%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP042^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 08:55:05 AM UTC 2026
% Result : Theorem 13.17s 3.13s
% Output : Refutation 13.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP042^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 08:23:55 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : ITP042^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.45 % Domain : Interactive Theorem Proving
% 0.29/0.45 % Problem : Sledgehammer Coincidence problem prob_99__7210728_1
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Des21]
% 0.29/0.45 % Names : Coincidence/prob_99__7210728_1 [Des21]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v7.5.0
% 0.29/0.45 % Syntax : Number of formulae : 430 ( 130 unt; 71 typ; 0 def)
% 0.29/0.45 % Number of atoms : 1008 ( 205 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 15 ( 2 avg)
% 0.29/0.45 % Number of connectives : 4766 ( 34 ~; 7 |; 123 &;4185 @)
% 0.29/0.45 % ( 0 <=>; 417 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 22 ( 8 avg)
% 0.29/0.45 % Number of types : 9 ( 8 usr)
% 0.29/0.45 % Number of type conns : 398 ( 398 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 66 ( 63 usr; 8 con; 0-8 aty)
% 0.29/0.45 % Number of variables : 1333 ( 154 ^;1073 !; 23 ?;1333 :)
% 0.29/0.45 % ( 83 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.45 % SPC : TH1_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:22:00.421
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % Could-be-implicit typings (17)
% 0.29/0.45 thf(ty_t_Denotational__Semantics_Ointerp_Ointerp__ext,type,
% 0.29/0.45 denota1663640101rp_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Frechet__Correctness_Oids_Ogood__interp,type,
% 0.29/0.45 frechet_good_interp: $tType > $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Bounded__Linear__Function_Oblinfun,type,
% 0.29/0.45 bounde2145540817linfun: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Frechet__Correctness_Oids_Ostrm,type,
% 0.29/0.45 frechet_strm: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 0.29/0.45 finite_Cartesian_vec: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Product__Type_Ounit,type,
% 0.29/0.45 product_unit: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Product__Type_Oprod,type,
% 0.29/0.45 product_prod: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Sum__Type_Osum,type,
% 0.29/0.45 sum_sum: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Syntax_Otrm,type,
% 0.29/0.45 trm: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Real_Oreal,type,
% 0.29/0.45 real: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Set_Oset,type,
% 0.29/0.45 set: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_sz,type,
% 0.29/0.45 sz: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_sf,type,
% 0.29/0.45 sf: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_sc,type,
% 0.29/0.45 sc: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_c,type,
% 0.29/0.45 c: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_b,type,
% 0.29/0.45 b: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_a,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 % Explicit typings (54)
% 0.29/0.45 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 0.29/0.45 real_V55928688vector:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Cardinality_OCARD__1,type,
% 0.29/0.45 cARD_1:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 0.29/0.45 ordere890947078_space:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.29/0.45 bounded_lattice:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_HOL_Otype,type,
% 0.29/0.45 type:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Osup,type,
% 0.29/0.45 sup:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.29/0.45 ord:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Otop,type,
% 0.29/0.45 top:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.45 order:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Olattice,type,
% 0.29/0.45 lattice:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.29/0.45 finite_finite:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.45 linorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.29/0.45 preorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oorder__top,type,
% 0.29/0.45 order_top:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.29/0.45 semilattice_sup:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.29/0.45 bounded_lattice_top:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Topological__Spaces_Odiscrete__topology,type,
% 0.29/0.45 topolo2133971006pology:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 0.29/0.45 topolo503727757_space:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BNF__Def_Orel__fun,type,
% 0.29/0.45 bNF_rel_fun:
% 0.29/0.45 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Denotational__Semantics_OIagree,type,
% 0.29/0.45 denotational_Iagree:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Denotational__Semantics_OVagree,type,
% 0.29/0.45 denotational_Vagree:
% 0.29/0.45 !>[C: $tType] : ( ( product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) ) > ( product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) ) > ( set @ ( sum_sum @ C @ C ) ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Denotational__Semantics_Ointerp_OFunctions,type,
% 0.29/0.45 denota593628964ctions:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType,Z: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ Z ) > A > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Denotational__Semantics_Ois__interp,type,
% 0.29/0.45 denota2077489681interp:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Denotational__Semantics_Osterm__sem,type,
% 0.29/0.45 denota126604975rm_sem:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Oblin__frechet,type,
% 0.29/0.45 frechet_blin_frechet:
% 0.29/0.45 !>[Sf: $tType,Sc: $tType,Sz: $tType] : ( ( frechet_good_interp @ Sf @ Sc @ Sz ) > ( frechet_strm @ Sf @ Sz ) > ( finite_Cartesian_vec @ real @ Sz ) > ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ Sz ) @ real ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Ocr__good__interp,type,
% 0.29/0.45 freche457001096interp:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm,type,
% 0.29/0.45 frechet_cr_strm:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( ( trm @ A @ B ) > ( frechet_strm @ A @ B ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Ogood__interp,type,
% 0.29/0.45 freche227871258interp:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Oraw__interp,type,
% 0.29/0.45 freche229654227interp:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( frechet_good_interp @ A @ B @ C ) > ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Oraw__term,type,
% 0.29/0.45 frechet_raw_term:
% 0.29/0.45 !>[A: $tType,C: $tType] : ( ( frechet_strm @ A @ C ) > ( trm @ A @ C ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Osimple__term,type,
% 0.29/0.45 frechet_simple_term:
% 0.29/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( frechet_strm @ A @ C ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_If,type,
% 0.29/0.45 if:
% 0.29/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.29/0.45 sup_sup:
% 0.29/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Lifting_Orel__pred__comp,type,
% 0.29/0.45 rel_pred_comp:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( B > $o ) > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/0.45 ord_less_eq:
% 0.29/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.29/0.45 top_top:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.29/0.45 product_fst:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Relation_ODomainp,type,
% 0.29/0.45 domainp:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_OCollect,type,
% 0.29/0.45 collect:
% 0.29/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Static__Semantics_OFVT,type,
% 0.29/0.45 static_FVT:
% 0.29/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ ( sum_sum @ C @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Static__Semantics_OSIGT,type,
% 0.29/0.45 static_SIGT:
% 0.29/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Sum__Type_OInl,type,
% 0.29/0.45 sum_Inl:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.29/0.45 sum_rec_sum:
% 0.29/0.45 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Syntax_Odfree,type,
% 0.29/0.45 dfree:
% 0.29/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.29/0.45 times:
% 0.29/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( trm @ A @ C ) > ( trm @ A @ C ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Topological__Spaces_Ocontinuous__on,type,
% 0.29/0.45 topolo2071040574ous_on:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Typedef_Otype__definition,type,
% 0.29/0.45 type_definition:
% 0.29/0.45 !>[B: $tType,A: $tType] : ( ( B > A ) > ( A > B ) > ( set @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_member,type,
% 0.29/0.45 member:
% 0.29/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_I,type,
% 0.29/0.45 i: denota1663640101rp_ext @ a @ c @ b @ product_unit ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_J,type,
% 0.29/0.45 j: denota1663640101rp_ext @ a @ c @ b @ product_unit ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v__092_060nu_062,type,
% 0.29/0.45 nu: product_prod @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v__092_060nu_062_H,type,
% 0.29/0.45 nu2: product_prod @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v__092_060theta_062_092_060_094sub_0621____,type,
% 0.29/0.45 theta_1: trm @ a @ b ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v__092_060theta_062_092_060_094sub_0622____,type,
% 0.29/0.45 theta_2: trm @ a @ b ).
% 0.29/0.45
% 0.29/0.45 % Relevant facts (256)
% 0.29/0.45 thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [I: denota1663640101rp_ext @ a @ B @ C @ product_unit,J: denota1663640101rp_ext @ a @ B @ C @ product_unit] :
% 0.29/0.45 ( ( denotational_Iagree @ a @ B @ C @ I @ J
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
% 0.29/0.45 => ( denotational_Iagree @ a @ B @ C @ I @ J
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % \<open>\<And>J I. Iagree I J {Inl x |x. x \<in> SIGT (Times \<theta>\<^sub>1 \<theta>\<^sub>2)} \<Longrightarrow> Iagree I J {Inl x |x. x \<in> SIGT \<theta>\<^sub>1}\<close>
% 0.29/0.45 thf(fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [I: denota1663640101rp_ext @ a @ B @ C @ product_unit,J: denota1663640101rp_ext @ a @ B @ C @ product_unit] :
% 0.29/0.45 ( ( denotational_Iagree @ a @ B @ C @ I @ J
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
% 0.29/0.45 => ( denotational_Iagree @ a @ B @ C @ I @ J
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % \<open>\<And>J I. Iagree I J {Inl x |x. x \<in> SIGT (Times \<theta>\<^sub>1 \<theta>\<^sub>2)} \<Longrightarrow> Iagree I J {Inl x |x. x \<in> SIGT \<theta>\<^sub>2}\<close>
% 0.29/0.45 thf(fact_2_IA,axiom,
% 0.29/0.45 ( denotational_Iagree @ a @ c @ b @ i @ j
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 0.29/0.45 & ( ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) )
% 0.29/0.45 | ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % IA
% 0.29/0.45 thf(fact_3_dfree__Times_Oprems_I2_J,axiom,
% 0.29/0.45 ( denotational_Iagree @ a @ c @ b @ i @ j
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dfree_Times.prems(2)
% 0.29/0.45 thf(fact_4_dfree__Times_Ohyps_I1_J,axiom,
% 0.29/0.45 dfree @ a @ b @ theta_1 ).
% 0.29/0.45
% 0.29/0.45 % dfree_Times.hyps(1)
% 0.29/0.45 thf(fact_5_sum_Oinject_I1_J,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.29/0.45 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.29/0.45 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.29/0.45 = ( X1 = Y1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % sum.inject(1)
% 0.29/0.45 thf(fact_6_old_Osum_Oinject_I1_J,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,A2: A,A3: A] :
% 0.29/0.45 ( ( ( sum_Inl @ A @ B @ A2 )
% 0.29/0.45 = ( sum_Inl @ A @ B @ A3 ) )
% 0.29/0.45 = ( A2 = A3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.sum.inject(1)
% 0.29/0.45 thf(fact_7_Isubs_I2_J,axiom,
% 0.29/0.45 ! [E: $tType] :
% 0.29/0.45 ( ord_less_eq @ ( set @ ( sum_sum @ a @ E ) )
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ E )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ E] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ E @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) )
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ E )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ E] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ E @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Isubs(2)
% 0.29/0.45 thf(fact_8_Isubs_I1_J,axiom,
% 0.29/0.45 ! [D2: $tType] :
% 0.29/0.45 ( ord_less_eq @ ( set @ ( sum_sum @ a @ D2 ) )
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ D2 )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ D2] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ D2 @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) )
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ D2 )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ D2] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ D2 @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Isubs(1)
% 0.29/0.45 thf(fact_9_Iagree__comm,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [A4: denota1663640101rp_ext @ A @ B @ C @ product_unit,B2: denota1663640101rp_ext @ A @ B @ C @ product_unit,V: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] :
% 0.29/0.45 ( ( denotational_Iagree @ A @ B @ C @ A4 @ B2 @ V )
% 0.29/0.45 => ( denotational_Iagree @ A @ B @ C @ B2 @ A4 @ V ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Iagree_comm
% 0.29/0.45 thf(fact_10_Iagree__refl,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,A4: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] : ( denotational_Iagree @ A @ B @ C @ I @ I @ A4 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Iagree_refl
% 0.29/0.45 thf(fact_11_Inl__inject,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.29/0.45 ( ( ( sum_Inl @ A @ B @ X2 )
% 0.29/0.45 = ( sum_Inl @ A @ B @ Y ) )
% 0.29/0.45 => ( X2 = Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % Inl_inject
% 0.29/0.45 thf(fact_12_IH1,axiom,
% 0.29/0.45 ( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ) )
% 0.29/0.45 => ( ( denotational_Iagree @ a @ c @ b @ i @ j
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) )
% 0.29/0.45 => ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
% 0.29/0.45 = ( denota126604975rm_sem @ a @ c @ b @ j @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % IH1
% 0.29/0.45 thf(fact_13_rel__pred__comp__def,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( rel_pred_comp @ A @ B )
% 0.29/0.45 = ( ^ [R: A > B > $o,P: B > $o,X: A] :
% 0.29/0.45 ? [Y2: B] :
% 0.29/0.45 ( ( R @ X @ Y2 )
% 0.29/0.45 & ( P @ Y2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % rel_pred_comp_def
% 0.29/0.45 thf(fact_14_IH2,axiom,
% 0.29/0.45 ( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ) )
% 0.29/0.45 => ( ( denotational_Iagree @ a @ c @ b @ i @ j
% 0.29/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 0.29/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 0.29/0.45 ? [X: a] :
% 0.29/0.45 ( ( Uu
% 0.29/0.45 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 0.29/0.45 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) )
% 0.29/0.45 => ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
% 0.29/0.45 = ( denota126604975rm_sem @ a @ c @ b @ j @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % IH2
% 0.29/0.45 thf(fact_15_Iagree__Func,axiom,
% 0.29/0.45 ! [B: $tType,C: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ C )
% 0.29/0.45 & ( finite_finite @ B ) )
% 0.29/0.45 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,J: denota1663640101rp_ext @ A @ B @ C @ product_unit,V: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),F: A] :
% 0.29/0.45 ( ( denotational_Iagree @ A @ B @ C @ I @ J @ V )
% 0.29/0.45 => ( ( member @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) @ ( sum_Inl @ A @ ( sum_sum @ B @ C ) @ F ) @ V )
% 0.29/0.45 => ( ( denota593628964ctions @ A @ B @ C @ product_unit @ I @ F )
% 0.29/0.45 = ( denota593628964ctions @ A @ B @ C @ product_unit @ J @ F ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Iagree_Func
% 0.29/0.45 thf(fact_16_raw__interp__inject,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [X2: frechet_good_interp @ A @ B @ C,Y: frechet_good_interp @ A @ B @ C] :
% 0.29/0.45 ( ( ( freche229654227interp @ A @ B @ C @ X2 )
% 0.29/0.45 = ( freche229654227interp @ A @ B @ C @ Y ) )
% 0.29/0.45 = ( X2 = Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_interp_inject
% 0.29/0.45 thf(fact_17_dfree__Times_Ohyps_I2_J,axiom,
% 0.29/0.45 dfree @ a @ b @ theta_2 ).
