/12.82 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)). % 12.93/12.82 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)). % 12.93/12.82 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_z))=V_z. % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),V_a_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),V_a_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2. % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2. % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(c_RealVector_Oof__real(T_a),V_r))=hAPP(c_RealVector_Oof__real(T_a),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)). % 12.93/12.82 0 [] hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_x. % 12.93/12.82 0 [] hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_y. % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.82 0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] -class_SEQ_Ocomplete__space(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,V_X_2). % 12.93/12.82 0 [] -class_SEQ_Ocomplete__space(T_a)|c_SEQ_OCauchy(T_a,V_X_2)| -c_SEQ_Oconvergent(T_a,V_X_2). % 12.93/12.82 0 [] -class_SEQ_Ocomplete__space(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Ometric__space(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)|c_SEQ_OCauchy(T_a,V_X_2). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)). % 12.93/12.82 0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.82 0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.82 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)). % 12.93/12.82 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)). % 12.93/12.82 0 [] -c_SEQ_OCauchy(tc_RealDef_Oreal,V_X_2)|c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)| -c_SEQ_Oconvergent(T_a,V_Y_2)|c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2)). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2)). % 12.93/12.82 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_Oconvergent(T_a,V_X_2)| -c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_X_2)). % 12.93/12.82 0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),V_x_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] hAPP(c_Complex_OIm,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_z))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),hAPP(c_RealVector_Oof__real(T_a),V_y)). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),hAPP(c_RealVector_Oof__real(T_a),V_y)). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(T_a). % 12.93/12.82 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),V_n). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)). % 12.93/12.82 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)). % 12.93/12.82 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.82 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)). % 12.93/12.82 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|hAPP(c_RealVector_Oof__real(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_m_2=V_n_2. % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a. % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),V_r))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2),V_b_2). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z))=V_z. % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_a_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_a_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)). % 12.93/12.83 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b))=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_b)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OCauchy(tc_RealDef_Oreal,V_X_2)|c_SEQ_OCauchy(T_a,c_COMBB(tc_RealDef_Oreal,T_a,tc_Nat_Onat,c_RealVector_Oof__real(T_a),V_X_2)). % 12.93/12.83 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)). % 12.93/12.83 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)). % 12.93/12.83 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))). % 12.93/12.83 0 [] -c_SEQ_OBse_q(tc_RealDef_Oreal,V_X_2)| -c_SEQ_Omonose_q(tc_RealDef_Oreal,V_X_2)|c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2). % 12.93/12.83 0 [] -class_Groups_Oabs__if(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a). % 12.93/12.83 0 [] -class_Groups_Oabs__if(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a. % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Oone__class_Oone(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s)). % 12.93/12.83 0 [] V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] V_a!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2),V_y_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x_2),V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_x_2),V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_r). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=V_r. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_a). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=V_a. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_a_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_a_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -class_SEQ_Ocomplete__space(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)| -c_SEQ_Osubse_q(V_fa_2)|c_SEQ_Oconvergent(T_a,c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,V_fa_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Osgn__class_Osgn(T_a,V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)). % 12.93/12.83 0 [] -class_Groups_Osgn__if(T_a)|V_x!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a). % 12.93/12.83 0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))). % 12.93/12.83 0 [] c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f17(V_X_2,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_X_2,B_n)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),$f16(V_X_2,T_a)))),$f17(V_X_2,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_X_2,$f18(V_X_2,T_a,B_k,B_x))),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),B_x))),B_k). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f20(V_X_2,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_X_2,B_n)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_X_2,$f19(V_X_2,T_a))))),$f20(V_X_2,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_X_2,$f21(V_X_2,T_a,B_k,B_N))),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_X_2,B_N)))),B_k). % 12.93/12.83 0 [] c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2). % 12.93/12.83 0 [] c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n). % 12.93/12.83 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x). % 12.93/12.83 0 [] V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2). % 12.93/12.83 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_n_2=V_m_2. % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_n_2!=V_m_2. % 12.93/12.83 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2). % 12.93/12.83 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2,V_fa_2). % 12.93/12.83 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2,V_fa_2). % 12.93/12.83 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.83 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_i). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_i). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n. % 12.93/12.83 0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)). % 12.93/12.83 0 [] -c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)). % 12.93/12.83 0 [] c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f23(V_fa_2),$f22(V_fa_2)). % 12.93/12.83 0 [] c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f23(V_fa_2)),hAPP(V_fa_2,$f22(V_fa_2))). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] V_x!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a). % 12.93/12.83 0 [] -c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)|c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2)). % 12.93/12.83 0 [] -c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)|c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_a=V_b. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=V_n. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f24(V_X_2,V_K_2,T_a))),V_K_2)|c_SEQ_OBse_q(T_a,V_X_2). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f25(V_X_2,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),$f25(V_X_2,T_a)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f26(V_n_2,V_P_2),V_n_2). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,$f26(V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,B_i)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f26(V_n_2,V_P_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.83 0 [] V_i!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.83 0 [] V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|V_z_2!=V_w_2. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)|V_z_2=V_w_2. % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_RealVector_Oof__real(T_a),V_x)),hAPP(c_RealVector_Oof__real(T_a),V_y)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=V_i. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Ono__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Ono__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)). % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2=V_b_2|V_c_2=V_d_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)). % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2!=V_b_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)). % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_c_2!=V_d_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m). % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_w_2=V_x_2|V_y_2=V_z_2. % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_w_2!=V_x_2. % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_y_2!=V_z_2. % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)). % 12.93/12.83 0 [] -class_Rings_Osemiring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a. % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a. % 12.93/12.83 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a. % 12.93/12.83 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a. % 12.93/12.83 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a. % 12.93/12.83 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a. % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2=V_b_2|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2). % 12.93/12.83 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2!=V_b_2. % 12.93/12.83 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)). % 12.93/12.83 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.83 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)). % 12.93/12.83 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)|V_a_2=V_b_2. % 12.93/12.83 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)|V_a_2!=V_b_2. % 12.93/12.83 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)|V_a_2=V_b_2. % 12.93/12.83 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)|V_a_2!=V_b_2. % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)). % 12.93/12.83 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)). % 12.93/12.83 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a). % 12.93/12.83 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x. % 12.93/12.83 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)). % 12.93/12.83 0 [] -class_Groups_Oab__semigroup__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z. % 12.93/12.83 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)| -c_SEQ_Oconvergent(T_a,V_Y_2)|c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_OCauchy(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_OCauchy(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Lim_OisUCont(T_a,T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Lim_OisUCont(T_a,T_a,c_COMBC(T_a,T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_y_2)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 12.93/12.83 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__comm__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)). % 12.93/12.83 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)). % 12.93/12.83 0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)). % 12.93/12.83 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m). % 12.93/12.83 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)). % 12.93/12.83 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a). % 12.93/12.83 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)). % 12.93/12.83 0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)). % 12.93/12.83 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x))=V_x. % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x)=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))). % 12.93/12.83 0 [] -class_Rings_Oring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__1(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))|V_x=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_y_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n). % 12.93/12.83 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n. % 12.93/12.83 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)). % 12.93/12.83 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)). % 12.93/12.83 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))=V_z. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)|V_z=V_w. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.83 0 [] V_m!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)|V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 12.93/12.83 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)). % 12.93/12.83 0 [] c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_x,V_y)),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_r)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)),c_Complex_Ocomplex_OComplex(V_x,V_y))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_y)). % 12.93/12.83 0 [] hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),$f27(V_n,V_b)),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c4). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c4)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c5). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c5)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f28(T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),$f28(T_a))). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c6). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c6)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c7). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c7)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f29(T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),$f29(T_a))). % 12.93/12.83 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)). % 12.93/12.83 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2. % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f30(V_y,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f30(V_y,T_a))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f31(V_x,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f31(V_x,T_a))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f32(T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f32(T_a))). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c8)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c9)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_RealVector_Oof__real(T_a),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),$f33(T_a))). % 12.93/12.83 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n)=c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Ominus__class_Ominus(T_a,V_b,V_a). % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b)=V_a. % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=V_a. % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a). % 12.93/12.83 0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)). % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)). % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_RealVector_Oof__real(T_a),V_x),hAPP(c_RealVector_Oof__real(T_a),V_y)). % 12.93/12.83 0 [] -class_RealVector_Oreal__algebra__1(T_a)|hAPP(c_RealVector_Oof__real(T_a),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_RealVector_Oof__real(T_a),V_x),hAPP(c_RealVector_Oof__real(T_a),V_y)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)). % 12.93/12.83 0 [] -class_Groups_Ominus(T_a)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)). % 12.93/12.83 0 [] -class_Groups_Ominus(T_a)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2!=V_b_2|V_c_2=V_d_2. % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2=V_b_2|V_c_2!=V_d_2. % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2). % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a. % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a). % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=V_b_2. % 12.93/12.83 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=V_b_2. % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_y)). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_s)). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)=V_d_2. % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)!=V_d_2. % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|V_c_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2). % 12.93/12.83 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|V_c_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2),V_d_2). