%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT124^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:44:51 AM UTC 2026
% Result : Theorem 3.09s 1.99s
% Output : Refutation 3.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT124^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n015.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 06:08:46 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : DAT124^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.39 % Domain : Data Structures
% 0.16/0.39 % Problem : Coinductive list 2275
% 0.16/0.39 % Version : [Bla16] axioms : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.16/0.39 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.39 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bla16]
% 0.16/0.39 % Names : coinductive_list__2275.p [Bla16]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.33 v9.1.0, 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.16/0.39 % Syntax : Number of formulae : 322 ( 57 unt; 49 typ; 0 def)
% 0.16/0.39 % Number of atoms : 878 ( 199 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 13 ( 3 avg)
% 0.16/0.39 % Number of connectives : 3697 ( 79 ~; 22 |; 42 &;3073 @)
% 0.16/0.39 % ( 0 <=>; 481 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 21 ( 9 avg)
% 0.16/0.39 % Number of types : 3 ( 2 usr)
% 0.16/0.39 % Number of type conns : 109 ( 109 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 48 ( 47 usr; 4 con; 0-3 aty)
% 0.16/0.39 % Number of variables : 1022 ( 31 ^; 917 !; 33 ?;1022 :)
% 0.16/0.39 % ( 41 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.39 % SPC : TH1_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.39 % 2016-07-13 14:55:40.237
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 %----Could-be-implicit typings (4)
% 0.16/0.39 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.16/0.39 coindu1593790203_llist: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_Extended__Nat_Oenat,type,
% 0.16/0.39 extended_enat: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_itself,type,
% 0.16/0.39 itself: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_tf_a,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 %----Explicit typings (45)
% 0.16/0.39 thf(sy_cl_HOL_Otype,type,
% 0.16/0.39 type:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Oord,type,
% 0.16/0.39 ord:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Oorder,type,
% 0.16/0.39 order:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Ogroup__add,type,
% 0.16/0.39 group_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Ono__bot,type,
% 0.16/0.39 no_bot:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Ono__top,type,
% 0.16/0.39 no_top:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Olinorder,type,
% 0.16/0.39 linorder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Opreorder,type,
% 0.16/0.39 preorder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oab__group__add,type,
% 0.16/0.39 ab_group_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Owellorder,type,
% 0.16/0.39 wellorder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.16/0.39 semigroup_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Odense__order,type,
% 0.16/0.39 dense_order:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.16/0.39 linordered_idom:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.16/0.39 ab_semigroup_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.16/0.39 dense_linorder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.16/0.39 linordered_semidom:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.16/0.39 cancel_semigroup_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.16/0.39 ordered_ab_group_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.16/0.39 cancel1352612707id_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.16/0.39 cancel146912293up_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.16/0.39 ordere779506340up_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.16/0.39 canoni770627133id_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.16/0.39 ordere236663937imp_le:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.16/0.39 ordere223160158up_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff,type,
% 0.16/0.39 ordere623563068d_diff:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.16/0.39 strict2144017051up_add:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.16/0.39 condit1656338222tinuum:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.16/0.39 condit1037483654norder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.16/0.39 coindu268472904append:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oldrop,type,
% 0.16/0.39 coindu191418589_ldrop:
% 0.16/0.39 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength,type,
% 0.16/0.39 coindu1018505716length:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.16/0.39 coindu1598213697e_LNil:
% 0.16/0.39 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.16/0.39 coindu335574135_lnull:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.16/0.39 coindu1696667936prefix:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.16/0.39 coindu574146665prefix:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake,type,
% 0.16/0.39 coindu1802687541_ltake:
% 0.16/0.39 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.16/0.39 minus_minus:
% 0.16/0.39 !>[A: $tType] : ( A > A > A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.16/0.39 plus_plus:
% 0.16/0.39 !>[A: $tType] : ( A > A > A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.16/0.39 ord_less:
% 0.16/0.39 !>[A: $tType] : ( A > A > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.16/0.39 ord_less_eq:
% 0.16/0.39 !>[A: $tType] : ( A > A > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Pure_Otype,type,
% 0.16/0.39 type2:
% 0.16/0.39 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_xs,type,
% 0.16/0.39 xs: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_xs_H____,type,
% 0.16/0.39 xs2: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_ys,type,
% 0.16/0.39 ys: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_zs,type,
% 0.16/0.39 zs: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 %----Relevant facts (254)
% 0.16/0.39 thf(fact_0__092_060open_062_092_060not_062_Allength_Ays_A_092_060le_062_Allength_Axs_092_060close_062,axiom,
% 0.16/0.39 ~ ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ ys ) @ ( coindu1018505716length @ a @ xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<not> llength ys \<le> llength xs\<close>
% 0.16/0.39 thf(fact_1__092_060open_062_092_060not_062_A_Ixs_A_092_060sqsubseteq_062_Ays_A_092_060or_062_Ays_A_092_060sqsubseteq_062_Axs_J_092_060close_062,axiom,
% 0.16/0.39 ~ ( ( coindu1696667936prefix @ a @ xs @ ys )
% 0.16/0.39 | ( coindu1696667936prefix @ a @ ys @ xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<not> (xs \<sqsubseteq> ys \<or> ys \<sqsubseteq> xs)\<close>
% 0.16/0.39 thf(fact_2__092_060open_062_092_060not_062_Axs_A_092_060sqsubseteq_062_Ays_092_060close_062,axiom,
% 0.16/0.39 ~ ( coindu1696667936prefix @ a @ xs @ ys ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<not> xs \<sqsubseteq> ys\<close>
% 0.16/0.39 thf(fact_3__092_060open_062_092_060not_062_Ays_A_092_060sqsubseteq_062_Axs_092_060close_062,axiom,
% 0.16/0.39 ~ ( coindu1696667936prefix @ a @ ys @ xs ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<not> ys \<sqsubseteq> xs\<close>
% 0.16/0.39 thf(fact_4__092_060open_062lappend_Axs_Axs_H_A_061_Alappend_Ays_Azs_092_060close_062,axiom,
% 0.16/0.39 ( ( coindu268472904append @ a @ xs @ xs2 )
% 0.16/0.39 = ( coindu268472904append @ a @ ys @ zs ) ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>lappend xs xs' = lappend ys zs\<close>
% 0.16/0.39 thf(fact_5_lstrict__prefix__llength__less,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ord_less @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_llength_less
% 0.16/0.39 thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_O_Alappend_Axs_Axs_H_A_061_Alappend_Ays_Azs_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.16/0.39 ~ ! [Xs2: coindu1593790203_llist @ a] :
% 0.16/0.39 ( ( coindu268472904append @ a @ xs @ Xs2 )
% 0.16/0.39 != ( coindu268472904append @ a @ ys @ zs ) ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<And>thesis. (\<And>xs'. lappend xs xs' = lappend ys zs \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.16/0.39 thf(fact_7_enat__less__induct,axiom,
% 0.16/0.39 ! [P: extended_enat > $o,N: extended_enat] :
% 0.16/0.39 ( ! [N2: extended_enat] :
% 0.16/0.39 ( ! [M: extended_enat] :
% 0.16/0.39 ( ( ord_less @ extended_enat @ M @ N2 )
% 0.16/0.39 => ( P @ M ) )
% 0.16/0.39 => ( P @ N2 ) )
% 0.16/0.39 => ( P @ N ) ) ).
% 0.16/0.39
% 0.16/0.39 % enat_less_induct
% 0.16/0.39 thf(fact_8_minf_I11_J,axiom,
% 0.16/0.39 ! [C: $tType,D: $tType] :
% 0.16/0.39 ( ( ord @ C @ ( type2 @ C ) )
% 0.16/0.39 => ! [F: D] :
% 0.16/0.39 ? [Z: C] :
% 0.16/0.39 ! [X: C] :
% 0.16/0.39 ( ( ord_less @ C @ X @ Z )
% 0.16/0.39 => ( F = F ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(11)
% 0.16/0.39 thf(fact_9_minf_I7_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ~ ( ord_less @ A @ T @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(7)
% 0.16/0.39 thf(fact_10_minf_I5_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ( ord_less @ A @ X @ T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(5)
% 0.16/0.39 thf(fact_11_minf_I4_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ( X != T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(4)
% 0.16/0.39 thf(fact_12_minf_I3_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ( X != T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(3)
% 0.16/0.39 thf(fact_13_minf_I2_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.16/0.39 ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Z2 )
% 0.16/0.39 => ( ( P @ X2 )
% 0.16/0.39 = ( P2 @ X2 ) ) )
% 0.16/0.39 => ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Z2 )
% 0.16/0.39 => ( ( Q @ X2 )
% 0.16/0.39 = ( Q2 @ X2 ) ) )
% 0.16/0.39 => ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ( ( ( P @ X )
% 0.16/0.39 | ( Q @ X ) )
% 0.16/0.39 = ( ( P2 @ X )
% 0.16/0.39 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(2)
% 0.16/0.39 thf(fact_14_lprefix__refl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_refl
% 0.16/0.39 thf(fact_15_llist_Oleq__refl,axiom,
% 0.16/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X3 @ X3 ) ).
% 0.16/0.39
% 0.16/0.39 % llist.leq_refl
% 0.16/0.39 thf(fact_16_assms,axiom,
% 0.16/0.39 coindu1696667936prefix @ a @ xs @ ( coindu268472904append @ a @ ys @ zs ) ).
% 0.16/0.39
% 0.16/0.39 % assms
% 0.16/0.39 thf(fact_17_lappend__assoc,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.16/0.39 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_assoc
% 0.16/0.39 thf(fact_18_lprefix__trans,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_trans
% 0.16/0.39 thf(fact_19_llist_Oleq__trans,axiom,
% 0.16/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Y @ Z3 )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ X3 @ Z3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.leq_trans
% 0.16/0.39 thf(fact_20_lprefix__antisym,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.16/0.39 => ( Xs = Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_antisym
% 0.16/0.39 thf(fact_21_lprefix__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lappend
% 0.16/0.39 thf(fact_22_lappend__lprefixE,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.16/0.39 => ~ ! [Zs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Zs
% 0.16/0.39 != ( coindu268472904append @ A @ Xs @ Zs2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_lprefixE
% 0.16/0.39 thf(fact_23_llist_Oleq__antisym,axiom,
% 0.16/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Y @ X3 )
% 0.16/0.39 => ( X3 = Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.leq_antisym
% 0.16/0.39 thf(fact_24_lstrict__prefix__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu574146665prefix @ A )
% 0.16/0.39 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs3 @ Ys2 )
% 0.16/0.39 & ( Xs3 != Ys2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_def
% 0.16/0.39 thf(fact_25_lprefix__down__linear,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_down_linear
% 0.16/0.39 thf(fact_26_lprefix__conv__lappend,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A )
% 0.16/0.39 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.16/0.39 ? [Zs3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Ys2
% 0.16/0.39 = ( coindu268472904append @ A @ Xs3 @ Zs3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_conv_lappend
% 0.16/0.39 thf(fact_27_lprefix__lappend__sameI,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lappend_sameI
% 0.16/0.39 thf(fact_28_llist__less__induct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ! [Xs4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ! [Ys3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Ys3 @ Xs4 )
% 0.16/0.39 => ( P @ Ys3 ) )
% 0.16/0.39 => ( P @ Xs4 ) )
% 0.16/0.39 => ( P @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist_less_induct
% 0.16/0.39 thf(fact_29_lprefix__llength__le,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_llength_le
% 0.16/0.39 thf(fact_30_lprefix__llength__eq__imp__eq,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( ( coindu1018505716length @ A @ Xs )
% 0.16/0.39 = ( coindu1018505716length @ A @ Ys ) )
% 0.16/0.39 => ( Xs = Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_llength_eq_imp_eq
% 0.16/0.39 thf(fact_31_wlog__linorder__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > A > $o,B: A,A2: A] :
% 0.16/0.39 ( ! [A3: A,B2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.16/0.39 => ( P @ A3 @ B2 ) )
% 0.16/0.39 => ( ( ( P @ B @ A2 )
% 0.16/0.39 => ( P @ A2 @ B ) )
% 0.16/0.39 => ( P @ A2 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % wlog_linorder_le
% 0.16/0.39 thf(fact_32_pinf_I6_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ X @ T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(6)
% 0.16/0.39 thf(fact_33_pinf_I8_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ( ord_less_eq @ A @ T @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(8)
% 0.16/0.39 thf(fact_34_minf_I6_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ( ord_less_eq @ A @ X @ T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(6)
% 0.16/0.39 thf(fact_35_minf_I8_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ T @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(8)
% 0.16/0.39 thf(fact_36_pinf_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.16/0.39 ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z2 @ X2 )
% 0.16/0.39 => ( ( P @ X2 )
% 0.16/0.39 = ( P2 @ X2 ) ) )
% 0.16/0.39 => ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z2 @ X2 )
% 0.16/0.39 => ( ( Q @ X2 )
% 0.16/0.39 = ( Q2 @ X2 ) ) )
% 0.16/0.39 => ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ( ( ( P @ X )
% 0.16/0.39 & ( Q @ X ) )
% 0.16/0.39 = ( ( P2 @ X )
% 0.16/0.39 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(1)
% 0.16/0.39 thf(fact_37_pinf_I2_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.16/0.39 ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z2 @ X2 )
% 0.16/0.39 => ( ( P @ X2 )
% 0.16/0.39 = ( P2 @ X2 ) ) )
% 0.16/0.39 => ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z2 @ X2 )
% 0.16/0.39 => ( ( Q @ X2 )
% 0.16/0.39 = ( Q2 @ X2 ) ) )
% 0.16/0.39 => ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ( ( ( P @ X )
% 0.16/0.39 | ( Q @ X ) )
% 0.16/0.39 = ( ( P2 @ X )
% 0.16/0.39 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(2)
% 0.16/0.39 thf(fact_38_pinf_I3_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ( X != T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(3)
% 0.16/0.39 thf(fact_39_pinf_I4_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ( X != T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(4)
% 0.16/0.39 thf(fact_40_pinf_I5_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ~ ( ord_less @ A @ X @ T ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(5)
% 0.16/0.39 thf(fact_41_pinf_I7_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [T: A] :
% 0.16/0.39 ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z @ X )
% 0.16/0.39 => ( ord_less @ A @ T @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(7)
% 0.16/0.39 thf(fact_42_pinf_I11_J,axiom,
% 0.16/0.39 ! [C: $tType,D: $tType] :
% 0.16/0.39 ( ( ord @ C @ ( type2 @ C ) )
% 0.16/0.39 => ! [F: D] :
% 0.16/0.39 ? [Z: C] :
% 0.16/0.39 ! [X: C] :
% 0.16/0.39 ( ( ord_less @ C @ Z @ X )
% 0.16/0.39 => ( F = F ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % pinf(11)
% 0.16/0.39 thf(fact_43_minf_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.16/0.39 ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Z2 )
% 0.16/0.39 => ( ( P @ X2 )
% 0.16/0.39 = ( P2 @ X2 ) ) )
% 0.16/0.39 => ( ? [Z2: A] :
% 0.16/0.39 ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Z2 )
% 0.16/0.39 => ( ( Q @ X2 )
% 0.16/0.39 = ( Q2 @ X2 ) ) )
% 0.16/0.39 => ? [Z: A] :
% 0.16/0.39 ! [X: A] :
% 0.16/0.39 ( ( ord_less @ A @ X @ Z )
% 0.16/0.39 => ( ( ( P @ X )
% 0.16/0.39 & ( Q @ X ) )
% 0.16/0.39 = ( ( P2 @ X )
% 0.16/0.39 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % minf(1)
% 0.16/0.39 thf(fact_44_eq,axiom,
% 0.16/0.39 ( ( coindu268472904append @ a @ ( coindu1802687541_ltake @ a @ ( coindu1018505716length @ a @ ys ) @ xs ) @ ( coindu268472904append @ a @ ( coindu191418589_ldrop @ a @ ( coindu1018505716length @ a @ ys ) @ xs ) @ xs2 ) )
% 0.16/0.39 = ( coindu268472904append @ a @ ys @ zs ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq
% 0.16/0.39 thf(fact_45_order__refl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_refl
% 0.16/0.39 thf(fact_46_complete__interval,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,P: A > $o] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( P @ A2 )
% 0.16/0.39 => ( ~ ( P @ B )
% 0.16/0.39 => ? [C2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.16/0.39 & ( ord_less_eq @ A @ C2 @ B )
% 0.16/0.39 & ! [X: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ A2 @ X )
% 0.16/0.39 & ( ord_less @ A @ X @ C2 ) )
% 0.16/0.39 => ( P @ X ) )
% 0.16/0.39 & ! [D2: A] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.16/0.39 & ( ord_less @ A @ X2 @ D2 ) )
% 0.16/0.39 => ( P @ X2 ) )
% 0.16/0.39 => ( ord_less_eq @ A @ D2 @ C2 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % complete_interval
% 0.16/0.39 thf(fact_47_order_Onot__eq__order__implies__strict,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( A2 != B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.not_eq_order_implies_strict
% 0.16/0.39 thf(fact_48_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A] :
% 0.16/0.39 ( ( ord_less @ A @ B @ A2 )
% 0.16/0.39 => ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.strict_implies_order
% 0.16/0.39 thf(fact_49_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less @ A )
% 0.16/0.39 = ( ^ [B3: A,A4: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.16/0.39 & ( A4 != B3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.strict_iff_order
% 0.16/0.39 thf(fact_50_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less_eq @ A )
% 0.16/0.39 = ( ^ [B3: A,A4: A] :
% 0.16/0.39 ( ( ord_less @ A @ B3 @ A4 )
% 0.16/0.39 | ( A4 = B3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.order_iff_strict
% 0.16/0.39 thf(fact_51_order_Ostrict__implies__order,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.strict_implies_order
% 0.16/0.39 thf(fact_52_dense__le__bounded,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,Z3: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ! [W: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ W )
% 0.16/0.39 => ( ( ord_less @ A @ W @ Y )
% 0.16/0.39 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dense_le_bounded
% 0.16/0.39 thf(fact_53_dense__ge__bounded,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Z3: A,X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z3 @ X3 )
% 0.16/0.39 => ( ! [W: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z3 @ W )
% 0.16/0.39 => ( ( ord_less @ A @ W @ X3 )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dense_ge_bounded
% 0.16/0.39 thf(fact_54_dual__order_Ostrict__trans2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ B @ A2 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ C3 @ B )
% 0.16/0.39 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.strict_trans2
% 0.16/0.39 thf(fact_55_ltake__is__lprefix,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_is_lprefix
% 0.16/0.39 thf(fact_56_lprefix__ltake__same,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,M2: extended_enat] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ M2 @ Xs ) )
% 0.16/0.39 = ( ( ord_less_eq @ extended_enat @ N @ M2 )
% 0.16/0.39 | ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_ltake_same
% 0.16/0.39 thf(fact_57_lappend__ltake__ldrop,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu191418589_ldrop @ A @ N @ Xs ) )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_ltake_ldrop
% 0.16/0.39 thf(fact_58_ltake__eq__ltake__antimono,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,M2: extended_enat] :
% 0.16/0.39 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.16/0.39 = ( coindu1802687541_ltake @ A @ N @ Ys ) )
% 0.16/0.39 => ( ( ord_less_eq @ extended_enat @ M2 @ N )
% 0.16/0.39 => ( ( coindu1802687541_ltake @ A @ M2 @ Xs )
% 0.16/0.39 = ( coindu1802687541_ltake @ A @ M2 @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_eq_ltake_antimono
% 0.16/0.39 thf(fact_59_ltake__all,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,M2: extended_enat] :
% 0.16/0.39 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M2 )
% 0.16/0.39 => ( ( coindu1802687541_ltake @ A @ M2 @ Xs )
% 0.16/0.39 = Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_all
% 0.16/0.39 thf(fact_60_dual__order_Oantisym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( A2 = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.antisym
% 0.16/0.39 thf(fact_61_dual__order_Otrans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ C3 @ B )
% 0.16/0.39 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.trans
% 0.16/0.39 thf(fact_62_linorder__wlog,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > A > $o,A2: A,B: A] :
% 0.16/0.39 ( ! [A3: A,B2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.16/0.39 => ( P @ A3 @ B2 ) )
% 0.16/0.39 => ( ! [A3: A,B2: A] :
% 0.16/0.39 ( ( P @ B2 @ A3 )
% 0.16/0.39 => ( P @ A3 @ B2 ) )
% 0.16/0.39 => ( P @ A2 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % linorder_wlog
% 0.16/0.39 thf(fact_63_dual__order_Orefl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.refl
% 0.16/0.39 thf(fact_64_order__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,Z3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.16/0.39 => ( ord_less_eq @ A @ X3 @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_trans
% 0.16/0.39 thf(fact_65_order__class_Oorder_Oantisym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( A2 = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_class.order.antisym
% 0.16/0.39 thf(fact_66_ord__le__eq__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( B = C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_le_eq_trans
% 0.16/0.39 thf(fact_67_ord__eq__le__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( A2 = B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B @ C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_eq_le_trans
% 0.16/0.39 thf(fact_68_antisym__conv,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Y: A,X3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 = ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym_conv
% 0.16/0.39 thf(fact_69_le__cases3,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,Z3: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Y @ Z3 ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ X3 @ Z3 ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ X3 @ Z3 )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Z3 @ Y ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ Z3 @ Y )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Z3 @ X3 ) )
% 0.16/0.39 => ~ ( ( ord_less_eq @ A @ Z3 @ X3 )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_cases3
% 0.16/0.39 thf(fact_70_order_Otrans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B @ C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.trans
% 0.16/0.39 thf(fact_71_le__cases,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_cases
% 0.16/0.39 thf(fact_72_eq__refl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( X3 = Y )
% 0.16/0.39 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_refl
% 0.16/0.39 thf(fact_73_linear,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % linear
% 0.16/0.39 thf(fact_74_antisym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ A @ Y @ X3 )
% 0.16/0.39 => ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym
% 0.16/0.39 thf(fact_75_eq__iff,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ^ [Y2: A,Z4: A] : ( Y2 = Z4 ) )
% 0.16/0.39 = ( ^ [X4: A,Y3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.16/0.39 & ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_iff
% 0.16/0.39 thf(fact_76_ord__le__eq__subst,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,B: A,F2: A > B4,C3: B4] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ( F2 @ B )
% 0.16/0.39 = C3 )
% 0.16/0.39 => ( ! [X2: A,Y4: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less_eq @ B4 @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less_eq @ B4 @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_le_eq_subst
% 0.16/0.39 thf(fact_77_ord__eq__le__subst,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 0.16/0.39 ( ( A2
% 0.16/0.39 = ( F2 @ B ) )
% 0.16/0.39 => ( ( ord_less_eq @ B4 @ B @ C3 )
% 0.16/0.39 => ( ! [X2: B4,Y4: B4] :
% 0.16/0.39 ( ( ord_less_eq @ B4 @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_eq_le_subst
% 0.16/0.39 thf(fact_78_order__subst2,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType] :
% 0.16/0.39 ( ( ( order @ C @ ( type2 @ C ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ C @ ( F2 @ B ) @ C3 )
% 0.16/0.39 => ( ! [X2: A,Y4: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less_eq @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_subst2
% 0.16/0.39 thf(fact_79_order__subst1,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B ) )
% 0.16/0.39 => ( ( ord_less_eq @ B4 @ B @ C3 )
% 0.16/0.39 => ( ! [X2: B4,Y4: B4] :
% 0.16/0.39 ( ( ord_less_eq @ B4 @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_subst1
% 0.16/0.39 thf(fact_80_le__fun__def,axiom,
% 0.16/0.39 ! [B4: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 => ( ( ord_less_eq @ ( A > B4 ) )
% 0.16/0.39 = ( ^ [F3: A > B4,G: A > B4] :
% 0.16/0.39 ! [X4: A] : ( ord_less_eq @ B4 @ ( F3 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_fun_def
% 0.16/0.39 thf(fact_81_le__funI,axiom,
% 0.16/0.39 ! [B4: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 => ! [F2: A > B4,G2: A > B4] :
% 0.16/0.39 ( ! [X2: A] : ( ord_less_eq @ B4 @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 0.16/0.39 => ( ord_less_eq @ ( A > B4 ) @ F2 @ G2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_funI
% 0.16/0.39 thf(fact_82_le__funE,axiom,
% 0.16/0.39 ! [B4: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 => ! [F2: A > B4,G2: A > B4,X3: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B4 ) @ F2 @ G2 )
% 0.16/0.39 => ( ord_less_eq @ B4 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_funE
% 0.16/0.39 thf(fact_83_le__funD,axiom,
% 0.16/0.39 ! [B4: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 => ! [F2: A > B4,G2: A > B4,X3: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B4 ) @ F2 @ G2 )
% 0.16/0.39 => ( ord_less_eq @ B4 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_funD
% 0.16/0.39 thf(fact_84_ltake__lappend1,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ord_less_eq @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 0.16/0.39 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_lappend1
% 0.16/0.39 thf(fact_85_ord__eq__less__subst,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 0.16/0.39 ( ( A2
% 0.16/0.39 = ( F2 @ B ) )
% 0.16/0.39 => ( ( ord_less @ B4 @ B @ C3 )
% 0.16/0.39 => ( ! [X2: B4,Y4: B4] :
% 0.16/0.39 ( ( ord_less @ B4 @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_eq_less_subst
% 0.16/0.39 thf(fact_86_ord__less__eq__subst,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,B: A,F2: A > B4,C3: B4] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ( F2 @ B )
% 0.16/0.39 = C3 )
% 0.16/0.39 => ( ! [X2: A,Y4: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less @ B4 @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ B4 @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_less_eq_subst
% 0.16/0.39 thf(fact_87_order__less__subst1,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ ( F2 @ B ) )
% 0.16/0.39 => ( ( ord_less @ B4 @ B @ C3 )
% 0.16/0.39 => ( ! [X2: B4,Y4: B4] :
% 0.16/0.39 ( ( ord_less @ B4 @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_less_subst1
% 0.16/0.39 thf(fact_88_order__less__subst2,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType] :
% 0.16/0.39 ( ( ( order @ C @ ( type2 @ C ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ C @ ( F2 @ B ) @ C3 )
% 0.16/0.39 => ( ! [X2: A,Y4: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_less_subst2
% 0.16/0.39 thf(fact_89_lt__ex,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A] :
% 0.16/0.39 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % lt_ex
% 0.16/0.39 thf(fact_90_gt__ex,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( no_top @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A] :
% 0.16/0.39 ? [X1: A] : ( ord_less @ A @ X3 @ X1 ) ) ).