% 0.29/0.45
% 0.29/0.45 % dfree_Times.hyps(2)
% 0.29/0.45 thf(fact_18_coincidence__sterm,axiom,
% 0.29/0.45 ! [B: $tType,C: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ C )
% 0.29/0.45 & ( finite_finite @ B ) )
% 0.29/0.45 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Theta: trm @ B @ A,I: denota1663640101rp_ext @ B @ C @ A @ product_unit] :
% 0.29/0.45 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ Theta ) )
% 0.29/0.45 => ( ( denota126604975rm_sem @ B @ C @ A @ I @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu ) )
% 0.29/0.45 = ( denota126604975rm_sem @ B @ C @ A @ I @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coincidence_sterm
% 0.29/0.45 thf(fact_19_dfree__Times_Oprems_I1_J,axiom,
% 0.29/0.45 denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % dfree_Times.prems(1)
% 0.29/0.45 thf(fact_20_VAs_I2_J,axiom,
% 0.29/0.45 denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ) ).
% 0.29/0.45
% 0.29/0.45 % VAs(2)
% 0.29/0.45 thf(fact_21_VAs_I1_J,axiom,
% 0.29/0.45 denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ) ).
% 0.29/0.45
% 0.29/0.45 % VAs(1)
% 0.29/0.45 thf(fact_22_VA,axiom,
% 0.29/0.45 denotational_Vagree @ b @ nu @ nu2 @ ( sup_sup @ ( set @ ( sum_sum @ b @ b ) ) @ ( static_FVT @ a @ b @ theta_1 ) @ ( static_FVT @ a @ b @ theta_2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % VA
% 0.29/0.45 thf(fact_23_agree__sub,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( finite_finite @ A )
% 0.29/0.45 => ! [A4: set @ ( sum_sum @ A @ A ),B2: set @ ( sum_sum @ A @ A ),Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Omega: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A )] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ A4 @ B2 )
% 0.29/0.45 => ( ( denotational_Vagree @ A @ Nu @ Omega @ B2 )
% 0.29/0.45 => ( denotational_Vagree @ A @ Nu @ Omega @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % agree_sub
% 0.29/0.45 thf(fact_24_agree__comm,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( finite_finite @ A )
% 0.29/0.45 => ! [A4: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),B2: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),V: set @ ( sum_sum @ A @ A )] :
% 0.29/0.45 ( ( denotational_Vagree @ A @ A4 @ B2 @ V )
% 0.29/0.45 => ( denotational_Vagree @ A @ B2 @ A4 @ V ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % agree_comm
% 0.29/0.45 thf(fact_25_agree__refl,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( finite_finite @ A )
% 0.29/0.45 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),A4: set @ ( sum_sum @ A @ A )] : ( denotational_Vagree @ A @ Nu @ Nu @ A4 ) ) ).
% 0.29/0.45
% 0.29/0.45 % agree_refl
% 0.29/0.45 thf(fact_26_agree__supset,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( finite_finite @ A )
% 0.29/0.45 => ! [B2: set @ ( sum_sum @ A @ A ),A4: set @ ( sum_sum @ A @ A ),Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A )] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ B2 @ A4 )
% 0.29/0.45 => ( ( denotational_Vagree @ A @ Nu @ Nu2 @ A4 )
% 0.29/0.45 => ( denotational_Vagree @ A @ Nu @ Nu2 @ B2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % agree_supset
% 0.29/0.45 thf(fact_27_cr__good__interp__def,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ( ( freche457001096interp @ A @ B @ C )
% 0.29/0.45 = ( ^ [X: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y2: frechet_good_interp @ A @ B @ C] :
% 0.29/0.45 ( X
% 0.29/0.45 = ( freche229654227interp @ A @ B @ C @ Y2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % cr_good_interp_def
% 0.29/0.45 thf(fact_28_dfree__Times__simps,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,A2: trm @ A @ B,B3: trm @ A @ B] :
% 0.29/0.45 ( ( dfree @ A @ B @ ( times @ A @ B @ A2 @ B3 ) )
% 0.29/0.45 = ( ( dfree @ A @ B @ A2 )
% 0.29/0.45 & ( dfree @ A @ B @ B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dfree_Times_simps
% 0.29/0.45 thf(fact_29_simple__term__inject,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,X2: trm @ A @ C,Y: trm @ A @ C] :
% 0.29/0.45 ( ( member @ ( trm @ A @ C ) @ X2 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.29/0.45 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.29/0.45 => ( ( ( frechet_simple_term @ A @ C @ X2 )
% 0.29/0.45 = ( frechet_simple_term @ A @ C @ Y ) )
% 0.29/0.45 = ( X2 = Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % simple_term_inject
% 0.29/0.45 thf(fact_30_simple__term__induct,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,P2: ( frechet_strm @ A @ C ) > $o,X2: frechet_strm @ A @ C] :
% 0.29/0.45 ( ! [Y3: trm @ A @ C] :
% 0.29/0.45 ( ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.29/0.45 => ( P2 @ ( frechet_simple_term @ A @ C @ Y3 ) ) )
% 0.29/0.45 => ( P2 @ X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % simple_term_induct
% 0.29/0.45 thf(fact_31_simple__term__cases,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C] :
% 0.29/0.45 ~ ! [Y3: trm @ A @ C] :
% 0.29/0.45 ( ( X2
% 0.29/0.45 = ( frechet_simple_term @ A @ C @ Y3 ) )
% 0.29/0.45 => ~ ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % simple_term_cases
% 0.29/0.45 thf(fact_32_raw__interp__inverse,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [X2: frechet_good_interp @ A @ B @ C] :
% 0.29/0.45 ( ( freche227871258interp @ A @ B @ C @ ( freche229654227interp @ A @ B @ C @ X2 ) )
% 0.29/0.45 = X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_interp_inverse
% 0.29/0.45 thf(fact_33_raw__term__induct,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,Y: trm @ A @ C,P2: ( trm @ A @ C ) > $o] :
% 0.29/0.45 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.29/0.45 => ( ! [X3: frechet_strm @ A @ C] : ( P2 @ ( frechet_raw_term @ A @ C @ X3 ) )
% 0.29/0.45 => ( P2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_term_induct
% 0.29/0.45 thf(fact_34_raw__term__cases,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 0.29/0.45 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.29/0.45 => ~ ! [X3: frechet_strm @ A @ C] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( frechet_raw_term @ A @ C @ X3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_term_cases
% 0.29/0.45 thf(fact_35_raw__term,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C] : ( member @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C @ X2 ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_term
% 0.29/0.45 thf(fact_36_trm_Oinject_I5_J,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,X51: trm @ A @ C,X52: trm @ A @ C,Y51: trm @ A @ C,Y52: trm @ A @ C] :
% 0.29/0.45 ( ( ( times @ A @ C @ X51 @ X52 )
% 0.29/0.45 = ( times @ A @ C @ Y51 @ Y52 ) )
% 0.29/0.45 = ( ( X51 = Y51 )
% 0.29/0.45 & ( X52 = Y52 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % trm.inject(5)
% 0.29/0.45 thf(fact_37_raw__term__inject,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C,Y: frechet_strm @ A @ C] :
% 0.29/0.45 ( ( ( frechet_raw_term @ A @ C @ X2 )
% 0.29/0.45 = ( frechet_raw_term @ A @ C @ Y ) )
% 0.29/0.45 = ( X2 = Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_term_inject
% 0.29/0.45 thf(fact_38_raw__term__inverse,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C] :
% 0.29/0.45 ( ( frechet_simple_term @ A @ C @ ( frechet_raw_term @ A @ C @ X2 ) )
% 0.29/0.45 = X2 ) ).
% 0.29/0.45
% 0.29/0.45 % raw_term_inverse
% 0.29/0.45 thf(fact_39_simple__term__inverse,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 0.29/0.45 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.29/0.45 => ( ( frechet_raw_term @ A @ C @ ( frechet_simple_term @ A @ C @ Y ) )
% 0.29/0.45 = Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % simple_term_inverse
% 0.29/0.45 thf(fact_40_agree__union,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( finite_finite @ A )
% 0.29/0.45 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Omega: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),A4: set @ ( sum_sum @ A @ A ),B2: set @ ( sum_sum @ A @ A )] :
% 0.29/0.45 ( ( denotational_Vagree @ A @ Nu @ Omega @ A4 )
% 0.29/0.45 => ( ( denotational_Vagree @ A @ Nu @ Omega @ B2 )
% 0.29/0.45 => ( denotational_Vagree @ A @ Nu @ Omega @ ( sup_sup @ ( set @ ( sum_sum @ A @ A ) ) @ A4 @ B2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % agree_union
% 0.29/0.45 thf(fact_41_Iagree__sub,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [A4: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),B2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),I: denota1663640101rp_ext @ A @ B @ C @ product_unit,J: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) ) @ A4 @ B2 )
% 0.29/0.45 => ( ( denotational_Iagree @ A @ B @ C @ I @ J @ B2 )
% 0.29/0.45 => ( denotational_Iagree @ A @ B @ C @ I @ J @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Iagree_sub
% 0.29/0.45 thf(fact_42_dfree_Odfree__Times,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,Theta_1: trm @ A @ C,Theta_2: trm @ A @ C] :
% 0.29/0.45 ( ( dfree @ A @ C @ Theta_1 )
% 0.29/0.45 => ( ( dfree @ A @ C @ Theta_2 )
% 0.29/0.45 => ( dfree @ A @ C @ ( times @ A @ C @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dfree.dfree_Times
% 0.29/0.45 thf(fact_43_cr__strm__def,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( frechet_cr_strm @ A @ B )
% 0.29/0.45 = ( ^ [X: trm @ A @ B,Y2: frechet_strm @ A @ B] :
% 0.29/0.45 ( X
% 0.29/0.45 = ( frechet_raw_term @ A @ B @ Y2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % cr_strm_def
% 0.29/0.45 thf(fact_44_fst__sup,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( sup @ A )
% 0.29/0.45 & ( sup @ B ) )
% 0.29/0.45 => ! [X2: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 0.29/0.45 ( ( product_fst @ A @ B @ ( sup_sup @ ( product_prod @ A @ B ) @ X2 @ Y ) )
% 0.29/0.45 = ( sup_sup @ A @ ( product_fst @ A @ B @ X2 ) @ ( product_fst @ A @ B @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % fst_sup
% 0.29/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,P2: A > $o] :
% 0.29/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.29/0.45 = ( P2 @ A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mem_Collect_eq
% 0.29/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A] :
% 0.29/0.45 ( ( collect @ A
% 0.29/0.45 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.29/0.45 = A4 ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_mem_eq
% 0.29/0.45 thf(fact_47_Collect__cong,axiom,
% 0.29/0.45 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.45 ( ! [X3: A] :
% 0.29/0.45 ( ( P2 @ X3 )
% 0.29/0.45 = ( Q @ X3 ) )
% 0.29/0.45 => ( ( collect @ A @ P2 )
% 0.29/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_cong
% 0.29/0.45 thf(fact_48_ext,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.45 ( ! [X3: A] :
% 0.29/0.45 ( ( F @ X3 )
% 0.29/0.45 = ( G @ X3 ) )
% 0.29/0.45 => ( F = G ) ) ).