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2),V_d_2). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2)). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2),V_d_2). % 12.93/12.83 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2),V_d_2). % 12.93/12.83 0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 12.93/12.83 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2)). % 12.93/12.83 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b))). % 12.93/12.83 0 [] c_Complex_Orcis(V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)). % 12.93/12.83 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r). % 12.93/12.83 0 [] c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))). % 12.93/12.83 0 [] hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b))=c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(V_e_2,V_X_2,T_a),B_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(V_e_2,V_X_2,T_a),B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))),V_e_2). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f35(V_X_2,T_a,B_e),B_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f35(V_X_2,T_a,B_e),B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))),B_e). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OCauchy(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f38(V_X_2,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OCauchy(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_M,$f37(V_X_2,T_a,B_M)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OCauchy(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_M,$f36(V_X_2,T_a,B_M)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OCauchy(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(V_X_2,$f37(V_X_2,T_a,B_M)),hAPP(V_X_2,$f36(V_X_2,T_a,B_M)))),$f38(V_X_2,T_a)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n)=V_m. % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n)=V_m. % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.83 0 [] hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)). % 12.93/12.83 0 [] hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m. % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n)=V_m. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_y)). % 12.93/12.83 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.83 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f39(V_b_2,V_a_2,V_P_2)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f39(V_b_2,V_a_2,V_P_2))). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f39(V_b_2,V_a_2,V_P_2)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f39(V_b_2,V_a_2,V_P_2))). % 12.93/12.83 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 12.93/12.83 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f40(V_b_2,V_a_2,V_P_2)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f40(V_b_2,V_a_2,V_P_2))). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f40(V_b_2,V_a_2,V_P_2)). % 12.93/12.83 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f40(V_b_2,V_a_2,V_P_2))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|V_m_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|V_m_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)!=V_n_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2),V_n_2). % 12.93/12.83 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.83 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)). % 12.93/12.83 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.93/12.83 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a). % 12.93/12.83 0 [] -class_Groups_Omonoid__mult(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y))))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))). % 12.93/12.83 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j). % 12.93/12.83 0 [] -class_Power_Opower(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a). % 12.93/12.83 0 [] -class_Power_Opower(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). % 12.93/12.83 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] hAPP(c_Complex_ORe,c_Complex_Oii)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] hAPP(c_Complex_OIm,c_Complex_Oii)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). % 12.93/12.83 0 [] c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V_x). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)!=c_Complex_Oii|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)!=c_Complex_Oii|V_y_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)=c_Complex_Oii|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] c_Complex_Oii=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Ocomplex_OComplex(V_a,V_b))=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_b),V_a). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Oii)=c_Complex_Ocomplex_OComplex(hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),V_b),V_a). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r)),c_Complex_Oii)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r). % 12.93/12.83 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),V_r))=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f41(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,$f41(V_r))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,$f42(V_X_2,V_M_2,T_a,T_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,$f42(V_X_2,V_M_2,T_a,T_b)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y). % 12.93/12.83 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)|hBOOL(hAPP(V_P_2,$f43(V_k_2,V_P_2,V_d_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)| -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,$f43(V_k_2,V_P_2,V_d_2),V_d_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f44(V_b,V_x,V_a)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f44(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_a,B_y). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f44(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_y,V_b). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)|hBOOL(hAPP(V_P_2,$f45(V_k_2,V_P_2,V_d_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),$f45(V_k_2,V_P_2,V_d_2)),V_d_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f46(V_a,V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f46(V_a,V_n)),V_n)=V_a. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)!=V_a|B_y=$f46(V_a,V_n). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f47(V_a,V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f47(V_a,V_n)),V_n)=V_a. % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f48(T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f48(T_a))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f49(V_x,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f49(V_x,T_a))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f50(V_y,T_a)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f50(V_y,T_a))). % 12.93/12.83 0 [] -c_SEQ_OBse_q(tc_RealDef_Oreal,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f52(V_X_2),$f51(V_X_2))|c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2). % 12.93/12.83 0 [] -c_SEQ_OBse_q(tc_RealDef_Oreal,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(V_X_2,$f52(V_X_2)),hAPP(V_X_2,$f51(V_X_2)))|c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_Oconvergent(T_a,V_gb_2)|c_SEQ_Olim(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(T_a),V_gb_2))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_SEQ_Olim(T_a,V_gb_2)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|c_Transcendental_Oln(V_x_2)!=c_Transcendental_Oln(V_y_2)|V_x_2=V_y_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|c_Transcendental_Oln(V_x_2)=c_Transcendental_Oln(V_y_2)|V_x_2!=V_y_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),V_x). % 12.93/12.83 0 [] c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Transcendental_Oln(V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Transcendental_Oln(V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)),V_x). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f53(V_k_2,V_fa_2,V_n_2),V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f54(V_k_2,V_fa_2,V_n_2),V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f53(V_k_2,V_fa_2,V_n_2),V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|hAPP(V_fa_2,$f54(V_k_2,V_fa_2,V_n_2))=V_k_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_fa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f53(V_k_2,V_fa_2,V_n_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(V_fa_2,$f53(V_k_2,V_fa_2,V_n_2)))),c_Groups_Oone__class_Oone(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f54(V_k_2,V_fa_2,V_n_2),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_fa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f53(V_k_2,V_fa_2,V_n_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(V_fa_2,$f53(V_k_2,V_fa_2,V_n_2)))),c_Groups_Oone__class_Oone(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|hAPP(V_fa_2,$f54(V_k_2,V_fa_2,V_n_2))=V_k_2. % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f55(V_k_2,V_fa_2,V_n_2),V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f56(V_k_2,V_fa_2,V_n_2),V_n_2). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f55(V_k_2,V_fa_2,V_n_2),V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|hAPP(V_fa_2,$f56(V_k_2,V_fa_2,V_n_2))=V_k_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_fa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f55(V_k_2,V_fa_2,V_n_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(V_fa_2,$f55(V_k_2,V_fa_2,V_n_2)))),c_Groups_Oone__class_Oone(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f56(V_k_2,V_fa_2,V_n_2),V_n_2). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_fa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f55(V_k_2,V_fa_2,V_n_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(V_fa_2,$f55(V_k_2,V_fa_2,V_n_2)))),c_Groups_Oone__class_Oone(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(V_fa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,hAPP(V_fa_2,V_n_2))|hAPP(V_fa_2,$f56(V_k_2,V_fa_2,V_n_2))=V_k_2. % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f57(V_b,V_x,V_a)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f57(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f57(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f58(V_X_2,T_b,B_K))),B_K)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f59(V_X_2,T_b)))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f60(V_X_2,T_b))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f61(V_X_2,T_b,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))). % 12.93/12.83 0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,X3)),$f60(V_X_2,T_b))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f61(V_X_2,T_b,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)). % 12.93/12.83 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)). % 12.93/12.83 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n. % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j)). % 12.93/12.84 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)). % 12.93/12.84 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n. % 12.93/12.84 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n). % 12.93/12.84 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k). % 12.93/12.84 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)). % 12.93/12.84 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 12.93/12.84 0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|V_a=V_b. % 12.93/12.84 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))). % 12.93/12.84 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2=V_y_2|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2). % 12.93/12.84 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=V_y_2. % 12.93/12.84 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2). % 12.93/12.84 0 [] -c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))). % 12.93/12.84 0 [] c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f62(V_fa_2)),hAPP(V_fa_2,c_Nat_OSuc($f62(V_fa_2)))). % 12.93/12.84 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_m_2=V_n_2. % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_m_2!=V_n_2. % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)). % 12.93/12.84 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)). % 12.93/12.84 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Nat_OSuc($f63(V_n_2,V_m_2)). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f63(V_n_2,V_m_2),V_n_2). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Nat_OSuc(B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=c_Nat_OSuc($f64(V_n_2)). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=c_Nat_OSuc(B_m). % 12.93/12.84 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))). % 12.93/12.84 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))). % 12.93/12.84 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ocomm__ring(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ocomm__ring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ocomm__ring(tc_Int_Oint). % 12.93/12.84 0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)). % 12.93/12.84 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)). % 12.93/12.84 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)). % 12.93/12.84 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)). % 12.93/12.84 0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)). % 12.93/12.84 0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)). % 12.93/12.84 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oordered__semiring(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oordered__ring__abs(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__ring(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Olinordered__idom(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oab__group__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oordered__ring(tc_Int_Oint). % 12.93/12.84 0 [] class_Orderings_Opreorder(tc_Int_Oint). % 12.93/12.84 0 [] class_Orderings_Olinorder(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Omonoid__mult(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Omonoid__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Osemiring__0(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ogroup__add(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Omult__zero(tc_Int_Oint). % 12.93/12.84 0 [] class_Orderings_Oorder(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Osemiring(tc_Int_Oint). % 12.93/12.84 0 [] class_Orderings_Oord(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ouminus(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Osgn__if(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oabs__if(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oring__1(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ominus(tc_Int_Oint). % 12.93/12.84 0 [] class_Power_Opower(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Ozero(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oring(tc_Int_Oint). % 12.93/12.84 0 [] class_Rings_Oidom(tc_Int_Oint). % 12.93/12.84 0 [] class_Groups_Oone(tc_Int_Oint). % 12.93/12.84 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Oordered__semiring(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat). % 12.93/12.84 0 [] class_Orderings_Opreorder(tc_Nat_Onat). % 12.93/12.84 0 [] class_Orderings_Olinorder(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Omonoid__add(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Osemiring__0(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Omult__zero(tc_Nat_Onat). % 12.93/12.84 0 [] class_Orderings_Oorder(tc_Nat_Onat). % 12.93/12.84 0 [] class_Rings_Osemiring(tc_Nat_Onat). % 12.93/12.84 0 [] class_Orderings_Oord(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ominus(tc_Nat_Onat). % 12.93/12.84 0 [] class_Power_Opower(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Ozero(tc_Nat_Onat). % 12.93/12.84 0 [] class_Groups_Oone(tc_Nat_Onat). % 12.93/12.84 0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool). % 12.93/12.84 0 [] class_Orderings_Opreorder(tc_HOL_Obool). % 12.93/12.84 0 [] class_Orderings_Oorder(tc_HOL_Obool). % 12.93/12.84 0 [] class_Orderings_Oord(tc_HOL_Obool). % 12.93/12.84 0 [] class_Groups_Ouminus(tc_HOL_Obool). % 12.93/12.84 0 [] class_Groups_Ominus(tc_HOL_Obool). % 12.93/12.84 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_RealVector_Ometric__space(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oordered__ring__abs(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_SEQ_Ocomplete__space(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Orderings_Opreorder(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Orderings_Olinorder(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Omult__zero(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Orderings_Oorder(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Osemiring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Orderings_Oord(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ouminus(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Osgn__if(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oabs__if(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oring__1(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ominus(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Power_Opower(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Ozero(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oring(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Rings_Oidom(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Groups_Oone(tc_RealDef_Oreal). % 