% 0.16/0.39
% 0.16/0.39 % gt_ex
% 0.16/0.39 thf(fact_91_neqE,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( X3 != Y )
% 0.16/0.39 => ( ~ ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % neqE
% 0.16/0.39 thf(fact_92_neq__iff,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( X3 != Y )
% 0.16/0.39 = ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 | ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % neq_iff
% 0.16/0.39 thf(fact_93_order_Oasym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.asym
% 0.16/0.39 thf(fact_94_dense,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ? [Z: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Z )
% 0.16/0.39 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dense
% 0.16/0.39 thf(fact_95_less__imp__neq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( X3 != Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_imp_neq
% 0.16/0.39 thf(fact_96_less__asym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_asym
% 0.16/0.39 thf(fact_97_less__asym_H,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_asym'
% 0.16/0.39 thf(fact_98_less__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,Z3: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less @ A @ Y @ Z3 )
% 0.16/0.39 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_trans
% 0.16/0.39 thf(fact_99_less__linear,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 | ( X3 = Y )
% 0.16/0.39 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_linear
% 0.16/0.39 thf(fact_100_less__irrefl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A] :
% 0.16/0.39 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_irrefl
% 0.16/0.39 thf(fact_101_ord__eq__less__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( A2 = B )
% 0.16/0.39 => ( ( ord_less @ A @ B @ C3 )
% 0.16/0.39 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_eq_less_trans
% 0.16/0.39 thf(fact_102_ord__less__eq__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( B = C3 )
% 0.16/0.39 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_less_eq_trans
% 0.16/0.39 thf(fact_103_dual__order_Oasym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A] :
% 0.16/0.39 ( ( ord_less @ A @ B @ A2 )
% 0.16/0.39 => ~ ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.asym
% 0.16/0.39 thf(fact_104_less__imp__not__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( X3 != Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_imp_not_eq
% 0.16/0.39 thf(fact_105_less__not__sym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_not_sym
% 0.16/0.39 thf(fact_106_less__induct,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > $o,A2: A] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ! [Y5: A] :
% 0.16/0.39 ( ( ord_less @ A @ Y5 @ X2 )
% 0.16/0.39 => ( P @ Y5 ) )
% 0.16/0.39 => ( P @ X2 ) )
% 0.16/0.39 => ( P @ A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_induct
% 0.16/0.39 thf(fact_107_antisym__conv3,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Y: A,X3: A] :
% 0.16/0.39 ( ~ ( ord_less @ A @ Y @ X3 )
% 0.16/0.39 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.16/0.39 = ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym_conv3
% 0.16/0.39 thf(fact_108_less__imp__not__eq2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( Y != X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_imp_not_eq2
% 0.16/0.39 thf(fact_109_less__imp__triv,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,P: $o] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less @ A @ Y @ X3 )
% 0.16/0.39 => P ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_imp_triv
% 0.16/0.39 thf(fact_110_linorder__cases,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ( X3 != Y )
% 0.16/0.39 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % linorder_cases
% 0.16/0.39 thf(fact_111_dual__order_Oirrefl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A] :
% 0.16/0.39 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.irrefl
% 0.16/0.39 thf(fact_112_order_Ostrict__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ A @ B @ C3 )
% 0.16/0.39 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.strict_trans
% 0.16/0.39 thf(fact_113_less__imp__not__less,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_imp_not_less
% 0.16/0.39 thf(fact_114_dual__order_Ostrict__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ B @ A2 )
% 0.16/0.39 => ( ( ord_less @ A @ C3 @ B )
% 0.16/0.39 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.strict_trans
% 0.16/0.39 thf(fact_115_not__less__iff__gr__or__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.16/0.39 = ( ( ord_less @ A @ Y @ X3 )
% 0.16/0.39 | ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % not_less_iff_gr_or_eq
% 0.16/0.39 thf(fact_116_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( A2 != B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.strict_implies_not_eq
% 0.16/0.39 thf(fact_117_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A] :
% 0.16/0.39 ( ( ord_less @ A @ B @ A2 )
% 0.16/0.39 => ( A2 != B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.strict_implies_not_eq
% 0.16/0.39 thf(fact_118_ex__gt__or__lt,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A] :
% 0.16/0.39 ? [B2: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B2 )
% 0.16/0.39 | ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ex_gt_or_lt
% 0.16/0.39 thf(fact_119_leD,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Y: A,X3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.16/0.39 => ~ ( ord_less @ A @ X3 @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % leD
% 0.16/0.39 thf(fact_120_leI,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % leI
% 0.16/0.39 thf(fact_121_le__less,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less_eq @ A )
% 0.16/0.39 = ( ^ [X4: A,Y3: A] :
% 0.16/0.39 ( ( ord_less @ A @ X4 @ Y3 )
% 0.16/0.39 | ( X4 = Y3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_less
% 0.16/0.39 thf(fact_122_less__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less @ A )
% 0.16/0.39 = ( ^ [X4: A,Y3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.16/0.39 & ( X4 != Y3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_le
% 0.16/0.39 thf(fact_123_order__le__less__subst1,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B ) )
% 0.16/0.39 => ( ( ord_less @ B4 @ B @ C3 )
% 0.16/0.39 => ( ! [X2: B4,Y4: B4] :
% 0.16/0.39 ( ( ord_less @ B4 @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_le_less_subst1
% 0.16/0.39 thf(fact_124_order__le__less__subst2,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType] :
% 0.16/0.39 ( ( ( order @ C @ ( type2 @ C ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ C @ ( F2 @ B ) @ C3 )
% 0.16/0.39 => ( ! [X2: A,Y4: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_le_less_subst2
% 0.16/0.39 thf(fact_125_order__less__le__subst1,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType] :
% 0.16/0.39 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ ( F2 @ B ) )
% 0.16/0.39 => ( ( ord_less_eq @ B4 @ B @ C3 )
% 0.16/0.39 => ( ! [X2: B4,Y4: B4] :
% 0.16/0.39 ( ( ord_less_eq @ B4 @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_less_le_subst1
% 0.16/0.39 thf(fact_126_order__less__le__subst2,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType] :
% 0.16/0.39 ( ( ( order @ C @ ( type2 @ C ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ C @ ( F2 @ B ) @ C3 )
% 0.16/0.39 => ( ! [X2: A,Y4: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Y4 )
% 0.16/0.39 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 0.16/0.39 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_less_le_subst2
% 0.16/0.39 thf(fact_127_not__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ~ ( ord_less_eq @ A @ X3 @ Y ) )
% 0.16/0.39 = ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % not_le
% 0.16/0.39 thf(fact_128_not__less,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.16/0.39 = ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % not_less
% 0.16/0.39 thf(fact_129_le__neq__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( A2 != B )
% 0.16/0.39 => ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_neq_trans
% 0.16/0.39 thf(fact_130_less__imp__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_imp_le
% 0.16/0.39 thf(fact_131_antisym__conv1,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 = ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym_conv1
% 0.16/0.39 thf(fact_132_antisym__conv2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.16/0.39 = ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym_conv2
% 0.16/0.39 thf(fact_133_le__less__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,Z3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less @ A @ Y @ Z3 )
% 0.16/0.39 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_less_trans
% 0.16/0.39 thf(fact_134_less__le__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A,Z3: A] :
% 0.16/0.39 ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.16/0.39 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_le_trans
% 0.16/0.39 thf(fact_135_dense__ge,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Z3: A,Y: A] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ Z3 @ X2 )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ X2 ) )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dense_ge
% 0.16/0.39 thf(fact_136_dense__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Y: A,Z3: A] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( ord_less @ A @ X2 @ Y )
% 0.16/0.39 => ( ord_less_eq @ A @ X2 @ Z3 ) )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dense_le
% 0.16/0.39 thf(fact_137_le__less__linear,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_less_linear
% 0.16/0.39 thf(fact_138_le__imp__less__or__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.16/0.39 => ( ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 | ( X3 = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_imp_less_or_eq
% 0.16/0.39 thf(fact_139_less__le__not__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less @ A )
% 0.16/0.39 = ( ^ [X4: A,Y3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.16/0.39 & ~ ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_le_not_le
% 0.16/0.39 thf(fact_140_not__le__imp__less,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Y: A,X3: A] :
% 0.16/0.39 ( ~ ( ord_less_eq @ A @ Y @ X3 )
% 0.16/0.39 => ( ord_less @ A @ X3 @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % not_le_imp_less
% 0.16/0.39 thf(fact_141_order_Ostrict__trans1,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ A @ B @ C3 )
% 0.16/0.39 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.strict_trans1
% 0.16/0.39 thf(fact_142_order_Ostrict__trans2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B @ C3 )
% 0.16/0.39 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.strict_trans2
% 0.16/0.39 thf(fact_143_order_Oorder__iff__strict,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less_eq @ A )
% 0.16/0.39 = ( ^ [A4: A,B3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.39 | ( A4 = B3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.order_iff_strict
% 0.16/0.39 thf(fact_144_order_Ostrict__iff__order,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less @ A )
% 0.16/0.39 = ( ^ [A4: A,B3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.16/0.39 & ( A4 != B3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.strict_iff_order
% 0.16/0.39 thf(fact_145_dual__order_Ostrict__trans1,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( ( ord_less @ A @ C3 @ B )
% 0.16/0.39 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.strict_trans1
% 0.16/0.39 thf(fact_146_ldrop__lappend,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( ord_less @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 0.16/0.39 => ( ( coindu191418589_ldrop @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu268472904append @ A @ ( coindu191418589_ldrop @ A @ N @ Xs ) @ Ys ) ) )
% 0.16/0.39 & ( ~ ( ord_less @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 0.16/0.39 => ( ( coindu191418589_ldrop @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu191418589_ldrop @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_lappend
% 0.16/0.39 thf(fact_147_ltake__lappend2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: extended_enat,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N )
% 0.16/0.39 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu268472904append @ A @ Xs @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_lappend2
% 0.16/0.39 thf(fact_148_ldrop__eq__LNil,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu191418589_ldrop @ A @ N @ Xs )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_eq_LNil
% 0.16/0.39 thf(fact_149_lnull__ldrop,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ ( coindu191418589_ldrop @ A @ N @ Xs ) )
% 0.16/0.39 = ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_ldrop
% 0.16/0.39 thf(fact_150_ltake__plus__conv__lappend,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1802687541_ltake @ A @ ( plus_plus @ extended_enat @ N @ M2 ) @ Xs )
% 0.16/0.39 = ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ M2 @ ( coindu191418589_ldrop @ A @ N @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_plus_conv_lappend
% 0.16/0.39 thf(fact_151_ltake__lappend,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_lappend
% 0.16/0.39 thf(fact_152_ldrop__all,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,M2: extended_enat] :
% 0.16/0.39 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M2 )
% 0.16/0.39 => ( ( coindu191418589_ldrop @ A @ M2 @ Xs )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_all
% 0.16/0.39 thf(fact_153_lprefix__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_code(1)
% 0.16/0.39 thf(fact_154_lappend_Odisc__iff_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.16/0.39 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc_iff(2)
% 0.16/0.39 thf(fact_155_lnull__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_lappend
% 0.16/0.39 thf(fact_156_lappend__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.16/0.39 = Ys ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_code(1)
% 0.16/0.39 thf(fact_157_lappend__LNil2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_LNil2
% 0.16/0.39 thf(fact_158_ltake__LNil,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat] :
% 0.16/0.39 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_LNil
% 0.16/0.39 thf(fact_159_ldrop__LNil,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat] :
% 0.16/0.39 ( ( coindu191418589_ldrop @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_LNil
% 0.16/0.39 thf(fact_160_ldrop__ldrop,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu191418589_ldrop @ A @ N @ ( coindu191418589_ldrop @ A @ M2 @ Xs ) )
% 0.16/0.39 = ( coindu191418589_ldrop @ A @ ( plus_plus @ extended_enat @ N @ M2 ) @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_ldrop
% 0.16/0.39 thf(fact_161_lstrict__prefix__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(1)
% 0.16/0.39 thf(fact_162_lprefix__LNil,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_LNil
% 0.16/0.39 thf(fact_163_llength__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1018505716length @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( plus_plus @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llength_lappend
% 0.16/0.39 thf(fact_164_less__fun__def,axiom,
% 0.16/0.39 ! [B4: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 0.16/0.39 => ( ( ord_less @ ( A > B4 ) )
% 0.16/0.39 = ( ^ [F3: A > B4,G: A > B4] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B4 ) @ F3 @ G )
% 0.16/0.39 & ~ ( ord_less_eq @ ( A > B4 ) @ G @ F3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_fun_def
% 0.16/0.39 thf(fact_165_ldrop__lnull,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: extended_enat] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu191418589_ldrop @ A @ N @ Xs )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_lnull
% 0.16/0.39 thf(fact_166_lappend_Octr_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.ctr(1)
% 0.16/0.39 thf(fact_167_llist_Odisc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.disc(1)
% 0.16/0.39 thf(fact_168_llist_OdiscI_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Llist
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.discI(1)
% 0.16/0.39 thf(fact_169_llist_Ocollapse_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Llist )
% 0.16/0.39 => ( Llist
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.collapse(1)
% 0.16/0.39 thf(fact_170_lzip_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,B4: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B4] :
% 0.16/0.39 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ( coindu335574135_lnull @ B4 @ Ys ) )
% 0.16/0.39 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu335574135_lnull @ B4 @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lzip.exhaust
% 0.16/0.39 thf(fact_171_lappend_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.16/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.exhaust
% 0.16/0.39 thf(fact_172_lnull__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A )
% 0.16/0.39 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Llist2
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_def
% 0.16/0.39 thf(fact_173_lnull__lprefix,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_lprefix
% 0.16/0.39 thf(fact_174_lprefix__lnull,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lnull
% 0.16/0.39 thf(fact_175_lprefix__lnullD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lnullD
% 0.16/0.39 thf(fact_176_lprefix__not__lnullD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_not_lnullD
% 0.16/0.39 thf(fact_177_LNil__lprefix,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % LNil_lprefix
% 0.16/0.39 thf(fact_178_lappend_Odisc_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc(2)
% 0.16/0.39 thf(fact_179_lappend_Odisc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc(1)
% 0.16/0.39 thf(fact_180_lappend__lnull1,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_lnull1
% 0.16/0.39 thf(fact_181_lappend__lnull2,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_lnull2
% 0.16/0.39 thf(fact_182_lappend__LNil__LNil,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_LNil_LNil
% 0.16/0.39 thf(fact_183_LNil__eq__lappend__iff,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu1598213697e_LNil @ A )
% 0.16/0.39 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % LNil_eq_lappend_iff
% 0.16/0.39 thf(fact_184_lappend__eq__LNil__iff,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_eq_LNil_iff
% 0.16/0.39 thf(fact_185_ldrop__ltake,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu191418589_ldrop @ A @ N @ ( coindu1802687541_ltake @ A @ M2 @ Xs ) )
% 0.16/0.39 = ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ M2 @ N ) @ ( coindu191418589_ldrop @ A @ N @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ldrop_ltake
% 0.16/0.39 thf(fact_186_ltake__ldrop,axiom,
% 0.16/0.39 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1802687541_ltake @ A @ N @ ( coindu191418589_ldrop @ A @ M2 @ Xs ) )
% 0.16/0.39 = ( coindu191418589_ldrop @ A @ M2 @ ( coindu1802687541_ltake @ A @ ( plus_plus @ extended_enat @ N @ M2 ) @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltake_ldrop
% 0.16/0.39 thf(fact_187_le__add__diff__inverse,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( ( plus_plus @ A @ B @ ( minus_minus @ A @ A2 @ B ) )
% 0.16/0.39 = A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_add_diff_inverse
% 0.16/0.39 thf(fact_188_le__add__diff__inverse2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.16/0.39 = A2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_add_diff_inverse2
% 0.16/0.39 thf(fact_189_add__diff__cancel,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.16/0.39 = A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_diff_cancel
% 0.16/0.39 thf(fact_190_add__right__cancel,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ B @ A2 )
% 0.16/0.39 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.16/0.39 = ( B = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_right_cancel
% 0.16/0.39 thf(fact_191_add__left__cancel,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ A2 @ B )
% 0.16/0.39 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.16/0.39 = ( B = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_left_cancel
% 0.16/0.39 thf(fact_192_add__le__cancel__left,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [C3: A,A2: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 0.16/0.39 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_le_cancel_left
% 0.16/0.39 thf(fact_193_add__le__cancel__right,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 0.16/0.39 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_le_cancel_right
% 0.16/0.39 thf(fact_194_add__less__cancel__right,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 0.16/0.39 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_less_cancel_right
% 0.16/0.39 thf(fact_195_add__less__cancel__left,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [C3: A,A2: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 0.16/0.39 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_less_cancel_left
% 0.16/0.39 thf(fact_196_add__diff__cancel__right_H,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.16/0.39 = A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_diff_cancel_right'
% 0.16/0.39 thf(fact_197_add__diff__cancel__right,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 0.16/0.39 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_diff_cancel_right
% 0.16/0.39 thf(fact_198_add__diff__cancel__left_H,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ A2 )
% 0.16/0.39 = B ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_diff_cancel_left'
% 0.16/0.39 thf(fact_199_add__diff__cancel__left,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [C3: A,A2: A,B: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 0.16/0.39 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_diff_cancel_left
% 0.16/0.39 thf(fact_200_diff__add__cancel,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.16/0.39 = A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_add_cancel
% 0.16/0.39 thf(fact_201_linorder__neqE__linordered__idom,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X3: A,Y: A] :
% 0.16/0.39 ( ( X3 != Y )
% 0.16/0.39 => ( ~ ( ord_less @ A @ X3 @ Y )
% 0.16/0.39 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % linorder_neqE_linordered_idom
% 0.16/0.39 thf(fact_202_add__right__imp__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ B @ A2 )
% 0.16/0.39 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.16/0.39 => ( B = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_right_imp_eq
% 0.16/0.39 thf(fact_203_add__left__imp__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ A2 @ B )
% 0.16/0.39 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.16/0.39 => ( B = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_left_imp_eq
% 0.16/0.39 thf(fact_204_add_Oleft__commute,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C3 ) )
% 0.16/0.39 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add.left_commute
% 0.16/0.39 thf(fact_205_add_Ocommute,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( plus_plus @ A )