% 0.29/0.45
% 0.29/0.45 % ext
% 0.29/0.45 thf(fact_49_Un__subset__iff,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ C2 )
% 0.29/0.45 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 0.29/0.45 & ( ord_less_eq @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_subset_iff
% 0.29/0.45 thf(fact_50_sup_Obounded__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,C3: A,A2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A2 )
% 0.29/0.45 = ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.45 & ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.bounded_iff
% 0.29/0.45 thf(fact_51_le__sup__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X2 @ Y ) @ Z2 )
% 0.29/0.45 = ( ( ord_less_eq @ A @ X2 @ Z2 )
% 0.29/0.45 & ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % le_sup_iff
% 0.29/0.45 thf(fact_52_FVT_Osimps_I5_J,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,F: trm @ A @ C,G: trm @ A @ C] :
% 0.29/0.45 ( ( static_FVT @ A @ C @ ( times @ A @ C @ F @ G ) )
% 0.29/0.45 = ( sup_sup @ ( set @ ( sum_sum @ C @ C ) ) @ ( static_FVT @ A @ C @ F ) @ ( static_FVT @ A @ C @ G ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % FVT.simps(5)
% 0.29/0.45 thf(fact_53_SIGT_Osimps_I5_J,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType,T1: trm @ A @ C,T2: trm @ A @ C] :
% 0.29/0.45 ( ( static_SIGT @ A @ C @ ( times @ A @ C @ T1 @ T2 ) )
% 0.29/0.45 = ( sup_sup @ ( set @ A ) @ ( static_SIGT @ A @ C @ T1 ) @ ( static_SIGT @ A @ C @ T2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % SIGT.simps(5)
% 0.29/0.45 thf(fact_54_type__definition__strm,axiom,
% 0.29/0.45 ! [C: $tType,A: $tType] : ( type_definition @ ( frechet_strm @ A @ C ) @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C ) @ ( frechet_simple_term @ A @ C ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_definition_strm
% 0.29/0.45 thf(fact_55_good__interp__inverse,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.29/0.45 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.29/0.45 => ( ( freche229654227interp @ A @ B @ C @ ( freche227871258interp @ A @ B @ C @ Y ) )
% 0.29/0.45 = Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % good_interp_inverse
% 0.29/0.45 thf(fact_56_raw__interp__induct,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit,P2: ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o] :
% 0.29/0.45 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.29/0.45 => ( ! [X3: frechet_good_interp @ A @ B @ C] : ( P2 @ ( freche229654227interp @ A @ B @ C @ X3 ) )
% 0.29/0.45 => ( P2 @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_interp_induct
% 0.29/0.45 thf(fact_57_raw__interp__cases,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.29/0.45 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.29/0.45 => ~ ! [X3: frechet_good_interp @ A @ B @ C] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( freche229654227interp @ A @ B @ C @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_interp_cases
% 0.29/0.45 thf(fact_58_raw__interp,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [X2: frechet_good_interp @ A @ B @ C] : ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C @ X2 ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % raw_interp
% 0.29/0.45 thf(fact_59_good__interp__inject,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [X2: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.29/0.45 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ X2 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.29/0.45 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.29/0.45 => ( ( ( freche227871258interp @ A @ B @ C @ X2 )
% 0.29/0.45 = ( freche227871258interp @ A @ B @ C @ Y ) )
% 0.29/0.45 = ( X2 = Y ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % good_interp_inject
% 0.29/0.45 thf(fact_60_good__interp__induct,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [P2: ( frechet_good_interp @ A @ B @ C ) > $o,X2: frechet_good_interp @ A @ B @ C] :
% 0.29/0.45 ( ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.29/0.45 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.29/0.45 => ( P2 @ ( freche227871258interp @ A @ B @ C @ Y3 ) ) )
% 0.29/0.45 => ( P2 @ X2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % good_interp_induct
% 0.29/0.45 thf(fact_61_good__interp__cases,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ! [X2: frechet_good_interp @ A @ B @ C] :
% 0.29/0.45 ~ ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.29/0.45 ( ( X2
% 0.29/0.45 = ( freche227871258interp @ A @ B @ C @ Y3 ) )
% 0.29/0.45 => ~ ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % good_interp_cases
% 0.29/0.45 thf(fact_62_subsetI,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ! [X3: A] :
% 0.29/0.45 ( ( member @ A @ X3 @ A4 )
% 0.29/0.45 => ( member @ A @ X3 @ B2 ) )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % subsetI
% 0.29/0.45 thf(fact_63_subset__antisym,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A4 )
% 0.29/0.45 => ( A4 = B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subset_antisym
% 0.29/0.45 thf(fact_64_sup__apply,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ B )
% 0.29/0.45 => ( ( sup_sup @ ( A > B ) )
% 0.29/0.45 = ( ^ [F2: A > B,G2: A > B,X: A] : ( sup_sup @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_apply
% 0.29/0.45 thf(fact_65_sup_Oidem,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ A2 @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.idem
% 0.29/0.45 thf(fact_66_sup__idem,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ X2 @ X2 )
% 0.29/0.45 = X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_idem
% 0.29/0.45 thf(fact_67_sup_Oleft__idem,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) )
% 0.29/0.45 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.left_idem
% 0.29/0.45 thf(fact_68_sup__left__idem,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,Y: A] :
% 0.29/0.45 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) )
% 0.29/0.45 = ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_left_idem
% 0.29/0.45 thf(fact_69_sup_Oright__idem,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ B3 )
% 0.29/0.45 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.right_idem
% 0.29/0.45 thf(fact_70_UnCI,axiom,
% 0.29/0.45 ! [A: $tType,C3: A,B2: set @ A,A4: set @ A] :
% 0.29/0.45 ( ( ~ ( member @ A @ C3 @ B2 )
% 0.29/0.45 => ( member @ A @ C3 @ A4 ) )
% 0.29/0.45 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % UnCI
% 0.29/0.45 thf(fact_71_Un__iff,axiom,
% 0.29/0.45 ! [A: $tType,C3: A,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 0.29/0.45 = ( ( member @ A @ C3 @ A4 )
% 0.29/0.45 | ( member @ A @ C3 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_iff
% 0.29/0.45 thf(fact_72_sup__set__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ( collect @ A
% 0.29/0.45 @ ( sup_sup @ ( A > $o )
% 0.29/0.45 @ ^ [X: A] : ( member @ A @ X @ A5 )
% 0.29/0.45 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_set_def
% 0.29/0.45 thf(fact_73_less__eq__set__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ( ord_less_eq @ ( A > $o )
% 0.29/0.45 @ ^ [X: A] : ( member @ A @ X @ A5 )
% 0.29/0.45 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_eq_set_def
% 0.29/0.45 thf(fact_74_in__mono,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,X2: A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 => ( ( member @ A @ X2 @ A4 )
% 0.29/0.45 => ( member @ A @ X2 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % in_mono
% 0.29/0.45 thf(fact_75_subsetD,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C3: A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 => ( ( member @ A @ C3 @ A4 )
% 0.29/0.45 => ( member @ A @ C3 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subsetD
% 0.29/0.45 thf(fact_76_equalityE,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( A4 = B2 )
% 0.29/0.45 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % equalityE
% 0.29/0.45 thf(fact_77_subset__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ! [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ A5 )
% 0.29/0.45 => ( member @ A @ X @ B4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subset_eq
% 0.29/0.45 thf(fact_78_equalityD1,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( A4 = B2 )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % equalityD1
% 0.29/0.45 thf(fact_79_equalityD2,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( A4 = B2 )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ).
% 0.29/0.45
% 0.29/0.45 % equalityD2
% 0.29/0.45 thf(fact_80_subset__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ! [T3: A] :
% 0.29/0.45 ( ( member @ A @ T3 @ A5 )
% 0.29/0.45 => ( member @ A @ T3 @ B4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subset_iff
% 0.29/0.45 thf(fact_81_subset__refl,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.29/0.45
% 0.29/0.45 % subset_refl
% 0.29/0.45 thf(fact_82_Collect__mono,axiom,
% 0.29/0.45 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.45 ( ! [X3: A] :
% 0.29/0.45 ( ( P2 @ X3 )
% 0.29/0.45 => ( Q @ X3 ) )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_mono
% 0.29/0.45 thf(fact_83_subset__trans,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subset_trans
% 0.29/0.45 thf(fact_84_set__eq__subset,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B4 )
% 0.29/0.45 & ( ord_less_eq @ ( set @ A ) @ B4 @ A5 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % set_eq_subset
% 0.29/0.45 thf(fact_85_Collect__mono__iff,axiom,
% 0.29/0.45 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 0.29/0.45 = ( ! [X: A] :
% 0.29/0.45 ( ( P2 @ X )
% 0.29/0.45 => ( Q @ X ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_mono_iff
% 0.29/0.45 thf(fact_86_inf__sup__aci_I8_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( lattice @ A )
% 0.29/0.45 => ! [X2: A,Y: A] :
% 0.29/0.45 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) )
% 0.29/0.45 = ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % inf_sup_aci(8)
% 0.29/0.45 thf(fact_87_inf__sup__aci_I7_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( lattice @ A )
% 0.29/0.45 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) )
% 0.29/0.45 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X2 @ Z2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % inf_sup_aci(7)
% 0.29/0.45 thf(fact_88_inf__sup__aci_I6_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( lattice @ A )
% 0.29/0.45 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y ) @ Z2 )
% 0.29/0.45 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % inf_sup_aci(6)
% 0.29/0.45 thf(fact_89_inf__sup__aci_I5_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( lattice @ A )
% 0.29/0.45 => ( ( sup_sup @ A )
% 0.29/0.45 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % inf_sup_aci(5)
% 0.29/0.45 thf(fact_90_sup__fun__def,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ B )
% 0.29/0.45 => ( ( sup_sup @ ( A > B ) )
% 0.29/0.45 = ( ^ [F2: A > B,G2: A > B,X: A] : ( sup_sup @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_fun_def
% 0.29/0.45 thf(fact_91_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A4: A,K: A,A2: A,B3: A] :
% 0.29/0.45 ( ( A4
% 0.29/0.45 = ( sup_sup @ A @ K @ A2 ) )
% 0.29/0.45 => ( ( sup_sup @ A @ A4 @ B3 )
% 0.29/0.45 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % boolean_algebra_cancel.sup1
% 0.29/0.45 thf(fact_92_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B2: A,K: A,B3: A,A2: A] :
% 0.29/0.45 ( ( B2
% 0.29/0.45 = ( sup_sup @ A @ K @ B3 ) )
% 0.29/0.45 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.29/0.45 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % boolean_algebra_cancel.sup2
% 0.29/0.45 thf(fact_93_sup_Oassoc,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A,C3: A] :
% 0.29/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ C3 )
% 0.29/0.45 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.assoc
% 0.29/0.45 thf(fact_94_sup__assoc,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y ) @ Z2 )
% 0.29/0.45 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_assoc
% 0.29/0.45 thf(fact_95_sup_Ocommute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ( ( sup_sup @ A )
% 0.29/0.45 = ( ^ [A6: A,B5: A] : ( sup_sup @ A @ B5 @ A6 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.commute
% 0.29/0.45 thf(fact_96_sup__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ( ( sup_sup @ A )
% 0.29/0.45 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_commute
% 0.29/0.45 thf(fact_97_sup_Oleft__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,A2: A,C3: A] :
% 0.29/0.45 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A2 @ C3 ) )
% 0.29/0.45 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.left_commute
% 0.29/0.45 thf(fact_98_sup__left__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) )
% 0.29/0.45 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X2 @ Z2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_left_commute
% 0.29/0.45 thf(fact_99_UnE,axiom,
% 0.29/0.45 ! [A: $tType,C3: A,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 0.29/0.45 => ( ~ ( member @ A @ C3 @ A4 )
% 0.29/0.45 => ( member @ A @ C3 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % UnE
% 0.29/0.45 thf(fact_100_UnI1,axiom,
% 0.29/0.45 ! [A: $tType,C3: A,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( member @ A @ C3 @ A4 )
% 0.29/0.45 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % UnI1
% 0.29/0.45 thf(fact_101_UnI2,axiom,
% 0.29/0.45 ! [A: $tType,C3: A,B2: set @ A,A4: set @ A] :
% 0.29/0.45 ( ( member @ A @ C3 @ B2 )
% 0.29/0.45 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % UnI2
% 0.29/0.45 thf(fact_102_bex__Un,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,P2: A > $o] :
% 0.29/0.45 ( ( ? [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 0.29/0.45 & ( P2 @ X ) ) )
% 0.29/0.45 = ( ? [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ A4 )
% 0.29/0.45 & ( P2 @ X ) )
% 0.29/0.45 | ? [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ B2 )
% 0.29/0.45 & ( P2 @ X ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bex_Un
% 0.29/0.45 thf(fact_103_ball__Un,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,P2: A > $o] :
% 0.29/0.45 ( ( ! [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 0.29/0.45 => ( P2 @ X ) ) )
% 0.29/0.45 = ( ! [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ A4 )
% 0.29/0.45 => ( P2 @ X ) )
% 0.29/0.45 & ! [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ B2 )
% 0.29/0.45 => ( P2 @ X ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ball_Un
% 0.29/0.45 thf(fact_104_Un__assoc,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ C2 )
% 0.29/0.45 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_assoc
% 0.29/0.45 thf(fact_105_Un__absorb,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 0.29/0.45 = A4 ) ).