12.93/12.84 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_RealVector_Ometric__space(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_SEQ_Ocomplete__space(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Osemiring(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ouminus(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Oring__1(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ominus(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Power_Opower(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Ozero(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Oring(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Rings_Oidom(tc_Complex_Ocomplex). % 12.93/12.84 0 [] class_Groups_Oone(tc_Complex_Ocomplex). % 12.93/12.84 0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)). % 12.93/12.84 0 [] hAPP(c_COMBK(T_a,T_b,V_P),V_Q)=V_P. % 12.93/12.84 0 [] hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2)). % 12.93/12.84 0 [] hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2). % 12.93/12.84 0 [] hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)). % 12.93/12.84 0 [] -c_SEQ_OBse_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))). % 12.93/12.84 end_of_list. % 12.93/12.84 % 12.93/12.84 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7. % 12.93/12.84 % 12.93/12.84 This ia a non-Horn set with equality. The strategy will be % 12.93/12.84 Knuth-Bendix, ordered hyper_res, factoring, and unit % 12.93/12.84 deletion, with positive clauses in sos and nonpositive % 12.93/12.84 clauses in usable. % 12.93/12.84 % 12.93/12.84 dependent: set(knuth_bendix). % 12.93/12.84 dependent: set(anl_eq). % 12.93/12.84 dependent: set(para_from). % 12.93/12.84 dependent: set(para_into). % 12.93/12.84 dependent: clear(para_from_right). % 12.93/12.84 dependent: clear(para_into_right). % 12.93/12.84 dependent: set(para_from_vars). % 12.93/12.84 dependent: set(eq_units_both_ways). % 12.93/12.84 dependent: set(dynamic_demod_all). % 12.93/12.84 dependent: set(dynamic_demod). % 12.93/12.84 dependent: set(order_eq). % 12.93/12.84 dependent: set(back_demod). % 12.93/12.84 dependent: set(lrpo). % 12.93/12.84 dependent: set(hyper_res). % 12.93/12.84 dependent: set(unit_deletion). % 12.93/12.84 dependent: set(factor). % 12.93/12.84 % 12.93/12.84 ------------> process usable: % 12.93/12.84 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B. % 12.93/12.84 ** KEPT (pick-wt=19): 2 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_SEQ_OBse_q(A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C))). % 12.93/12.84 ** KEPT (pick-wt=19): 3 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C)))|c_SEQ_OBse_q(A,B). % 12.93/12.84 ** KEPT (pick-wt=14): 4 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B))|c_SEQ_OBse_q(A,B). % 12.93/12.84 ** KEPT (pick-wt=14): 5 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B))| -c_SEQ_OBse_q(A,B). % 12.93/12.84 ** KEPT (pick-wt=8): 6 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_OBse_q(A,B). % 12.93/12.84 ** KEPT (pick-wt=29): 7 [] -class_Orderings_Oorder(A)| -c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,E,F)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,F),hAPP(B,E)). % 12.93/12.84 ** KEPT (pick-wt=13): 8 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f3(B,A),$f2(B,A)). % 12.93/12.84 ** KEPT (pick-wt=17): 9 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f3(B,A)),hAPP(B,$f2(B,A))). % 12.93/12.84 ** KEPT (pick-wt=13): 10 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f5(B,A),$f4(B,A)). % 12.93/12.84 ** KEPT (pick-wt=17): 11 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f4(B,A)),hAPP(B,$f5(B,A))). % 12.93/12.84 ** KEPT (pick-wt=11): 12 [] -c_SEQ_OCauchy(tc_Complex_Ocomplex,A)|c_SEQ_OCauchy(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,A)). % 12.93/12.84 ** KEPT (pick-wt=14): 13 [] -class_Groups_Oordered__ab__group__add(A)| -c_SEQ_Omonose_q(A,B)|c_SEQ_Omonose_q(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=15): 14 [] -class_RealVector_Ometric__space(A)| -c_SEQ_OCauchy(A,B)| -c_SEQ_Osubse_q(C)|c_SEQ_OCauchy(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)). % 12.93/12.84 ** KEPT (pick-wt=11): 15 [] -c_SEQ_OCauchy(tc_Complex_Ocomplex,A)|c_SEQ_OCauchy(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,A)). % 12.93/12.84 ** KEPT (pick-wt=17): 16 [] hAPP(c_Complex_ORe,A)!=hAPP(c_Complex_ORe,B)|hAPP(c_Complex_OIm,A)!=hAPP(c_Complex_OIm,B)|A=B. % 12.93/12.84 ** KEPT (pick-wt=10): 17 [] A!=B|hAPP(c_Complex_ORe,A)=hAPP(c_Complex_ORe,B). % 12.93/12.84 ** KEPT (pick-wt=10): 18 [] A!=B|hAPP(c_Complex_OIm,A)=hAPP(c_Complex_OIm,B). % 12.93/12.84 Following clause subsumed by 16 during input processing: 0 [] A=B|hAPP(c_Complex_ORe,A)!=hAPP(c_Complex_ORe,B)|hAPP(c_Complex_OIm,A)!=hAPP(c_Complex_OIm,B). % 12.93/12.84 ** KEPT (pick-wt=22): 19 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))). % 12.93/12.84 ** KEPT (pick-wt=12): 20 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=15): 22 [copy,21,flip.3] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=c_Groups_Oabs__class_Oabs(A,B). % 12.93/12.84 ** KEPT (pick-wt=9): 23 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.84 ** KEPT (pick-wt=11): 24 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),c_Groups_Oabs__class_Oabs(A,B)). % 12.93/12.84 ** KEPT (pick-wt=12): 25 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.84 ** KEPT (pick-wt=15): 26 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C). % 12.93/12.84 ** KEPT (pick-wt=19): 27 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C). % 12.93/12.84 Following clause subsumed by 27 during input processing: 0 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C). % 12.93/12.84 Following clause subsumed by 26 during input processing: 0 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C). % 12.93/12.84 ** KEPT (pick-wt=13): 28 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=13): 29 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=22): 30 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))). % 12.93/12.84 ** KEPT (pick-wt=5): 31 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.84 ** KEPT (pick-wt=15): 32 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=B. % 12.93/12.84 ** KEPT (pick-wt=15): 33 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=B. % 12.93/12.84 ** KEPT (pick-wt=15): 34 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A). % 12.93/12.84 ** KEPT (pick-wt=15): 35 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A). % 12.93/12.84 ** KEPT (pick-wt=9): 36 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)). % 12.93/12.84 ** KEPT (pick-wt=17): 37 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). % 12.93/12.84 ** KEPT (pick-wt=17): 38 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). % 12.93/12.84 ** KEPT (pick-wt=17): 39 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B). % 12.93/12.84 ** KEPT (pick-wt=17): 40 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B). % 12.93/12.84 ** KEPT (pick-wt=8): 41 [] -c_SEQ_Osubse_q(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,hAPP(A,B)). % 12.93/12.84 ** KEPT (pick-wt=10): 42 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=10): 43 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=18): 44 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D. % 12.93/12.84 ** KEPT (pick-wt=18): 45 [] -class_Groups_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D. % 12.93/12.84 ** KEPT (pick-wt=18): 46 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D. % 12.93/12.84 Following clause subsumed by 44 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D. % 12.93/12.84 ** KEPT (pick-wt=18): 47 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B!=D. % 12.93/12.84 Following clause subsumed by 46 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D. % 12.93/12.84 ** KEPT (pick-wt=18): 48 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C!=D. % 12.93/12.84 ** KEPT (pick-wt=25): 49 [] -class_Groups_Oab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.84 ** KEPT (pick-wt=10): 50 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A). % 12.93/12.84 ** KEPT (pick-wt=10): 51 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A). % 12.93/12.84 ** KEPT (pick-wt=14): 52 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|B=C. % 12.93/12.84 ** KEPT (pick-wt=14): 53 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|B!=C. % 12.93/12.84 ** KEPT (pick-wt=14): 54 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=C|hAPP(c_Groups_Ouminus__class_Ouminus(A),C)=B. % 12.93/12.84 Following clause subsumed by 54 during input processing: 0 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=C|hAPP(c_Groups_Ouminus__class_Ouminus(A),C)!=B. % 12.93/12.84 ** KEPT (pick-wt=14): 55 [] -class_Groups_Ogroup__add(A)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|C=hAPP(c_Groups_Ouminus__class_Ouminus(A),B). % 12.93/12.84 Following clause subsumed by 55 during input processing: 0 [] -class_Groups_Ogroup__add(A)|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|C!=hAPP(c_Groups_Ouminus__class_Ouminus(A),B). % 12.93/12.84 ** KEPT (pick-wt=11): 56 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=B. % 12.93/12.84 ** KEPT (pick-wt=11): 57 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,A)|A=B. % 12.93/12.84 ** KEPT (pick-wt=12): 58 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,C). % 12.93/12.84 ** KEPT (pick-wt=11): 59 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oabs__class_Oabs(A,B))=c_Groups_Oabs__class_Oabs(A,B). % 12.93/12.84 ** KEPT (pick-wt=11): 60 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B. % 12.93/12.84 ** KEPT (pick-wt=11): 61 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B. % 12.93/12.84 ** KEPT (pick-wt=15): 62 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=15): 63 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=11): 64 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B. % 12.93/12.84 ** KEPT (pick-wt=11): 65 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B. % 12.93/12.84 ** KEPT (pick-wt=20): 66 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))|c_Orderings_Oord__class_Oless__e_q(A,C,D). % 12.93/12.84 ** KEPT (pick-wt=20): 67 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 12.93/12.84 ** KEPT (pick-wt=24): 68 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)). % 12.93/12.84 ** KEPT (pick-wt=20): 69 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)). % 12.93/12.84 ** KEPT (pick-wt=20): 70 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.84 Following clause subsumed by 66 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))|c_Orderings_Oord__class_Oless__e_q(A,C,D). % 12.93/12.84 ** KEPT (pick-wt=20): 71 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D). % 12.93/12.84 Following clause subsumed by 67 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 12.93/12.84 ** KEPT (pick-wt=20): 72 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))| -c_Orderings_Oord__class_Oless__e_q(A,B,D). % 12.93/12.84 ** KEPT (pick-wt=12): 73 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=B|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=12): 74 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=B|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=13): 75 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=13): 76 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 Following clause subsumed by 73 during input processing: 0 [flip.2] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=B|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 Following clause subsumed by 74 during input processing: 0 [flip.2] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=B|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=13): 77 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)!=hAPP(c_Groups_Ouminus__class_Ouminus(A),B)|c_Groups_Ozero__class_Ozero(A)=B. % 12.93/12.84 ** KEPT (pick-wt=13): 78 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)=hAPP(c_Groups_Ouminus__class_Ouminus(A),B)|c_Groups_Ozero__class_Ozero(A)!=B. % 12.93/12.84 ** KEPT (pick-wt=10): 79 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=16): 80 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=16): 81 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 Following clause subsumed by 80 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 ** KEPT (pick-wt=16): 82 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C),B). % 12.93/12.84 Following clause subsumed by 82 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C),B). % 12.93/12.84 ** KEPT (pick-wt=16): 83 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),C))|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 Following clause subsumed by 83 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),C))| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=18): 84 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))=C. % 12.93/12.84 ** KEPT (pick-wt=18): 85 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C))=C. % 12.93/12.84 ** KEPT (pick-wt=24): 86 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=24): 88 [copy,87,flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)). % 12.93/12.84 ** KEPT (pick-wt=12): 89 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=12): 90 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=9): 91 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=12): 92 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=12): 93 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=9): 94 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.84 Following clause subsumed by 25 during input processing: 0 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.84 ** KEPT (pick-wt=8): 95 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oabs__class_Oabs(A,B)). % 12.93/12.84 ** KEPT (pick-wt=25): 96 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)). % 12.93/12.84 ** KEPT (pick-wt=12): 97 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=c_Groups_Oabs__class_Oabs(A,B). % 12.93/12.84 ** KEPT (pick-wt=12): 98 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=c_RealVector_Onorm__class_Onorm(A,B). % 12.93/12.84 ** KEPT (pick-wt=18): 99 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B)). % 12.93/12.84 ** KEPT (pick-wt=13): 100 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),A). % 12.93/12.84 ** KEPT (pick-wt=10): 101 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B). % 12.93/12.84 ** KEPT (pick-wt=17): 102 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B). % 12.93/12.84 ** KEPT (pick-wt=11): 103 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B))=c_RealVector_Onorm__class_Onorm(A,B). % 12.93/12.84 ** KEPT (pick-wt=22): 104 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=20): 105 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)). % 12.93/12.84 ** KEPT (pick-wt=20): 106 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)). % 12.93/12.84 ** KEPT (pick-wt=25): 107 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=25): 108 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=29): 109 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 Following clause subsumed by 106 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)). % 12.93/12.84 ** KEPT (pick-wt=17): 110 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=17): 111 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=17): 112 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.84 ** KEPT (pick-wt=17): 113 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.84 ** KEPT (pick-wt=14): 114 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.84 ** KEPT (pick-wt=14): 115 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.84 ** KEPT (pick-wt=15): 116 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.84 ** KEPT (pick-wt=15): 117 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.84 ** KEPT (pick-wt=14): 118 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=14): 119 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),B))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=15): 120 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=15): 121 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=17): 122 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=C. % 12.93/12.84 ** KEPT (pick-wt=17): 123 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C=hAPP(c_Groups_Ouminus__class_Ouminus(A),B). % 12.93/12.84 ** KEPT (pick-wt=17): 124 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=hAPP(c_Groups_Ouminus__class_Ouminus(A),B). % 12.93/12.84 ** KEPT (pick-wt=14): 125 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=14): 126 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=17): 127 [] -class_Groups_Ogroup__add(A)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=17): 128 [] -class_Groups_Ogroup__add(A)|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=14): 129 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=12): 130 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,B)=B. % 12.93/12.84 ** KEPT (pick-wt=13): 131 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=13): 132 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=9): 133 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)). % 12.93/12.84 ** KEPT (pick-wt=19): 134 [] -class_RealVector_Ometric__space(A)| -class_RealVector_Ometric__space(B)| -c_Lim_OisUCont(B,A,C)| -c_SEQ_OCauchy(B,D)|c_SEQ_OCauchy(A,c_COMBB(B,A,tc_Nat_Onat,C,D)). % 12.93/12.84 ** KEPT (pick-wt=8): 135 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)). % 12.93/12.84 ** KEPT (pick-wt=8): 136 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.84 ** KEPT (pick-wt=6): 137 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B). % 12.93/12.84 ** KEPT (pick-wt=13): 138 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 12.93/12.84 ** KEPT (pick-wt=13): 139 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.93/12.84 Following clause subsumed by 138 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 12.93/12.84 Following clause subsumed by 139 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.93/12.84 ** KEPT (pick-wt=22): 140 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). % 12.93/12.84 ** KEPT (pick-wt=18): 141 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). % 12.93/12.84 ** KEPT (pick-wt=13): 142 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)). % 12.93/12.84 ** KEPT (pick-wt=16): 143 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)). % 12.93/12.84 ** KEPT (pick-wt=24): 144 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f6(D,C,B,A)),hAPP(D,$f6(D,C,B,A))). % 12.93/12.84 ** KEPT (pick-wt=10): 145 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 ** KEPT (pick-wt=9): 146 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.84 ** KEPT (pick-wt=9): 147 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 ** KEPT (pick-wt=13): 148 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 ** KEPT (pick-wt=9): 149 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.84 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)). % 12.93/12.84 Following clause subsumed by 148 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B. % 12.93/12.84 Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B. % 12.93/12.84 ** KEPT (pick-wt=13): 150 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 12.93/12.84 ** KEPT (pick-wt=13): 151 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B). % 12.93/12.84 ** KEPT (pick-wt=13): 152 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 12.93/12.84 ** KEPT (pick-wt=13): 153 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C). % 12.93/12.84 Following clause subsumed by 148 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C. % 12.93/12.84 ** KEPT (pick-wt=14): 154 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 12.93/12.84 Following clause subsumed by 148 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B. % 12.93/12.84 ** KEPT (pick-wt=14): 155 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C). % 12.93/12.84 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)). % 12.93/12.84 Following clause subsumed by 145 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 ** KEPT (pick-wt=16): 156 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B=C. % 12.93/12.84 ** KEPT (pick-wt=16): 157 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B!=C. % 12.93/12.84 ** KEPT (pick-wt=16): 158 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A=C. % 12.93/12.84 ** KEPT (pick-wt=16): 159 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A!=C. % 12.93/12.84 ** KEPT (pick-wt=11): 160 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B. % 12.93/12.84 ** KEPT (pick-wt=12): 161 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 12.93/12.84 ** KEPT (pick-wt=7): 162 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.84 ** KEPT (pick-wt=28): 163 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(c_Fun_Ocomp(G,H,I,A,B),C)=hAPP(c_Fun_Ocomp(J,H,K,D,E),F). % 12.93/12.84 ** KEPT (pick-wt=7): 165 [copy,164,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A). % 12.93/12.84 Following clause subsumed by 165 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A). % 12.93/12.84 ** KEPT (pick-wt=13): 166 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 ** KEPT (pick-wt=13): 167 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 ** KEPT (pick-wt=17): 168 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 ** KEPT (pick-wt=12): 169 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 ** KEPT (pick-wt=9): 170 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 Following clause subsumed by 162 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.84 ** KEPT (pick-wt=9): 171 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A). % 12.93/12.84 ** KEPT (pick-wt=14): 173 [copy,172,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f7(B,A))=B. % 12.93/12.84 ** KEPT (pick-wt=12): 174 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C). % 12.93/12.84 ** KEPT (pick-wt=18): 175 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.93/12.84 ** KEPT (pick-wt=18): 176 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.93/12.84 ** KEPT (pick-wt=13): 177 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). % 12.93/12.84 Following clause subsumed by 142 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)). % 12.93/12.84 Following clause subsumed by 177 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). % 12.93/12.84 ** KEPT (pick-wt=14): 179 [copy,178,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f8(B,A))=B. % 12.93/12.84 Following clause subsumed by 174 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C). % 12.93/12.84 ** KEPT (pick-wt=17): 180 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,D),hAPP(B,C)). % 12.93/12.84 ** KEPT (pick-wt=13): 181 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f10(B,A),$f9(B,A)). % 12.93/12.84 ** KEPT (pick-wt=17): 182 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f9(B,A)),hAPP(B,$f10(B,A))). % 12.93/12.84 ** KEPT (pick-wt=16): 183 [] -class_Lattices_Oboolean__algebra(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 ** KEPT (pick-wt=16): 184 [] -class_Lattices_Oboolean__algebra(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.84 Following clause subsumed by 184 during input processing: 0 [] -class_Lattices_Oboolean__algebra(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=11): 185 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B. % 12.93/12.84 ** KEPT (pick-wt=11): 186 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B. % 12.93/12.84 ** KEPT (pick-wt=14): 188 [copy,187,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=B|C=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=14): 190 [copy,189,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=B|C!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=15): 191 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=15): 192 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.84 ** KEPT (pick-wt=17): 193 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D)). % 12.93/12.84 ** KEPT (pick-wt=13): 194 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f12(B,A),$f11(B,A)). % 12.93/12.84 ** KEPT (pick-wt=17): 195 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f12(B,A)),hAPP(B,$f11(B,A))). % 12.93/12.84 ** KEPT (pick-wt=14): 196 [] -class_Groups_Oordered__ab__group__add(A)| -c_SEQ_Odecse_q(A,B)|c_SEQ_Oincse_q(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=14): 197 [] -class_Groups_Oordered__ab__group__add(A)|c_SEQ_Odecse_q(A,B)| -c_SEQ_Oincse_q(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.84 ** KEPT (pick-wt=35): 198 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)). % 12.93/12.84 ** KEPT (pick-wt=25): 199 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C). % 12.93/12.84 ** KEPT (pick-wt=25): 200 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.84 Following clause subsumed by 200 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.84 ** KEPT (pick-wt=25): 201 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)). % 12.93/12.84 ** KEPT (pick-wt=15): 202 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B). % 12.93/12.84 ** KEPT (pick-wt=14): 203 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|B=C. % 12.93/12.84 ** KEPT (pick-wt=14): 204 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|B!=C. % 12.93/12.84 ** KEPT (pick-wt=17): 205 [] -class_Groups_Ouminus(A)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A)),C),D)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(C,D)). % 12.93/12.84 ** KEPT (pick-wt=11): 206 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=B. % 12.93/12.84 ** KEPT (pick-wt=8): 207 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)|c_SEQ_Omonose_q(A,B). % 12.93/12.84 ** KEPT (pick-wt=8): 208 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)|c_SEQ_Omonose_q(A,B). % 12.93/12.84 Following clause subsumed by 205 during input processing: 0 [] -class_Groups_Ouminus(A)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A)),C),D)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(C,D)). % 12.93/12.84 ** KEPT (pick-wt=13): 209 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,$f13(C,D,B,A))|c_SEQ_OBse_q(A,D). % 12.93/12.84 ** KEPT (pick-wt=17): 210 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f13(C,B,D,A))),C)|c_SEQ_OBse_q(A,B). % 12.93/12.84 ** KEPT (pick-wt=14): 211 [] -class_RealVector_Oreal__normed__vector(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.84 ** KEPT (pick-wt=14): 212 [] -class_RealVector_Oreal__normed__vector(A)|B=c_Groups_Ozero__class_Ozero(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.84 ** KEPT (pick-wt=13): 213 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). % 12.93/12.84 ** KEPT (pick-wt=13): 214 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). % 12.93/12.84 ** KEPT (pick-wt=16): 215 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_SEQ_OBse_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A)). % 12.93/12.84 ** KEPT (pick-wt=16): 216 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_SEQ_Omonose_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A)). % 12.93/12.84 ** KEPT (pick-wt=11): 217 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B. % 12.93/12.84 ** KEPT (pick-wt=19): 218 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C). % 12.93/12.84 ** KEPT (pick-wt=11): 219 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Osgn__class_Osgn(A,B). % 12.93/12.84 ** KEPT (pick-wt=20): 220 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C)). % 12.93/12.85 ** KEPT (pick-wt=12): 221 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=12): 222 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=9): 223 [] -class_Groups_Osgn__if(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=9): 224 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=12): 225 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=12): 226 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=9): 227 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=15): 229 [copy,228,flip.2] -class_RealVector_Oreal__normed__vector(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Osgn__class_Osgn(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.85 ** KEPT (pick-wt=12): 230 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=17): 231 [] c_Fun_Ocomp(A,B,C,D,E)!=F|hAPP(D,hAPP(E,G))=hAPP(F,G). % 12.93/12.85 ** KEPT (pick-wt=24): 232 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,B,C,G,H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)). % 12.93/12.85 Following clause subsumed by 232 during input processing: 0 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,B,C,G,H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)). % 12.93/12.85 ** KEPT (pick-wt=30): 233 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)). % 12.93/12.85 ** KEPT (pick-wt=25): 234 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)). % 12.93/12.85 ** KEPT (pick-wt=14): 235 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oabs__class_Oabs(A,B)),C)). % 12.93/12.85 ** KEPT (pick-wt=18): 236 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=18): 237 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=22): 238 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=12): 239 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=21): 240 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=21): 241 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=25): 242 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=11): 243 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B. % 12.93/12.85 ** KEPT (pick-wt=15): 244 [] -class_Rings_Oring__1__no__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=12): 245 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B)=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=19): 247 [copy,246,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oabs__class_Oabs(A,B)),C)=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=25): 248 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)). % 12.93/12.85 ** KEPT (pick-wt=17): 249 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=17): 250 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=22): 251 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.85 ** KEPT (pick-wt=22): 252 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.85 ** KEPT (pick-wt=16): 253 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A)). % 12.93/12.85 ** KEPT (pick-wt=12): 254 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f14(B,A)). % 12.93/12.85 ** KEPT (pick-wt=15): 255 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),$f14(B,A)). % 12.93/12.85 ** KEPT (pick-wt=21): 256 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f15(B,A,C))),C). % 12.93/12.85 ** KEPT (pick-wt=8): 257 [] -class_RealVector_Ometric__space(A)|c_SEQ_Oconvergent(A,c_COMBK(A,tc_Nat_Onat,B)). % 12.93/12.85 ** KEPT (pick-wt=14): 258 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),B)!=hAPP(c_RealVector_Oof__real(A),C)|B=C. % 12.93/12.85 ** KEPT (pick-wt=14): 259 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),B)=hAPP(c_RealVector_Oof__real(A),C)|B!=C. % 12.93/12.85 ** KEPT (pick-wt=16): 260 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_Oconvergent(tc_RealDef_Oreal,B)|c_SEQ_Oconvergent(A,c_COMBB(tc_RealDef_Oreal,A,tc_Nat_Onat,c_RealVector_Oof__real(A),B)). % 12.93/12.85 ** KEPT (pick-wt=10): 261 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Complex_Ocomplex_OComplex(C,D)|A=C. % 12.93/12.85 ** KEPT (pick-wt=10): 262 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Complex_Ocomplex_OComplex(C,D)|B=D. % 12.93/12.85 ** KEPT (pick-wt=13): 263 [] c_Complex_Ocomplex_OComplex(A,B)=c_Complex_Ocomplex_OComplex(C,D)|A!=C|B!=D. % 12.93/12.85 ** KEPT (pick-wt=9): 264 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_Lim_OisUCont(tc_RealDef_Oreal,A,c_RealVector_Oof__real(A)). % 12.93/12.85 ** KEPT (pick-wt=13): 265 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=10): 266 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=14): 267 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.85 ** KEPT (pick-wt=14): 268 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=13): 269 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.85 ** KEPT (pick-wt=13): 270 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=13): 271 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B). % 12.93/12.85 ** KEPT (pick-wt=13): 272 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=10): 273 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 266 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=9): 274 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B. % 12.93/12.85 ** KEPT (pick-wt=9): 275 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 12.93/12.85 Following clause subsumed by 266 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 266 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 275 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 12.93/12.85 ** KEPT (pick-wt=13): 276 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B. % 12.93/12.85 ** KEPT (pick-wt=13): 277 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B. % 12.93/12.85 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C. % 12.93/12.85 ** KEPT (pick-wt=10): 278 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=9): 279 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 12.93/12.85 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 279 during input processing: 0 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C). % 12.93/12.85 ** KEPT (pick-wt=9): 280 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=6): 281 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B). % 12.93/12.85 ** KEPT (pick-wt=11): 282 [] c_Complex_Ocomplex_OComplex(A,B)!=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),C)|A=C. % 12.93/12.85 ** KEPT (pick-wt=12): 283 [] c_Complex_Ocomplex_OComplex(A,B)!