% 0.16/0.39 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add.commute
% 0.16/0.39 thf(fact_206_add_Oright__cancel,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ B @ A2 )
% 0.16/0.39 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.16/0.39 = ( B = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add.right_cancel
% 0.16/0.39 thf(fact_207_add_Oleft__cancel,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ A2 @ B )
% 0.16/0.39 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.16/0.39 = ( B = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add.left_cancel
% 0.16/0.39 thf(fact_208_add_Oassoc,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C3 )
% 0.16/0.39 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add.assoc
% 0.16/0.39 thf(fact_209_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( I = J )
% 0.16/0.39 & ( K = L ) )
% 0.16/0.39 => ( ( plus_plus @ A @ I @ K )
% 0.16/0.39 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_semiring(4)
% 0.16/0.39 thf(fact_210_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C3 )
% 0.16/0.39 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ab_semigroup_add_class.add_ac(1)
% 0.16/0.39 thf(fact_211_diff__right__commute,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C3 ) @ B )
% 0.16/0.39 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_right_commute
% 0.16/0.39 thf(fact_212_diff__eq__diff__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ( minus_minus @ A @ A2 @ B )
% 0.16/0.39 = ( minus_minus @ A @ C3 @ D3 ) )
% 0.16/0.39 => ( ( A2 = B )
% 0.16/0.39 = ( C3 = D3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_eq_diff_eq
% 0.16/0.39 thf(fact_213_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ I @ J )
% 0.16/0.39 & ( K = L ) )
% 0.16/0.39 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_semiring(3)
% 0.16/0.39 thf(fact_214_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( I = J )
% 0.16/0.39 & ( ord_less_eq @ A @ K @ L ) )
% 0.16/0.39 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_semiring(2)
% 0.16/0.39 thf(fact_215_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ I @ J )
% 0.16/0.39 & ( ord_less_eq @ A @ K @ L ) )
% 0.16/0.39 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_semiring(1)
% 0.16/0.39 thf(fact_216_add__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono
% 0.16/0.39 thf(fact_217_add__left__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_left_mono
% 0.16/0.39 thf(fact_218_add__right__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_right_mono
% 0.16/0.39 thf(fact_219_le__iff__add,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ord_less_eq @ A )
% 0.16/0.39 = ( ^ [A4: A,B3: A] :
% 0.16/0.39 ? [C4: A] :
% 0.16/0.39 ( B3
% 0.16/0.39 = ( plus_plus @ A @ A4 @ C4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_iff_add
% 0.16/0.39 thf(fact_220_add__le__imp__le__left,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [C3: A,A2: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_le_imp_le_left
% 0.16/0.39 thf(fact_221_add__le__imp__le__right,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 0.16/0.39 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_le_imp_le_right
% 0.16/0.39 thf(fact_222_diff__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,D3: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ D3 @ C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ D3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_mono
% 0.16/0.39 thf(fact_223_diff__left__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B @ A2 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( minus_minus @ A @ C3 @ A2 ) @ ( minus_minus @ A @ C3 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_left_mono
% 0.16/0.39 thf(fact_224_diff__right__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_right_mono
% 0.16/0.39 thf(fact_225_diff__eq__diff__less__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ( minus_minus @ A @ A2 @ B )
% 0.16/0.39 = ( minus_minus @ A @ C3 @ D3 ) )
% 0.16/0.39 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 = ( ord_less_eq @ A @ C3 @ D3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_eq_diff_less_eq
% 0.16/0.39 thf(fact_226_add__less__imp__less__right,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 0.16/0.39 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_less_imp_less_right
% 0.16/0.39 thf(fact_227_add__less__imp__less__left,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [C3: A,A2: A,B: A] :
% 0.16/0.39 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 0.16/0.39 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_less_imp_less_left
% 0.16/0.39 thf(fact_228_add__strict__right__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_strict_right_mono
% 0.16/0.39 thf(fact_229_add__strict__left__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_strict_left_mono
% 0.16/0.39 thf(fact_230_add__strict__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ A @ C3 @ D3 )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_strict_mono
% 0.16/0.39 thf(fact_231_add__mono__thms__linordered__field_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( ord_less @ A @ I @ J )
% 0.16/0.39 & ( K = L ) )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_field(1)
% 0.16/0.39 thf(fact_232_add__mono__thms__linordered__field_I2_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( I = J )
% 0.16/0.39 & ( ord_less @ A @ K @ L ) )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_field(2)
% 0.16/0.39 thf(fact_233_add__mono__thms__linordered__field_I5_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( ord_less @ A @ I @ J )
% 0.16/0.39 & ( ord_less @ A @ K @ L ) )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_field(5)
% 0.16/0.39 thf(fact_234_diff__strict__right__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_strict_right_mono
% 0.16/0.39 thf(fact_235_diff__strict__left__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B: A,A2: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ B @ A2 )
% 0.16/0.39 => ( ord_less @ A @ ( minus_minus @ A @ C3 @ A2 ) @ ( minus_minus @ A @ C3 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_strict_left_mono
% 0.16/0.39 thf(fact_236_diff__eq__diff__less,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ( minus_minus @ A @ A2 @ B )
% 0.16/0.39 = ( minus_minus @ A @ C3 @ D3 ) )
% 0.16/0.39 => ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 = ( ord_less @ A @ C3 @ D3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_eq_diff_less
% 0.16/0.39 thf(fact_237_diff__strict__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,D3: A,C3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ A @ D3 @ C3 )
% 0.16/0.39 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ D3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_strict_mono
% 0.16/0.39 thf(fact_238_add__implies__diff,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [C3: A,B: A,A2: A] :
% 0.16/0.39 ( ( ( plus_plus @ A @ C3 @ B )
% 0.16/0.39 = A2 )
% 0.16/0.39 => ( C3
% 0.16/0.39 = ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_implies_diff
% 0.16/0.39 thf(fact_239_diff__diff__add,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C3 )
% 0.16/0.39 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_diff_add
% 0.16/0.39 thf(fact_240_diff__add__eq__diff__diff__swap,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) )
% 0.16/0.39 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C3 ) @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_add_eq_diff_diff_swap
% 0.16/0.39 thf(fact_241_diff__add__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ C3 )
% 0.16/0.39 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_add_eq
% 0.16/0.39 thf(fact_242_diff__diff__eq2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B @ C3 ) )
% 0.16/0.39 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_diff_eq2
% 0.16/0.39 thf(fact_243_add__diff__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ C3 ) )
% 0.16/0.39 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_diff_eq
% 0.16/0.39 thf(fact_244_eq__diff__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,C3: A,B: A] :
% 0.16/0.39 ( ( A2
% 0.16/0.39 = ( minus_minus @ A @ C3 @ B ) )
% 0.16/0.39 = ( ( plus_plus @ A @ A2 @ B )
% 0.16/0.39 = C3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_diff_eq
% 0.16/0.39 thf(fact_245_diff__eq__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( group_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ( minus_minus @ A @ A2 @ B )
% 0.16/0.39 = C3 )
% 0.16/0.39 = ( A2
% 0.16/0.39 = ( plus_plus @ A @ C3 @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % diff_eq_eq
% 0.16/0.39 thf(fact_246_add__mono__thms__linordered__field_I4_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ I @ J )
% 0.16/0.39 & ( ord_less @ A @ K @ L ) )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_field(4)
% 0.16/0.39 thf(fact_247_add__mono__thms__linordered__field_I3_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [I: A,J: A,K: A,L: A] :
% 0.16/0.39 ( ( ( ord_less @ A @ I @ J )
% 0.16/0.39 & ( ord_less_eq @ A @ K @ L ) )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_mono_thms_linordered_field(3)
% 0.16/0.39 thf(fact_248_add__le__less__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less @ A @ C3 @ D3 )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_le_less_mono
% 0.16/0.39 thf(fact_249_add__less__le__mono,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A,D3: A] :
% 0.16/0.39 ( ( ord_less @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.16/0.39 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % add_less_le_mono
% 0.16/0.39 thf(fact_250_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( ( minus_minus @ A @ B @ A2 )
% 0.16/0.39 = C3 )
% 0.16/0.39 = ( B
% 0.16/0.39 = ( plus_plus @ A @ C3 @ A2 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.16/0.39 thf(fact_251_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ A2 ) )
% 0.16/0.39 = B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.16/0.39 thf(fact_252_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( minus_minus @ A @ C3 @ ( minus_minus @ A @ B @ A2 ) )
% 0.16/0.39 = ( minus_minus @ A @ ( plus_plus @ A @ C3 @ A2 ) @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.16/0.39 thf(fact_253_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A2: A,B: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B )
% 0.16/0.39 => ( ( minus_minus @ A @ ( plus_plus @ A @ B @ C3 ) @ A2 )
% 0.16/0.39 = ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.16/0.39
% 0.16/0.39 %----Type constructors (18)
% 0.16/0.39 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.16/0.39 ! [A5: $tType,A6: $tType] :
% 0.16/0.39 ( ( preorder @ A6 @ ( type2 @ A6 ) )
% 0.16/0.39 => ( preorder @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.16/0.39 ! [A5: $tType,A6: $tType] :
% 0.16/0.39 ( ( order @ A6 @ ( type2 @ A6 ) )
% 0.16/0.39 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_fun___Orderings_Oord,axiom,
% 0.16/0.39 ! [A5: $tType,A6: $tType] :
% 0.16/0.39 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 0.16/0.39 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Opreorder_1,axiom,
% 0.16/0.39 preorder @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.16/0.39 linorder @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.16/0.39 order @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Oord_3,axiom,
% 0.16/0.39 ord @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.16/0.39 condit1037483654norder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.16/0.39 strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.16/0.39 canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.16/0.39 ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add,axiom,
% 0.16/0.39 ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add,axiom,
% 0.16/0.39 semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Orderings_Owellorder,axiom,
% 0.16/0.39 wellorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_4,axiom,
% 0.16/0.39 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_5,axiom,
% 0.16/0.39 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_6,axiom,
% 0.16/0.39 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_7,axiom,
% 0.16/0.39 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.16/0.39
% 0.16/0.39 %----Conjectures (1)
% 0.16/0.39 thf(conj_0,conjecture,
% 0.16/0.39 ord_less @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ a @ ys ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 3.01/1.64 ---- Embedded in THF ---
% 3.01/1.64 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.01/1.64 %%% Generated on Tue Feb 24 06:08:47 EST 2026
% 3.01/1.64 %%% using '$$dhol' embedding, version 1.3.0.
% 3.01/1.64 %%% Logic specification used:
% 3.01/1.64 %%% thf(spec, logic, $$dhol).
% 3.01/1.64
% 3.01/1.64 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2HsJS0n40S/DTF2DTF24777.p
% 3.01/1.64 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 3.01/1.64 thf(ty_t_Extended__Nat_Oenat, type, extended_enat: $tType).
% 3.01/1.64 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.01/1.64 thf(ty_tf_a, type, a: $tType).
% 3.01/1.64 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff, type, ordere623563068d_diff: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oldrop, type, coindu191418589_ldrop: (!> [A:$tType]: ((extended_enat > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength, type, coindu1018505716length: (!> [A:$tType]: (((coindu1593790203_llist @ A) > extended_enat)))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix, type, coindu574146665prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 3.01/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake, type, coindu1802687541_ltake: (!> [A:$tType]: ((extended_enat > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.01/1.64 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 3.01/1.64 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 3.01/1.64 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 3.01/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.01/1.64 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 3.01/1.64 thf(sy_v_xs, type, xs: (coindu1593790203_llist @ a)).
% 3.01/1.64 thf(sy_v_xs_H____, type, xs2: (coindu1593790203_llist @ a)).
% 3.01/1.64 thf(sy_v_ys, type, ys: (coindu1593790203_llist @ a)).
% 3.01/1.64 thf(sy_v_zs, type, zs: (coindu1593790203_llist @ a)).
% 3.01/1.64 thf(fact_0__092_060open_062_092_060not_062_Allength_Ays_A_092_060le_062_Allength_Axs_092_060close_062, axiom, (~ ((((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ a) @ ys)) @ ((coindu1018505716length @ a) @ xs))))).
% 3.01/1.64 thf(fact_1__092_060open_062_092_060not_062_A_Ixs_A_092_060sqsubseteq_062_Ays_A_092_060or_062_Ays_A_092_060sqsubseteq_062_Axs_J_092_060close_062, axiom, (~ (((((coindu1696667936prefix @ a) @ xs) @ ys) | (((coindu1696667936prefix @ a) @ ys) @ xs))))).
% 3.01/1.64 thf(fact_2__092_060open_062_092_060not_062_Axs_A_092_060sqsubseteq_062_Ays_092_060close_062, axiom, (~ ((((coindu1696667936prefix @ a) @ xs) @ ys)))).
% 3.01/1.64 thf(fact_3__092_060open_062_092_060not_062_Ays_A_092_060sqsubseteq_062_Axs_092_060close_062, axiom, (~ ((((coindu1696667936prefix @ a) @ ys) @ xs)))).
% 3.01/1.64 thf(fact_4__092_060open_062lappend_Axs_Axs_H_A_061_Alappend_Ays_Azs_092_060close_062, axiom, ((((coindu268472904append @ a) @ xs) @ xs2) = (((coindu268472904append @ a) @ ys) @ zs))).
% 3.01/1.64 thf(fact_5_lstrict__prefix__llength__less, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Xs) @ Ys) => (((ord_less @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ ((coindu1018505716length @ A) @ Ys)))))).
% 3.01/1.64 thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_O_Alappend_Axs_Axs_H_A_061_Alappend_Ays_Azs_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Xs2:(coindu1593790203_llist @ a)]: (((((coindu268472904append @ a) @ xs) @ Xs2) != (((coindu268472904append @ a) @ ys) @ zs))))))).
% 3.01/1.64 thf(fact_7_enat__less__induct, axiom, (! [P:(extended_enat > $o),N:extended_enat]: (((! [N2:extended_enat]: (((! [M:extended_enat]: (((((ord_less @ extended_enat) @ M) @ N2) => (P @ M)))) => (P @ N2)))) => (P @ N))))).
% 3.01/1.64 thf(fact_8_minf_I11_J, axiom, (! [C:$tType,D:$tType]: ((((ord @ C) @ (type2 @ C)) => (! [F:D]: ((? [Z:C]: ((! [X:C]: (((((ord_less @ C) @ X) @ Z) => (F = F)))))))))))).
% 3.01/1.64 thf(fact_9_minf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (~ ((((ord_less @ A) @ T) @ X)))))))))))))).
% 3.01/1.64 thf(fact_10_minf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((ord_less @ A) @ X) @ T)))))))))))).
% 3.01/1.64 thf(fact_11_minf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (X != T)))))))))))).
% 3.01/1.64 thf(fact_12_minf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (X != T)))))))))))).
% 3.01/1.64 thf(fact_13_minf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((P @ X) | (Q @ X)) = ((P2 @ X) | (Q2 @ X)))))))))))))))).
% 3.01/1.64 thf(fact_14_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 3.01/1.64 thf(fact_15_llist_Oleq__refl, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ X3) @ X3)))).
% 3.01/1.64 thf(fact_16_assms, axiom, (((coindu1696667936prefix @ a) @ xs) @ (((coindu268472904append @ a) @ ys) @ zs))).
% 3.01/1.64 thf(fact_17_lappend__assoc, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) = (((coindu268472904append @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs)))))).
% 3.01/1.64 thf(fact_18_lprefix__trans, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => (((coindu1696667936prefix @ A) @ Xs) @ Zs)))))).
% 3.01/1.64 thf(fact_19_llist_Oleq__trans, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A),Z3:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X3) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ Z3) => (((coindu1696667936prefix @ A) @ X3) @ Z3)))))).
% 3.01/1.64 thf(fact_20_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 3.01/1.64 thf(fact_21_lprefix__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 3.01/1.64 thf(fact_22_lappend__lprefixE, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) => (~ ((! [Zs2:(coindu1593790203_llist @ A)]: ((Zs != (((coindu268472904append @ A) @ Xs) @ Zs2)))))))))).
% 3.01/1.64 thf(fact_23_llist_Oleq__antisym, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X3) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ X3) => (X3 = Y)))))).
% 3.01/1.64 thf(fact_24_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu574146665prefix @ A) = (^ [Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs3) @ Ys2) & (Xs3 != Ys2)))))))).
% 3.01/1.64 thf(fact_25_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Zs) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) | (((coindu1696667936prefix @ A) @ Ys) @ Xs))))))).
% 3.01/1.64 thf(fact_26_lprefix__conv__lappend, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: ((? [Zs3:(coindu1593790203_llist @ A)]: ((Ys2 = (((coindu268472904append @ A) @ Xs3) @ Zs3)))))))))).
% 3.01/1.64 thf(fact_27_lprefix__lappend__sameI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Zs) @ Xs)) @ (((coindu268472904append @ A) @ Zs) @ Ys)))))).
% 3.01/1.64 thf(fact_28_llist__less__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((! [Xs4:(coindu1593790203_llist @ A)]: (((! [Ys3:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys3) @ Xs4) => (P @ Ys3)))) => (P @ Xs4)))) => (P @ Xs))))).
% 3.01/1.64 thf(fact_29_lprefix__llength__le, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ ((coindu1018505716length @ A) @ Ys)))))).
% 3.01/1.64 thf(fact_30_lprefix__llength__eq__imp__eq, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1018505716length @ A) @ Xs) = ((coindu1018505716length @ A) @ Ys)) => (Xs = Ys)))))).
% 3.01/1.64 thf(fact_31_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B:A,A2:A]: (((! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((P @ A3) @ B2)))) => ((((P @ B) @ A2) => ((P @ A2) @ B)) => ((P @ A2) @ B))))))))).
% 3.01/1.64 thf(fact_32_pinf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ T)))))))))))))).
% 3.01/1.64 thf(fact_33_pinf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((ord_less_eq @ A) @ T) @ X)))))))))))).
% 3.01/1.64 thf(fact_34_minf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((ord_less_eq @ A) @ X) @ T)))))))))))).
% 3.01/1.64 thf(fact_35_minf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ T) @ X)))))))))))))).
% 3.01/1.64 thf(fact_36_pinf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((P @ X) & (Q @ X)) = ((P2 @ X) & (Q2 @ X)))))))))))))))).
% 3.01/1.64 thf(fact_37_pinf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((P @ X) | (Q @ X)) = ((P2 @ X) | (Q2 @ X)))))))))))))))).
% 3.01/1.64 thf(fact_38_pinf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (X != T)))))))))))).
% 3.01/1.64 thf(fact_39_pinf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (X != T)))))))))))).
% 3.01/1.64 thf(fact_40_pinf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (~ ((((ord_less @ A) @ X) @ T)))))))))))))).
% 3.01/1.64 thf(fact_41_pinf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((ord_less @ A) @ T) @ X)))))))))))).
% 3.01/1.64 thf(fact_42_pinf_I11_J, axiom, (! [C:$tType,D:$tType]: ((((ord @ C) @ (type2 @ C)) => (! [F:D]: ((? [Z:C]: ((! [X:C]: (((((ord_less @ C) @ Z) @ X) => (F = F)))))))))))).
% 3.01/1.64 thf(fact_43_minf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((P @ X) & (Q @ X)) = ((P2 @ X) & (Q2 @ X)))))))))))))))).
% 3.01/1.64 thf(fact_44_eq, axiom, ((((coindu268472904append @ a) @ (((coindu1802687541_ltake @ a) @ ((coindu1018505716length @ a) @ ys)) @ xs)) @ (((coindu268472904append @ a) @ (((coindu191418589_ldrop @ a) @ ((coindu1018505716length @ a) @ ys)) @ xs)) @ xs2)) = (((coindu268472904append @ a) @ ys) @ zs))).
% 3.01/1.64 thf(fact_45_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 3.01/1.64 thf(fact_46_complete__interval, axiom, (! [A:$tType]: ((((condit1037483654norder @ A) @ (type2 @ A)) => (! [A2:A,B:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B) => ((P @ A2) => ((~ ((P @ B))) => (? [C2:A]: (((((ord_less_eq @ A) @ A2) @ C2) & ((((ord_less_eq @ A) @ C2) @ B) & ((! [X:A]: ((((((ord_less_eq @ A) @ A2) @ X) & (((ord_less @ A) @ X) @ C2)) => (P @ X)))) & (! [D2:A]: (((! [X2:A]: ((((((ord_less_eq @ A) @ A2) @ X2) & (((ord_less @ A) @ X2) @ D2)) => (P @ X2)))) => (((ord_less_eq @ A) @ D2) @ C2)))))))))))))))))).
% 3.01/1.64 thf(fact_47_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((A2 != B) => ((((ord_less_eq @ A) @ A2) @ B) => (((ord_less @ A) @ A2) @ B))))))))).
% 3.01/1.64 thf(fact_48_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less @ A) @ B) @ A2) => (((ord_less_eq @ A) @ B) @ A2)))))))).
% 3.01/1.64 thf(fact_49_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [B3:A,A4:A]: (((((ord_less_eq @ A) @ B3) @ A4) & (A4 != B3))))))))).
% 3.01/1.64 thf(fact_50_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) | (A4 = B3))))))))).
% 3.01/1.64 thf(fact_51_order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_52_dense__le__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y) => ((! [W:A]: (((((ord_less @ A) @ X3) @ W) => ((((ord_less @ A) @ W) @ Y) => (((ord_less_eq @ A) @ W) @ Z3))))) => (((ord_less_eq @ A) @ Y) @ Z3))))))))).
% 3.01/1.64 thf(fact_53_dense__ge__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z3:A,X3:A,Y:A]: (((((ord_less @ A) @ Z3) @ X3) => ((! [W:A]: (((((ord_less @ A) @ Z3) @ W) => ((((ord_less @ A) @ W) @ X3) => (((ord_less_eq @ A) @ Y) @ W))))) => (((ord_less_eq @ A) @ Y) @ Z3))))))))).