% 0.29/0.45
% 0.29/0.45 % Un_absorb
% 0.29/0.45 thf(fact_106_Un__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A5 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_commute
% 0.29/0.45 thf(fact_107_Un__left__absorb,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 0.29/0.45 = ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_left_absorb
% 0.29/0.45 thf(fact_108_Un__left__commute,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) )
% 0.29/0.45 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_left_commute
% 0.29/0.45 thf(fact_109_Collect__subset,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,P2: A > $o] :
% 0.29/0.45 ( ord_less_eq @ ( set @ A )
% 0.29/0.45 @ ( collect @ A
% 0.29/0.45 @ ^ [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ A4 )
% 0.29/0.45 & ( P2 @ X ) ) )
% 0.29/0.45 @ A4 ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_subset
% 0.29/0.45 thf(fact_110_Un__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ( collect @ A
% 0.29/0.45 @ ^ [X: A] :
% 0.29/0.45 ( ( member @ A @ X @ A5 )
% 0.29/0.45 | ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_def
% 0.29/0.45 thf(fact_111_Collect__disj__eq,axiom,
% 0.29/0.45 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.45 ( ( collect @ A
% 0.29/0.45 @ ^ [X: A] :
% 0.29/0.45 ( ( P2 @ X )
% 0.29/0.45 | ( Q @ X ) ) )
% 0.29/0.45 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_disj_eq
% 0.29/0.45 thf(fact_112_inf__sup__ord_I4_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( lattice @ A )
% 0.29/0.45 => ! [Y: A,X2: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % inf_sup_ord(4)
% 0.29/0.45 thf(fact_113_inf__sup__ord_I3_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( lattice @ A )
% 0.29/0.45 => ! [X2: A,Y: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % inf_sup_ord(3)
% 0.29/0.45 thf(fact_114_le__supE,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A,X2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X2 )
% 0.29/0.45 => ~ ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.29/0.45 => ~ ( ord_less_eq @ A @ B3 @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % le_supE
% 0.29/0.45 thf(fact_115_le__supI,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,X2: A,B3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.29/0.45 => ( ( ord_less_eq @ A @ B3 @ X2 )
% 0.29/0.45 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % le_supI
% 0.29/0.45 thf(fact_116_sup__ge1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,Y: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_ge1
% 0.29/0.45 thf(fact_117_sup__ge2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [Y: A,X2: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_ge2
% 0.29/0.45 thf(fact_118_le__supI1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,A2: A,B3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ X2 @ A2 )
% 0.29/0.45 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % le_supI1
% 0.29/0.45 thf(fact_119_le__supI2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,B3: A,A2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ X2 @ B3 )
% 0.29/0.45 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % le_supI2
% 0.29/0.45 thf(fact_120_sup_Omono,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [C3: A,A2: A,D3: A,B3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ C3 @ A2 )
% 0.29/0.45 => ( ( ord_less_eq @ A @ D3 @ B3 )
% 0.29/0.45 => ( ord_less_eq @ A @ ( sup_sup @ A @ C3 @ D3 ) @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.mono
% 0.29/0.45 thf(fact_121_sup__mono,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,C3: A,B3: A,D3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.29/0.45 => ( ( ord_less_eq @ A @ B3 @ D3 )
% 0.29/0.45 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ ( sup_sup @ A @ C3 @ D3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_mono
% 0.29/0.45 thf(fact_122_sup__least,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [Y: A,X2: A,Z2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.29/0.45 => ( ( ord_less_eq @ A @ Z2 @ X2 )
% 0.29/0.45 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z2 ) @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_least
% 0.29/0.45 thf(fact_123_le__iff__sup,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ( ( ord_less_eq @ A )
% 0.29/0.45 = ( ^ [X: A,Y2: A] :
% 0.29/0.45 ( ( sup_sup @ A @ X @ Y2 )
% 0.29/0.45 = Y2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % le_iff_sup
% 0.29/0.45 thf(fact_124_sup_OorderE,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,A2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.45 => ( A2
% 0.29/0.45 = ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.orderE
% 0.29/0.45 thf(fact_125_sup_OorderI,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 = ( sup_sup @ A @ A2 @ B3 ) )
% 0.29/0.45 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.orderI
% 0.29/0.45 thf(fact_126_sup__unique,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [F: A > A > A,X2: A,Y: A] :
% 0.29/0.45 ( ! [X3: A,Y3: A] : ( ord_less_eq @ A @ X3 @ ( F @ X3 @ Y3 ) )
% 0.29/0.45 => ( ! [X3: A,Y3: A] : ( ord_less_eq @ A @ Y3 @ ( F @ X3 @ Y3 ) )
% 0.29/0.45 => ( ! [X3: A,Y3: A,Z4: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.29/0.45 => ( ( ord_less_eq @ A @ Z4 @ X3 )
% 0.29/0.45 => ( ord_less_eq @ A @ ( F @ Y3 @ Z4 ) @ X3 ) ) )
% 0.29/0.45 => ( ( sup_sup @ A @ X2 @ Y )
% 0.29/0.45 = ( F @ X2 @ Y ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_unique
% 0.29/0.45 thf(fact_127_sup_Oabsorb1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,A2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.45 => ( ( sup_sup @ A @ A2 @ B3 )
% 0.29/0.45 = A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.absorb1
% 0.29/0.45 thf(fact_128_sup_Oabsorb2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.45 => ( ( sup_sup @ A @ A2 @ B3 )
% 0.29/0.45 = B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.absorb2
% 0.29/0.45 thf(fact_129_sup__absorb1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [Y: A,X2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.29/0.45 => ( ( sup_sup @ A @ X2 @ Y )
% 0.29/0.45 = X2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_absorb1
% 0.29/0.45 thf(fact_130_sup__absorb2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [X2: A,Y: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.45 => ( ( sup_sup @ A @ X2 @ Y )
% 0.29/0.45 = Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup_absorb2
% 0.29/0.45 thf(fact_131_sup_OboundedE,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,C3: A,A2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A2 )
% 0.29/0.45 => ~ ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.45 => ~ ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.boundedE
% 0.29/0.45 thf(fact_132_sup_OboundedI,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,A2: A,C3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.45 => ( ( ord_less_eq @ A @ C3 @ A2 )
% 0.29/0.45 => ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.boundedI
% 0.29/0.45 thf(fact_133_sup_Oorder__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ( ( ord_less_eq @ A )
% 0.29/0.45 = ( ^ [B5: A,A6: A] :
% 0.29/0.45 ( A6
% 0.29/0.45 = ( sup_sup @ A @ A6 @ B5 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.order_iff
% 0.29/0.45 thf(fact_134_sup_Ocobounded1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.cobounded1
% 0.29/0.45 thf(fact_135_sup_Ocobounded2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [B3: A,A2: A] : ( ord_less_eq @ A @ B3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.cobounded2
% 0.29/0.45 thf(fact_136_sup_Oabsorb__iff1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ( ( ord_less_eq @ A )
% 0.29/0.45 = ( ^ [B5: A,A6: A] :
% 0.29/0.45 ( ( sup_sup @ A @ A6 @ B5 )
% 0.29/0.45 = A6 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.absorb_iff1
% 0.29/0.45 thf(fact_137_sup_Oabsorb__iff2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ( ( ord_less_eq @ A )
% 0.29/0.45 = ( ^ [A6: A,B5: A] :
% 0.29/0.45 ( ( sup_sup @ A @ A6 @ B5 )
% 0.29/0.45 = B5 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.absorb_iff2
% 0.29/0.45 thf(fact_138_sup_OcoboundedI1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [C3: A,A2: A,B3: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ C3 @ A2 )
% 0.29/0.45 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.coboundedI1
% 0.29/0.45 thf(fact_139_sup_OcoboundedI2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semilattice_sup @ A )
% 0.29/0.45 => ! [C3: A,B3: A,A2: A] :
% 0.29/0.45 ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.29/0.45 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sup.coboundedI2
% 0.29/0.45 thf(fact_140_fst__mono,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( ord @ A )
% 0.29/0.45 & ( ord @ B ) )
% 0.29/0.45 => ! [X2: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 0.29/0.45 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X2 @ Y )
% 0.29/0.45 => ( ord_less_eq @ A @ ( product_fst @ A @ B @ X2 ) @ ( product_fst @ A @ B @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % fst_mono
% 0.29/0.45 thf(fact_141_Un__mono,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,C2: set @ A,B2: set @ A,D4: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 0.29/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D4 )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C2 @ D4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_mono
% 0.29/0.45 thf(fact_142_Un__least,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,C2: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 0.29/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 0.29/0.45 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_least
% 0.29/0.45 thf(fact_143_Un__upper1,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_upper1
% 0.29/0.45 thf(fact_144_Un__upper2,axiom,
% 0.29/0.45 ! [A: $tType,B2: set @ A,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_upper2
% 0.29/0.45 thf(fact_145_Un__absorb1,axiom,
% 0.29/0.45 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 => ( ( sup_sup @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 = B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_absorb1
% 0.29/0.45 thf(fact_146_Un__absorb2,axiom,
% 0.29/0.45 ! [A: $tType,B2: set @ A,A4: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A4 )
% 0.29/0.45 => ( ( sup_sup @ ( set @ A ) @ A4 @ B2 )
% 0.29/0.45 = A4 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Un_absorb2
% 0.29/0.45 thf(fact_147_subset__UnE,axiom,
% 0.29/0.45 ! [A: $tType,C2: set @ A,A4: set @ A,B2: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 0.29/0.45 => ~ ! [A7: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ A7 @ A4 )
% 0.29/0.45 => ! [B6: set @ A] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B2 )
% 0.29/0.45 => ( C2
% 0.29/0.45 != ( sup_sup @ ( set @ A ) @ A7 @ B6 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subset_UnE
% 0.29/0.45 thf(fact_148_subset__Un__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B4: set @ A] :
% 0.29/0.45 ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 0.29/0.45 = B4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subset_Un_eq
% 0.29/0.45 thf(fact_149_type__definition__good__interp,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ B )
% 0.29/0.45 & ( finite_finite @ C ) )
% 0.29/0.45 => ( type_definition @ ( frechet_good_interp @ A @ B @ C ) @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C ) @ ( freche227871258interp @ A @ B @ C ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_definition_good_interp
% 0.29/0.45 thf(fact_150_order__refl,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % order_refl
% 0.29/0.45 thf(fact_151_sterm__continuous_H,axiom,
% 0.29/0.45 ! [B: $tType,C: $tType,A: $tType] :
% 0.29/0.45 ( ( ( finite_finite @ A )
% 0.29/0.45 & ( finite_finite @ C )
% 0.29/0.45 & ( finite_finite @ B ) )
% 0.29/0.46 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C,S: set @ ( finite_Cartesian_vec @ real @ C )] :
% 0.29/0.46 ( ( denota2077489681interp @ A @ B @ C @ I )
% 0.29/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.29/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ S @ ( denota126604975rm_sem @ A @ B @ C @ I @ Theta ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sterm_continuous'
% 0.29/0.46 thf(fact_152_old_Osum_Osimps_I7_J,axiom,
% 0.29/0.46 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A2: A] :
% 0.29/0.46 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.29/0.46 = ( F1 @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.sum.simps(7)
% 0.29/0.46 thf(fact_153_strm_Orep__transfer,axiom,
% 0.29/0.46 ! [C: $tType,A: $tType] :
% 0.29/0.46 ( bNF_rel_fun @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( trm @ A @ C ) @ ( trm @ A @ C ) @ ( frechet_cr_strm @ A @ C )
% 0.29/0.46 @ ^ [Y4: trm @ A @ C,Z3: trm @ A @ C] : ( Y4 = Z3 )
% 0.29/0.46 @ ^ [X: trm @ A @ C] : X
% 0.29/0.46 @ ( frechet_raw_term @ A @ C ) ) ).