=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),C)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=15): 284 [] c_Complex_Ocomplex_OComplex(A,B)=hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),C)|A!=C|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=25): 285 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 12.93/12.85 ** KEPT (pick-wt=25): 286 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 12.93/12.85 Following clause subsumed by 285 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 12.93/12.85 Following clause subsumed by 286 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)). % 12.93/12.85 ** KEPT (pick-wt=10): 287 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=10): 288 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.85 Following clause subsumed by 287 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 288 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 287 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=10): 289 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.85 Following clause subsumed by 275 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 12.93/12.85 ** KEPT (pick-wt=13): 290 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C. % 12.93/12.85 ** KEPT (pick-wt=10): 291 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.85 ** KEPT (pick-wt=10): 292 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=14): 293 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.85 Following clause subsumed by 290 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C. % 12.93/12.85 Following clause subsumed by 289 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C). % 12.93/12.85 Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C. % 12.93/12.85 Following clause subsumed by 287 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 12.93/12.85 Following clause subsumed by 287 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=13): 294 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C. % 12.93/12.85 ** KEPT (pick-wt=13): 295 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C. % 12.93/12.85 Following clause subsumed by 290 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C). % 12.93/12.85 ** KEPT (pick-wt=13): 296 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 288 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 Following clause subsumed by 291 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 12.93/12.85 Following clause subsumed by 294 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C. % 12.93/12.85 Following clause subsumed by 279 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 12.93/12.85 Following clause subsumed by 290 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C. % 12.93/12.85 Following clause subsumed by 290 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C). % 12.93/12.85 Following clause subsumed by 296 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C). % 12.93/12.85 ** KEPT (pick-wt=14): 297 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=14): 298 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.85 ** KEPT (pick-wt=14): 299 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=14): 300 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.85 ** KEPT (pick-wt=20): 301 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=20): 302 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))| -c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=20): 303 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D). % 12.93/12.85 ** KEPT (pick-wt=20): 304 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))| -c_Orderings_Oord__class_Oless(A,C,D). % 12.93/12.85 ** KEPT (pick-wt=20): 305 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.85 ** KEPT (pick-wt=20): 306 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)). % 12.93/12.85 ** KEPT (pick-wt=24): 307 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)). % 12.93/12.85 Following clause subsumed by 301 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 Following clause subsumed by 303 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D). % 12.93/12.85 ** KEPT (pick-wt=16): 308 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),C))|c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.85 Following clause subsumed by 308 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),C))| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.85 ** KEPT (pick-wt=16): 309 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C),B). % 12.93/12.85 Following clause subsumed by 309 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C),B). % 12.93/12.85 ** KEPT (pick-wt=16): 310 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))|c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=16): 311 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))| -c_Orderings_Oord__class_Oless(A,C,B). % 12.93/12.85 ** KEPT (pick-wt=8): 312 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B). % 12.93/12.85 ** KEPT (pick-wt=7): 313 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B. % 12.93/12.85 ** KEPT (pick-wt=11): 314 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A=B. % 12.93/12.85 Following clause subsumed by 314 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B. % 12.93/12.85 Following clause subsumed by 312 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). % 12.93/12.85 ** KEPT (pick-wt=7): 315 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B. % 12.93/12.85 ** KEPT (pick-wt=15): 317 [copy,316,flip.2] -class_RealVector_Oreal__normed__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,B))=c_Groups_Osgn__class_Osgn(A,hAPP(c_RealVector_Oof__real(A),B)). % 12.93/12.85 ** KEPT (pick-wt=30): 318 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)). % 12.93/12.85 ** KEPT (pick-wt=22): 319 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=8): 320 [] -class_SEQ_Ocomplete__space(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_Oconvergent(A,B). % 12.93/12.85 ** KEPT (pick-wt=8): 321 [] -class_SEQ_Ocomplete__space(A)|c_SEQ_OCauchy(A,B)| -c_SEQ_Oconvergent(A,B). % 12.93/12.85 Following clause subsumed by 320 during input processing: 0 [] -class_SEQ_Ocomplete__space(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_Oconvergent(A,B). % 12.93/12.85 ** KEPT (pick-wt=8): 322 [] -class_RealVector_Ometric__space(A)| -c_SEQ_Oconvergent(A,B)|c_SEQ_OCauchy(A,B). % 12.93/12.85 ** KEPT (pick-wt=10): 323 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_RComplete_Onatfloor(B)). % 12.93/12.85 ** KEPT (pick-wt=10): 324 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_RComplete_Onatceiling(B)). % 12.93/12.85 ** KEPT (pick-wt=6): 325 [] -c_SEQ_OCauchy(tc_RealDef_Oreal,A)|c_SEQ_Oconvergent(tc_RealDef_Oreal,A). % 12.93/12.85 ** KEPT (pick-wt=24): 326 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_Oconvergent(A,B)| -c_SEQ_Oconvergent(A,C)|c_SEQ_Oconvergent(A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=14): 327 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_Oconvergent(A,B)|c_SEQ_Oconvergent(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.85 ** KEPT (pick-wt=14): 328 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_Oconvergent(A,B)| -c_SEQ_Oconvergent(A,c_COMBB(A,A,tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(A),B)). % 12.93/12.85 ** KEPT (pick-wt=30): 329 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)). % 12.93/12.85 ** KEPT (pick-wt=10): 330 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 Following clause subsumed by 330 during input processing: 0 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|hAPP(c_RealVector_Oof__real(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=13): 331 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=13): 332 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=24): 334 [copy,333,flip.2] -class_RealVector_Oreal__algebra__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_RealVector_Oof__real(A),B)),hAPP(c_RealVector_Oof__real(A),C))=hAPP(c_RealVector_Oof__real(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). % 12.93/12.85 Following clause subsumed by 334 during input processing: 0 [flip.3] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_RealVector_Oof__real(A),B)),hAPP(c_RealVector_Oof__real(A),C))=hAPP(c_RealVector_Oof__real(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). % 12.93/12.85 ** KEPT (pick-wt=10): 335 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=21): 337 [copy,336,flip.2] -class_RealVector_Oreal__algebra__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_RealVector_Oof__real(A),B)),C)=hAPP(c_RealVector_Oof__real(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)). % 12.93/12.85 ** KEPT (pick-wt=20): 338 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)). % 12.93/12.85 ** KEPT (pick-wt=17): 339 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=17): 340 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=17): 341 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=17): 342 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=22): 343 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=22): 344 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=17): 345 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=17): 346 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=24): 347 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)). % 12.93/12.85 ** KEPT (pick-wt=24): 348 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)). % 12.93/12.85 ** KEPT (pick-wt=8): 349 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=8): 350 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)). % 12.93/12.85 ** KEPT (pick-wt=14): 351 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=14): 352 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=15): 353 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=15): 354 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=15): 355 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=15): 356 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=14): 357 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=14): 358 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=17): 359 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=17): 360 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_RealVector_Oof__real(A),B)). % 12.93/12.85 Following clause subsumed by 360 during input processing: 0 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|hAPP(c_RealVector_Oof__real(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_RealVector_Oof__real(A),B)). % 12.93/12.85 ** KEPT (pick-wt=12): 361 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))). % 12.93/12.85 ** KEPT (pick-wt=23): 362 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C=D. % 12.93/12.85 ** KEPT (pick-wt=23): 363 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C!=D. % 12.93/12.85 ** KEPT (pick-wt=9): 364 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=13): 365 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B))|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=13): 366 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B))|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=12): 367 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,B)=B. % 12.93/12.85 ** KEPT (pick-wt=12): 368 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(c_RealVector_Oof__real(A),B))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B). % 12.93/12.85 ** KEPT (pick-wt=12): 369 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless(A,B,C). % 12.93/12.85 ** KEPT (pick-wt=15): 370 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C). % 12.93/12.85 ** KEPT (pick-wt=19): 371 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C). % 12.93/12.85 ** KEPT (pick-wt=9): 372 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.85 ** KEPT (pick-wt=14): 373 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=14): 374 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=14): 375 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=14): 376 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=11): 377 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=10): 378 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=10): 379 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=14): 380 [] c_Complex_Ocomplex_OComplex(A,B)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=10): 381 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=10): 382 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=16): 383 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OCauchy(tc_RealDef_Oreal,B)|c_SEQ_OCauchy(A,c_COMBB(tc_RealDef_Oreal,A,tc_Nat_Onat,c_RealVector_Oof__real(A),B)). % 12.93/12.85 ** KEPT (pick-wt=22): 384 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=22): 385 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)). % 12.93/12.85 ** KEPT (pick-wt=20): 386 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)). % 12.93/12.85 ** KEPT (pick-wt=20): 387 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)). % 12.93/12.85 ** KEPT (pick-wt=22): 388 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=22): 389 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=25): 390 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.85 ** KEPT (pick-wt=14): 391 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))). % 12.93/12.85 ** KEPT (pick-wt=9): 392 [] -c_SEQ_OBse_q(tc_RealDef_Oreal,A)| -c_SEQ_Omonose_q(tc_RealDef_Oreal,A)|c_SEQ_Oconvergent(tc_RealDef_Oreal,A). % 12.93/12.85 ** KEPT (pick-wt=15): 394 [copy,393,flip.3] -class_Groups_Oabs__if(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=c_Groups_Oabs__class_Oabs(A,B). % 12.93/12.85 ** KEPT (pick-wt=12): 395 [] -class_Groups_Oabs__if(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Oabs__class_Oabs(A,B)=B. % 12.93/12.85 ** KEPT (pick-wt=15): 397 [copy,396,flip.3] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=c_Groups_Oabs__class_Oabs(A,B). % 12.93/12.85 ** KEPT (pick-wt=13): 398 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B))|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=13): 399 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B))|B=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=13): 400 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 ** KEPT (pick-wt=13): 401 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.85 Following clause subsumed by 401 during input processing: 0 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=30): 402 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),E)). % 12.93/12.85 ** KEPT (pick-wt=10): 403 [] A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 Following clause subsumed by 377 during input processing: 0 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.85 Following clause subsumed by 403 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 Following clause subsumed by 377 during input processing: 0 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=17): 404 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). % 12.93/12.85 ** KEPT (pick-wt=17): 405 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). % 12.93/12.85 ** KEPT (pick-wt=17): 406 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B). % 12.93/12.85 ** KEPT (pick-wt=17): 407 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B). % 12.93/12.85 ** KEPT (pick-wt=13): 409 [copy,408,flip.2] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A). % 12.93/12.85 Following clause subsumed by 409 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A). % 12.93/12.85 ** KEPT (pick-wt=11): 410 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 12.93/12.85 ** KEPT (pick-wt=11): 411 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 12.93/12.85 ** KEPT (pick-wt=12): 412 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). % 12.93/12.85 ** KEPT (pick-wt=10): 413 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|A=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=10): 414 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=14): 415 [] c_Complex_Ocomplex_OComplex(A,B)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|A!