% 3.01/1.64 thf(fact_54_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ C3) @ B) => (((ord_less @ A) @ C3) @ A2))))))))).
% 3.01/1.64 thf(fact_55_ltake__is__lprefix, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ Xs)))).
% 3.01/1.64 thf(fact_56_lprefix__ltake__same, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),M2:extended_enat]: (((((coindu1696667936prefix @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ (((coindu1802687541_ltake @ A) @ M2) @ Xs)) = ((((ord_less_eq @ extended_enat) @ N) @ M2) | (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ M2)))))).
% 3.01/1.64 thf(fact_57_lappend__ltake__ldrop, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ (((coindu191418589_ldrop @ A) @ N) @ Xs)) = Xs)))).
% 3.01/1.64 thf(fact_58_ltake__eq__ltake__antimono, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),M2:extended_enat]: ((((((coindu1802687541_ltake @ A) @ N) @ Xs) = (((coindu1802687541_ltake @ A) @ N) @ Ys)) => ((((ord_less_eq @ extended_enat) @ M2) @ N) => ((((coindu1802687541_ltake @ A) @ M2) @ Xs) = (((coindu1802687541_ltake @ A) @ M2) @ Ys))))))).
% 3.01/1.64 thf(fact_59_ltake__all, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),M2:extended_enat]: (((((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ M2) => ((((coindu1802687541_ltake @ A) @ M2) @ Xs) = Xs))))).
% 3.01/1.64 thf(fact_60_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ A2) @ B) => (A2 = B))))))))).
% 3.01/1.64 thf(fact_61_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ C3) @ B) => (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 3.01/1.64 thf(fact_62_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B:A]: (((! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((P @ A3) @ B2)))) => ((! [A3:A,B2:A]: ((((P @ B2) @ A3) => ((P @ A3) @ B2)))) => ((P @ A2) @ B))))))))).
% 3.01/1.64 thf(fact_63_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.01/1.64 thf(fact_64_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z3:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z3) => (((ord_less_eq @ A) @ X3) @ Z3))))))))).
% 3.01/1.64 thf(fact_65_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ A2) => (A2 = B))))))))).
% 3.01/1.64 thf(fact_66_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((B = C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_67_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((A2 = B) => ((((ord_less_eq @ A) @ B) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_68_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X3:A]: (((((ord_less_eq @ A) @ Y) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y) = (X3 = Y))))))))).
% 3.01/1.64 thf(fact_69_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z3:A]: ((((((ord_less_eq @ A) @ X3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z3)))) => (((((ord_less_eq @ A) @ Y) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z3)))) => (((((ord_less_eq @ A) @ X3) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y)))) => (((((ord_less_eq @ A) @ Z3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X3)))) => (((((ord_less_eq @ A) @ Y) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y))))))))))))))))).
% 3.01/1.64 thf(fact_70_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_71_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y))) => (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 3.01/1.64 thf(fact_72_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((X3 = Y) => (((ord_less_eq @ A) @ X3) @ Y)))))))).
% 3.01/1.64 thf(fact_73_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) | (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 3.01/1.64 thf(fact_74_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ X3) => (X3 = Y))))))))).
% 3.01/1.64 thf(fact_75_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y2:A,Z4:A]: ((Y2 = Z4))) = (^ [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X4))))))))).
% 3.01/1.64 thf(fact_76_ord__le__eq__subst, axiom, (! [A:$tType,B4:$tType]: (((((ord @ B4) @ (type2 @ B4)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B:A,F2:(A > B4),C3:B4]: (((((ord_less_eq @ A) @ A2) @ B) => (((F2 @ B) = C3) => ((! [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) => (((ord_less_eq @ B4) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less_eq @ B4) @ (F2 @ A2)) @ C3)))))))))).
% 3.01/1.64 thf(fact_77_ord__eq__le__subst, axiom, (! [A:$tType,B4:$tType]: (((((ord @ B4) @ (type2 @ B4)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F2:(B4 > A),B:B4,C3:B4]: (((A2 = (F2 @ B)) => ((((ord_less_eq @ B4) @ B) @ C3) => ((! [X2:B4,Y4:B4]: (((((ord_less_eq @ B4) @ X2) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C3))))))))))).
% 3.01/1.64 thf(fact_78_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B:A,F2:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ C) @ (F2 @ B)) @ C3) => ((! [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) => (((ord_less_eq @ C) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less_eq @ C) @ (F2 @ A2)) @ C3)))))))))).
% 3.01/1.64 thf(fact_79_order__subst1, axiom, (! [A:$tType,B4:$tType]: (((((order @ B4) @ (type2 @ B4)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F2:(B4 > A),B:B4,C3:B4]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B)) => ((((ord_less_eq @ B4) @ B) @ C3) => ((! [X2:B4,Y4:B4]: (((((ord_less_eq @ B4) @ X2) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C3))))))))))).
% 3.01/1.64 thf(fact_80_le__fun__def, axiom, (! [B4:$tType,A:$tType]: ((((ord @ B4) @ (type2 @ B4)) => ((ord_less_eq @ (A > B4)) = (^ [F3:(A > B4),G:(A > B4)]: ((! [X4:A]: ((((ord_less_eq @ B4) @ (F3 @ X4)) @ (G @ X4))))))))))).
% 3.01/1.64 thf(fact_81_le__funI, axiom, (! [B4:$tType,A:$tType]: ((((ord @ B4) @ (type2 @ B4)) => (! [F2:(A > B4),G2:(A > B4)]: (((! [X2:A]: ((((ord_less_eq @ B4) @ (F2 @ X2)) @ (G2 @ X2)))) => (((ord_less_eq @ (A > B4)) @ F2) @ G2)))))))).
% 3.01/1.64 thf(fact_82_le__funE, axiom, (! [B4:$tType,A:$tType]: ((((ord @ B4) @ (type2 @ B4)) => (! [F2:(A > B4),G2:(A > B4),X3:A]: (((((ord_less_eq @ (A > B4)) @ F2) @ G2) => (((ord_less_eq @ B4) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 3.01/1.64 thf(fact_83_le__funD, axiom, (! [B4:$tType,A:$tType]: ((((ord @ B4) @ (type2 @ B4)) => (! [F2:(A > B4),G2:(A > B4),X3:A]: (((((ord_less_eq @ (A > B4)) @ F2) @ G2) => (((ord_less_eq @ B4) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 3.01/1.64 thf(fact_84_ltake__lappend1, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((ord_less_eq @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs)) => ((((coindu1802687541_ltake @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1802687541_ltake @ A) @ N) @ Xs)))))).
% 3.01/1.64 thf(fact_85_ord__eq__less__subst, axiom, (! [A:$tType,B4:$tType]: (((((ord @ B4) @ (type2 @ B4)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F2:(B4 > A),B:B4,C3:B4]: (((A2 = (F2 @ B)) => ((((ord_less @ B4) @ B) @ C3) => ((! [X2:B4,Y4:B4]: (((((ord_less @ B4) @ X2) @ Y4) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 3.01/1.64 thf(fact_86_ord__less__eq__subst, axiom, (! [A:$tType,B4:$tType]: (((((ord @ B4) @ (type2 @ B4)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B:A,F2:(A > B4),C3:B4]: (((((ord_less @ A) @ A2) @ B) => (((F2 @ B) = C3) => ((! [X2:A,Y4:A]: (((((ord_less @ A) @ X2) @ Y4) => (((ord_less @ B4) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ B4) @ (F2 @ A2)) @ C3)))))))))).
% 3.01/1.64 thf(fact_87_order__less__subst1, axiom, (! [A:$tType,B4:$tType]: (((((order @ B4) @ (type2 @ B4)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F2:(B4 > A),B:B4,C3:B4]: (((((ord_less @ A) @ A2) @ (F2 @ B)) => ((((ord_less @ B4) @ B) @ C3) => ((! [X2:B4,Y4:B4]: (((((ord_less @ B4) @ X2) @ Y4) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 3.01/1.64 thf(fact_88_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B:A,F2:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ C) @ (F2 @ B)) @ C3) => ((! [X2:A,Y4:A]: (((((ord_less @ A) @ X2) @ Y4) => (((ord_less @ C) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ C) @ (F2 @ A2)) @ C3)))))))))).
% 3.01/1.64 thf(fact_89_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X3:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X3))))))))).
% 3.01/1.64 thf(fact_90_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X3:A]: ((? [X1:A]: ((((ord_less @ A) @ X3) @ X1))))))))).
% 3.01/1.64 thf(fact_91_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((X3 != Y) => ((~ ((((ord_less @ A) @ X3) @ Y))) => (((ord_less @ A) @ Y) @ X3))))))))).
% 3.01/1.64 thf(fact_92_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((X3 != Y) = ((((ord_less @ A) @ X3) @ Y) | (((ord_less @ A) @ Y) @ X3))))))))).
% 3.01/1.64 thf(fact_93_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (~ ((((ord_less @ A) @ B) @ A2)))))))))).
% 3.01/1.64 thf(fact_94_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X3) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 3.01/1.64 thf(fact_95_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (X3 != Y)))))))).
% 3.01/1.64 thf(fact_96_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 3.01/1.64 thf(fact_97_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (~ ((((ord_less @ A) @ B) @ A2)))))))))).
% 3.01/1.64 thf(fact_98_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 3.01/1.64 thf(fact_99_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) | ((X3 = Y) | (((ord_less @ A) @ Y) @ X3))))))))).
% 3.01/1.64 thf(fact_100_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 3.01/1.64 thf(fact_101_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((A2 = B) => ((((ord_less @ A) @ B) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_102_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => ((B = C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_103_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less @ A) @ B) @ A2) => (~ ((((ord_less @ A) @ A2) @ B)))))))))).
% 3.01/1.64 thf(fact_104_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (X3 != Y)))))))).
% 3.01/1.64 thf(fact_105_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 3.01/1.64 thf(fact_106_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A2:A]: (((! [X2:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X2) => (P @ Y5)))) => (P @ X2)))) => (P @ A2)))))))).
% 3.01/1.64 thf(fact_107_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X3:A]: (((~ ((((ord_less @ A) @ Y) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y))) = (X3 = Y))))))))).
% 3.01/1.64 thf(fact_108_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (Y != X3)))))))).
% 3.01/1.64 thf(fact_109_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,P:$o]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ X3) => P)))))))).
% 3.01/1.64 thf(fact_110_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((X3 != Y) => (((ord_less @ A) @ Y) @ X3))))))))).
% 3.01/1.64 thf(fact_111_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 3.01/1.64 thf(fact_112_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ B) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_113_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 3.01/1.64 thf(fact_114_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less @ A) @ C3) @ B) => (((ord_less @ A) @ C3) @ A2))))))))).
% 3.01/1.64 thf(fact_115_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) = ((((ord_less @ A) @ Y) @ X3) | (X3 = Y))))))))).
% 3.01/1.64 thf(fact_116_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (A2 != B)))))))).
% 3.01/1.64 thf(fact_117_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less @ A) @ B) @ A2) => (A2 != B)))))))).
% 3.01/1.64 thf(fact_118_ex__gt__or__lt, axiom, (! [A:$tType]: ((((condit1656338222tinuum @ A) @ (type2 @ A)) => (! [A2:A]: ((? [B2:A]: (((((ord_less @ A) @ A2) @ B2) | (((ord_less @ A) @ B2) @ A2)))))))))).
% 3.01/1.64 thf(fact_119_leD, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X3:A]: (((((ord_less_eq @ A) @ Y) @ X3) => (~ ((((ord_less @ A) @ X3) @ Y)))))))))).
% 3.01/1.64 thf(fact_120_leI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) => (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 3.01/1.64 thf(fact_121_le__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X4:A,Y3:A]: (((((ord_less @ A) @ X4) @ Y3) | (X4 = Y3))))))))).
% 3.01/1.64 thf(fact_122_less__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) & (X4 != Y3))))))))).
% 3.01/1.64 thf(fact_123_order__le__less__subst1, axiom, (! [A:$tType,B4:$tType]: (((((order @ B4) @ (type2 @ B4)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F2:(B4 > A),B:B4,C3:B4]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B)) => ((((ord_less @ B4) @ B) @ C3) => ((! [X2:B4,Y4:B4]: (((((ord_less @ B4) @ X2) @ Y4) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 3.01/1.64 thf(fact_124_order__le__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B:A,F2:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less @ C) @ (F2 @ B)) @ C3) => ((! [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) => (((ord_less_eq @ C) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ C) @ (F2 @ A2)) @ C3)))))))))).
% 3.01/1.64 thf(fact_125_order__less__le__subst1, axiom, (! [A:$tType,B4:$tType]: (((((order @ B4) @ (type2 @ B4)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F2:(B4 > A),B:B4,C3:B4]: (((((ord_less @ A) @ A2) @ (F2 @ B)) => ((((ord_less_eq @ B4) @ B) @ C3) => ((! [X2:B4,Y4:B4]: (((((ord_less_eq @ B4) @ X2) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 3.01/1.64 thf(fact_126_order__less__le__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B:A,F2:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less_eq @ C) @ (F2 @ B)) @ C3) => ((! [X2:A,Y4:A]: (((((ord_less @ A) @ X2) @ Y4) => (((ord_less @ C) @ (F2 @ X2)) @ (F2 @ Y4))))) => (((ord_less @ C) @ (F2 @ A2)) @ C3)))))))))).
% 3.01/1.64 thf(fact_127_not__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y))) = (((ord_less @ A) @ Y) @ X3)))))))).
% 3.01/1.64 thf(fact_128_not__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) = (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 3.01/1.64 thf(fact_129_le__neq__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((A2 != B) => (((ord_less @ A) @ A2) @ B))))))))).
% 3.01/1.64 thf(fact_130_less__imp__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (((ord_less_eq @ A) @ X3) @ Y)))))))).
% 3.01/1.64 thf(fact_131_antisym__conv1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((((ord_less_eq @ A) @ X3) @ Y) = (X3 = Y))))))))).
% 3.01/1.64 thf(fact_132_antisym__conv2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((~ ((((ord_less @ A) @ X3) @ Y))) = (X3 = Y))))))))).
% 3.01/1.64 thf(fact_133_le__less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z3:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 3.01/1.64 thf(fact_134_less__le__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 3.01/1.64 thf(fact_135_dense__ge, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z3:A,Y:A]: (((! [X2:A]: (((((ord_less @ A) @ Z3) @ X2) => (((ord_less_eq @ A) @ Y) @ X2)))) => (((ord_less_eq @ A) @ Y) @ Z3)))))))).
% 3.01/1.64 thf(fact_136_dense__le, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Y:A,Z3:A]: (((! [X2:A]: (((((ord_less @ A) @ X2) @ Y) => (((ord_less_eq @ A) @ X2) @ Z3)))) => (((ord_less_eq @ A) @ Y) @ Z3)))))))).
% 3.01/1.64 thf(fact_137_le__less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) | (((ord_less @ A) @ Y) @ X3)))))))).
% 3.01/1.64 thf(fact_138_le__imp__less__or__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less @ A) @ X3) @ Y) | (X3 = Y))))))))).
% 3.01/1.64 thf(fact_139_less__le__not__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) & (~ ((((ord_less_eq @ A) @ Y3) @ X4))))))))))).
% 3.01/1.64 thf(fact_140_not__le__imp__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X3:A]: (((~ ((((ord_less_eq @ A) @ Y) @ X3))) => (((ord_less @ A) @ X3) @ Y)))))))).
% 3.01/1.64 thf(fact_141_order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less @ A) @ B) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_142_order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 3.01/1.64 thf(fact_143_order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) | (A4 = B3))))))))).
% 3.01/1.64 thf(fact_144_order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) & (A4 != B3))))))))).
% 3.01/1.64 thf(fact_145_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less @ A) @ C3) @ B) => (((ord_less @ A) @ C3) @ A2))))))))).
% 3.01/1.64 thf(fact_146_ldrop__lappend, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((ord_less @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs)) => ((((coindu191418589_ldrop @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ (((coindu191418589_ldrop @ A) @ N) @ Xs)) @ Ys))) & ((~ ((((ord_less @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs)))) => ((((coindu191418589_ldrop @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu191418589_ldrop @ A) @ (((minus_minus @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs))) @ Ys))))))).
% 3.01/1.64 thf(fact_147_ltake__lappend2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),N:extended_enat,Ys:(coindu1593790203_llist @ A)]: (((((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ N) => ((((coindu1802687541_ltake @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ Xs) @ (((coindu1802687541_ltake @ A) @ (((minus_minus @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs))) @ Ys))))))).
% 3.01/1.64 thf(fact_148_ldrop__eq__LNil, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((((coindu191418589_ldrop @ A) @ N) @ Xs) = (coindu1598213697e_LNil @ A)) = (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ N))))).
% 3.01/1.64 thf(fact_149_lnull__ldrop, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu191418589_ldrop @ A) @ N) @ Xs)) = (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ N))))).
% 3.01/1.64 thf(fact_150_ltake__plus__conv__lappend, axiom, (! [A:$tType,N:extended_enat,M2:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ (((plus_plus @ extended_enat) @ N) @ M2)) @ Xs) = (((coindu268472904append @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ (((coindu1802687541_ltake @ A) @ M2) @ (((coindu191418589_ldrop @ A) @ N) @ Xs))))))).
% 3.01/1.64 thf(fact_151_ltake__lappend, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ (((coindu1802687541_ltake @ A) @ (((minus_minus @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs))) @ Ys)))))).
% 3.01/1.64 thf(fact_152_ldrop__all, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),M2:extended_enat]: (((((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ M2) => ((((coindu191418589_ldrop @ A) @ M2) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 3.01/1.64 thf(fact_153_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 3.01/1.64 thf(fact_154_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.01/1.64 thf(fact_155_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 3.01/1.64 thf(fact_156_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 3.01/1.64 thf(fact_157_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 3.01/1.64 thf(fact_158_ltake__LNil, axiom, (! [A:$tType,N:extended_enat]: (((((coindu1802687541_ltake @ A) @ N) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.01/1.64 thf(fact_159_ldrop__LNil, axiom, (! [A:$tType,N:extended_enat]: (((((coindu191418589_ldrop @ A) @ N) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.01/1.64 thf(fact_160_ldrop__ldrop, axiom, (! [A:$tType,N:extended_enat,M2:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu191418589_ldrop @ A) @ N) @ (((coindu191418589_ldrop @ A) @ M2) @ Xs)) = (((coindu191418589_ldrop @ A) @ (((plus_plus @ extended_enat) @ N) @ M2)) @ Xs))))).
% 3.01/1.64 thf(fact_161_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu574146665prefix @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A))))))).
% 3.01/1.64 thf(fact_162_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 3.01/1.64 thf(fact_163_llength__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1018505716length @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((plus_plus @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ ((coindu1018505716length @ A) @ Ys)))))).
% 3.01/1.64 thf(fact_164_less__fun__def, axiom, (! [B4:$tType,A:$tType]: ((((ord @ B4) @ (type2 @ B4)) => ((ord_less @ (A > B4)) = (^ [F3:(A > B4),G:(A > B4)]: (((((ord_less_eq @ (A > B4)) @ F3) @ G) & (~ ((((ord_less_eq @ (A > B4)) @ G) @ F3))))))))))).
% 3.01/1.64 thf(fact_165_ldrop__lnull, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),N:extended_enat]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu191418589_ldrop @ A) @ N) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 3.01/1.64 thf(fact_166_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 3.01/1.64 thf(fact_167_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 3.01/1.64 thf(fact_168_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 3.01/1.64 thf(fact_169_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 3.01/1.64 thf(fact_170_lzip_Oexhaust, axiom, (! [A:$tType,B4:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B4)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B4) @ Ys)))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((coindu335574135_lnull @ B4) @ Ys)))))))).
% 3.01/1.64 thf(fact_171_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.01/1.64 thf(fact_172_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist2:(coindu1593790203_llist @ A)]: ((Llist2 = (coindu1598213697e_LNil @ A)))))))).
% 3.01/1.64 thf(fact_173_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 3.01/1.64 thf(fact_174_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.01/1.64 thf(fact_175_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.01/1.64 thf(fact_176_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.01/1.64 thf(fact_177_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 3.01/1.64 thf(fact_178_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 3.01/1.64 thf(fact_179_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 3.01/1.64 thf(fact_180_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 3.01/1.64 thf(fact_181_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 3.01/1.64 thf(fact_182_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.01/1.64 thf(fact_183_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 3.01/1.64 thf(fact_184_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 3.01/1.64 thf(fact_185_ldrop__ltake, axiom, (! [A:$tType,N:extended_enat,M2:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu191418589_ldrop @ A) @ N) @ (((coindu1802687541_ltake @ A) @ M2) @ Xs)) = (((coindu1802687541_ltake @ A) @ (((minus_minus @ extended_enat) @ M2) @ N)) @ (((coindu191418589_ldrop @ A) @ N) @ Xs)))))).
% 3.01/1.64 thf(fact_186_ltake__ldrop, axiom, (! [A:$tType,N:extended_enat,M2:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ N) @ (((coindu191418589_ldrop @ A) @ M2) @ Xs)) = (((coindu191418589_ldrop @ A) @ M2) @ (((coindu1802687541_ltake @ A) @ (((plus_plus @ extended_enat) @ N) @ M2)) @ Xs)))))).
% 3.01/1.64 thf(fact_187_le__add__diff__inverse, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((plus_plus @ A) @ B) @ (((minus_minus @ A) @ A2) @ B)) = A2)))))))).
% 3.01/1.64 thf(fact_188_le__add__diff__inverse2, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ B) = A2)))))))).
% 3.01/1.64 thf(fact_189_add__diff__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ B) = A2))))))).
% 3.01/1.64 thf(fact_190_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B = C3)))))))).
% 3.01/1.64 thf(fact_191_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C3)) = (B = C3)))))))).
% 3.01/1.64 thf(fact_192_add__le__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_193_add__le__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_194_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3)) = (((ord_less @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_195_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B)) = (((ord_less @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_196_add__diff__cancel__right_H, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ B) = A2))))))).
% 3.01/1.64 thf(fact_197_add__diff__cancel__right, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3)) = (((minus_minus @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_198_add__diff__cancel__left_H, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ A2) = B))))))).