% 0.29/0.46
% 0.29/0.46 % strm.rep_transfer
% 0.29/0.46 thf(fact_154_good__interp_Orep__transfer,axiom,
% 0.29/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A )
% 0.29/0.46 & ( finite_finite @ B )
% 0.29/0.46 & ( finite_finite @ C ) )
% 0.29/0.46 => ( bNF_rel_fun @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche457001096interp @ A @ B @ C )
% 0.29/0.46 @ ^ [Y4: denota1663640101rp_ext @ A @ B @ C @ product_unit,Z3: denota1663640101rp_ext @ A @ B @ C @ product_unit] : ( Y4 = Z3 )
% 0.29/0.46 @ ^ [X: denota1663640101rp_ext @ A @ B @ C @ product_unit] : X
% 0.29/0.46 @ ( freche229654227interp @ A @ B @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % good_interp.rep_transfer
% 0.29/0.46 thf(fact_155_good__interp_Odomain,axiom,
% 0.29/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A )
% 0.29/0.46 & ( finite_finite @ B )
% 0.29/0.46 & ( finite_finite @ C ) )
% 0.29/0.46 => ( ( domainp @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( freche457001096interp @ A @ B @ C ) )
% 0.29/0.46 = ( denota2077489681interp @ A @ B @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % good_interp.domain
% 0.29/0.46 thf(fact_156_strm_Odomain,axiom,
% 0.29/0.46 ! [C: $tType,A: $tType] :
% 0.29/0.46 ( ( domainp @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( frechet_cr_strm @ A @ C ) )
% 0.29/0.46 = ( dfree @ A @ C ) ) ).
% 0.29/0.46
% 0.29/0.46 % strm.domain
% 0.29/0.46 thf(fact_157_predicate1I,axiom,
% 0.29/0.46 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( P2 @ X3 )
% 0.29/0.46 => ( Q @ X3 ) )
% 0.29/0.46 => ( ord_less_eq @ ( A > $o ) @ P2 @ Q ) ) ).
% 0.29/0.46
% 0.29/0.46 % predicate1I
% 0.29/0.46 thf(fact_158_sup1CI,axiom,
% 0.29/0.46 ! [A: $tType,B2: A > $o,X2: A,A4: A > $o] :
% 0.29/0.46 ( ( ~ ( B2 @ X2 )
% 0.29/0.46 => ( A4 @ X2 ) )
% 0.29/0.46 => ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup1CI
% 0.29/0.46 thf(fact_159_fun__mono,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,D: $tType,C: $tType,C2: A > B > $o,A4: A > B > $o,B2: C > D > $o,D4: C > D > $o] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > B > $o ) @ C2 @ A4 )
% 0.29/0.46 => ( ( ord_less_eq @ ( C > D > $o ) @ B2 @ D4 )
% 0.29/0.46 => ( ord_less_eq @ ( ( A > C ) > ( B > D ) > $o ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 ) @ ( bNF_rel_fun @ A @ B @ C @ D @ C2 @ D4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun_mono
% 0.29/0.46 thf(fact_160_predicate1D,axiom,
% 0.29/0.46 ! [A: $tType,P2: A > $o,Q: A > $o,X2: A] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > $o ) @ P2 @ Q )
% 0.29/0.46 => ( ( P2 @ X2 )
% 0.29/0.46 => ( Q @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % predicate1D
% 0.29/0.46 thf(fact_161_rev__predicate1D,axiom,
% 0.29/0.46 ! [A: $tType,P2: A > $o,X2: A,Q: A > $o] :
% 0.29/0.46 ( ( P2 @ X2 )
% 0.29/0.46 => ( ( ord_less_eq @ ( A > $o ) @ P2 @ Q )
% 0.29/0.46 => ( Q @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rev_predicate1D
% 0.29/0.46 thf(fact_162_sup1I2,axiom,
% 0.29/0.46 ! [A: $tType,B2: A > $o,X2: A,A4: A > $o] :
% 0.29/0.46 ( ( B2 @ X2 )
% 0.29/0.46 => ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup1I2
% 0.29/0.46 thf(fact_163_sup1I1,axiom,
% 0.29/0.46 ! [A: $tType,A4: A > $o,X2: A,B2: A > $o] :
% 0.29/0.46 ( ( A4 @ X2 )
% 0.29/0.46 => ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup1I1
% 0.29/0.46 thf(fact_164_sup1E,axiom,
% 0.29/0.46 ! [A: $tType,A4: A > $o,B2: A > $o,X2: A] :
% 0.29/0.46 ( ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 )
% 0.29/0.46 => ( ~ ( A4 @ X2 )
% 0.29/0.46 => ( B2 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup1E
% 0.29/0.46 thf(fact_165_apply__rsp_H,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o,F: A > C,G: B > D,X2: A,Y: B] :
% 0.29/0.46 ( ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 @ F @ G )
% 0.29/0.46 => ( ( R1 @ X2 @ Y )
% 0.29/0.46 => ( R2 @ ( F @ X2 ) @ ( G @ Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % apply_rsp'
% 0.29/0.46 thf(fact_166_typedef__rep__transfer,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,Rep: B > A,Abs: A > B,A4: set @ A,T4: A > B > $o] :
% 0.29/0.46 ( ( type_definition @ B @ A @ Rep @ Abs @ A4 )
% 0.29/0.46 => ( ( T4
% 0.29/0.46 = ( ^ [X: A,Y2: B] :
% 0.29/0.46 ( X
% 0.29/0.46 = ( Rep @ Y2 ) ) ) )
% 0.29/0.46 => ( bNF_rel_fun @ A @ B @ A @ A @ T4
% 0.29/0.46 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 )
% 0.29/0.46 @ ^ [X: A] : X
% 0.29/0.46 @ Rep ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % typedef_rep_transfer
% 0.29/0.46 thf(fact_167_dual__order_Oantisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [B3: A,A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.46 => ( A2 = B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.antisym
% 0.29/0.46 thf(fact_168_dual__order_Oeq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.46 = ( ^ [A6: A,B5: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ B5 @ A6 )
% 0.29/0.46 & ( ord_less_eq @ A @ A6 @ B5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.eq_iff
% 0.29/0.46 thf(fact_169_dual__order_Otrans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [B3: A,A2: A,C3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.29/0.46 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.trans
% 0.29/0.46 thf(fact_170_linorder__wlog,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [P2: A > A > $o,A2: A,B3: A] :
% 0.29/0.46 ( ! [A8: A,B7: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A8 @ B7 )
% 0.29/0.46 => ( P2 @ A8 @ B7 ) )
% 0.29/0.46 => ( ! [A8: A,B7: A] :
% 0.29/0.46 ( ( P2 @ B7 @ A8 )
% 0.29/0.46 => ( P2 @ A8 @ B7 ) )
% 0.29/0.46 => ( P2 @ A2 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linorder_wlog
% 0.29/0.46 thf(fact_171_dual__order_Orefl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.refl
% 0.29/0.46 thf(fact_172_order__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( preorder @ A )
% 0.29/0.46 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.29/0.46 => ( ord_less_eq @ A @ X2 @ Z2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_trans
% 0.29/0.46 thf(fact_173_order__class_Oorder_Oantisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [A2: A,B3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.29/0.46 => ( A2 = B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_class.order.antisym
% 0.29/0.46 thf(fact_174_ord__le__eq__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [A2: A,B3: A,C3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.46 => ( ( B3 = C3 )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ord_le_eq_trans
% 0.29/0.46 thf(fact_175_ord__eq__le__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [A2: A,B3: A,C3: A] :
% 0.29/0.46 ( ( A2 = B3 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ord_eq_le_trans
% 0.29/0.46 thf(fact_176_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.46 = ( ^ [A6: A,B5: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A6 @ B5 )
% 0.29/0.46 & ( ord_less_eq @ A @ B5 @ A6 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_class.order.eq_iff
% 0.29/0.46 thf(fact_177_antisym__conv,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [Y: A,X2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.46 = ( X2 = Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % antisym_conv
% 0.29/0.46 thf(fact_178_le__cases3,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X2: A,Y: A,Z2: A] :
% 0.29/0.46 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ X2 @ Z2 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ X2 @ Z2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X2 ) )
% 0.29/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_cases3
% 0.29/0.46 thf(fact_179_order_Otrans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [A2: A,B3: A,C3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order.trans
% 0.29/0.46 thf(fact_180_le__cases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X2: A,Y: A] :
% 0.29/0.46 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.46 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_cases
% 0.29/0.46 thf(fact_181_eq__refl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( preorder @ A )
% 0.29/0.46 => ! [X2: A,Y: A] :
% 0.29/0.46 ( ( X2 = Y )
% 0.29/0.46 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_refl
% 0.29/0.46 thf(fact_182_linear,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X2: A,Y: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.46 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linear
% 0.29/0.46 thf(fact_183_antisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [X2: A,Y: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.29/0.46 => ( ( ord_less_eq @ A @ Y @ X2 )
% 0.29/0.46 => ( X2 = Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % antisym
% 0.29/0.46 thf(fact_184_eq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.46 = ( ^ [X: A,Y2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.29/0.46 & ( ord_less_eq @ A @ Y2 @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_iff
% 0.29/0.46 thf(fact_185_ord__le__eq__subst,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( ord @ B )
% 0.29/0.46 & ( ord @ A ) )
% 0.29/0.46 => ! [A2: A,B3: A,F: A > B,C3: B] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.46 => ( ( ( F @ B3 )
% 0.29/0.46 = C3 )
% 0.29/0.46 => ( ! [X3: A,Y3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.29/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.46 => ( ord_less_eq @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ord_le_eq_subst
% 0.29/0.46 thf(fact_186_ord__eq__le__subst,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( ord @ B )
% 0.29/0.46 & ( ord @ A ) )
% 0.29/0.46 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( F @ B3 ) )
% 0.29/0.46 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.29/0.46 => ( ! [X3: B,Y3: B] :
% 0.29/0.46 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ord_eq_le_subst
% 0.29/0.46 thf(fact_187_order__subst2,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType] :
% 0.29/0.46 ( ( ( order @ C )
% 0.29/0.46 & ( order @ A ) )
% 0.29/0.46 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.29/0.46 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 0.29/0.46 => ( ! [X3: A,Y3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.29/0.46 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.46 => ( ord_less_eq @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_subst2
% 0.29/0.46 thf(fact_188_order__subst1,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( order @ B )
% 0.29/0.46 & ( order @ A ) )
% 0.29/0.46 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.29/0.46 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.29/0.46 => ( ! [X3: B,Y3: B] :
% 0.29/0.46 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_subst1
% 0.29/0.46 thf(fact_189_le__fun__def,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ord @ B )
% 0.29/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.29/0.46 = ( ^ [F2: A > B,G2: A > B] :
% 0.29/0.46 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_fun_def
% 0.29/0.46 thf(fact_190_le__funI,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ord @ B )
% 0.29/0.46 => ! [F: A > B,G: A > B] :
% 0.29/0.46 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.29/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_funI
% 0.29/0.46 thf(fact_191_le__funE,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ord @ B )
% 0.29/0.46 => ! [F: A > B,G: A > B,X2: A] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.29/0.46 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_funE
% 0.29/0.46 thf(fact_192_le__funD,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ord @ B )
% 0.29/0.46 => ! [F: A > B,G: A > B,X2: A] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.29/0.46 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_funD
% 0.29/0.46 thf(fact_193_sterm__continuous,axiom,
% 0.29/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A )
% 0.29/0.46 & ( finite_finite @ C )
% 0.29/0.46 & ( finite_finite @ B ) )
% 0.29/0.46 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C] :
% 0.29/0.46 ( ( denota2077489681interp @ A @ B @ C @ I )
% 0.29/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.29/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ C ) ) ) @ ( denota126604975rm_sem @ A @ B @ C @ I @ Theta ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sterm_continuous
% 0.29/0.46 thf(fact_194_sup__Un__eq,axiom,
% 0.29/0.46 ! [A: $tType,R3: set @ A,S: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( A > $o )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ R3 )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 0.29/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ R3 @ S ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_Un_eq
% 0.29/0.46 thf(fact_195_pred__subset__eq,axiom,
% 0.29/0.46 ! [A: $tType,R3: set @ A,S: set @ A] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > $o )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ R3 )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 0.29/0.46 = ( ord_less_eq @ ( set @ A ) @ R3 @ S ) ) ).
