%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SCT149+1 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n007.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 : 600s % DateTime : Mon Jul 18 22:16:20 EDT 2022 % Result : Theorem 2.54s 2.70s % Output : Proof 2.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.12 % Problem : SCT149+1 : TPTP v8.1.0. Released v5.2.0. % 0.09/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n007.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 : 600 % 0.12/0.33 % DateTime : Fri Jul 1 21:20:54 EDT 2022 % 0.12/0.33 % CPUTime : % 2.54/2.70 % SZS status Theorem % 2.54/2.70 (* PROOF-FOUND *) % 2.54/2.70 (* BEGIN-PROOF *) % 2.54/2.70 % SZS output start Proof % 2.54/2.70 1. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ### Axiom % 2.54/2.70 2. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) ### Axiom % 2.54/2.70 3. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ### Equiv 1 2 % 2.54/2.70 4. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) ### Axiom % 2.54/2.70 5. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ### Equiv 3 4 % 2.54/2.70 6. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) ### Axiom % 2.54/2.70 7. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) ### Equiv 5 6 % 2.54/2.70 8. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) ### Axiom % 2.54/2.70 9. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ### Equiv 7 8 % 2.54/2.71 10. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____))))) ### Axiom % 2.54/2.71 11. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ### Axiom % 2.54/2.71 12. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ### Axiom % 2.54/2.71 13. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) ### Axiom % 2.54/2.71 14. (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))) ### Axiom % 2.54/2.71 15. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) ### Equiv 13 14 % 2.54/2.71 16. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) ### Equiv 12 15 % 2.54/2.71 17. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) ### Equiv 11 16 % 2.54/2.71 18. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) (-. (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) ### Equiv 10 17 % 2.54/2.71 19. (-. ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (v_P_H____))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____))))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_b____)) (v_a____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))) (v_b____))) (v_a____)))) (v_a____))) (v_c____)))))) ((hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_b____))) (hAPP (v_F) (v_P____)))) <=> (hBOOL (hAPP (hAPP (c_member (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt))) (hAPP (hAPP (c_Product__Type_OPair (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (v_a____)) (v_c____))) (hAPP (v_F) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool))) (hAPP (hAPP (c_COMBC (tc_Arrow__Order__Mirabelle_Oindi) (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (hAPP (hAPP (c_COMBB (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_Arrow__Order__Mirabelle_Oalt) (tc_fun (tc_prod (tc_Arrow__Order__Mirabelle_Oalt) (tc_Arrow__Order__Mirabelle_Oalt)) (tc_HOL_Obool)))) (tc_Arrow__Order__Mirabelle_Oindi)) (c_Arrow__Order__Mirabelle_Obelow)) (v_P____))) (v_c____))) (v_b____)))))) ### NotEquiv 9 18 % 2.54/2.71 % SZS output end Proof % 2.54/2.71 (* END-PROOF *) %------------------------------------------------------------------------------