% 3.01/1.64 thf(fact_199_add__diff__cancel__left, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B)) = (((minus_minus @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_200_diff__add__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ B) = A2))))))).
% 3.01/1.64 thf(fact_201_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((X3 != Y) => ((~ ((((ord_less @ A) @ X3) @ Y))) => (((ord_less @ A) @ Y) @ X3))))))))).
% 3.01/1.64 thf(fact_202_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C3) @ A2)) => (B = C3)))))))).
% 3.01/1.64 thf(fact_203_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C3)) => (B = C3)))))))).
% 3.01/1.64 thf(fact_204_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C3)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_205_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,B3:A]: ((((plus_plus @ A) @ B3) @ A4)))))))).
% 3.01/1.64 thf(fact_206_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B = C3)))))))).
% 3.01/1.64 thf(fact_207_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C3)) = (B = C3)))))))).
% 3.01/1.64 thf(fact_208_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_209_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_210_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_211_diff__right__commute, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C3)) @ B) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C3)))))))).
% 3.01/1.64 thf(fact_212_diff__eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: ((((((minus_minus @ A) @ A2) @ B) = (((minus_minus @ A) @ C3) @ D3)) => ((A2 = B) = (C3 = D3))))))))).
% 3.01/1.64 thf(fact_213_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_214_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_215_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_216_add__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C3) @ D3) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ D3)))))))))).
% 3.01/1.64 thf(fact_217_add__left__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B))))))))).
% 3.01/1.64 thf(fact_218_add__right__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_219_le__iff__add, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A4:A,B3:A]: ((? [C4:A]: ((B3 = (((plus_plus @ A) @ A4) @ C4))))))))))).
% 3.01/1.64 thf(fact_220_add__le__imp__le__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B)) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_221_add__le__imp__le__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3)) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_222_diff__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,D3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ D3) @ C3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C3)) @ (((minus_minus @ A) @ B) @ D3)))))))))).
% 3.01/1.64 thf(fact_223_diff__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B) @ A2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C3) @ A2)) @ (((minus_minus @ A) @ C3) @ B))))))))).
% 3.01/1.64 thf(fact_224_diff__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C3)) @ (((minus_minus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_225_diff__eq__diff__less__eq, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: ((((((minus_minus @ A) @ A2) @ B) = (((minus_minus @ A) @ C3) @ D3)) => ((((ord_less_eq @ A) @ A2) @ B) = (((ord_less_eq @ A) @ C3) @ D3))))))))).
% 3.01/1.64 thf(fact_226_add__less__imp__less__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3)) => (((ord_less @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_227_add__less__imp__less__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B)) => (((ord_less @ A) @ A2) @ B)))))))).
% 3.01/1.64 thf(fact_228_add__strict__right__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_229_add__strict__left__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B))))))))).
% 3.01/1.64 thf(fact_230_add__strict__mono, axiom, (! [A:$tType]: ((((strict2144017051up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ C3) @ D3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ D3)))))))))).
% 3.01/1.64 thf(fact_231_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_232_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_233_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_234_diff__strict__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((minus_minus @ A) @ A2) @ C3)) @ (((minus_minus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_235_diff__strict__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C3:A]: (((((ord_less @ A) @ B) @ A2) => (((ord_less @ A) @ (((minus_minus @ A) @ C3) @ A2)) @ (((minus_minus @ A) @ C3) @ B))))))))).
% 3.01/1.64 thf(fact_236_diff__eq__diff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: ((((((minus_minus @ A) @ A2) @ B) = (((minus_minus @ A) @ C3) @ D3)) => ((((ord_less @ A) @ A2) @ B) = (((ord_less @ A) @ C3) @ D3))))))))).
% 3.01/1.64 thf(fact_237_diff__strict__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,D3:A,C3:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ D3) @ C3) => (((ord_less @ A) @ (((minus_minus @ A) @ A2) @ C3)) @ (((minus_minus @ A) @ B) @ D3)))))))))).
% 3.01/1.64 thf(fact_238_add__implies__diff, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [C3:A,B:A,A2:A]: ((((((plus_plus @ A) @ C3) @ B) = A2) => (C3 = (((minus_minus @ A) @ A2) @ B))))))))).
% 3.01/1.64 thf(fact_239_diff__diff__add, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C3) = (((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C3))))))))).
% 3.01/1.64 thf(fact_240_diff__add__eq__diff__diff__swap, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C3)) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C3)) @ B)))))))).
% 3.01/1.64 thf(fact_241_diff__add__eq, axiom, (! [A:$tType]: ((((ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C3) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ B)))))))).
% 3.01/1.64 thf(fact_242_diff__diff__eq2, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((minus_minus @ A) @ A2) @ (((minus_minus @ A) @ B) @ C3)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ B)))))))).
% 3.01/1.64 thf(fact_243_add__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((plus_plus @ A) @ A2) @ (((minus_minus @ A) @ B) @ C3)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C3)))))))).
% 3.01/1.64 thf(fact_244_eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B:A]: (((A2 = (((minus_minus @ A) @ C3) @ B)) = ((((plus_plus @ A) @ A2) @ B) = C3)))))))).
% 3.01/1.64 thf(fact_245_diff__eq__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: ((((((minus_minus @ A) @ A2) @ B) = C3) = (A2 = (((plus_plus @ A) @ C3) @ B))))))))).
% 3.01/1.64 thf(fact_246_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_247_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 3.01/1.64 thf(fact_248_add__le__less__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less @ A) @ C3) @ D3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ D3)))))))))).
% 3.01/1.64 thf(fact_249_add__less__le__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A,D3:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C3) @ D3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B) @ D3)))))))))).
% 3.01/1.64 thf(fact_250_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, axiom, (! [A:$tType]: ((((ordere623563068d_diff @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ A2) @ B) => (((((minus_minus @ A) @ B) @ A2) = C3) = (B = (((plus_plus @ A) @ C3) @ A2))))))))))).
% 3.01/1.64 thf(fact_251_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, axiom, (! [A:$tType]: ((((ordere623563068d_diff @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((plus_plus @ A) @ A2) @ (((minus_minus @ A) @ B) @ A2)) = B)))))))).
% 3.01/1.64 thf(fact_252_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, axiom, (! [A:$tType]: ((((ordere623563068d_diff @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((minus_minus @ A) @ C3) @ (((minus_minus @ A) @ B) @ A2)) = (((minus_minus @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ B))))))))).
% 3.01/1.64 thf(fact_253_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, axiom, (! [A:$tType]: ((((ordere623563068d_diff @ A) @ (type2 @ A)) => (! [A2:A,B:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((minus_minus @ A) @ (((plus_plus @ A) @ B) @ C3)) @ A2) = (((plus_plus @ A) @ (((minus_minus @ A) @ B) @ A2)) @ C3))))))))).
% 3.01/1.64 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A5:$tType,A6:$tType]: ((((preorder @ A6) @ (type2 @ A6)) => ((preorder @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 3.01/1.64 thf(tcon_fun___Orderings_Oorder, axiom, (! [A5:$tType,A6:$tType]: ((((order @ A6) @ (type2 @ A6)) => ((order @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 3.01/1.64 thf(tcon_fun___Orderings_Oord, axiom, (! [A5:$tType,A6:$tType]: ((((ord @ A6) @ (type2 @ A6)) => ((ord @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 3.01/1.64 thf(tcon_HOL_Obool___Orderings_Opreorder_1, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 3.01/1.64 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 3.01/1.64 thf(tcon_HOL_Obool___Orderings_Oorder_2, axiom, ((order @ $o) @ (type2 @ $o))).
% 3.01/1.64 thf(tcon_HOL_Obool___Orderings_Oord_3, axiom, ((ord @ $o) @ (type2 @ $o))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, ((condit1037483654norder @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, ((strict2144017051up_add @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add, axiom, ((semigroup_add @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Orderings_Owellorder, axiom, ((wellorder @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_4, axiom, ((preorder @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_5, axiom, ((linorder @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_6, axiom, ((order @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_7, axiom, ((ord @ extended_enat) @ (type2 @ extended_enat))).
% 3.01/1.64 thf(conj_0, conjecture, (((ord_less @ extended_enat) @ ((coindu1018505716length @ a) @ xs)) @ ((coindu1018505716length @ a) @ ys))).
% 3.01/1.64 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2HsJS0n40S/DTF2DTF24777.p
% 3.01/1.64 ------------------------
% 3.01/1.68 ---- Cleaned THF ---
% 3.01/1.68 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 3.01/1.68 coindu1593790203_llist: $tType > $tType ).
% 3.01/1.68
% 3.01/1.68 thf(ty_t_Extended__Nat_Oenat,type,
% 3.01/1.68 extended_enat: $tType ).
% 3.01/1.68
% 3.01/1.68 thf(ty_t_itself,type,
% 3.01/1.68 itself: $tType > $tType ).
% 3.01/1.68
% 3.01/1.68 thf(ty_tf_a,type,
% 3.01/1.68 a: $tType ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_HOL_Otype,type,
% 3.01/1.68 type:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Oord,type,
% 3.01/1.68 ord:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Oorder,type,
% 3.01/1.68 order:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Ogroup__add,type,
% 3.01/1.68 group_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Ono__bot,type,
% 3.01/1.68 no_bot:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Ono__top,type,
% 3.01/1.68 no_top:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Olinorder,type,
% 3.01/1.68 linorder:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Opreorder,type,
% 3.01/1.68 preorder:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oab__group__add,type,
% 3.01/1.68 ab_group_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Owellorder,type,
% 3.01/1.68 wellorder:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Osemigroup__add,type,
% 3.01/1.68 semigroup_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Odense__order,type,
% 3.01/1.68 dense_order:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Rings_Olinordered__idom,type,
% 3.01/1.68 linordered_idom:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 3.01/1.68 ab_semigroup_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Orderings_Odense__linorder,type,
% 3.01/1.68 dense_linorder:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Rings_Olinordered__semidom,type,
% 3.01/1.68 linordered_semidom:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 3.01/1.68 cancel_semigroup_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 3.01/1.68 ordered_ab_group_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 3.01/1.68 cancel1352612707id_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 3.01/1.68 cancel146912293up_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 3.01/1.68 ordere779506340up_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 3.01/1.68 canoni770627133id_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 3.01/1.68 ordere236663937imp_le:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 3.01/1.68 ordere223160158up_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff,type,
% 3.01/1.68 ordere623563068d_diff:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 3.01/1.68 strict2144017051up_add:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 3.01/1.68 condit1656338222tinuum:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 3.01/1.68 condit1037483654norder:
% 3.01/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 3.01/1.68 coindu268472904append:
% 3.01/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oldrop,type,
% 3.01/1.68 coindu191418589_ldrop:
% 3.01/1.68 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength,type,
% 3.01/1.68 coindu1018505716length:
% 3.01/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 3.01/1.68 coindu1598213697e_LNil:
% 3.01/1.68 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 3.01/1.68 coindu335574135_lnull:
% 3.01/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 3.01/1.68 coindu1696667936prefix:
% 3.01/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 3.01/1.68 coindu574146665prefix:
% 3.01/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake,type,
% 3.01/1.68 coindu1802687541_ltake:
% 3.01/1.68 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 3.01/1.68 minus_minus:
% 3.01/1.68 !>[A: $tType] : ( A > A > A ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 3.01/1.68 plus_plus:
% 3.01/1.68 !>[A: $tType] : ( A > A > A ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.01/1.68 ord_less:
% 3.01/1.68 !>[A: $tType] : ( A > A > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.01/1.68 ord_less_eq:
% 3.01/1.68 !>[A: $tType] : ( A > A > $o ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_c_Pure_Otype,type,
% 3.01/1.68 type2:
% 3.01/1.68 !>[A: $tType] : ( itself @ A ) ).
% 3.01/1.68
% 3.01/1.68 thf(sy_v_xs,type,
% 3.01/1.68 xs: coindu1593790203_llist @ a ).
% 3.01/1.68
% 3.01/1.68 thf(sy_v_xs_H____,type,
% 3.01/1.68 xs2: coindu1593790203_llist @ a ).
% 3.01/1.68
% 3.01/1.68 thf(sy_v_ys,type,
% 3.01/1.68 ys: coindu1593790203_llist @ a ).
% 3.01/1.68
% 3.01/1.68 thf(sy_v_zs,type,
% 3.01/1.68 zs: coindu1593790203_llist @ a ).
% 3.01/1.68
% 3.01/1.68 thf(fact_0__092_060open_062_092_060not_062_Allength_Ays_A_092_060le_062_Allength_Axs_092_060close_062,axiom,
% 3.01/1.68 ~ ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ ys ) @ ( coindu1018505716length @ a @ xs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_1__092_060open_062_092_060not_062_A_Ixs_A_092_060sqsubseteq_062_Ays_A_092_060or_062_Ays_A_092_060sqsubseteq_062_Axs_J_092_060close_062,axiom,
% 3.01/1.68 ~ ( ( coindu1696667936prefix @ a @ xs @ ys )
% 3.01/1.68 | ( coindu1696667936prefix @ a @ ys @ xs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_2__092_060open_062_092_060not_062_Axs_A_092_060sqsubseteq_062_Ays_092_060close_062,axiom,
% 3.01/1.68 ~ ( coindu1696667936prefix @ a @ xs @ ys ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_3__092_060open_062_092_060not_062_Ays_A_092_060sqsubseteq_062_Axs_092_060close_062,axiom,
% 3.01/1.68 ~ ( coindu1696667936prefix @ a @ ys @ xs ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_4__092_060open_062lappend_Axs_Axs_H_A_061_Alappend_Ays_Azs_092_060close_062,axiom,
% 3.01/1.68 ( ( coindu268472904append @ a @ xs @ xs2 )
% 3.01/1.68 = ( coindu268472904append @ a @ ys @ zs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_5_lstrict__prefix__llength__less,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 3.01/1.68 => ( ord_less @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_O_Alappend_Axs_Axs_H_A_061_Alappend_Ays_Azs_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.01/1.68 ~ ! [Xs2: coindu1593790203_llist @ a] :
% 3.01/1.68 ( ( coindu268472904append @ a @ xs @ Xs2 )
% 3.01/1.68 != ( coindu268472904append @ a @ ys @ zs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_7_enat__less__induct,axiom,
% 3.01/1.68 ! [P: extended_enat > $o,N: extended_enat] :
% 3.01/1.68 ( ! [N2: extended_enat] :
% 3.01/1.68 ( ! [M: extended_enat] :
% 3.01/1.68 ( ( ord_less @ extended_enat @ M @ N2 )
% 3.01/1.68 => ( P @ M ) )
% 3.01/1.68 => ( P @ N2 ) )
% 3.01/1.68 => ( P @ N ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_8_minf_I11_J,axiom,
% 3.01/1.68 ! [C: $tType,D: $tType] :
% 3.01/1.68 ( ( ord @ C @ ( type2 @ C ) )
% 3.01/1.68 => ! [F: D] :
% 3.01/1.68 ? [Z: C] :
% 3.01/1.68 ! [X: C] :
% 3.01/1.68 ( ( ord_less @ C @ X @ Z )
% 3.01/1.68 => ( F = F ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_9_minf_I7_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ~ ( ord_less @ A @ T @ X ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_10_minf_I5_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ( ord_less @ A @ X @ T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_11_minf_I4_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ( X != T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_12_minf_I3_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ( X != T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_13_minf_I2_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 3.01/1.68 ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Z2 )
% 3.01/1.68 => ( ( P @ X2 )
% 3.01/1.68 = ( P2 @ X2 ) ) )
% 3.01/1.68 => ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Z2 )
% 3.01/1.68 => ( ( Q @ X2 )
% 3.01/1.68 = ( Q2 @ X2 ) ) )
% 3.01/1.68 => ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ( ( ( P @ X )
% 3.01/1.68 | ( Q @ X ) )
% 3.01/1.68 = ( ( P2 @ X )
% 3.01/1.68 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_14_lprefix__refl,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_15_llist_Oleq__refl,axiom,
% 3.01/1.68 ! [A: $tType,X3: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X3 @ X3 ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_16_assms,axiom,
% 3.01/1.68 coindu1696667936prefix @ a @ xs @ ( coindu268472904append @ a @ ys @ zs ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_17_lappend__assoc,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 3.01/1.68 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_18_lprefix__trans,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.68 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 3.01/1.68 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_19_llist_Oleq__trans,axiom,
% 3.01/1.68 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z3: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 3.01/1.68 => ( ( coindu1696667936prefix @ A @ Y @ Z3 )
% 3.01/1.68 => ( coindu1696667936prefix @ A @ X3 @ Z3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_20_lprefix__antisym,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.68 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 3.01/1.68 => ( Xs = Ys ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_21_lprefix__lappend,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_22_lappend__lprefixE,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 3.01/1.68 => ~ ! [Zs2: coindu1593790203_llist @ A] :
% 3.01/1.68 ( Zs
% 3.01/1.68 != ( coindu268472904append @ A @ Xs @ Zs2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_23_llist_Oleq__antisym,axiom,
% 3.01/1.68 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 3.01/1.68 => ( ( coindu1696667936prefix @ A @ Y @ X3 )
% 3.01/1.68 => ( X3 = Y ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_24_lstrict__prefix__def,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( coindu574146665prefix @ A )
% 3.01/1.68 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs3 @ Ys2 )
% 3.01/1.68 & ( Xs3 != Ys2 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_25_lprefix__down__linear,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 3.01/1.68 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 3.01/1.68 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.68 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_26_lprefix__conv__lappend,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A )
% 3.01/1.68 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 3.01/1.68 ? [Zs3: coindu1593790203_llist @ A] :
% 3.01/1.68 ( Ys2
% 3.01/1.68 = ( coindu268472904append @ A @ Xs3 @ Zs3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_27_lprefix__lappend__sameI,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.68 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_28_llist__less__induct,axiom,
% 3.01/1.68 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ! [Xs4: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ! [Ys3: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu574146665prefix @ A @ Ys3 @ Xs4 )
% 3.01/1.68 => ( P @ Ys3 ) )
% 3.01/1.68 => ( P @ Xs4 ) )
% 3.01/1.68 => ( P @ Xs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_29_lprefix__llength__le,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.68 => ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_30_lprefix__llength__eq__imp__eq,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.68 => ( ( ( coindu1018505716length @ A @ Xs )
% 3.01/1.68 = ( coindu1018505716length @ A @ Ys ) )
% 3.01/1.68 => ( Xs = Ys ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_31_wlog__linorder__le,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > A > $o,B: A,A2: A] :
% 3.01/1.68 ( ! [A3: A,B2: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.01/1.68 => ( P @ A3 @ B2 ) )
% 3.01/1.68 => ( ( ( P @ B @ A2 )
% 3.01/1.68 => ( P @ A2 @ B ) )
% 3.01/1.68 => ( P @ A2 @ B ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_32_pinf_I6_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ X @ T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_33_pinf_I8_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ( ord_less_eq @ A @ T @ X ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_34_minf_I6_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ( ord_less_eq @ A @ X @ T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_35_minf_I8_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ T @ X ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_36_pinf_I1_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 3.01/1.68 ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z2 @ X2 )
% 3.01/1.68 => ( ( P @ X2 )
% 3.01/1.68 = ( P2 @ X2 ) ) )
% 3.01/1.68 => ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z2 @ X2 )
% 3.01/1.68 => ( ( Q @ X2 )
% 3.01/1.68 = ( Q2 @ X2 ) ) )
% 3.01/1.68 => ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ( ( ( P @ X )
% 3.01/1.68 & ( Q @ X ) )
% 3.01/1.68 = ( ( P2 @ X )
% 3.01/1.68 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_37_pinf_I2_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 3.01/1.68 ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z2 @ X2 )
% 3.01/1.68 => ( ( P @ X2 )
% 3.01/1.68 = ( P2 @ X2 ) ) )
% 3.01/1.68 => ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z2 @ X2 )
% 3.01/1.68 => ( ( Q @ X2 )
% 3.01/1.68 = ( Q2 @ X2 ) ) )
% 3.01/1.68 => ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ( ( ( P @ X )
% 3.01/1.68 | ( Q @ X ) )
% 3.01/1.68 = ( ( P2 @ X )
% 3.01/1.68 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_38_pinf_I3_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ( X != T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_39_pinf_I4_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ( X != T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_40_pinf_I5_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ~ ( ord_less @ A @ X @ T ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_41_pinf_I7_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [T: A] :
% 3.01/1.68 ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z @ X )
% 3.01/1.68 => ( ord_less @ A @ T @ X ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_42_pinf_I11_J,axiom,
% 3.01/1.68 ! [C: $tType,D: $tType] :
% 3.01/1.68 ( ( ord @ C @ ( type2 @ C ) )
% 3.01/1.68 => ! [F: D] :
% 3.01/1.68 ? [Z: C] :
% 3.01/1.68 ! [X: C] :
% 3.01/1.68 ( ( ord_less @ C @ Z @ X )
% 3.01/1.68 => ( F = F ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_43_minf_I1_J,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 3.01/1.68 ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Z2 )
% 3.01/1.68 => ( ( P @ X2 )
% 3.01/1.68 = ( P2 @ X2 ) ) )
% 3.01/1.68 => ( ? [Z2: A] :
% 3.01/1.68 ! [X2: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Z2 )
% 3.01/1.68 => ( ( Q @ X2 )
% 3.01/1.68 = ( Q2 @ X2 ) ) )
% 3.01/1.68 => ? [Z: A] :
% 3.01/1.68 ! [X: A] :
% 3.01/1.68 ( ( ord_less @ A @ X @ Z )
% 3.01/1.68 => ( ( ( P @ X )
% 3.01/1.68 & ( Q @ X ) )
% 3.01/1.68 = ( ( P2 @ X )
% 3.01/1.68 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_44_eq,axiom,
% 3.01/1.68 ( ( coindu268472904append @ a @ ( coindu1802687541_ltake @ a @ ( coindu1018505716length @ a @ ys ) @ xs ) @ ( coindu268472904append @ a @ ( coindu191418589_ldrop @ a @ ( coindu1018505716length @ a @ ys ) @ xs ) @ xs2 ) )
% 3.01/1.68 = ( coindu268472904append @ a @ ys @ zs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_45_order__refl,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_46_complete__interval,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,P: A > $o] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ( P @ A2 )
% 3.01/1.68 => ( ~ ( P @ B )
% 3.01/1.68 => ? [C2: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ C2 )
% 3.01/1.68 & ( ord_less_eq @ A @ C2 @ B )
% 3.01/1.68 & ! [X: A] :
% 3.01/1.68 ( ( ( ord_less_eq @ A @ A2 @ X )
% 3.01/1.68 & ( ord_less @ A @ X @ C2 ) )
% 3.01/1.68 => ( P @ X ) )
% 3.01/1.68 & ! [D2: A] :
% 3.01/1.68 ( ! [X2: A] :
% 3.01/1.68 ( ( ( ord_less_eq @ A @ A2 @ X2 )
% 3.01/1.68 & ( ord_less @ A @ X2 @ D2 ) )
% 3.01/1.68 => ( P @ X2 ) )
% 3.01/1.68 => ( ord_less_eq @ A @ D2 @ C2 ) ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_47_order_Onot__eq__order__implies__strict,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A] :
% 3.01/1.68 ( ( A2 != B )
% 3.01/1.68 => ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_48_dual__order_Ostrict__implies__order,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A] :
% 3.01/1.68 ( ( ord_less @ A @ B @ A2 )
% 3.01/1.68 => ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_49_dual__order_Ostrict__iff__order,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ( ( ord_less @ A )
% 3.01/1.68 = ( ^ [B3: A,A4: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ B3 @ A4 )