% 0.29/0.46
% 0.29/0.46 % pred_subset_eq
% 0.29/0.46 thf(fact_196_top__apply,axiom,
% 0.29/0.46 ! [C: $tType,D: $tType] :
% 0.29/0.46 ( ( top @ C )
% 0.29/0.46 => ( ( top_top @ ( D > C ) )
% 0.29/0.46 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % top_apply
% 0.29/0.46 thf(fact_197_UNIV__I,axiom,
% 0.29/0.46 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UNIV_I
% 0.29/0.46 thf(fact_198_predicate2I,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,P2: A > B > $o,Q: A > B > $o] :
% 0.29/0.46 ( ! [X3: A,Y3: B] :
% 0.29/0.46 ( ( P2 @ X3 @ Y3 )
% 0.29/0.46 => ( Q @ X3 @ Y3 ) )
% 0.29/0.46 => ( ord_less_eq @ ( A > B > $o ) @ P2 @ Q ) ) ).
% 0.29/0.46
% 0.29/0.46 % predicate2I
% 0.29/0.46 thf(fact_199_sup__top__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounded_lattice_top @ A )
% 0.29/0.46 => ! [X2: A] :
% 0.29/0.46 ( ( sup_sup @ A @ X2 @ ( top_top @ A ) )
% 0.29/0.46 = ( top_top @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_top_right
% 0.29/0.46 thf(fact_200_sup__top__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounded_lattice_top @ A )
% 0.29/0.46 => ! [X2: A] :
% 0.29/0.46 ( ( sup_sup @ A @ ( top_top @ A ) @ X2 )
% 0.29/0.46 = ( top_top @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_top_left
% 0.29/0.46 thf(fact_201_fst__top,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( top @ A )
% 0.29/0.46 & ( top @ B ) )
% 0.29/0.46 => ( ( product_fst @ A @ B @ ( top_top @ ( product_prod @ A @ B ) ) )
% 0.29/0.46 = ( top_top @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fst_top
% 0.29/0.46 thf(fact_202_predicate2D,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,P2: A > B > $o,Q: A > B > $o,X2: A,Y: B] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > B > $o ) @ P2 @ Q )
% 0.29/0.46 => ( ( P2 @ X2 @ Y )
% 0.29/0.46 => ( Q @ X2 @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % predicate2D
% 0.29/0.46 thf(fact_203_rev__predicate2D,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,P2: A > B > $o,X2: A,Y: B,Q: A > B > $o] :
% 0.29/0.46 ( ( P2 @ X2 @ Y )
% 0.29/0.46 => ( ( ord_less_eq @ ( A > B > $o ) @ P2 @ Q )
% 0.29/0.46 => ( Q @ X2 @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rev_predicate2D
% 0.29/0.46 thf(fact_204_top_Oextremum__uniqueI,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order_top @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 0.29/0.46 => ( A2
% 0.29/0.46 = ( top_top @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % top.extremum_uniqueI
% 0.29/0.46 thf(fact_205_top_Oextremum__unique,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order_top @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( top_top @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % top.extremum_unique
% 0.29/0.46 thf(fact_206_top__greatest,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order_top @ A )
% 0.29/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( top_top @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % top_greatest
% 0.29/0.46 thf(fact_207_subset__UNIV,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % subset_UNIV
% 0.29/0.46 thf(fact_208_Un__UNIV__left,axiom,
% 0.29/0.46 ! [A: $tType,B2: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.29/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_UNIV_left
% 0.29/0.46 thf(fact_209_Un__UNIV__right,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ A4 @ ( top_top @ ( set @ A ) ) )
% 0.29/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_UNIV_right
% 0.29/0.46 thf(fact_210_UNIV__witness,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UNIV_witness
% 0.29/0.46 thf(fact_211_UNIV__eq__I,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A] :
% 0.29/0.46 ( ! [X3: A] : ( member @ A @ X3 @ A4 )
% 0.29/0.46 => ( ( top_top @ ( set @ A ) )
% 0.29/0.46 = A4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % UNIV_eq_I
% 0.29/0.46 thf(fact_212_UNIV__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( top_top @ ( set @ A ) )
% 0.29/0.46 = ( collect @ A
% 0.29/0.46 @ ^ [X: A] : $true ) ) ).
% 0.29/0.46
% 0.29/0.46 % UNIV_def
% 0.29/0.46 thf(fact_213_DomainpE,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,R4: A > B > $o,A2: A] :
% 0.29/0.46 ( ( domainp @ A @ B @ R4 @ A2 )
% 0.29/0.46 => ~ ! [B7: B] :
% 0.29/0.46 ~ ( R4 @ A2 @ B7 ) ) ).
% 0.29/0.46
% 0.29/0.46 % DomainpE
% 0.29/0.46 thf(fact_214_Domainp_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,R4: A > B > $o,A2: A] :
% 0.29/0.46 ( ( domainp @ A @ B @ R4 @ A2 )
% 0.29/0.46 => ~ ! [B7: B] :
% 0.29/0.46 ~ ( R4 @ A2 @ B7 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domainp.cases
% 0.29/0.46 thf(fact_215_Domainp_Osimps,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( domainp @ A @ B )
% 0.29/0.46 = ( ^ [R5: A > B > $o,A6: A] :
% 0.29/0.46 ? [B5: A,C4: B] :
% 0.29/0.46 ( ( A6 = B5 )
% 0.29/0.46 & ( R5 @ B5 @ C4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domainp.simps
% 0.29/0.46 thf(fact_216_Domainp_ODomainI,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,R4: A > B > $o,A2: A,B3: B] :
% 0.29/0.46 ( ( R4 @ A2 @ B3 )
% 0.29/0.46 => ( domainp @ A @ B @ R4 @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domainp.DomainI
% 0.29/0.46 thf(fact_217_Domainp_Oinducts,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,R4: A > B > $o,X2: A,P2: A > $o] :
% 0.29/0.46 ( ( domainp @ A @ B @ R4 @ X2 )
% 0.29/0.46 => ( ! [A8: A,B7: B] :
% 0.29/0.46 ( ( R4 @ A8 @ B7 )
% 0.29/0.46 => ( P2 @ A8 ) )
% 0.29/0.46 => ( P2 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domainp.inducts
% 0.29/0.46 thf(fact_218_fun_Orel__mono,axiom,
% 0.29/0.46 ! [D: $tType,B: $tType,A: $tType,R3: A > B > $o,Ra: A > B > $o] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > B > $o ) @ R3 @ Ra )
% 0.29/0.46 => ( ord_less_eq @ ( ( D > A ) > ( D > B ) > $o )
% 0.29/0.46 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 0.29/0.46 @ R3 )
% 0.29/0.46 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 0.29/0.46 @ Ra ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun.rel_mono
% 0.29/0.46 thf(fact_219_continuous__on__cases__le,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ B ) )
% 0.29/0.46 => ! [S2: set @ A,H: A > real,A2: real,F: A > B,G: A > B] :
% 0.29/0.46 ( ( topolo2071040574ous_on @ A @ B
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [T3: A] :
% 0.29/0.46 ( ( member @ A @ T3 @ S2 )
% 0.29/0.46 & ( ord_less_eq @ real @ ( H @ T3 ) @ A2 ) ) )
% 0.29/0.46 @ F )
% 0.29/0.46 => ( ( topolo2071040574ous_on @ A @ B
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [T3: A] :
% 0.29/0.46 ( ( member @ A @ T3 @ S2 )
% 0.29/0.46 & ( ord_less_eq @ real @ A2 @ ( H @ T3 ) ) ) )
% 0.29/0.46 @ G )
% 0.29/0.46 => ( ( topolo2071040574ous_on @ A @ real @ S2 @ H )
% 0.29/0.46 => ( ! [T5: A] :
% 0.29/0.46 ( ( member @ A @ T5 @ S2 )
% 0.29/0.46 => ( ( ( H @ T5 )
% 0.29/0.46 = A2 )
% 0.29/0.46 => ( ( F @ T5 )
% 0.29/0.46 = ( G @ T5 ) ) ) )
% 0.29/0.46 => ( topolo2071040574ous_on @ A @ B @ S2
% 0.29/0.46 @ ^ [T3: A] : ( if @ B @ ( ord_less_eq @ real @ ( H @ T3 ) @ A2 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_cases_le
% 0.29/0.46 thf(fact_220_continuous__on__cases__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ A )
% 0.29/0.46 => ! [S2: set @ real,A2: real,F: real > A,G: real > A] :
% 0.29/0.46 ( ( topolo2071040574ous_on @ real @ A
% 0.29/0.46 @ ( collect @ real
% 0.29/0.46 @ ^ [T3: real] :
% 0.29/0.46 ( ( member @ real @ T3 @ S2 )
% 0.29/0.46 & ( ord_less_eq @ real @ T3 @ A2 ) ) )
% 0.29/0.46 @ F )
% 0.29/0.46 => ( ( topolo2071040574ous_on @ real @ A
% 0.29/0.46 @ ( collect @ real
% 0.29/0.46 @ ^ [T3: real] :
% 0.29/0.46 ( ( member @ real @ T3 @ S2 )
% 0.29/0.46 & ( ord_less_eq @ real @ A2 @ T3 ) ) )
% 0.29/0.46 @ G )
% 0.29/0.46 => ( ( ( member @ real @ A2 @ S2 )
% 0.29/0.46 => ( ( F @ A2 )
% 0.29/0.46 = ( G @ A2 ) ) )
% 0.29/0.46 => ( topolo2071040574ous_on @ real @ A @ S2
% 0.29/0.46 @ ^ [T3: real] : ( if @ A @ ( ord_less_eq @ real @ T3 @ A2 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_cases_1
% 0.29/0.46 thf(fact_221_agree__UNIV__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( finite_finite @ A )
% 0.29/0.46 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Omega: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A )] :
% 0.29/0.46 ( ( denotational_Vagree @ A @ Nu @ Omega @ ( top_top @ ( set @ ( sum_sum @ A @ A ) ) ) )
% 0.29/0.46 => ( Nu = Omega ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % agree_UNIV_eq
% 0.29/0.46 thf(fact_222_top__empty__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( top_top @ ( A > $o ) )
% 0.29/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % top_empty_eq
% 0.29/0.46 thf(fact_223_top__set__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( top_top @ ( set @ A ) )
% 0.29/0.46 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % top_set_def
% 0.29/0.46 thf(fact_224_fun_Orel__transfer,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,C: $tType,E2: $tType,D: $tType,Sa: A > C > $o,Sc2: B > E2 > $o] :
% 0.29/0.46 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > E2 > $o ) @ ( ( D > A ) > ( D > B ) > $o ) @ ( ( D > C ) > ( D > E2 ) > $o )
% 0.29/0.46 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( E2 > $o ) @ Sa
% 0.29/0.46 @ ( bNF_rel_fun @ B @ E2 @ $o @ $o @ Sc2
% 0.29/0.46 @ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
% 0.29/0.46 @ ( bNF_rel_fun @ ( D > A ) @ ( D > C ) @ ( ( D > B ) > $o ) @ ( ( D > E2 ) > $o )
% 0.29/0.46 @ ( bNF_rel_fun @ D @ D @ A @ C
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 0.29/0.46 @ Sa )
% 0.29/0.46 @ ( bNF_rel_fun @ ( D > B ) @ ( D > E2 ) @ $o @ $o
% 0.29/0.46 @ ( bNF_rel_fun @ D @ D @ B @ E2
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 0.29/0.46 @ Sc2 )
% 0.29/0.46 @ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
% 0.29/0.46 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 ) )
% 0.29/0.46 @ ( bNF_rel_fun @ D @ D @ C @ E2
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun.rel_transfer
% 0.29/0.46 thf(fact_225_fun_Orel__refl,axiom,
% 0.29/0.46 ! [B: $tType,D: $tType,Ra: B > B > $o,X2: D > B] :
% 0.29/0.46 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 0.29/0.46 => ( bNF_rel_fun @ D @ D @ B @ B
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 0.29/0.46 @ Ra
% 0.29/0.46 @ X2
% 0.29/0.46 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun.rel_refl
% 0.29/0.46 thf(fact_226_fun_Orel__eq,axiom,
% 0.29/0.46 ! [A: $tType,D: $tType] :
% 0.29/0.46 ( ( bNF_rel_fun @ D @ D @ A @ A
% 0.29/0.46 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 0.29/0.46 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.46 = ( ^ [Y4: D > A,Z3: D > A] : ( Y4 = Z3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun.rel_eq
% 0.29/0.46 thf(fact_227_frechet__continuous,axiom,
% 0.29/0.46 ! [I: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Theta: trm @ sf @ sz] :
% 0.29/0.46 ( ( denota2077489681interp @ sf @ sc @ sz @ I )
% 0.29/0.46 => ( ( dfree @ sf @ sz @ Theta )
% 0.29/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ sz ) @ ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real ) @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ sz ) ) ) @ ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ I ) @ ( frechet_simple_term @ sf @ sz @ Theta ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % frechet_continuous
% 0.29/0.46 thf(fact_228_rel__funI,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 0.29/0.46 ( ! [X3: A,Y3: B] :
% 0.29/0.46 ( ( A4 @ X3 @ Y3 )
% 0.29/0.46 => ( B2 @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.29/0.46 => ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 @ F @ G ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_funI
% 0.29/0.46 thf(fact_229_top1I,axiom,
% 0.29/0.46 ! [A: $tType,X2: A] : ( top_top @ ( A > $o ) @ X2 ) ).