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.93/12.85 ** KEPT (pick-wt=15): 416 [] -class_SEQ_Ocomplete__space(A)| -c_SEQ_Oconvergent(A,B)| -c_SEQ_Osubse_q(C)|c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)). % 12.93/12.85 ** KEPT (pick-wt=11): 417 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.85 ** KEPT (pick-wt=11): 418 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 12.93/12.85 ** KEPT (pick-wt=25): 419 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D). % 12.93/12.85 ** KEPT (pick-wt=25): 420 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D). % 12.93/12.85 Following clause subsumed by 419 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D). % 12.93/12.85 ** KEPT (pick-wt=16): 421 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 ** KEPT (pick-wt=16): 422 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.85 Following clause subsumed by 422 during input processing: 0 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Osgn__class_Osgn(A,B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)). % 12.93/12.85 ** KEPT (pick-wt=12): 423 [] -class_Groups_Osgn__if(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.85 ** KEPT (pick-wt=17): 424 [] -class_Groups_Osgn__if(A)|B=c_Groups_Ozero__class_Ozero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A). % 12.93/12.85 ** KEPT (pick-wt=20): 425 [] -class_Groups_Osgn__if(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)). % 12.93/12.85 ** KEPT (pick-wt=12): 426 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f17(B,A)). % 12.93/12.85 ** KEPT (pick-wt=25): 427 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),$f16(B,A)))),$f17(B,A)). % 12.93/12.85 ** KEPT (pick-wt=30): 428 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(B,$f18(B,A,C,D))),hAPP(c_Groups_Ouminus__class_Ouminus(A),D))),C). % 12.93/12.85 ** KEPT (pick-wt=12): 429 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f20(B,A)). % 12.93/12.85 ** KEPT (pick-wt=27): 430 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(B,$f19(B,A))))),$f20(B,A)). % 12.93/12.85 ** KEPT (pick-wt=32): 431 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(B,$f21(B,A,C,D))),hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(B,D)))),C). % 12.93/12.85 ** KEPT (pick-wt=28): 432 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 12.93/12.85 ** KEPT (pick-wt=5): 433 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.85 ** KEPT (pick-wt=12): 434 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 12.93/12.85 ** KEPT (pick-wt=12): 435 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 12.93/12.85 ** KEPT (pick-wt=7): 436 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B. % 12.93/12.85 ** KEPT (pick-wt=7): 437 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A. % 12.93/12.85 ** KEPT (pick-wt=4): 438 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A). % 12.93/12.85 Following clause subsumed by 436 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 12.93/12.85 Following clause subsumed by 437 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). % 12.93/12.85 Following clause subsumed by 438 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A). % 12.93/12.85 ** KEPT (pick-wt=10): 439 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_RealDef_Oreal(tc_Nat_Onat,B)|A=B. % 12.93/12.85 ** KEPT (pick-wt=10): 440 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_RealDef_Oreal(tc_Nat_Onat,B)|A!=B. % 12.93/12.85 ** KEPT (pick-wt=14): 441 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D). % 12.93/12.85 ** KEPT (pick-wt=14): 442 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C). % 12.93/12.85 ** KEPT (pick-wt=20): 443 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C). % 12.93/12.85 ** KEPT (pick-wt=20): 444 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),B))|A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=16): 445 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=23): 446 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.93/12.85 ** KEPT (pick-wt=19): 447 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=15): 448 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.85 ** KEPT (pick-wt=14): 449 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 ** KEPT (pick-wt=8): 450 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.85 Following clause subsumed by 433 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.85 Following clause subsumed by 450 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.85 Following clause subsumed by 433 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 12.93/12.85 ** KEPT (pick-wt=13): 451 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). % 12.93/12.85 ** KEPT (pick-wt=21): 452 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 12.93/12.85 ** KEPT (pick-wt=22): 453 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). % 12.93/12.85 ** KEPT (pick-wt=18): 454 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). % 12.93/12.85 ** KEPT (pick-wt=13): 455 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)). % 12.93/12.85 ** KEPT (pick-wt=13): 456 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). % 12.93/12.85 Following clause subsumed by 455 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)). % 12.93/12.85 Following clause subsumed by 456 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). % 12.93/12.85 ** KEPT (pick-wt=18): 457 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.93/12.85 ** KEPT (pick-wt=18): 458 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.93/12.85 ** KEPT (pick-wt=9): 459 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),B). % 12.93/12.85 ** KEPT (pick-wt=9): 460 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),A). % 12.93/12.85 ** KEPT (pick-wt=8): 461 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.85 Following clause subsumed by 436 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B. % 12.93/12.85 ** KEPT (pick-wt=11): 462 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B. % 12.93/12.85 Following clause subsumed by 462 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B. % 12.93/12.85 Following clause subsumed by 461 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 12.93/12.85 Following clause subsumed by 162 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B. % 12.93/12.85 Following clause subsumed by 461 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.85 Following clause subsumed by 461 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.86 Following clause subsumed by 462 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 12.93/12.86 Following clause subsumed by 461 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.86 Following clause subsumed by 162 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.86 ** KEPT (pick-wt=12): 463 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.86 ** KEPT (pick-wt=12): 464 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.86 ** KEPT (pick-wt=18): 465 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,B)). % 12.93/12.86 ** KEPT (pick-wt=18): 466 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,B)). % 12.93/12.86 ** KEPT (pick-wt=14): 467 [] -c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). % 12.93/12.86 ** KEPT (pick-wt=12): 468 [] c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f23(A)),hAPP(A,$f22(A))). % 12.93/12.86 ** KEPT (pick-wt=10): 469 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.86 ** KEPT (pick-wt=10): 470 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.86 ** KEPT (pick-wt=16): 471 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(A),B). % 12.93/12.86 ** KEPT (pick-wt=7): 472 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.93/12.86 ** KEPT (pick-wt=12): 473 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.86 ** KEPT (pick-wt=12): 474 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.93/12.86 ** KEPT (pick-wt=20): 475 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 12.93/12.86 Following clause subsumed by 456 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.86 Following clause subsumed by 455 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 12.93/12.86 ** KEPT (pick-wt=21): 477 [copy,476,flip.1] c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A))!=A|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(A)),B). % 12.93/12.86 ** KEPT (pick-wt=11): 478 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.86 ** KEPT (pick-wt=11): 479 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.86 ** KEPT (pick-wt=12): 480 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A)),A). % 12.93/12.86 ** KEPT (pick-wt=11): 481 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_RComplete_Onatfloor(B)). % 12.93/12.86 ** KEPT (pick-wt=11): 482 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B). % 12.93/12.86 ** KEPT (pick-wt=11): 483 [] -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A)|c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,A)). % 12.93/12.86 ** KEPT (pick-wt=11): 484 [] -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A)|c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,A)). % 12.93/12.86 ** KEPT (pick-wt=18): 485 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.86 ** KEPT (pick-wt=18): 486 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 12.93/12.86 ** KEPT (pick-wt=16): 487 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_RComplete_Onatfloor(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A). % 12.93/12.86 Following clause subsumed by 481 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_RComplete_Onatfloor(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A). % 12.93/12.86 ** KEPT (pick-wt=33): 488 [] -class_Rings_Olinordered__semidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|B=D. % 12.93/12.86 ** KEPT (pick-wt=16): 489 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)). % 12.93/12.86 Following clause subsumed by 482 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)). % 12.93/12.86 ** KEPT (pick-wt=22): 490 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_RealDef_Oreal(tc_Nat_Onat,B)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(A)),B). % 12.93/12.86 ** KEPT (pick-wt=17): 491 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)). % 12.93/12.86 ** KEPT (pick-wt=22): 492 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(B)=A. % 12.93/12.86 ** KEPT (pick-wt=22): 493 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_RealDef_Oreal(tc_Nat_Onat,B)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(A)),B). % 12.93/12.86 Following clause subsumed by 447 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.86 Following clause subsumed by 449 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.93/12.86 Following clause subsumed by 448 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.93/12.86 ** KEPT (pick-wt=21): 494 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,$f24(C,B,A))),B)|c_SEQ_OBse_q(A,C). % 12.93/12.86 ** KEPT (pick-wt=12): 495 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f25(B,A)). % 12.93/12.86 ** KEPT (pick-wt=15): 496 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),$f25(B,A)). % 12.93/12.86 ** KEPT (pick-wt=33): 497 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),B)). % 12.93/12.86 ** KEPT (pick-wt=15): 498 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f26(B,A),B). % 12.93/12.86 ** KEPT (pick-wt=19): 499 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,$f26(B,A))| -hBOOL(hAPP(A,C)). % 12.93/12.86 ** KEPT (pick-wt=21): 500 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f26(B,A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). % 12.93/12.86 ** KEPT (pick-wt=10): 501 [] A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.86 ** KEPT (pick-wt=15): 502 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.86 ** KEPT (pick-wt=10): 503 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). % 12.93/12.86 ** KEPT (pick-wt=10): 504 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). % 12.93/12.86 ** KEPT (pick-wt=11): 505 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))|A=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.86 ** KEPT (pick-wt=11): 506 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))|A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.86 ** KEPT (pick-wt=21): 507 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.86 ** KEPT (pick-wt=21): 508 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.93/12.86 ** KEPT (pick-wt=16): 509 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)). % 12.93/12.86 ** KEPT (pick-wt=14): 510 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)),B). % 12.93/12.86 ** KEPT (pick-wt=14): 511 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)),B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 12.93/12.86 Following clause subsumed by 510 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)),B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 12.93/12.86 ** KEPT (pick-wt=17): 512 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A=B. % 12.93/12.86 ** KEPT (pick-wt=14): 513 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 12.93/12.86 ** KEPT (pick-wt=13): 514 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint)))|A!=B. % 12.93/12.86 ** KEPT (pick-wt=14): 515 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 12.93/12.86 ** KEPT (pick-wt=14): 516 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 12.93/12.86 ** KEPT (pick-wt=18): 517 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)). % 12.93/12.86 ** KEPT (pick-wt=22): 518 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C,D)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D)). % 12.93/12.86 ** KEPT (pick-wt=8): 519 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 12.93/12.86 ** KEPT (pick-wt=7): 520 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A!=B. % 12.93/12.86 ** KEPT (pick-wt=11): 521 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|A=B. % 12.93/12.86 ** KEPT (pick-wt=24): 523 [copy,522,flip.2] -class_RealVector_Oreal__algebra__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_RealVector_Oof__real(A),B)),hAPP(c_RealVector_Oof__real(A),C))=hAPP(c_RealVector_Oof__real(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). % 12.93/12.86 ** KEPT (pick-wt=13): 525 [copy,524,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,A). % 12.93/12.86 ** KEPT (pick-wt=22): 526 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))). % 12.93/12.86 ** KEPT (pick-wt=30): 527 [] -class_RealVector_Oreal__normed__algebra(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E)). % 12.93/12.86 ** KEPT (pick-wt=12): 528 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=12): 529 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=12): 530 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 Following clause subsumed by 530 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=12): 531 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 Following clause subsumed by 531 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=19): 532 [] -class_Rings_Ono__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 Following clause subsumed by 532 during input processing: 0 [] -class_Rings_Ono__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=19): 533 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=15): 534 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=15): 535 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=12): 536 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=12): 537 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A). % 12.93/12.86 ** KEPT (pick-wt=30): 539 [copy,538,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=41): 540 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=38): 541 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=38): 542 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)). % 12.93/12.86 ** KEPT (pick-wt=30): 543 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=30): 544 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C). % 12.93/12.86 Following clause subsumed by 540 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B=D|C=E. % 12.93/12.86 Following clause subsumed by 541 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B!=D. % 12.93/12.86 Following clause subsumed by 542 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=E. % 12.93/12.86 ** KEPT (pick-wt=30): 545 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 Following clause subsumed by 545 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=30): 547 [copy,546,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.86 Following clause subsumed by 547 during input processing: 0 [flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=40): 549 [copy,548,flip.2] -class_Rings_Osemiring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)),E)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),E)). % 12.93/12.86 ** KEPT (pick-wt=30): 550 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=11): 551 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B. % 12.93/12.86 ** KEPT (pick-wt=11): 552 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B. % 12.93/12.86 ** KEPT (pick-wt=11): 553 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B. % 12.93/12.86 ** KEPT (pick-wt=11): 554 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B. % 12.93/12.86 ** KEPT (pick-wt=11): 555 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B. % 12.93/12.86 ** KEPT (pick-wt=11): 556 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B. % 12.93/12.86 ** KEPT (pick-wt=21): 557 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 Following clause subsumed by 557 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=21): 558 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 Following clause subsumed by 558 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=24): 559 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B=C|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),C). % 12.93/12.86 ** KEPT (pick-wt=18): 560 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=C. % 12.93/12.86 ** KEPT (pick-wt=21): 561 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C). % 12.93/12.86 ** KEPT (pick-wt=21): 562 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C). % 12.93/12.86 ** KEPT (pick-wt=21): 563 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)). % 12.93/12.86 ** KEPT (pick-wt=21): 565 [copy,564,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=21): 566 [] -class_Rings_Oring(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)). % 12.93/12.86 ** KEPT (pick-wt=25): 567 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=30): 568 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=30): 569 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=20): 570 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B=C. % 12.93/12.86 ** KEPT (pick-wt=20): 571 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B!