% 3.01/1.68 & ( A4 != B3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_50_dual__order_Oorder__iff__strict,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ( ( ord_less_eq @ A )
% 3.01/1.68 = ( ^ [B3: A,A4: A] :
% 3.01/1.68 ( ( ord_less @ A @ B3 @ A4 )
% 3.01/1.68 | ( A4 = B3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_51_order_Ostrict__implies__order,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_52_dense__le__bounded,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A,Z3: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( ! [W: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ W )
% 3.01/1.68 => ( ( ord_less @ A @ W @ Y )
% 3.01/1.68 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 3.01/1.68 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_53_dense__ge__bounded,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [Z3: A,X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z3 @ X3 )
% 3.01/1.68 => ( ! [W: A] :
% 3.01/1.68 ( ( ord_less @ A @ Z3 @ W )
% 3.01/1.68 => ( ( ord_less @ A @ W @ X3 )
% 3.01/1.68 => ( ord_less_eq @ A @ Y @ W ) ) )
% 3.01/1.68 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_54_dual__order_Ostrict__trans2,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A,C3: A] :
% 3.01/1.68 ( ( ord_less @ A @ B @ A2 )
% 3.01/1.68 => ( ( ord_less_eq @ A @ C3 @ B )
% 3.01/1.68 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_55_ltake__is__lprefix,axiom,
% 3.01/1.68 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ Xs ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_56_lprefix__ltake__same,axiom,
% 3.01/1.68 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,M2: extended_enat] :
% 3.01/1.68 ( ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ M2 @ Xs ) )
% 3.01/1.68 = ( ( ord_less_eq @ extended_enat @ N @ M2 )
% 3.01/1.68 | ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_57_lappend__ltake__ldrop,axiom,
% 3.01/1.68 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu191418589_ldrop @ A @ N @ Xs ) )
% 3.01/1.68 = Xs ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_58_ltake__eq__ltake__antimono,axiom,
% 3.01/1.68 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,M2: extended_enat] :
% 3.01/1.68 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.01/1.68 = ( coindu1802687541_ltake @ A @ N @ Ys ) )
% 3.01/1.68 => ( ( ord_less_eq @ extended_enat @ M2 @ N )
% 3.01/1.68 => ( ( coindu1802687541_ltake @ A @ M2 @ Xs )
% 3.01/1.68 = ( coindu1802687541_ltake @ A @ M2 @ Ys ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_59_ltake__all,axiom,
% 3.01/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,M2: extended_enat] :
% 3.01/1.68 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M2 )
% 3.01/1.68 => ( ( coindu1802687541_ltake @ A @ M2 @ Xs )
% 3.01/1.68 = Xs ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_60_dual__order_Oantisym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.68 => ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( A2 = B ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_61_dual__order_Otrans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A,C3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.68 => ( ( ord_less_eq @ A @ C3 @ B )
% 3.01/1.68 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_62_linorder__wlog,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > A > $o,A2: A,B: A] :
% 3.01/1.68 ( ! [A3: A,B2: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.01/1.68 => ( P @ A3 @ B2 ) )
% 3.01/1.68 => ( ! [A3: A,B2: A] :
% 3.01/1.68 ( ( P @ B2 @ A3 )
% 3.01/1.68 => ( P @ A3 @ B2 ) )
% 3.01/1.68 => ( P @ A2 @ B ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_63_dual__order_Orefl,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_64_order__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A,Z3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.68 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 3.01/1.68 => ( ord_less_eq @ A @ X3 @ Z3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_65_order__class_Oorder_Oantisym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.68 => ( A2 = B ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_66_ord__le__eq__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( ord @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,C3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ( B = C3 )
% 3.01/1.68 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_67_ord__eq__le__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( ord @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,C3: A] :
% 3.01/1.68 ( ( A2 = B )
% 3.01/1.68 => ( ( ord_less_eq @ A @ B @ C3 )
% 3.01/1.68 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_68_antisym__conv,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [Y: A,X3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ Y @ X3 )
% 3.01/1.68 => ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.68 = ( X3 = Y ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_69_le__cases3,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A,Z3: A] :
% 3.01/1.68 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ Y @ Z3 ) )
% 3.01/1.68 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ X3 @ Z3 ) )
% 3.01/1.68 => ( ( ( ord_less_eq @ A @ X3 @ Z3 )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ Z3 @ Y ) )
% 3.01/1.68 => ( ( ( ord_less_eq @ A @ Z3 @ Y )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 3.01/1.68 => ( ( ( ord_less_eq @ A @ Y @ Z3 )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ Z3 @ X3 ) )
% 3.01/1.68 => ~ ( ( ord_less_eq @ A @ Z3 @ X3 )
% 3.01/1.68 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_70_order_Otrans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,C3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less_eq @ A @ B @ C3 )
% 3.01/1.68 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_71_le__cases,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.68 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_72_eq__refl,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( X3 = Y )
% 3.01/1.68 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_73_linear,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.68 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_74_antisym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.68 => ( ( ord_less_eq @ A @ Y @ X3 )
% 3.01/1.68 => ( X3 = Y ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_75_eq__iff,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ( ( ^ [Y2: A,Z4: A] : ( Y2 = Z4 ) )
% 3.01/1.68 = ( ^ [X4: A,Y3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.01/1.68 & ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_76_ord__le__eq__subst,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( ord @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,B: A,F2: A > B4,C3: B4] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ( ( F2 @ B )
% 3.01/1.68 = C3 )
% 3.01/1.68 => ( ! [X2: A,Y4: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less_eq @ B4 @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less_eq @ B4 @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_77_ord__eq__le__subst,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( ord @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 3.01/1.68 ( ( A2
% 3.01/1.68 = ( F2 @ B ) )
% 3.01/1.68 => ( ( ord_less_eq @ B4 @ B @ C3 )
% 3.01/1.68 => ( ! [X2: B4,Y4: B4] :
% 3.01/1.68 ( ( ord_less_eq @ B4 @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_78_order__subst2,axiom,
% 3.01/1.68 ! [A: $tType,C: $tType] :
% 3.01/1.68 ( ( ( order @ C @ ( type2 @ C ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less_eq @ C @ ( F2 @ B ) @ C3 )
% 3.01/1.68 => ( ! [X2: A,Y4: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less_eq @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_79_order__subst1,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B ) )
% 3.01/1.68 => ( ( ord_less_eq @ B4 @ B @ C3 )
% 3.01/1.68 => ( ! [X2: B4,Y4: B4] :
% 3.01/1.68 ( ( ord_less_eq @ B4 @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_80_le__fun__def,axiom,
% 3.01/1.68 ! [B4: $tType,A: $tType] :
% 3.01/1.68 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 => ( ( ord_less_eq @ ( A > B4 ) )
% 3.01/1.68 = ( ^ [F3: A > B4,G: A > B4] :
% 3.01/1.68 ! [X4: A] : ( ord_less_eq @ B4 @ ( F3 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_81_le__funI,axiom,
% 3.01/1.68 ! [B4: $tType,A: $tType] :
% 3.01/1.68 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 => ! [F2: A > B4,G2: A > B4] :
% 3.01/1.68 ( ! [X2: A] : ( ord_less_eq @ B4 @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 3.01/1.68 => ( ord_less_eq @ ( A > B4 ) @ F2 @ G2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_82_le__funE,axiom,
% 3.01/1.68 ! [B4: $tType,A: $tType] :
% 3.01/1.68 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 => ! [F2: A > B4,G2: A > B4,X3: A] :
% 3.01/1.68 ( ( ord_less_eq @ ( A > B4 ) @ F2 @ G2 )
% 3.01/1.68 => ( ord_less_eq @ B4 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_83_le__funD,axiom,
% 3.01/1.68 ! [B4: $tType,A: $tType] :
% 3.01/1.68 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 => ! [F2: A > B4,G2: A > B4,X3: A] :
% 3.01/1.68 ( ( ord_less_eq @ ( A > B4 ) @ F2 @ G2 )
% 3.01/1.68 => ( ord_less_eq @ B4 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_84_ltake__lappend1,axiom,
% 3.01/1.68 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.68 ( ( ord_less_eq @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 3.01/1.68 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.68 = ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_85_ord__eq__less__subst,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( ord @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 3.01/1.68 ( ( A2
% 3.01/1.68 = ( F2 @ B ) )
% 3.01/1.68 => ( ( ord_less @ B4 @ B @ C3 )
% 3.01/1.68 => ( ! [X2: B4,Y4: B4] :
% 3.01/1.68 ( ( ord_less @ B4 @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_86_ord__less__eq__subst,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( ord @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,B: A,F2: A > B4,C3: B4] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ( ( F2 @ B )
% 3.01/1.68 = C3 )
% 3.01/1.68 => ( ! [X2: A,Y4: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less @ B4 @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ B4 @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_87_order__less__subst1,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ ( F2 @ B ) )
% 3.01/1.68 => ( ( ord_less @ B4 @ B @ C3 )
% 3.01/1.68 => ( ! [X2: B4,Y4: B4] :
% 3.01/1.68 ( ( ord_less @ B4 @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_88_order__less__subst2,axiom,
% 3.01/1.68 ! [A: $tType,C: $tType] :
% 3.01/1.68 ( ( ( order @ C @ ( type2 @ C ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less @ C @ ( F2 @ B ) @ C3 )
% 3.01/1.68 => ( ! [X2: A,Y4: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_89_lt__ex,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( no_bot @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A] :
% 3.01/1.68 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_90_gt__ex,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( no_top @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A] :
% 3.01/1.68 ? [X1: A] : ( ord_less @ A @ X3 @ X1 ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_91_neqE,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( X3 != Y )
% 3.01/1.68 => ( ~ ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_92_neq__iff,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( X3 != Y )
% 3.01/1.68 = ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 | ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_93_order_Oasym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_94_dense,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( dense_order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ? [Z: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Z )
% 3.01/1.68 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_95_less__imp__neq,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( X3 != Y ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_96_less__asym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_97_less__asym_H,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_98_less__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A,Z3: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( ( ord_less @ A @ Y @ Z3 )
% 3.01/1.68 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_99_less__linear,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 | ( X3 = Y )
% 3.01/1.68 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_100_less__irrefl,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A] :
% 3.01/1.68 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_101_ord__eq__less__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( ord @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,C3: A] :
% 3.01/1.68 ( ( A2 = B )
% 3.01/1.68 => ( ( ord_less @ A @ B @ C3 )
% 3.01/1.68 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_102_ord__less__eq__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( ord @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,C3: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ( B = C3 )
% 3.01/1.68 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_103_dual__order_Oasym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A] :
% 3.01/1.68 ( ( ord_less @ A @ B @ A2 )
% 3.01/1.68 => ~ ( ord_less @ A @ A2 @ B ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_104_less__imp__not__eq,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( X3 != Y ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_105_less__not__sym,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_106_less__induct,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( wellorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [P: A > $o,A2: A] :
% 3.01/1.68 ( ! [X2: A] :
% 3.01/1.68 ( ! [Y5: A] :
% 3.01/1.68 ( ( ord_less @ A @ Y5 @ X2 )
% 3.01/1.68 => ( P @ Y5 ) )
% 3.01/1.68 => ( P @ X2 ) )
% 3.01/1.68 => ( P @ A2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_107_antisym__conv3,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [Y: A,X3: A] :
% 3.01/1.68 ( ~ ( ord_less @ A @ Y @ X3 )
% 3.01/1.68 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 3.01/1.68 = ( X3 = Y ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_108_less__imp__not__eq2,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( Y != X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_109_less__imp__triv,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A,P: $o] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( ( ord_less @ A @ Y @ X3 )
% 3.01/1.68 => P ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_110_linorder__cases,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( ( X3 != Y )
% 3.01/1.68 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_111_dual__order_Oirrefl,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A] :
% 3.01/1.68 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_112_order_Ostrict__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A,C3: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less @ A @ B @ C3 )
% 3.01/1.68 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_113_less__imp__not__less,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_114_dual__order_Ostrict__trans,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A,C3: A] :
% 3.01/1.68 ( ( ord_less @ A @ B @ A2 )
% 3.01/1.68 => ( ( ord_less @ A @ C3 @ B )
% 3.01/1.68 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_115_not__less__iff__gr__or__eq,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 3.01/1.68 = ( ( ord_less @ A @ Y @ X3 )
% 3.01/1.68 | ( X3 = Y ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_116_order_Ostrict__implies__not__eq,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A,B: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( A2 != B ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_117_dual__order_Ostrict__implies__not__eq,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [B: A,A2: A] :
% 3.01/1.68 ( ( ord_less @ A @ B @ A2 )
% 3.01/1.68 => ( A2 != B ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_118_ex__gt__or__lt,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [A2: A] :
% 3.01/1.68 ? [B2: A] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B2 )
% 3.01/1.68 | ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_119_leD,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [Y: A,X3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ Y @ X3 )
% 3.01/1.68 => ~ ( ord_less @ A @ X3 @ Y ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_120_leI,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.68 => ! [X3: A,Y: A] :
% 3.01/1.68 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.01/1.68 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_121_le__less,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ( ( ord_less_eq @ A )
% 3.01/1.68 = ( ^ [X4: A,Y3: A] :
% 3.01/1.68 ( ( ord_less @ A @ X4 @ Y3 )
% 3.01/1.68 | ( X4 = Y3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_122_less__le,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.68 => ( ( ord_less @ A )
% 3.01/1.68 = ( ^ [X4: A,Y3: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.01/1.68 & ( X4 != Y3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_123_order__le__less__subst1,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B ) )
% 3.01/1.68 => ( ( ord_less @ B4 @ B @ C3 )
% 3.01/1.68 => ( ! [X2: B4,Y4: B4] :
% 3.01/1.68 ( ( ord_less @ B4 @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_124_order__le__less__subst2,axiom,
% 3.01/1.68 ! [A: $tType,C: $tType] :
% 3.01/1.68 ( ( ( order @ C @ ( type2 @ C ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 3.01/1.68 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less @ C @ ( F2 @ B ) @ C3 )
% 3.01/1.68 => ( ! [X2: A,Y4: A] :
% 3.01/1.68 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_125_order__less__le__subst1,axiom,
% 3.01/1.68 ! [A: $tType,B4: $tType] :
% 3.01/1.68 ( ( ( order @ B4 @ ( type2 @ B4 ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,F2: B4 > A,B: B4,C3: B4] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ ( F2 @ B ) )
% 3.01/1.68 => ( ( ord_less_eq @ B4 @ B @ C3 )
% 3.01/1.68 => ( ! [X2: B4,Y4: B4] :
% 3.01/1.68 ( ( ord_less_eq @ B4 @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_126_order__less__le__subst2,axiom,
% 3.01/1.68 ! [A: $tType,C: $tType] :
% 3.01/1.68 ( ( ( order @ C @ ( type2 @ C ) )
% 3.01/1.68 & ( order @ A @ ( type2 @ A ) ) )
% 3.01/1.68 => ! [A2: A,B: A,F2: A > C,C3: C] :
% 3.01/1.68 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.68 => ( ( ord_less_eq @ C @ ( F2 @ B ) @ C3 )
% 3.01/1.68 => ( ! [X2: A,Y4: A] :
% 3.01/1.68 ( ( ord_less @ A @ X2 @ Y4 )
% 3.01/1.68 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y4 ) ) )
% 3.01/1.68 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 3.01/1.68
% 3.01/1.68 thf(fact_127_not__le,axiom,
% 3.01/1.68 ! [A: $tType] :
% 3.01/1.68 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( ~ ( ord_less_eq @ A @ X3 @ Y ) )
% 3.01/1.69 = ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_128_not__less,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 3.01/1.69 = ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_129_le__neq__trans,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( A2 != B )
% 3.01/1.69 => ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_130_less__imp__le,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.69 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_131_antisym__conv1,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.01/1.69 => ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.69 = ( X3 = Y ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_132_antisym__conv2,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.69 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 3.01/1.69 = ( X3 = Y ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_133_le__less__trans,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A,Z3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.69 => ( ( ord_less @ A @ Y @ Z3 )
% 3.01/1.69 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_134_less__le__trans,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A,Z3: A] :
% 3.01/1.69 ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.69 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 3.01/1.69 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_135_dense__ge,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [Z3: A,Y: A] :
% 3.01/1.69 ( ! [X2: A] :
% 3.01/1.69 ( ( ord_less @ A @ Z3 @ X2 )
% 3.01/1.69 => ( ord_less_eq @ A @ Y @ X2 ) )
% 3.01/1.69 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_136_dense__le,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [Y: A,Z3: A] :
% 3.01/1.69 ( ! [X2: A] :
% 3.01/1.69 ( ( ord_less @ A @ X2 @ Y )
% 3.01/1.69 => ( ord_less_eq @ A @ X2 @ Z3 ) )
% 3.01/1.69 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_137_le__less__linear,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.69 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_138_le__imp__less__or__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.69 => ( ( ord_less @ A @ X3 @ Y )
% 3.01/1.69 | ( X3 = Y ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_139_less__le__not__le,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( preorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ( ( ord_less @ A )
% 3.01/1.69 = ( ^ [X4: A,Y3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.01/1.69 & ~ ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_140_not__le__imp__less,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linorder @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [Y: A,X3: A] :
% 3.01/1.69 ( ~ ( ord_less_eq @ A @ Y @ X3 )
% 3.01/1.69 => ( ord_less @ A @ X3 @ Y ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_141_order_Ostrict__trans1,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less @ A @ B @ C3 )
% 3.01/1.69 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_142_order_Ostrict__trans2,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less_eq @ A @ B @ C3 )
% 3.01/1.69 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_143_order_Oorder__iff__strict,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ( ( ord_less_eq @ A )
% 3.01/1.69 = ( ^ [A4: A,B3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A4 @ B3 )
% 3.01/1.69 | ( A4 = B3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_144_order_Ostrict__iff__order,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ( ( ord_less @ A )
% 3.01/1.69 = ( ^ [A4: A,B3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A4 @ B3 )
% 3.01/1.69 & ( A4 != B3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_145_dual__order_Ostrict__trans1,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( order @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.69 => ( ( ord_less @ A @ C3 @ B )
% 3.01/1.69 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_146_ldrop__lappend,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ( ord_less @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 3.01/1.69 => ( ( coindu191418589_ldrop @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( coindu268472904append @ A @ ( coindu191418589_ldrop @ A @ N @ Xs ) @ Ys ) ) )
% 3.01/1.69 & ( ~ ( ord_less @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 3.01/1.69 => ( ( coindu191418589_ldrop @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( coindu191418589_ldrop @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_147_ltake__lappend2,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: extended_enat,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N )
% 3.01/1.69 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( coindu268472904append @ A @ Xs @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_148_ldrop__eq__LNil,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ( coindu191418589_ldrop @ A @ N @ Xs )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_149_lnull__ldrop,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ ( coindu191418589_ldrop @ A @ N @ Xs ) )
% 3.01/1.69 = ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_150_ltake__plus__conv__lappend,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1802687541_ltake @ A @ ( plus_plus @ extended_enat @ N @ M2 ) @ Xs )
% 3.01/1.69 = ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ M2 @ ( coindu191418589_ldrop @ A @ N @ Xs ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_151_ltake__lappend,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_152_ldrop__all,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,M2: extended_enat] :
% 3.01/1.69 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M2 )
% 3.01/1.69 => ( ( coindu191418589_ldrop @ A @ M2 @ Xs )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_153_lprefix__code_I1_J,axiom,
% 3.01/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_154_lappend_Odisc__iff_I2_J,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 3.01/1.69 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_155_lnull__lappend,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_156_lappend__code_I1_J,axiom,
% 3.01/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 3.01/1.69 = Ys ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_157_lappend__LNil2,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = Xs ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_158_ltake__LNil,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat] :
% 3.01/1.69 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_159_ldrop__LNil,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat] :
% 3.01/1.69 ( ( coindu191418589_ldrop @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_160_ldrop__ldrop,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu191418589_ldrop @ A @ N @ ( coindu191418589_ldrop @ A @ M2 @ Xs ) )
% 3.01/1.69 = ( coindu191418589_ldrop @ A @ ( plus_plus @ extended_enat @ N @ M2 ) @ Xs ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_161_lstrict__prefix__code_I1_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_162_lprefix__LNil,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_163_llength__lappend,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1018505716length @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( plus_plus @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_164_less__fun__def,axiom,
% 3.01/1.69 ! [B4: $tType,A: $tType] :
% 3.01/1.69 ( ( ord @ B4 @ ( type2 @ B4 ) )
% 3.01/1.69 => ( ( ord_less @ ( A > B4 ) )
% 3.01/1.69 = ( ^ [F3: A > B4,G: A > B4] :
% 3.01/1.69 ( ( ord_less_eq @ ( A > B4 ) @ F3 @ G )
% 3.01/1.69 & ~ ( ord_less_eq @ ( A > B4 ) @ G @ F3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_165_ldrop__lnull,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: extended_enat] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ( ( coindu191418589_ldrop @ A @ N @ Xs )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_166_lappend_Octr_I1_J,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.01/1.69 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_167_llist_Odisc_I1_J,axiom,