% 0.29/0.46
% 0.29/0.46 % top1I
% 0.29/0.46 thf(fact_230_rel__funD,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y: B] :
% 0.29/0.46 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 @ F @ G )
% 0.29/0.46 => ( ( A4 @ X2 @ Y )
% 0.29/0.46 => ( B2 @ ( F @ X2 ) @ ( G @ Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_funD
% 0.29/0.46 thf(fact_231_rel__fun__mono,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,X4: A > B > $o,A4: C > D > $o,F: A > C,G: B > D,Y5: A > B > $o,B2: C > D > $o] :
% 0.29/0.46 ( ( bNF_rel_fun @ A @ B @ C @ D @ X4 @ A4 @ F @ G )
% 0.29/0.46 => ( ! [X3: A,Y3: B] :
% 0.29/0.46 ( ( Y5 @ X3 @ Y3 )
% 0.29/0.46 => ( X4 @ X3 @ Y3 ) )
% 0.29/0.46 => ( ! [X3: C,Y3: D] :
% 0.29/0.46 ( ( A4 @ X3 @ Y3 )
% 0.29/0.46 => ( B2 @ X3 @ Y3 ) )
% 0.29/0.46 => ( bNF_rel_fun @ A @ B @ C @ D @ Y5 @ B2 @ F @ G ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_fun_mono
% 0.29/0.46 thf(fact_232_rel__fun__mono_H,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,Y5: A > B > $o,X4: A > B > $o,A4: C > D > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 0.29/0.46 ( ! [X3: A,Y3: B] :
% 0.29/0.46 ( ( Y5 @ X3 @ Y3 )
% 0.29/0.46 => ( X4 @ X3 @ Y3 ) )
% 0.29/0.46 => ( ! [X3: C,Y3: D] :
% 0.29/0.46 ( ( A4 @ X3 @ Y3 )
% 0.29/0.46 => ( B2 @ X3 @ Y3 ) )
% 0.29/0.46 => ( ( bNF_rel_fun @ A @ B @ C @ D @ X4 @ A4 @ F @ G )
% 0.29/0.46 => ( bNF_rel_fun @ A @ B @ C @ D @ Y5 @ B2 @ F @ G ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_fun_mono'
% 0.29/0.46 thf(fact_233_ge__eq__refl,axiom,
% 0.29/0.46 ! [A: $tType,R3: A > A > $o,X2: A] :
% 0.29/0.46 ( ( ord_less_eq @ ( A > A > $o )
% 0.29/0.46 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 )
% 0.29/0.46 @ R3 )
% 0.29/0.46 => ( R3 @ X2 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % ge_eq_refl
% 0.29/0.46 thf(fact_234_refl__ge__eq,axiom,
% 0.29/0.46 ! [A: $tType,R3: A > A > $o] :
% 0.29/0.46 ( ! [X3: A] : ( R3 @ X3 @ X3 )
% 0.29/0.46 => ( ord_less_eq @ ( A > A > $o )
% 0.29/0.46 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 )
% 0.29/0.46 @ R3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % refl_ge_eq
% 0.29/0.46 thf(fact_235_let__rsp,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o] :
% 0.29/0.46 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 ) @ R2 )
% 0.29/0.46 @ ^ [S3: A,F2: A > C] : ( F2 @ S3 )
% 0.29/0.46 @ ^ [S3: B,F2: B > D] : ( F2 @ S3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % let_rsp
% 0.29/0.46 thf(fact_236_Let__transfer,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o] :
% 0.29/0.46 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ A4 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 ) @ B2 )
% 0.29/0.46 @ ^ [S3: A,F2: A > C] : ( F2 @ S3 )
% 0.29/0.46 @ ^ [S3: B,F2: B > D] : ( F2 @ S3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Let_transfer
% 0.29/0.46 thf(fact_237_rel__funD2,axiom,
% 0.29/0.46 ! [B: $tType,C: $tType,A: $tType,A4: A > A > $o,B2: B > C > $o,F: A > B,G: A > C,X2: A] :
% 0.29/0.46 ( ( bNF_rel_fun @ A @ A @ B @ C @ A4 @ B2 @ F @ G )
% 0.29/0.46 => ( ( A4 @ X2 @ X2 )
% 0.29/0.46 => ( B2 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_funD2
% 0.29/0.46 thf(fact_238_rel__funE,axiom,
% 0.29/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y: B] :
% 0.29/0.46 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 @ F @ G )
% 0.29/0.46 => ( ( A4 @ X2 @ Y )
% 0.29/0.46 => ( B2 @ ( F @ X2 ) @ ( G @ Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_funE
% 0.29/0.46 thf(fact_239_Domainp__refl,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( domainp @ A @ B )
% 0.29/0.46 = ( domainp @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domainp_refl
% 0.29/0.46 thf(fact_240_Domainp__iff,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( domainp @ A @ B )
% 0.29/0.46 = ( ^ [T6: A > B > $o,X: A] :
% 0.29/0.46 ? [X5: B] : ( T6 @ X @ X5 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domainp_iff
% 0.29/0.46 thf(fact_241_Domain__eq__top,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( domainp @ A @ A
% 0.29/0.46 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.46 = ( top_top @ ( A > $o ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Domain_eq_top
% 0.29/0.46 thf(fact_242_iso__tuple__UNIV__I,axiom,
% 0.29/0.46 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % iso_tuple_UNIV_I
% 0.29/0.46 thf(fact_243_continuous__on__fst,axiom,
% 0.29/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ B )
% 0.29/0.46 & ( topolo503727757_space @ C ) )
% 0.29/0.46 => ! [S2: set @ A,F: A > ( product_prod @ B @ C )] :
% 0.29/0.46 ( ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S2 @ F )
% 0.29/0.46 => ( topolo2071040574ous_on @ A @ B @ S2
% 0.29/0.46 @ ^ [X: A] : ( product_fst @ B @ C @ ( F @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_fst
% 0.29/0.46 thf(fact_244_continuous__on__cong,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ B ) )
% 0.29/0.46 => ! [S2: set @ A,T7: set @ A,F: A > B,G: A > B] :
% 0.29/0.46 ( ( S2 = T7 )
% 0.29/0.46 => ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ T7 )
% 0.29/0.46 => ( ( F @ X3 )
% 0.29/0.46 = ( G @ X3 ) ) )
% 0.29/0.46 => ( ( topolo2071040574ous_on @ A @ B @ S2 @ F )
% 0.29/0.46 = ( topolo2071040574ous_on @ A @ B @ T7 @ G ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_cong
% 0.29/0.46 thf(fact_245_continuous__on__discrete,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo2133971006pology @ A )
% 0.29/0.46 & ( topolo503727757_space @ B ) )
% 0.29/0.46 => ! [A4: set @ A,F: A > B] : ( topolo2071040574ous_on @ A @ B @ A4 @ F ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_discrete
% 0.29/0.46 thf(fact_246_continuous__on__id,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ A )
% 0.29/0.46 => ! [S2: set @ A] :
% 0.29/0.46 ( topolo2071040574ous_on @ A @ A @ S2
% 0.29/0.46 @ ^ [X: A] : X ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_id
% 0.29/0.46 thf(fact_247_continuous__on__const,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ B ) )
% 0.29/0.46 => ! [S2: set @ A,C3: B] :
% 0.29/0.46 ( topolo2071040574ous_on @ A @ B @ S2
% 0.29/0.46 @ ^ [X: A] : C3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_const
% 0.29/0.46 thf(fact_248_continuous__on__subset,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ B ) )
% 0.29/0.46 => ! [S2: set @ A,F: A > B,T7: set @ A] :
% 0.29/0.46 ( ( topolo2071040574ous_on @ A @ B @ S2 @ F )
% 0.29/0.46 => ( ( ord_less_eq @ ( set @ A ) @ T7 @ S2 )
% 0.29/0.46 => ( topolo2071040574ous_on @ A @ B @ T7 @ F ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_subset
% 0.29/0.46 thf(fact_249_continuous__on__product__then__coordinatewise__UNIV,axiom,
% 0.29/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ C ) )
% 0.29/0.46 => ! [F: A > B > C,I2: B] :
% 0.29/0.46 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ ( top_top @ ( set @ A ) ) @ F )
% 0.29/0.46 => ( topolo2071040574ous_on @ A @ C @ ( top_top @ ( set @ A ) )
% 0.29/0.46 @ ^ [X: A] : ( F @ X @ I2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_product_then_coordinatewise_UNIV
% 0.29/0.46 thf(fact_250_type__copy__ex__RepI,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A,F3: B > $o] :
% 0.29/0.46 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.29/0.46 => ( ( ? [X5: B] : ( F3 @ X5 ) )
% 0.29/0.46 = ( ? [B5: A] : ( F3 @ ( Rep @ B5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % type_copy_ex_RepI
% 0.29/0.46 thf(fact_251_conj__subset__def,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,P2: A > $o,Q: A > $o] :
% 0.29/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( P2 @ X )
% 0.29/0.46 & ( Q @ X ) ) ) )
% 0.29/0.46 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ P2 ) )
% 0.29/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % conj_subset_def
% 0.29/0.46 thf(fact_252_continuous__on__product__then__coordinatewise,axiom,
% 0.29/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ C ) )
% 0.29/0.46 => ! [S: set @ A,F: A > B > C,I2: B] :
% 0.29/0.46 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ S @ F )
% 0.29/0.46 => ( topolo2071040574ous_on @ A @ C @ S
% 0.29/0.46 @ ^ [X: A] : ( F @ X @ I2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_product_then_coordinatewise
% 0.29/0.46 thf(fact_253_continuous__on__coordinatewise__then__product,axiom,
% 0.29/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A )
% 0.29/0.46 & ( topolo503727757_space @ C ) )
% 0.29/0.46 => ! [S: set @ A,F: A > B > C] :
% 0.29/0.46 ( ! [I3: B] :
% 0.29/0.46 ( topolo2071040574ous_on @ A @ C @ S
% 0.29/0.46 @ ^ [X: A] : ( F @ X @ I3 ) )
% 0.29/0.46 => ( topolo2071040574ous_on @ A @ ( B > C ) @ S @ F ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % continuous_on_coordinatewise_then_product
% 0.29/0.46 thf(fact_254_type__copy__obj__one__point__absE,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,S2: A] :
% 0.29/0.46 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.29/0.46 => ~ ! [X3: B] :
% 0.29/0.46 ( S2
% 0.29/0.46 != ( Abs @ X3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % type_copy_obj_one_point_absE
% 0.29/0.46 thf(fact_255_rel__fun__def__butlast,axiom,
% 0.29/0.46 ! [B: $tType,D: $tType,C: $tType,E2: $tType,F4: $tType,A: $tType,R3: A > B > $o,S: C > E2 > $o,T4: D > F4 > $o,F: A > C > D,G: B > E2 > F4] :
% 0.29/0.46 ( ( bNF_rel_fun @ A @ B @ ( C > D ) @ ( E2 > F4 ) @ R3 @ ( bNF_rel_fun @ C @ E2 @ D @ F4 @ S @ T4 ) @ F @ G )
% 0.29/0.46 = ( ! [X: A,Y2: B] :
% 0.29/0.46 ( ( R3 @ X @ Y2 )
% 0.29/0.46 => ( bNF_rel_fun @ C @ E2 @ D @ F4 @ S @ T4 @ ( F @ X ) @ ( G @ Y2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rel_fun_def_butlast
% 0.29/0.46
% 0.29/0.46 % Subclasses (5)
% 0.29/0.46 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( finite_finite @ A )
% 0.29/0.46 => ( type @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ( type @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ( ord @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ( order @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ( preorder @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % Type constructors (87)
% 0.29/0.46 thf(tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( real_V55928688vector @ A9 )
% 0.29/0.46 & ( real_V55928688vector @ A10 ) )
% 0.29/0.46 => ( real_V55928688vector @ ( bounde2145540817linfun @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( ordere890947078_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( real_V55928688vector @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice,axiom,
% 0.29/0.46 bounded_lattice @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Lattices_Obounded__lattice_2,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( bounded_lattice @ A9 )
% 0.29/0.46 & ( bounded_lattice @ A10 ) )
% 0.29/0.46 => ( bounded_lattice @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space_3,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.46 & ( ordere890947078_space @ A10 ) )
% 0.29/0.46 => ( ordere890947078_space @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_4,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( real_V55928688vector @ A9 )
% 0.29/0.46 & ( real_V55928688vector @ A10 ) )
% 0.29/0.46 => ( real_V55928688vector @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_5,axiom,