=C. % 12.93/12.86 ** KEPT (pick-wt=20): 572 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B=C. % 12.93/12.86 ** KEPT (pick-wt=20): 573 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B!=C. % 12.93/12.86 ** KEPT (pick-wt=19): 574 [] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,B))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B). % 12.93/12.86 ** KEPT (pick-wt=21): 576 [copy,575,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=5): 577 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.93/12.86 ** KEPT (pick-wt=15): 578 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 12.93/12.86 ** KEPT (pick-wt=35): 579 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)). % 12.93/12.86 ** KEPT (pick-wt=35): 580 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),E)). % 12.93/12.86 ** KEPT (pick-wt=35): 581 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))). % 12.93/12.86 ** KEPT (pick-wt=25): 582 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C). % 12.93/12.86 ** KEPT (pick-wt=25): 583 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 Following clause subsumed by 583 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=25): 584 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)). % 12.93/12.86 ** KEPT (pick-wt=20): 585 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C). % 12.93/12.86 ** KEPT (pick-wt=15): 586 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B). % 12.93/12.86 ** KEPT (pick-wt=10): 587 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B. % 12.93/12.86 Following clause subsumed by 587 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B. % 12.93/12.86 ** KEPT (pick-wt=25): 588 [] -class_Groups_Oab__semigroup__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=21): 589 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)). % 12.93/12.86 ** KEPT (pick-wt=21): 591 [copy,590,flip.2] -class_RealVector_Oreal__normed__div__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C))=c_Groups_Osgn__class_Osgn(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=21): 593 [copy,592,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C))=c_Groups_Osgn__class_Osgn(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=24): 594 [] -class_RealVector_Oreal__normed__algebra(A)| -c_SEQ_Oconvergent(A,B)| -c_SEQ_Oconvergent(A,C)|c_SEQ_Oconvergent(A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=21): 595 [] -class_RealVector_Oreal__normed__algebra(A)| -c_SEQ_Oconvergent(A,B)|c_SEQ_Oconvergent(A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=16): 596 [] -class_RealVector_Oreal__normed__algebra(A)| -c_SEQ_Oconvergent(A,B)|c_SEQ_Oconvergent(A,c_COMBB(A,A,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(A),C),B)). % 12.93/12.86 ** KEPT (pick-wt=16): 597 [] -class_RealVector_Oreal__normed__algebra(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_OCauchy(A,c_COMBB(A,A,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(A),C),B)). % 12.93/12.86 ** KEPT (pick-wt=21): 598 [] -class_RealVector_Oreal__normed__algebra(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_OCauchy(A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=9): 599 [] -class_RealVector_Oreal__normed__algebra(A)|c_Lim_OisUCont(A,A,hAPP(c_Groups_Otimes__class_Otimes(A),B)). % 12.93/12.86 ** KEPT (pick-wt=12): 600 [] -class_RealVector_Oreal__normed__algebra(A)|c_Lim_OisUCont(A,A,c_COMBC(A,A,A,c_Groups_Otimes__class_Otimes(A),B)). % 12.93/12.86 ** KEPT (pick-wt=12): 601 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)). % 12.93/12.86 ** KEPT (pick-wt=22): 602 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 603 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 604 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 605 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 606 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 12.93/12.86 ** KEPT (pick-wt=22): 607 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 608 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 609 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 12.93/12.86 ** KEPT (pick-wt=22): 610 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 611 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 12.93/12.86 ** KEPT (pick-wt=22): 612 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 613 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 12.93/12.86 ** KEPT (pick-wt=22): 614 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=22): 615 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 616 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 Following clause subsumed by 616 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 617 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=25): 618 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=25): 619 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)). % 12.93/12.86 ** KEPT (pick-wt=25): 620 [] -class_Rings_Oordered__comm__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)). % 12.93/12.86 ** KEPT (pick-wt=25): 621 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)). % 12.93/12.86 ** KEPT (pick-wt=25): 622 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)). % 12.93/12.86 ** KEPT (pick-wt=34): 623 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)). % 12.93/12.86 ** KEPT (pick-wt=34): 624 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)). % 12.93/12.86 ** KEPT (pick-wt=22): 625 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 Following clause subsumed by 617 during input processing: 0 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 Following clause subsumed by 615 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 Following clause subsumed by 616 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=12): 626 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=26): 627 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=25): 628 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,D,B). % 12.93/12.86 ** KEPT (pick-wt=25): 629 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=24): 630 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,D,B). % 12.93/12.86 ** KEPT (pick-wt=25): 631 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,B,D). % 12.93/12.86 ** KEPT (pick-wt=25): 632 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,B). % 12.93/12.86 ** KEPT (pick-wt=26): 633 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=25): 634 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.86 ** KEPT (pick-wt=25): 635 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=24): 636 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.86 ** KEPT (pick-wt=25): 637 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D). % 12.93/12.86 ** KEPT (pick-wt=25): 638 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.86 ** KEPT (pick-wt=25): 639 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D). % 12.93/12.86 Following clause subsumed by 637 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,C,D). % 12.93/12.86 ** KEPT (pick-wt=22): 640 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=22): 641 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 642 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 643 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C). % 12.93/12.86 ** KEPT (pick-wt=22): 644 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 12.93/12.86 ** KEPT (pick-wt=25): 645 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.86 Following clause subsumed by 638 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,D,C). % 12.93/12.86 Following clause subsumed by 642 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)). % 12.93/12.86 ** KEPT (pick-wt=22): 646 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=25): 647 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.93/12.86 ** KEPT (pick-wt=25): 648 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)). % 12.93/12.86 ** KEPT (pick-wt=25): 649 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)). % 12.93/12.86 Following clause subsumed by 632 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)). % 12.93/12.86 Following clause subsumed by 638 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)). % 12.93/12.86 ** KEPT (pick-wt=35): 650 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)). % 12.93/12.86 ** KEPT (pick-wt=22): 651 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)). % 12.93/12.86 ** KEPT (pick-wt=22): 652 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))),B). % 12.93/12.86 ** KEPT (pick-wt=26): 653 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),c_Groups_Oone__class_Oone(A))),B). % 12.93/12.86 ** KEPT (pick-wt=26): 654 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),C). % 12.93/12.86 ** KEPT (pick-wt=22): 655 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)!=c_Groups_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A)|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)). % 12.93/12.86 ** KEPT (pick-wt=15): 656 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A). % 12.93/12.86 ** KEPT (pick-wt=18): 657 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)). % 12.93/12.86 ** KEPT (pick-wt=17): 659 [copy,658,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),B). % 12.93/12.87 ** KEPT (pick-wt=32): 660 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,D),E)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)). % 12.93/12.87 ** KEPT (pick-wt=30): 661 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)). % 12.93/12.87 ** KEPT (pick-wt=30): 663 [copy,662,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)). % 12.93/12.87 ** KEPT (pick-wt=23): 664 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). % 12.93/12.87 ** KEPT (pick-wt=20): 665 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). % 12.93/12.87 ** KEPT (pick-wt=23): 666 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). % 12.93/12.87 ** KEPT (pick-wt=23): 667 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). % 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-c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C). % 12.99/12.87 ** KEPT (pick-wt=31): 708 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). % 12.99/12.87 ** KEPT (pick-wt=24): 709 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_RealVector_Onorm__class_Onorm(A,D)))|C=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=48): 710 [] -class_Rings_Olinordered__semiring__1__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C). % 12.99/12.87 ** KEPT (pick-wt=22): 711 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)). % 12.99/12.87 ** KEPT (pick-wt=30): 712 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=26): 713 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|B=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=26): 714 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|C=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=22): 715 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))). % 12.99/12.87 ** KEPT (pick-wt=26): 716 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=26): 717 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A))|C=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=30): 718 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=20): 719 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=16): 720 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A!=C. % 12.99/12.87 ** KEPT (pick-wt=17): 721 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=20): 722 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=16): 723 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C. % 12.99/12.87 ** KEPT (pick-wt=17): 724 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=17): 725 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=13): 726 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=13): 727 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=25): 729 [copy,728,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)). % 12.99/12.87 ** KEPT (pick-wt=25): 730 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)). % 12.99/12.87 ** KEPT (pick-wt=18): 731 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). % 12.99/12.87 ** KEPT (pick-wt=18): 732 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)). % 12.99/12.87 ** KEPT (pick-wt=22): 733 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). % 12.99/12.87 ** KEPT (pick-wt=13): 735 [copy,734,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=13): 737 [copy,736,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=17): 739 [copy,738,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.99/12.87 Following clause subsumed by 735 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.99/12.87 Following clause subsumed by 737 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.99/12.87 Following clause subsumed by 739 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=17): 740 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.99/12.87 ** KEPT (pick-wt=12): 741 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,C). % 12.99/12.87 ** KEPT (pick-wt=11): 742 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,A)|A=B. % 12.99/12.87 ** KEPT (pick-wt=18): 743 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)). % 12.99/12.87 ** KEPT (pick-wt=15): 744 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.99/12.87 ** KEPT (pick-wt=15): 745 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 12.99/12.87 ** KEPT (pick-wt=20): 746 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 12.99/12.87 ** KEPT (pick-wt=19): 747 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 12.99/12.87 ** KEPT (pick-wt=18): 748 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.99/12.87 ** KEPT (pick-wt=23): 749 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.99/12.87 ** KEPT (pick-wt=19): 750 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 12.99/12.87 ** KEPT (pick-wt=18): 751 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). % 12.99/12.87 ** KEPT (pick-wt=23): 752 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). % 12.99/12.87 Following clause subsumed by 752 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). % 12.99/12.87 Following clause subsumed by 749 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)). % 12.99/12.87 ** KEPT (pick-wt=23): 753 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)). % 12.99/12.87 ** KEPT (pick-wt=18): 754 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.99/12.87 ** KEPT (pick-wt=18): 755 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.99/12.87 ** KEPT (pick-wt=22): 756 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)=c_Groups_Oone__class_Oone(tc_Int_Oint)|A!