% 3.01/1.69 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_168_llist_OdiscI_I1_J,axiom,
% 3.01/1.69 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( Llist
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_169_llist_Ocollapse_I1_J,axiom,
% 3.01/1.69 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Llist )
% 3.01/1.69 => ( Llist
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_170_lzip_Oexhaust,axiom,
% 3.01/1.69 ! [A: $tType,B4: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B4] :
% 3.01/1.69 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 | ( coindu335574135_lnull @ B4 @ Ys ) )
% 3.01/1.69 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ( coindu335574135_lnull @ B4 @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_171_lappend_Oexhaust,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 3.01/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_172_lnull__def,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A )
% 3.01/1.69 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 3.01/1.69 ( Llist2
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_173_lnull__lprefix,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_174_lprefix__lnull,axiom,
% 3.01/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Ys )
% 3.01/1.69 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.69 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_175_lprefix__lnullD,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.69 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.01/1.69 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_176_lprefix__not__lnullD,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.01/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_177_LNil__lprefix,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_178_lappend_Odisc_I2_J,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 3.01/1.69 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_179_lappend_Odisc_I1_J,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.01/1.69 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_180_lappend__lnull1,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.01/1.69 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.01/1.69 = Ys ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_181_lappend__lnull2,axiom,
% 3.01/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu335574135_lnull @ A @ Ys )
% 3.01/1.69 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.01/1.69 = Xs ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_182_lappend__LNil__LNil,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_183_LNil__eq__lappend__iff,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ( coindu1598213697e_LNil @ A )
% 3.01/1.69 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.01/1.69 = ( ( Xs
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 & ( Ys
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_184_lappend__eq__LNil__iff,axiom,
% 3.01/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 = ( ( Xs
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.01/1.69 & ( Ys
% 3.01/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_185_ldrop__ltake,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu191418589_ldrop @ A @ N @ ( coindu1802687541_ltake @ A @ M2 @ Xs ) )
% 3.01/1.69 = ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ M2 @ N ) @ ( coindu191418589_ldrop @ A @ N @ Xs ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_186_ltake__ldrop,axiom,
% 3.01/1.69 ! [A: $tType,N: extended_enat,M2: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.01/1.69 ( ( coindu1802687541_ltake @ A @ N @ ( coindu191418589_ldrop @ A @ M2 @ Xs ) )
% 3.01/1.69 = ( coindu191418589_ldrop @ A @ M2 @ ( coindu1802687541_ltake @ A @ ( plus_plus @ extended_enat @ N @ M2 ) @ Xs ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_187_le__add__diff__inverse,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.69 => ( ( plus_plus @ A @ B @ ( minus_minus @ A @ A2 @ B ) )
% 3.01/1.69 = A2 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_188_le__add__diff__inverse2,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.69 => ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 3.01/1.69 = A2 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_189_add__diff__cancel,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 3.01/1.69 = A2 ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_190_add__right__cancel,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ B @ A2 )
% 3.01/1.69 = ( plus_plus @ A @ C3 @ A2 ) )
% 3.01/1.69 = ( B = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_191_add__left__cancel,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ A2 @ B )
% 3.01/1.69 = ( plus_plus @ A @ A2 @ C3 ) )
% 3.01/1.69 = ( B = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_192_add__le__cancel__left,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [C3: A,A2: A,B: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 3.01/1.69 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_193_add__le__cancel__right,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 3.01/1.69 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_194_add__less__cancel__right,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 3.01/1.69 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_195_add__less__cancel__left,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [C3: A,A2: A,B: A] :
% 3.01/1.69 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 3.01/1.69 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_196_add__diff__cancel__right_H,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 3.01/1.69 = A2 ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_197_add__diff__cancel__right,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 3.01/1.69 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_198_add__diff__cancel__left_H,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ A2 )
% 3.01/1.69 = B ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_199_add__diff__cancel__left,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [C3: A,A2: A,B: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 3.01/1.69 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_200_diff__add__cancel,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A] :
% 3.01/1.69 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 3.01/1.69 = A2 ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_201_linorder__neqE__linordered__idom,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [X3: A,Y: A] :
% 3.01/1.69 ( ( X3 != Y )
% 3.01/1.69 => ( ~ ( ord_less @ A @ X3 @ Y )
% 3.01/1.69 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_202_add__right__imp__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ B @ A2 )
% 3.01/1.69 = ( plus_plus @ A @ C3 @ A2 ) )
% 3.01/1.69 => ( B = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_203_add__left__imp__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ A2 @ B )
% 3.01/1.69 = ( plus_plus @ A @ A2 @ C3 ) )
% 3.01/1.69 => ( B = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_204_add_Oleft__commute,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C3 ) )
% 3.01/1.69 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_205_add_Ocommute,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ( ( plus_plus @ A )
% 3.01/1.69 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_206_add_Oright__cancel,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ B @ A2 )
% 3.01/1.69 = ( plus_plus @ A @ C3 @ A2 ) )
% 3.01/1.69 = ( B = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_207_add_Oleft__cancel,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ A2 @ B )
% 3.01/1.69 = ( plus_plus @ A @ A2 @ C3 ) )
% 3.01/1.69 = ( B = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_208_add_Oassoc,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C3 )
% 3.01/1.69 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_209_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( I = J )
% 3.01/1.69 & ( K = L ) )
% 3.01/1.69 => ( ( plus_plus @ A @ I @ K )
% 3.01/1.69 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_210_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C3 )
% 3.01/1.69 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_211_diff__right__commute,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C3 ) @ B )
% 3.01/1.69 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_212_diff__eq__diff__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ( minus_minus @ A @ A2 @ B )
% 3.01/1.69 = ( minus_minus @ A @ C3 @ D3 ) )
% 3.01/1.69 => ( ( A2 = B )
% 3.01/1.69 = ( C3 = D3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_213_add__mono__thms__linordered__semiring_I3_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( ord_less_eq @ A @ I @ J )
% 3.01/1.69 & ( K = L ) )
% 3.01/1.69 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_214_add__mono__thms__linordered__semiring_I2_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( I = J )
% 3.01/1.69 & ( ord_less_eq @ A @ K @ L ) )
% 3.01/1.69 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_215_add__mono__thms__linordered__semiring_I1_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( ord_less_eq @ A @ I @ J )
% 3.01/1.69 & ( ord_less_eq @ A @ K @ L ) )
% 3.01/1.69 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_216_add__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 3.01/1.69 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_217_add__left__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_218_add__right__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_219_le__iff__add,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ( ( ord_less_eq @ A )
% 3.01/1.69 = ( ^ [A4: A,B3: A] :
% 3.01/1.69 ? [C4: A] :
% 3.01/1.69 ( B3
% 3.01/1.69 = ( plus_plus @ A @ A4 @ C4 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_220_add__le__imp__le__left,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [C3: A,A2: A,B: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 3.01/1.69 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_221_add__le__imp__le__right,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 3.01/1.69 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_222_diff__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,D3: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less_eq @ A @ D3 @ C3 )
% 3.01/1.69 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ D3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_223_diff__left__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ B @ A2 )
% 3.01/1.69 => ( ord_less_eq @ A @ ( minus_minus @ A @ C3 @ A2 ) @ ( minus_minus @ A @ C3 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_224_diff__right__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_225_diff__eq__diff__less__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ( minus_minus @ A @ A2 @ B )
% 3.01/1.69 = ( minus_minus @ A @ C3 @ D3 ) )
% 3.01/1.69 => ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 = ( ord_less_eq @ A @ C3 @ D3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_226_add__less__imp__less__right,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) )
% 3.01/1.69 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_227_add__less__imp__less__left,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [C3: A,A2: A,B: A] :
% 3.01/1.69 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) )
% 3.01/1.69 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_228_add__strict__right__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_229_add__strict__left__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_230_add__strict__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less @ A @ C3 @ D3 )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_231_add__mono__thms__linordered__field_I1_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( ord_less @ A @ I @ J )
% 3.01/1.69 & ( K = L ) )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_232_add__mono__thms__linordered__field_I2_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( I = J )
% 3.01/1.69 & ( ord_less @ A @ K @ L ) )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_233_add__mono__thms__linordered__field_I5_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( ord_less @ A @ I @ J )
% 3.01/1.69 & ( ord_less @ A @ K @ L ) )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_234_diff__strict__right__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_235_diff__strict__left__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [B: A,A2: A,C3: A] :
% 3.01/1.69 ( ( ord_less @ A @ B @ A2 )
% 3.01/1.69 => ( ord_less @ A @ ( minus_minus @ A @ C3 @ A2 ) @ ( minus_minus @ A @ C3 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_236_diff__eq__diff__less,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ( minus_minus @ A @ A2 @ B )
% 3.01/1.69 = ( minus_minus @ A @ C3 @ D3 ) )
% 3.01/1.69 => ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 = ( ord_less @ A @ C3 @ D3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_237_diff__strict__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,D3: A,C3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less @ A @ D3 @ C3 )
% 3.01/1.69 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C3 ) @ ( minus_minus @ A @ B @ D3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_238_add__implies__diff,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [C3: A,B: A,A2: A] :
% 3.01/1.69 ( ( ( plus_plus @ A @ C3 @ B )
% 3.01/1.69 = A2 )
% 3.01/1.69 => ( C3
% 3.01/1.69 = ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_239_diff__diff__add,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C3 )
% 3.01/1.69 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_240_diff__add__eq__diff__diff__swap,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C3 ) )
% 3.01/1.69 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C3 ) @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_241_diff__add__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ C3 )
% 3.01/1.69 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_242_diff__diff__eq2,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B @ C3 ) )
% 3.01/1.69 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_243_add__diff__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ C3 ) )
% 3.01/1.69 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_244_eq__diff__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,C3: A,B: A] :
% 3.01/1.69 ( ( A2
% 3.01/1.69 = ( minus_minus @ A @ C3 @ B ) )
% 3.01/1.69 = ( ( plus_plus @ A @ A2 @ B )
% 3.01/1.69 = C3 ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_245_diff__eq__eq,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( group_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ( minus_minus @ A @ A2 @ B )
% 3.01/1.69 = C3 )
% 3.01/1.69 = ( A2
% 3.01/1.69 = ( plus_plus @ A @ C3 @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_246_add__mono__thms__linordered__field_I4_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( ord_less_eq @ A @ I @ J )
% 3.01/1.69 & ( ord_less @ A @ K @ L ) )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_247_add__mono__thms__linordered__field_I3_J,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [I: A,J: A,K: A,L: A] :
% 3.01/1.69 ( ( ( ord_less @ A @ I @ J )
% 3.01/1.69 & ( ord_less_eq @ A @ K @ L ) )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_248_add__le__less__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less @ A @ C3 @ D3 )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_249_add__less__le__mono,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A,D3: A] :
% 3.01/1.69 ( ( ord_less @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 3.01/1.69 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B @ D3 ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_250_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( ( minus_minus @ A @ B @ A2 )
% 3.01/1.69 = C3 )
% 3.01/1.69 = ( B
% 3.01/1.69 = ( plus_plus @ A @ C3 @ A2 ) ) ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_251_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ A2 ) )
% 3.01/1.69 = B ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_252_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( minus_minus @ A @ C3 @ ( minus_minus @ A @ B @ A2 ) )
% 3.01/1.69 = ( minus_minus @ A @ ( plus_plus @ A @ C3 @ A2 ) @ B ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(fact_253_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 3.01/1.69 ! [A: $tType] :
% 3.01/1.69 ( ( ordere623563068d_diff @ A @ ( type2 @ A ) )
% 3.01/1.69 => ! [A2: A,B: A,C3: A] :
% 3.01/1.69 ( ( ord_less_eq @ A @ A2 @ B )
% 3.01/1.69 => ( ( minus_minus @ A @ ( plus_plus @ A @ B @ C3 ) @ A2 )
% 3.01/1.69 = ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C3 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.01/1.69 ! [A5: $tType,A6: $tType] :
% 3.01/1.69 ( ( preorder @ A6 @ ( type2 @ A6 ) )
% 3.01/1.69 => ( preorder @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.01/1.69 ! [A5: $tType,A6: $tType] :
% 3.01/1.69 ( ( order @ A6 @ ( type2 @ A6 ) )
% 3.01/1.69 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_fun___Orderings_Oord,axiom,
% 3.01/1.69 ! [A5: $tType,A6: $tType] :
% 3.01/1.69 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 3.01/1.69 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_HOL_Obool___Orderings_Opreorder_1,axiom,
% 3.01/1.69 preorder @ $o @ ( type2 @ $o ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.01/1.69 linorder @ $o @ ( type2 @ $o ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 3.01/1.69 order @ $o @ ( type2 @ $o ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_HOL_Obool___Orderings_Oord_3,axiom,
% 3.01/1.69 ord @ $o @ ( type2 @ $o ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 3.01/1.69 condit1037483654norder @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 3.01/1.69 strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 3.01/1.69 canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add,axiom,
% 3.01/1.69 ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add,axiom,
% 3.01/1.69 ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add,axiom,
% 3.01/1.69 semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Orderings_Owellorder,axiom,
% 3.01/1.69 wellorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_4,axiom,
% 3.01/1.69 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_5,axiom,
% 3.01/1.69 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_6,axiom,
% 3.01/1.69 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_7,axiom,
% 3.01/1.69 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.01/1.69
% 3.01/1.69 thf(conj_0,conjecture,
% 3.01/1.69 ord_less @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ a @ ys ) ).
% 3.01/1.69 ------------------------
% 3.09/1.72 % (24879)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/2Mi)
% 3.09/1.72 % (24878)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/27Mi)
% 3.09/1.72 % (24877)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/4Mi)
% 3.09/1.72 % (24882)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/18Mi)
% 3.09/1.72 % (24876)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/183Mi)
% 3.09/1.72 % (24881)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/275Mi)
% 3.09/1.72 % (24880)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/2Mi)
% 3.09/1.72 % (24879)Instruction limit reached!
% 3.09/1.72 % (24879)------------------------------
% 3.09/1.72 % (24879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (24879)Termination reason: Unknown
% 3.09/1.72 % (24879)Termination phase: shuffling
% 3.09/1.72
% 3.09/1.72 % (24880)Instruction limit reached!
% 3.09/1.72 % (24880)------------------------------
% 3.09/1.72 % (24880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (24880)Termination reason: Unknown
% 3.09/1.72 % (24880)Termination phase: shuffling
% 3.09/1.72
% 3.09/1.72 % (24880)Memory used [KB]: 1407
% 3.09/1.72 % (24880)Time elapsed: 0.003 s
% 3.09/1.72 % (24880)Instructions burned: 3 (million)
% 3.09/1.72 % (24880)------------------------------
% 3.09/1.72 % (24880)------------------------------
% 3.09/1.72 % (24879)Memory used [KB]: 1279
% 3.09/1.72 % (24879)Time elapsed: 0.004 s
% 3.09/1.72 % (24879)Instructions burned: 3 (million)
% 3.09/1.72 % (24879)------------------------------
% 3.09/1.72 % (24879)------------------------------
% 3.09/1.72 % (24877)Instruction limit reached!
% 3.09/1.72 % (24877)------------------------------
% 3.09/1.72 % (24877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (24877)Termination reason: Unknown
% 3.09/1.72 % (24877)Termination phase: shuffling
% 3.09/1.72
% 3.09/1.72 % (24877)Memory used [KB]: 1407
% 3.09/1.72 % (24877)Time elapsed: 0.005 s
% 3.09/1.72 % (24877)Instructions burned: 5 (million)
% 3.09/1.72 % (24877)------------------------------
% 3.09/1.72 % (24877)------------------------------
% 3.09/1.73 % (24882)Instruction limit reached!
% 3.09/1.73 % (24882)------------------------------
% 3.09/1.73 % (24882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.73 % (24882)Termination reason: Unknown
% 3.09/1.73 % (24882)Termination phase: shuffling
% 3.09/1.73
% 3.09/1.73 % (24882)Memory used [KB]: 1663
% 3.09/1.73 % (24882)Time elapsed: 0.011 s
% 3.09/1.73 % (24882)Instructions burned: 18 (million)
% 3.09/1.73 % (24882)------------------------------
% 3.09/1.73 % (24882)------------------------------
% 3.09/1.73 % (24878)Instruction limit reached!
% 3.09/1.73 % (24878)------------------------------
% 3.09/1.73 % (24878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.73 % (24878)Termination reason: Unknown
% 3.09/1.73 % (24878)Termination phase: Property scanning
% 3.09/1.73
% 3.09/1.73 % (24878)Memory used [KB]: 1663
% 3.09/1.73 % (24878)Time elapsed: 0.015 s
% 3.09/1.73 % (24878)Instructions burned: 28 (million)
% 3.09/1.73 % (24878)------------------------------
% 3.09/1.73 % (24878)------------------------------
% 3.09/1.74 % (24883)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/3Mi)
% 3.09/1.74 % (24884)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/37Mi)
% 3.09/1.74 % (24885)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/15Mi)
% 3.09/1.74 % (24883)Instruction limit reached!
% 3.09/1.74 % (24883)------------------------------
% 3.09/1.74 % (24883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.74 % (24883)Termination reason: Unknown
% 3.09/1.74 % (24883)Termination phase: shuffling
% 3.09/1.74
% 3.09/1.74 % (24883)Memory used [KB]: 1279
% 3.09/1.74 % (24883)Time elapsed: 0.003 s
% 3.09/1.74 % (24883)Instructions burned: 3 (million)
% 3.09/1.74 % (24883)------------------------------
% 3.09/1.74 % (24883)------------------------------
% 3.09/1.75 % (24886)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/3Mi)
% 3.09/1.75 % (24885)Instruction limit reached!
% 3.09/1.75 % (24885)------------------------------
% 3.09/1.75 % (24885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.75 % (24885)Termination reason: Unknown
% 3.09/1.75 % (24885)Termination phase: shuffling
% 3.09/1.75
% 3.09/1.75 % (24885)Memory used [KB]: 1663
% 3.09/1.75 % (24885)Time elapsed: 0.009 s
% 3.09/1.75 % (24885)Instructions burned: 16 (million)
% 3.09/1.75 % (24885)------------------------------
% 3.09/1.75 % (24885)------------------------------
% 3.09/1.75 % (24886)Instruction limit reached!
% 3.09/1.75 % (24886)------------------------------
% 3.09/1.75 % (24886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.75 % (24886)Termination reason: Unknown
% 3.09/1.75 % (24886)Termination phase: shuffling
% 3.09/1.75
% 3.09/1.75 % (24886)Memory used [KB]: 1279
% 3.09/1.75 % (24886)Time elapsed: 0.003 s
% 3.09/1.75 % (24886)Instructions burned: 3 (million)
% 3.09/1.75 % (24886)------------------------------
% 3.09/1.75 % (24886)------------------------------
% 3.09/1.75 % (24887)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/1041Mi)
% 3.09/1.76 % (24884)Instruction limit reached!
% 3.09/1.76 % (24884)------------------------------
% 3.09/1.76 % (24884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.76 % (24884)Termination reason: Unknown
% 3.09/1.76 % (24884)Termination phase: Property scanning
% 3.09/1.76
% 3.09/1.76 % (24884)Memory used [KB]: 2046
% 3.09/1.76 % (24884)Time elapsed: 0.019 s
% 3.09/1.76 % (24884)Instructions burned: 37 (million)
% 3.09/1.76 % (24884)------------------------------
% 3.09/1.76 % (24884)------------------------------
% 3.09/1.76 % (24888)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/7Mi)
% 3.09/1.76 % (24888)Instruction limit reached!
% 3.09/1.76 % (24888)------------------------------
% 3.09/1.76 % (24888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.76 % (24888)Termination reason: Unknown
% 3.09/1.76 % (24888)Termination phase: shuffling
% 3.09/1.76
% 3.09/1.76 % (24888)Memory used [KB]: 1535
% 3.09/1.76 % (24888)Time elapsed: 0.006 s
% 3.09/1.76 % (24888)Instructions burned: 8 (million)
% 3.09/1.76 % (24888)------------------------------
% 3.09/1.76 % (24888)------------------------------
% 3.09/1.76 % (24889)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/16Mi)
% 3.09/1.76 % (24890)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/3Mi)
% 3.09/1.76 % (24890)Instruction limit reached!
% 3.09/1.76 % (24890)------------------------------
% 3.09/1.76 % (24890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.76 % (24890)Termination reason: Unknown
% 3.09/1.76 % (24890)Termination phase: shuffling
% 3.09/1.76
% 3.09/1.76 % (24890)Memory used [KB]: 1279
% 3.09/1.76 % (24890)Time elapsed: 0.003 s
% 3.09/1.76 % (24890)Instructions burned: 3 (million)
% 3.09/1.76 % (24890)------------------------------
% 3.09/1.76 % (24890)------------------------------
% 3.09/1.77 % (24889)Instruction limit reached!
% 3.09/1.77 % (24889)------------------------------
% 3.09/1.77 % (24889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.77 % (24889)Termination reason: Unknown
% 3.09/1.77 % (24889)Termination phase: shuffling
% 3.09/1.77
% 3.09/1.77 % (24889)Memory used [KB]: 1663
% 3.09/1.77 % (24889)Time elapsed: 0.010 s
% 3.09/1.77 % (24889)Instructions burned: 17 (million)
% 3.09/1.77 % (24889)------------------------------
% 3.09/1.77 % (24889)------------------------------
% 3.09/1.77 % (24891)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/3Mi)
% 3.09/1.77 % (24891)Instruction limit reached!
% 3.09/1.77 % (24891)------------------------------
% 3.09/1.77 % (24891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.77 % (24891)Termination reason: Unknown
% 3.09/1.77 % (24891)Termination phase: shuffling
% 3.09/1.77
% 3.09/1.77 % (24891)Memory used [KB]: 1279
% 3.09/1.77 % (24891)Time elapsed: 0.003 s
% 3.09/1.77 % (24891)Instructions burned: 3 (million)
% 3.09/1.77 % (24891)------------------------------
% 3.09/1.77 % (24891)------------------------------
% 3.09/1.78 % (24892)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/7Mi)
% 3.09/1.78 % (24892)Instruction limit reached!