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 12.99/12.87 ** KEPT (pick-wt=16): 758 [copy,757,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=A|B=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 ** KEPT (pick-wt=23): 759 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.99/12.87 Following clause subsumed by 732 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.99/12.87 ** KEPT (pick-wt=23): 760 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 12.99/12.87 Following clause subsumed by 731 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 12.99/12.87 ** KEPT (pick-wt=27): 761 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(A)),c_RComplete_Onatfloor(B)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))). % 12.99/12.87 ** KEPT (pick-wt=25): 762 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=25): 763 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=29): 764 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=28): 766 [copy,765,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C,c_Groups_Oone__class_Oone(tc_Int_Oint)). % 12.99/12.87 ** KEPT (pick-wt=27): 768 [copy,767,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),C). % 12.99/12.87 ** KEPT (pick-wt=60): 769 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),F)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E,B). % 12.99/12.87 ** KEPT (pick-wt=29): 770 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 12.99/12.87 ** KEPT (pick-wt=30): 771 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.99/12.87 ** KEPT (pick-wt=41): 772 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,E,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,D). % 12.99/12.87 ** KEPT (pick-wt=60): 773 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,F,D)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,E). % 12.99/12.87 ** KEPT (pick-wt=41): 774 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,E)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D,B). % 12.99/12.87 Following clause subsumed by 759 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.99/12.87 Following clause subsumed by 732 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.99/12.87 Following clause subsumed by 722 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C. % 12.99/12.87 Following clause subsumed by 724 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.87 Following clause subsumed by 723 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C. % 12.99/12.87 Following clause subsumed by 748 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.99/12.87 Following clause subsumed by 749 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.99/12.87 ** KEPT (pick-wt=21): 775 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C. % 12.99/12.87 Following clause subsumed by 723 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C. % 12.99/12.87 ** KEPT (pick-wt=15): 776 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). % 12.99/12.87 ** KEPT (pick-wt=20): 777 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)). % 12.99/12.87 ** KEPT (pick-wt=20): 778 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)). % 12.99/12.87 ** KEPT (pick-wt=14): 779 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A))|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 12.99/12.87 ** KEPT (pick-wt=10): 780 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f28(A)). % 12.99/12.87 ** KEPT (pick-wt=21): 781 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(c_RealVector_Oof__real(A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),$f28(A))). % 12.99/12.87 ** KEPT (pick-wt=10): 782 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f29(A)). % 12.99/12.87 ** KEPT (pick-wt=21): 783 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(c_RealVector_Oof__real(A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),$f29(A))). % 12.99/12.87 ** KEPT (pick-wt=11): 784 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(A)=c_Power_Opower_Opower(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A)). % 12.99/12.87 ** KEPT (pick-wt=9): 785 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f30(B,A)). % 12.99/12.87 ** KEPT (pick-wt=22): 786 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),$f30(C,A))). % 12.99/12.87 ** KEPT (pick-wt=9): 787 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f31(B,A)). % 12.99/12.87 ** KEPT (pick-wt=22): 788 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),$f31(B,A))). % 12.99/12.87 ** KEPT (pick-wt=8): 789 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f32(A)). % 12.99/12.87 ** KEPT (pick-wt=28): 790 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),$f32(A))). % 12.99/12.87 ** KEPT (pick-wt=21): 791 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(c_RealVector_Oof__real(A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),$f33(A))). % 12.99/12.87 ** KEPT (pick-wt=20): 792 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 12.99/12.87 ** KEPT (pick-wt=14): 793 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Ominus__class_Ominus(A,B,C))=c_Groups_Ominus__class_Ominus(A,C,B). % 12.99/12.87 ** KEPT (pick-wt=13): 794 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,B,C)),C)=B. % 12.99/12.87 ** KEPT (pick-wt=13): 795 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),C)=B. % 12.99/12.87 ** KEPT (pick-wt=19): 796 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,E). % 12.99/12.87 ** KEPT (pick-wt=19): 797 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E). % 12.99/12.87 ** KEPT (pick-wt=18): 798 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 12.99/12.87 ** KEPT (pick-wt=14): 799 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 12.99/12.87 ** KEPT (pick-wt=14): 800 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 12.99/12.87 ** KEPT (pick-wt=14): 801 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 12.99/12.87 ** KEPT (pick-wt=14): 802 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 12.99/12.87 ** KEPT (pick-wt=12): 803 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Ozero__class_Ozero(A),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),B). % 12.99/12.87 ** KEPT (pick-wt=16): 805 [copy,804,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=c_Groups_Ominus__class_Ominus(A,B,C). % 12.99/12.87 ** KEPT (pick-wt=16): 806 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C). % 12.99/12.87 ** KEPT (pick-wt=16): 808 [copy,807,flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=c_Groups_Ominus__class_Ominus(A,B,C). % 12.99/12.87 ** KEPT (pick-wt=16): 810 [copy,809,flip.2] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=c_Groups_Ominus__class_Ominus(A,B,C). % 12.99/12.87 ** KEPT (pick-wt=18): 811 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B))). % 12.99/12.87 ** KEPT (pick-wt=18): 812 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 12.99/12.87 ** KEPT (pick-wt=20): 813 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 12.99/12.87 ** KEPT (pick-wt=12): 814 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.99/12.87 ** KEPT (pick-wt=12): 815 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 12.99/12.87 ** KEPT (pick-wt=22): 816 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|hAPP(c_RealVector_Oof__real(A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C))=c_Groups_Ominus__class_Ominus(A,hAPP(c_RealVector_Oof__real(A),B),hAPP(c_RealVector_Oof__real(A),C)). % 12.99/12.87 ** KEPT (pick-wt=20): 817 [] -class_RealVector_Oreal__algebra__1(A)|hAPP(c_RealVector_Oof__real(A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C))=c_Groups_Ominus__class_Ominus(A,hAPP(c_RealVector_Oof__real(A),B),hAPP(c_RealVector_Oof__real(A),C)). % 12.99/12.87 ** KEPT (pick-wt=15): 818 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,B)). % 12.99/12.87 ** KEPT (pick-wt=19): 819 [] -class_Groups_Ominus(A)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,A),C,D),E)=c_Groups_Ominus__class_Ominus(A,hAPP(C,E),hAPP(D,E)). % 12.99/12.87 Following clause subsumed by 819 during input processing: 0 [] -class_Groups_Ominus(A)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,A),C,D),E)=c_Groups_Ominus__class_Ominus(A,hAPP(C,E),hAPP(D,E)). % 12.99/12.87 ** KEPT (pick-wt=17): 820 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B!=C|D=E. % 12.99/12.87 ** KEPT (pick-wt=17): 821 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B=C|D!=E. % 12.99/12.87 ** KEPT (pick-wt=15): 822 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)). % 12.99/12.87 ** KEPT (pick-wt=19): 823 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E). % 12.99/12.87 ** KEPT (pick-wt=19): 824 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E). % 12.99/12.87 ** KEPT (pick-wt=9): 825 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A))=B. % 12.99/12.87 ** KEPT (pick-wt=9): 826 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,B)=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=12): 827 [] -class_Groups_Oab__group__add(A)|B!=C|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=12): 828 [] -class_Groups_Oab__group__add(A)|B=C|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A). % 12.99/12.87 ** KEPT (pick-wt=12): 829 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C. % 12.99/12.87 ** KEPT (pick-wt=12): 830 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C. % 12.99/12.87 ** KEPT (pick-wt=39): 832 [copy,831,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),D)). % 12.99/12.87 ** KEPT (pick-wt=55): 834 [copy,833,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ominus__class_Ominus(A,D,E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),c_Groups_Ominus__class_Ominus(A,D,E)))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)). % 12.99/12.87 ** KEPT (pick-wt=41): 835 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D)=F. % 12.99/12.87 ** KEPT (pick-wt=41): 836 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D)!=F. % 12.99/12.87 ** KEPT (pick-wt=41): 837 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|D=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F). % 12.99/12.88 ** KEPT (pick-wt=41): 838 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|D!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F). % 12.99/12.88 ** KEPT (pick-wt=26): 839 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)). % 12.99/12.88 Following clause subsumed by 839 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)). % 12.99/12.88 ** KEPT (pick-wt=26): 840 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.99/12.88 Following clause subsumed by 840 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). % 12.99/12.88 ** KEPT (pick-wt=43): 841 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D),F). % 12.99/12.88 ** KEPT (pick-wt=43): 842 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D),F). % 12.99/12.88 ** KEPT (pick-wt=43): 843 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))|c_Orderings_Oord__class_Oless__e_q(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F)). % 12.99/12.88 ** KEPT (pick-wt=43): 844 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))| -c_Orderings_Oord__class_Oless__e_q(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F)). % 12.99/12.88 ** KEPT (pick-wt=43): 845 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))|c_Orderings_Oord__class_Oless(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F)). % 12.99/12.88 ** KEPT (pick-wt=43): 846 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))| -c_Orderings_Oord__class_Oless(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F)). % 12.99/12.88 ** KEPT (pick-wt=43): 847 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D),F). % 12.99/12.88 ** KEPT (pick-wt=43): 848 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D),F). % 12.99/12.88 ** KEPT (pick-wt=29): 850 [copy,849,flip.2] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A)))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Oone__class_Oone(A)). % 12.99/12.88 ** KEPT (pick-wt=20): 851 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))). % 12.99/12.88 ** KEPT (pick-wt=36): 852 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,D))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,E)))). % 12.99/12.88 ** KEPT (pick-wt=18): 853 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,C,D),B). % 12.99/12.88 ** KEPT (pick-wt=20): 854 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)|c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.99/12.88 ** KEPT (pick-wt=27): 855 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,C,D),B)| -c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)). % 12.99/12.88 ** KEPT (pick-wt=20): 856 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))). % 12.99/12.88 ** KEPT (pick-wt=20): 857 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))). % 12.99/12.88 ** KEPT (pick-wt=36): 858 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,D))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,E)))). % 12.99/12.88 ** KEPT (pick-wt=37): 859 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OCauchy(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(C,B,A),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(C,B,A),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(B,D),hAPP(B,E))),C). % 12.99/12.88 ** KEPT (pick-wt=37): 860 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OCauchy(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f35(B,A,C),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f35(B,A,C),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(B,D),hAPP(B,E))),C). % 12.99/12.88 ** KEPT (pick-wt=12): 861 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OCauchy(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f38(B,A)). % 12.99/12.88 ** KEPT (pick-wt=12): 862 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OCauchy(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,$f37(B,A,C)). % 12.99/12.88 ** KEPT (pick-wt=12): 863 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OCauchy(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,$f36(B,A,C)). % 12.99/12.88 ** KEPT (pick-wt=26): 864 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OCauchy(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(B,$f37(B,A,C)),hAPP(B,$f36(B,A,C)))),$f38(B,A)). % 12.99/12.88 ** KEPT (pick-wt=22): 865 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.99/12.88 ** KEPT (pick-wt=22): 866 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 12.99/12.88 ** KEPT (pick-wt=23): 867 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C). % 12.99/12.88 ** KEPT (pick-wt=20): 868 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B=C. % 12.99/12.88 ** KEPT (pick-wt=20): 869 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B!=C. % 12.99/12.88 ** KEPT (pick-wt=13): 870 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A. % 12.99/12.88 ** KEPT (pick-wt=14): 871 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)). % 12.99/12.88 ** KEPT (pick-wt=14): 872 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)). % 12.99/12.88 ** KEPT (pick-wt=12): 873 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.99/12.88 ** KEPT (pick-wt=12): 874 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 12.99/12.88 ** KEPT (pick-wt=17): 875 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B. % 12.99/12.88 ** KEPT (pick-wt=11): 876 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B). % 12.99/12.88 ** KEPT (pick-wt=18): 877 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)). % 12.99/12.88 ** KEPT (pick-wt=21): 878 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A),B). % 12.99/12.88 ** KEPT (pick-wt=16): 879 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)). % 12.99/12.88 ** KEPT (pick-wt=16): 880 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)). % 12.99/12.88 ** KEPT (pick-wt=16): 881 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C),A)). % 12.99/12.88 ** KEPT (pick-wt=15): 882 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=B. % 12.99/12.88 ** KEPT (pick-wt=23): 883 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B),A). % 12.99/12.88 ** KEPT (pick-wt=20): 884 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A),B). % 12.99/12.88 ** KEPT (pick-wt=20): 885 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A),B). % 12.99/12.88 ** KEPT (pick-wt=15): 886 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),A)=B. % 12.99/12.88 ** KEPT (pick-wt=18): 887 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=C|B=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A). % 12.99/12.88 ** KEPT (pick-wt=18): 888 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=C|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A). % 12.99/12.88 Following clause subsumed by 883 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B),A). % 12.99/12.88 ** KEPT (pick-wt=23): 889 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), % 12.99/12.88 Search stopped in tp_alloc by max_mem option. % 12.99/12.88 B),C),A). % 12.99/12.88 Following clause subsumed by 889 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C),A). % 12.99/12.88 ** KEPT (pick-wt=18): 890 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)). % 12.99/12.88 ** KEPT (pick-wt=22): 891 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.99/12.88 Following clause subsumed by 890 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 12.99/12.88 ** KEPT (pick-wt=16): 892 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). % 12.99/12.88 ** KEPT (pick-wt=16): 893 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). % 12.99/12.88 ** KEPT (pick-wt=11): 894 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.99/12.88 ** KEPT (pick-wt=11): 895 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 12.99/12.88 Following clause subsumed by 895 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 12.99/12.88 ** KEPT (pick-wt=12): 896 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). % 12.99/12.88 ** KEPT (pick-wt=12): 897 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). % 12.99/12.88 ** KEPT (pick-wt=17): 898 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),B). % 12.99/12.88 % 12.99/12.88 Search stopped in tp_alloc by max_mem option. % 12.99/12.88 % 12.99/12.88 ============ end of search ============ % 12.99/12.88 % 12.99/12.88 -------------- statistics ------------- % 12.99/12.88 clauses given 0 % 12.99/12.88 clauses generated 0 % 12.99/12.88 clauses kept 853 % 12.99/12.88 clauses forward subsumed 148 % 12.99/12.88 clauses back subsumed 0 % 12.99/12.88 Kbytes malloced 11718 % 12.99/12.88 % 12.99/12.88 ----------- times (seconds) ----------- % 12.99/12.88 user CPU time 0.19 (0 hr, 0 min, 0 sec) % 12.99/12.88 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 12.99/12.88 wall-clock time 12 (0 hr, 0 min, 12 sec) % 12.99/12.88 % 12.99/12.88 Process 10326 finished Wed Jul 27 03:03:29 2022 % 12.99/12.88 Otter interrupted % 12.99/12.88 PROOF NOT FOUND %------------------------------------------------------------------------------