% 3.09/1.78 % (24892)------------------------------
% 3.09/1.78 % (24892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.78 % (24892)Termination reason: Unknown
% 3.09/1.78 % (24892)Termination phase: shuffling
% 3.09/1.78
% 3.09/1.78 % (24892)Memory used [KB]: 1407
% 3.09/1.78 % (24892)Time elapsed: 0.005 s
% 3.09/1.78 % (24892)Instructions burned: 7 (million)
% 3.09/1.78 % (24892)------------------------------
% 3.09/1.78 % (24892)------------------------------
% 3.09/1.78 % (24893)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/3Mi)
% 3.09/1.78 % (24893)Instruction limit reached!
% 3.09/1.78 % (24893)------------------------------
% 3.09/1.78 % (24893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.78 % (24893)Termination reason: Unknown
% 3.09/1.78 % (24893)Termination phase: shuffling
% 3.09/1.78
% 3.09/1.78 % (24893)Memory used [KB]: 1407
% 3.09/1.78 % (24893)Time elapsed: 0.003 s
% 3.09/1.78 % (24893)Instructions burned: 3 (million)
% 3.09/1.78 % (24893)------------------------------
% 3.09/1.78 % (24893)------------------------------
% 3.09/1.79 % (24894)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/4Mi)
% 3.09/1.79 % (24894)Instruction limit reached!
% 3.09/1.79 % (24894)------------------------------
% 3.09/1.79 % (24894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.79 % (24894)Termination reason: Unknown
% 3.09/1.79 % (24894)Termination phase: shuffling
% 3.09/1.79
% 3.09/1.79 % (24894)Memory used [KB]: 1407
% 3.09/1.79 % (24894)Time elapsed: 0.004 s
% 3.09/1.79 % (24894)Instructions burned: 5 (million)
% 3.09/1.79 % (24894)------------------------------
% 3.09/1.79 % (24894)------------------------------
% 3.09/1.79 % (24895)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/18Mi)
% 3.09/1.79 % (24896)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/710Mi)
% 3.09/1.80 % (24897)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/6Mi)
% 3.09/1.80 % (24895)Instruction limit reached!
% 3.09/1.80 % (24895)------------------------------
% 3.09/1.80 % (24895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.80 % (24895)Termination reason: Unknown
% 3.09/1.80 % (24895)Termination phase: shuffling
% 3.09/1.80
% 3.09/1.80 % (24895)Memory used [KB]: 1663
% 3.09/1.80 % (24895)Time elapsed: 0.011 s
% 3.09/1.80 % (24895)Instructions burned: 19 (million)
% 3.09/1.80 % (24895)------------------------------
% 3.09/1.80 % (24895)------------------------------
% 3.09/1.80 % (24897)Instruction limit reached!
% 3.09/1.80 % (24897)------------------------------
% 3.09/1.80 % (24897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.80 % (24897)Termination reason: Unknown
% 3.09/1.80 % (24897)Termination phase: shuffling
% 3.09/1.80
% 3.09/1.80 % (24897)Memory used [KB]: 1407
% 3.09/1.80 % (24897)Time elapsed: 0.005 s
% 3.09/1.80 % (24897)Instructions burned: 7 (million)
% 3.09/1.80 % (24897)------------------------------
% 3.09/1.80 % (24897)------------------------------
% 3.09/1.80 % (24898)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_24777 for (2999ds/902Mi)
% 3.09/1.81 % (24876)Instruction limit reached!
% 3.09/1.81 % (24876)------------------------------
% 3.09/1.81 % (24876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.81 % (24876)Termination reason: Unknown
% 3.09/1.81 % (24876)Termination phase: Saturation
% 3.09/1.81
% 3.09/1.81 % (24876)Memory used [KB]: 6908
% 3.09/1.81 % (24876)Time elapsed: 0.088 s
% 3.09/1.81 % (24876)Instructions burned: 183 (million)
% 3.09/1.81 % (24876)------------------------------
% 3.09/1.81 % (24876)------------------------------
% 3.09/1.81 % (24899)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/21Mi)
% 3.09/1.82 % (24900)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/5Mi)
% 3.09/1.82 % (24900)Instruction limit reached!
% 3.09/1.82 % (24900)------------------------------
% 3.09/1.82 % (24900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.82 % (24900)Termination reason: Unknown
% 3.09/1.82 % (24900)Termination phase: shuffling
% 3.09/1.82
% 3.09/1.82 % (24900)Memory used [KB]: 1407
% 3.09/1.82 % (24900)Time elapsed: 0.004 s
% 3.09/1.82 % (24900)Instructions burned: 6 (million)
% 3.09/1.82 % (24900)------------------------------
% 3.09/1.82 % (24900)------------------------------
% 3.09/1.82 % (24901)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/6Mi)
% 3.09/1.82 % (24901)Instruction limit reached!
% 3.09/1.82 % (24901)------------------------------
% 3.09/1.82 % (24901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.82 % (24901)Termination reason: Unknown
% 3.09/1.82 % (24901)Termination phase: shuffling
% 3.09/1.82
% 3.09/1.82 % (24901)Memory used [KB]: 1407
% 3.09/1.82 % (24901)Time elapsed: 0.005 s
% 3.09/1.82 % (24901)Instructions burned: 7 (million)
% 3.09/1.82 % (24901)------------------------------
% 3.09/1.82 % (24901)------------------------------
% 3.09/1.83 % (24899)Instruction limit reached!
% 3.09/1.83 % (24899)------------------------------
% 3.09/1.83 % (24899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.83 % (24899)Termination reason: Unknown
% 3.09/1.83 % (24899)Termination phase: Property scanning
% 3.09/1.83
% 3.09/1.83 % (24899)Memory used [KB]: 1791
% 3.09/1.83 % (24899)Time elapsed: 0.013 s
% 3.09/1.83 % (24899)Instructions burned: 22 (million)
% 3.09/1.83 % (24899)------------------------------
% 3.09/1.83 % (24899)------------------------------
% 3.09/1.84 % (24902)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/377Mi)
% 3.09/1.84 % (24903)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/779Mi)
% 3.09/1.84 % (24904)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/19Mi)
% 3.09/1.85 % (24904)Instruction limit reached!
% 3.09/1.85 % (24904)------------------------------
% 3.09/1.85 % (24904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.85 % (24904)Termination reason: Unknown
% 3.09/1.85 % (24904)Termination phase: shuffling
% 3.09/1.85
% 3.09/1.85 % (24904)Memory used [KB]: 1663
% 3.09/1.85 % (24904)Time elapsed: 0.010 s
% 3.09/1.85 % (24904)Instructions burned: 19 (million)
% 3.09/1.85 % (24904)------------------------------
% 3.09/1.85 % (24904)------------------------------
% 3.09/1.85 % (24881)Instruction limit reached!
% 3.09/1.85 % (24881)------------------------------
% 3.09/1.85 % (24881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.85 % (24881)Termination reason: Unknown
% 3.09/1.85 % (24881)Termination phase: Saturation
% 3.09/1.85
% 3.09/1.85 % (24881)Memory used [KB]: 6652
% 3.09/1.85 % (24881)Time elapsed: 0.134 s
% 3.09/1.85 % (24881)Instructions burned: 276 (million)
% 3.09/1.85 % (24881)------------------------------
% 3.09/1.85 % (24881)------------------------------
% 3.09/1.87 % (24905)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/879Mi)
% 3.09/1.87 % (24906)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/17Mi)
% 3.09/1.88 % (24906)Instruction limit reached!
% 3.09/1.88 % (24906)------------------------------
% 3.09/1.88 % (24906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.88 % (24906)Termination reason: Unknown
% 3.09/1.88 % (24906)Termination phase: shuffling
% 3.09/1.88
% 3.09/1.88 % (24906)Memory used [KB]: 1663
% 3.09/1.88 % (24906)Time elapsed: 0.010 s
% 3.09/1.88 % (24906)Instructions burned: 17 (million)
% 3.09/1.88 % (24906)------------------------------
% 3.09/1.88 % (24906)------------------------------
% 3.09/1.89 % (24907)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/3Mi)
% 3.09/1.89 % (24907)Instruction limit reached!
% 3.09/1.89 % (24907)------------------------------
% 3.09/1.89 % (24907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.89 % (24907)Termination reason: Unknown
% 3.09/1.89 % (24907)Termination phase: shuffling
% 3.09/1.89
% 3.09/1.89 % (24907)Memory used [KB]: 1279
% 3.09/1.89 % (24907)Time elapsed: 0.004 s
% 3.09/1.89 % (24907)Instructions burned: 4 (million)
% 3.09/1.89 % (24907)------------------------------
% 3.09/1.89 % (24907)------------------------------
% 3.09/1.91 % (24908)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_24777 for (2998ds/30Mi)
% 3.09/1.93 % (24908)Instruction limit reached!
% 3.09/1.93 % (24908)------------------------------
% 3.09/1.93 % (24908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.93 % (24908)Termination reason: Unknown
% 3.09/1.93 % (24908)Termination phase: Property scanning
% 3.09/1.93
% 3.09/1.93 % (24908)Memory used [KB]: 1791
% 3.09/1.93 % (24908)Time elapsed: 0.017 s
% 3.09/1.93 % (24908)Instructions burned: 31 (million)
% 3.09/1.93 % (24908)------------------------------
% 3.09/1.93 % (24908)------------------------------
% 3.09/1.94 % (24909)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_24777 for (2997ds/127Mi)
% 3.09/1.98 % (24903)First to succeed.
% 3.09/1.99 % (24903)Refutation found. Thanks to Tanya!
% 3.09/1.99 % SZS status Theorem for DTF2THF_24777
% 3.09/1.99 % SZS output start Proof for DTF2THF_24777
% 3.09/1.99 thf(type_def_5, type, itself: ($tType) > $tType).
% 3.09/1.99 thf(type_def_7, type, coindu1593790203_llist: ($tType) > $tType).
% 3.09/1.99 thf(type_def_8, type, extended_enat: $tType).
% 3.09/1.99 thf(type_def_9, type, a: $tType).
% 3.09/1.99 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 3.09/1.99 thf(func_def_1, type, extended_enat: $tType).
% 3.09/1.99 thf(func_def_2, type, itself: ($tType) > $tType).
% 3.09/1.99 thf(func_def_3, type, a: $tType).
% 3.09/1.99 thf(func_def_4, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_5, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_6, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_7, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_8, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_9, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_10, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_11, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_12, type, ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_13, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_14, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_15, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_16, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_17, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_18, type, dense_linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_19, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_20, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_21, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_22, type, cancel1352612707id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_23, type, cancel146912293up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_24, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_26, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_27, type, ordere223160158up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_28, type, ordere623563068d_diff: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_29, type, strict2144017051up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_30, type, condit1656338222tinuum: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_31, type, condit1037483654norder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.09/1.99 thf(func_def_32, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.09/1.99 thf(func_def_33, type, coindu191418589_ldrop: !>[X0: $tType]:(extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.09/1.99 thf(func_def_34, type, coindu1018505716length: !>[X0: $tType]:(coindu1593790203_llist @ X0 > extended_enat)).
% 3.09/1.99 thf(func_def_35, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 3.09/1.99 thf(func_def_36, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 3.09/1.99 thf(func_def_37, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 3.09/1.99 thf(func_def_38, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 3.09/1.99 thf(func_def_39, type, coindu1802687541_ltake: !>[X0: $tType]:(extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.09/1.99 thf(func_def_40, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.09/1.99 thf(func_def_41, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.09/1.99 thf(func_def_42, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.09/1.99 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.09/1.99 thf(func_def_44, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.09/1.99 thf(func_def_45, type, xs: coindu1593790203_llist @ a).
% 3.09/1.99 thf(func_def_46, type, xs2: coindu1593790203_llist @ a).
% 3.09/1.99 thf(func_def_47, type, ys: coindu1593790203_llist @ a).
% 3.09/1.99 thf(func_def_48, type, zs: coindu1593790203_llist @ a).
% 3.09/1.99 thf(func_def_67, type, sK1: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.09/1.99 thf(func_def_68, type, sK2: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_69, type, sK3: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_70, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.09/1.99 thf(func_def_71, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.09/1.99 thf(func_def_72, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.09/1.99 thf(func_def_73, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.09/1.99 thf(func_def_74, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.09/1.99 thf(func_def_75, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.09/1.99 thf(func_def_76, type, sK10: !>[X0: $tType]:(X0)).
% 3.09/1.99 thf(func_def_77, type, sK11: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_78, type, sK12: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_79, type, sK13: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_80, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.09/1.99 thf(func_def_81, type, sK15: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 3.09/1.99 thf(func_def_82, type, sK16: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_83, type, sK17: (extended_enat > $o) > extended_enat).
% 3.09/1.99 thf(func_def_84, type, sK18: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_85, type, sK19: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_86, type, sK20: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_87, type, sK21: !>[X0: $tType]:(X0 > X0)).
% 3.09/1.99 thf(func_def_88, type, sK22: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 3.09/1.99 thf(func_def_89, type, ph23: !>[X0: $tType]:(X0)).
% 3.09/1.99 thf(f3018,plain,(
% 3.09/1.99 $false),
% 3.09/1.99 inference(trivial_inequality_removal,[status(thm)],[f3017])).
% 3.09/1.99 thf(f3017,plain,(
% 3.09/1.99 ($true = $false)),
% 3.09/1.99 inference(forward_demodulation,[status(thm)],[f3016,f1960])).
% 3.09/1.99 thf(f1960,plain,(
% 3.09/1.99 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs)) = $false)),
% 3.09/1.99 inference(not_proxy_clausification,[status(thm)],[f1061])).
% 3.09/1.99 thf(f1061,plain,(
% 3.09/1.99 ($true = (~ (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs))))),
% 3.09/1.99 inference(cnf_transformation,[status(thm)],[f374])).
% 3.09/1.99 thf(f374,plain,(
% 3.09/1.99 ($true = (~ (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs))))),
% 3.09/1.99 inference(fool_elimination,[status(thm)],[f373])).
% 3.09/1.99 thf(f373,plain,(
% 3.09/1.99 ~(ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs))),
% 3.09/1.99 inference(rectify,[status(thm)],[f1])).
% 3.09/1.99 thf(f1,axiom,(
% 3.09/1.99 ~(ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs))),
% 3.09/1.99 file('/export/starexec/sandbox2/tmp/tmp.2HsJS0n40S/DTF2THF_24777.p',fact_0__092_060open_062_092_060not_062_Allength_Ays_A_092_060le_062_Allength_Axs_092_060close_062)).
% 3.09/1.99 thf(f3016,plain,(
% 3.09/1.99 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs)) = $true)),
% 3.09/1.99 inference(trivial_inequality_removal,[status(thm)],[f3015])).
% 3.09/1.99 thf(f3015,plain,(
% 3.09/1.99 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs)) = $true) | ($true = $false)),
% 3.09/1.99 inference(forward_demodulation,[status(thm)],[f3012,f983])).
% 3.09/1.99 thf(f983,plain,(
% 3.09/1.99 ((linorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 3.09/1.99 inference(cnf_transformation,[status(thm)],[f422])).
% 3.09/1.99 thf(f422,plain,(
% 3.09/1.99 ((linorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 3.09/1.99 inference(fool_elimination,[status(thm)],[f421])).
% 3.09/1.99 thf(f421,plain,(
% 3.09/1.99 (linorder @ extended_enat @ type2 @ extended_enat)),
% 3.09/1.99 inference(rectify,[status(thm)],[f270])).
% 3.09/1.99 thf(f270,axiom,(
% 3.09/1.99 (linorder @ extended_enat @ type2 @ extended_enat)),
% 3.09/1.99 file('/export/starexec/sandbox2/tmp/tmp.2HsJS0n40S/DTF2THF_24777.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_5)).
% 3.09/1.99 thf(f3012,plain,(
% 3.09/1.99 ((linorder @ extended_enat @ type2 @ extended_enat) = $false) | ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs)) = $true)),
% 3.09/1.99 inference(trivial_inequality_removal,[status(thm)],[f2986])).
% 3.09/1.99 thf(f2986,plain,(
% 3.09/1.99 ((linorder @ extended_enat @ type2 @ extended_enat) = $false) | ($true = $false) | ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ ys) @ (coindu1018505716length @ a @ xs)) = $true)),
% 3.09/1.99 inference(superposition,[status(thm)],[f2060,f1862])).
% 3.09/1.99 thf(f1862,plain,(
% 3.09/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (ord_less @ X0 @ X1 @ X2)) | ((ord_less_eq @ X0 @ X2 @ X1) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 3.09/1.99 inference(not_proxy_clausification,[status(thm)],[f1861])).
% 3.09/1.99 thf(f1861,plain,(
% 3.09/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (ord_less @ X0 @ X1 @ X2)) | ((linorder @ X0 @ type2 @ X0) = $false) | ($false = (~ (ord_less_eq @ X0 @ X2 @ X1)))) )),
% 3.09/1.99 inference(binary_proxy_clausification,[status(thm)],[f1860])).
% 3.09/1.99 thf(f1860,plain,(
% 3.09/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = ((~ (ord_less_eq @ X0 @ X2 @ X1)) => (ord_less @ X0 @ X1 @ X2))) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 3.09/1.99 inference(beta_eta_normalization,[status(thm)],[f1859])).
% 3.09/1.99 thf(f1859,plain,(
% 3.09/1.99 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = ((^[Y0 : X0]: ((~ (ord_less_eq @ X0 @ Y0 @ X1)) => (ord_less @ X0 @ X1 @ Y0))) @ X2)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 3.09/1.99 inference(pi_clausification,[status(thm)],[f1858])).
% 3.09/1.99 thf(f1858,plain,(
% 3.09/1.99 ( ! [X0 : $tType,X1 : X0] : (((!! @ X0 @ (^[Y0 : X0]: ((~ (ord_less_eq @ X0 @ Y0 @ X1)) => (ord_less @ X0 @ X1 @ Y0)))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 3.09/1.99 inference(beta_eta_normalization,[status(thm)],[f1857])).
% 3.09/1.99 thf(f1857,plain,(
% 3.09/1.99 ( ! [X0 : $tType,X1 : X0] : (($true = ((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((~ (ord_less_eq @ X0 @ Y1 @ Y0)) => (ord_less @ X0 @ Y0 @ Y1))))) @ X1)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 3.09/1.99 inference(pi_clausification,[status(thm)],[f1856])).
% 3.09/1.99 thf(f1856,plain,(
% 3.09/1.99 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((~ (ord_less_eq @ X0 @ Y1 @ Y0)) => (ord_less @ X0 @ Y0 @ Y1)))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 3.09/1.99 inference(binary_proxy_clausification,[status(thm)],[f1067])).
% 3.09/1.99 thf(f1067,plain,(
% 3.09/1.99 ( ! [X0 : $tType] : (($true = ((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((~ (ord_less_eq @ X0 @ Y1 @ Y0)) => (ord_less @ X0 @ Y0 @ Y1))))))))) )),
% 3.09/1.99 inference(cnf_transformation,[status(thm)],[f838])).
% 3.09/1.99 thf(f838,plain,(
% 3.09/1.99 ! [X0 : $tType] : ($true = ((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((~ (ord_less_eq @ X0 @ Y1 @ Y0)) => (ord_less @ X0 @ Y0 @ Y1))))))))),
% 3.09/1.99 inference(closure,[status(thm)],[f795])).
% 3.09/1.99 thf(f795,plain,(
% 3.09/1.99 ( ! [X0 : $tType] : (($true = ((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((~ (ord_less_eq @ X0 @ Y1 @ Y0)) => (ord_less @ X0 @ Y0 @ Y1))))))))) )),
% 3.09/1.99 inference(fool_elimination,[status(thm)],[f794])).
% 3.09/1.99 thf(f794,plain,(
% 3.09/1.99 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : (~(ord_less_eq @ X0 @ X1 @ X2) => (ord_less @ X0 @ X2 @ X1)))),
% 3.09/1.99 inference(rectify,[status(thm)],[f141])).
% 3.09/1.99 thf(f141,axiom,(
% 3.09/1.99 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X21 : X0,X19 : X0] : (~(ord_less_eq @ X0 @ X21 @ X19) => (ord_less @ X0 @ X19 @ X21)))),
% 3.09/1.99 file('/export/starexec/sandbox2/tmp/tmp.2HsJS0n40S/DTF2THF_24777.p',fact_140_not__le__imp__less)).
% 3.09/1.99 thf(f2060,plain,(
% 3.09/1.99 ((ord_less @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ ys)) = $false)),
% 3.09/1.99 inference(not_proxy_clausification,[status(thm)],[f1040])).
% 3.09/1.99 thf(f1040,plain,(
% 3.09/1.99 ((~ (ord_less @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ ys))) = $true)),
% 3.09/1.99 inference(cnf_transformation,[status(thm)],[f704])).
% 3.09/1.99 thf(f704,plain,(
% 3.09/1.99 ((~ (ord_less @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ ys))) = $true)),
% 3.09/1.99 inference(fool_elimination,[status(thm)],[f703])).
% 3.09/1.99 thf(f703,plain,(
% 3.09/1.99 ~(ord_less @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ ys))),
% 3.09/1.99 inference(rectify,[status(thm)],[f274])).
% 3.09/1.99 thf(f274,negated_conjecture,(
% 3.09/1.99 ~(ord_less @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ ys))),
% 3.09/1.99 inference(negated_conjecture,[status(cth)],[f273])).
% 3.09/1.99 thf(f273,conjecture,(
% 3.09/1.99 (ord_less @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ ys))),
% 3.09/1.99 file('/export/starexec/sandbox2/tmp/tmp.2HsJS0n40S/DTF2THF_24777.p',conj_0)).
% 3.09/1.99 % SZS output end Proof for DTF2THF_24777
% 3.09/1.99 % (24903)------------------------------
% 3.09/1.99 % (24903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.99 % (24903)Termination reason: Refutation
% 3.09/1.99
% 3.09/1.99 % (24903)Memory used [KB]: 7419
% 3.09/1.99 % (24903)Time elapsed: 0.145 s
% 3.09/1.99 % (24903)Instructions burned: 294 (million)
% 3.09/1.99 % (24903)------------------------------
% 3.09/1.99 % (24903)------------------------------
% 3.09/1.99 % (24875)Success in time 0.283 s
%------------------------------------------------------------------------------