% 0.29/0.46 ordere890947078_space @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_6,axiom,
% 0.29/0.46 real_V55928688vector @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_7,axiom,
% 0.29/0.46 bounded_lattice @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_8,axiom,
% 0.29/0.46 ! [A9: $tType] : ( bounded_lattice @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Obounded__lattice_9,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( bounded_lattice @ A10 )
% 0.29/0.46 => ( bounded_lattice @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ A10 )
% 0.29/0.46 => ( topolo503727757_space @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( bounded_lattice @ A10 )
% 0.29/0.46 => ( bounded_lattice_top @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A10 )
% 0.29/0.46 => ( semilattice_sup @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( order_top @ A10 )
% 0.29/0.46 => ( order_top @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( preorder @ A10 )
% 0.29/0.46 => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( lattice @ A10 )
% 0.29/0.46 => ( lattice @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( order @ A10 )
% 0.29/0.46 => ( order @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Otop,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( top @ A10 )
% 0.29/0.46 => ( top @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ord @ A10 )
% 0.29/0.46 => ( ord @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Osup,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A10 )
% 0.29/0.46 => ( sup @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_10,axiom,
% 0.29/0.46 ! [A9: $tType] : ( bounded_lattice_top @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_11,axiom,
% 0.29/0.46 ! [A9: $tType] : ( semilattice_sup @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Oorder__top_12,axiom,
% 0.29/0.46 ! [A9: $tType] : ( order_top @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_13,axiom,
% 0.29/0.46 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Finite__Set_Ofinite_14,axiom,
% 0.29/0.46 ! [A9: $tType] :
% 0.29/0.46 ( ( finite_finite @ A9 )
% 0.29/0.46 => ( finite_finite @ ( set @ A9 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Olattice_15,axiom,
% 0.29/0.46 ! [A9: $tType] : ( lattice @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Oorder_16,axiom,
% 0.29/0.46 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Otop_17,axiom,
% 0.29/0.46 ! [A9: $tType] : ( top @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Oord_18,axiom,
% 0.29/0.46 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Osup_19,axiom,
% 0.29/0.46 ! [A9: $tType] : ( sup @ ( set @ A9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_20,axiom,
% 0.29/0.46 topolo503727757_space @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology,axiom,
% 0.29/0.46 topolo2133971006pology @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_21,axiom,
% 0.29/0.46 bounded_lattice_top @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_22,axiom,
% 0.29/0.46 semilattice_sup @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__top_23,axiom,
% 0.29/0.46 order_top @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_24,axiom,
% 0.29/0.46 preorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.29/0.46 linorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Finite__Set_Ofinite_25,axiom,
% 0.29/0.46 finite_finite @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Olattice_26,axiom,
% 0.29/0.46 lattice @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_27,axiom,
% 0.29/0.46 order @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Otop_28,axiom,
% 0.29/0.46 top @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oord_29,axiom,
% 0.29/0.46 ord @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Osup_30,axiom,
% 0.29/0.46 sup @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_31,axiom,
% 0.29/0.46 topolo503727757_space @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Lattices_Osemilattice__sup_32,axiom,
% 0.29/0.46 semilattice_sup @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Opreorder_33,axiom,
% 0.29/0.46 preorder @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Olinorder_34,axiom,
% 0.29/0.46 linorder @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Lattices_Olattice_35,axiom,
% 0.29/0.46 lattice @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Oorder_36,axiom,
% 0.29/0.46 order @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Oord_37,axiom,
% 0.29/0.46 ord @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Lattices_Osup_38,axiom,
% 0.29/0.46 sup @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_39,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( finite_finite @ ( sum_sum @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_40,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A9 )
% 0.29/0.46 & ( topolo503727757_space @ A10 ) )
% 0.29/0.46 => ( topolo503727757_space @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Lattices_Obounded__lattice__top_41,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( bounded_lattice @ A9 )
% 0.29/0.46 & ( bounded_lattice @ A10 ) )
% 0.29/0.46 => ( bounded_lattice_top @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_42,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( semilattice_sup @ A9 )
% 0.29/0.46 & ( semilattice_sup @ A10 ) )
% 0.29/0.46 => ( semilattice_sup @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oorder__top_43,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( order_top @ A9 )
% 0.29/0.46 & ( order_top @ A10 ) )
% 0.29/0.46 => ( order_top @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_44,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( preorder @ A9 )
% 0.29/0.46 & ( preorder @ A10 ) )
% 0.29/0.46 => ( preorder @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_45,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( finite_finite @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Lattices_Olattice_46,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( lattice @ A9 )
% 0.29/0.46 & ( lattice @ A10 ) )
% 0.29/0.46 => ( lattice @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oorder_47,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( order @ A9 )
% 0.29/0.46 & ( order @ A10 ) )
% 0.29/0.46 => ( order @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Orderings_Otop_48,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( top @ A9 )
% 0.29/0.46 & ( top @ A10 ) )
% 0.29/0.46 => ( top @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oord_49,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ord @ A9 )
% 0.29/0.46 & ( ord @ A10 ) )
% 0.29/0.46 => ( ord @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Lattices_Osup_50,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( sup @ A9 )
% 0.29/0.46 & ( sup @ A10 ) )
% 0.29/0.46 => ( sup @ ( product_prod @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_51,axiom,
% 0.29/0.46 bounded_lattice_top @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_52,axiom,
% 0.29/0.46 semilattice_sup @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_53,axiom,
% 0.29/0.46 order_top @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_54,axiom,
% 0.29/0.46 preorder @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_55,axiom,
% 0.29/0.46 linorder @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Finite__Set_Ofinite_56,axiom,
% 0.29/0.46 finite_finite @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Lattices_Olattice_57,axiom,
% 0.29/0.46 lattice @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder_58,axiom,
% 0.29/0.46 order @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Otop_59,axiom,
% 0.29/0.46 top @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oord_60,axiom,
% 0.29/0.46 ord @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Lattices_Osup_61,axiom,
% 0.29/0.46 sup @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_62,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( topolo503727757_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( topolo503727757_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__sup_63,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( semilattice_sup @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_64,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( order @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( preorder @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_65,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( linorder @ A9 )
% 0.29/0.46 & ( cARD_1 @ A10 ) )
% 0.29/0.46 => ( linorder @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_66,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( finite_finite @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_67,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( lattice @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_68,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( order @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( order @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_69,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ord @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( ord @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osup_70,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( sup @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_71,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( real_V55928688vector @ A9 )
% 0.29/0.46 & ( real_V55928688vector @ A10 ) )
% 0.29/0.46 => ( topolo503727757_space @ ( bounde2145540817linfun @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Helper facts (3)
% 0.29/0.46 thf(help_If_3_1_T,axiom,
% 0.29/0.46 ! [P2: $o] :
% 0.29/0.46 ( ( P2 = $true )
% 0.29/0.46 | ( P2 = $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_2_1_T,axiom,
% 0.29/0.46 ! [A: $tType,X2: A,Y: A] :
% 0.29/0.46 ( ( if @ A @ $false @ X2 @ Y )
% 0.29/0.46 = Y ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_1_1_T,axiom,
% 0.29/0.46 ! [A: $tType,X2: A,Y: A] :
% 0.29/0.46 ( ( if @ A @ $true @ X2 @ Y )
% 0.29/0.46 = X2 ) ).
% 0.29/0.46
% 0.29/0.46 % Free types (7)
% 0.29/0.46 thf(tfree_0,hypothesis,
% 0.29/0.46 finite_finite @ b ).
% 0.29/0.46
% 0.29/0.46 thf(tfree_1,hypothesis,
% 0.29/0.46 finite_finite @ a ).
% 0.29/0.46
% 0.29/0.46 thf(tfree_2,hypothesis,
% 0.29/0.46 finite_finite @ c ).
% 0.29/0.46
% 0.29/0.46 thf(tfree_3,hypothesis,
% 0.29/0.46 finite_finite @ sc ).
% 0.29/0.46
% 0.29/0.46 thf(tfree_4,hypothesis,
% 0.29/0.46 finite_finite @ sz ).
% 0.29/0.46
% 0.29/0.46 thf(tfree_5,hypothesis,
% 0.29/0.46 linorder @ sz ).
% 0.29/0.46
% 0.29/0.46 thf(tfree_6,hypothesis,
% 0.29/0.46 finite_finite @ sf ).
% 0.29/0.46
% 0.29/0.46 % Conjectures (1)
% 0.29/0.46 thf(conj_0,conjecture,
% 0.29/0.46 ( denotational_Iagree @ a @ c @ b @ i @ j
% 0.29/0.46 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 0.29/0.46 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 0.29/0.46 ? [X: a] :
% 0.29/0.46 ( ( Uu
% 0.29/0.46 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 0.29/0.46 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.84/1.53 ---- Embedded in THF ---
% 2.84/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.84/1.53 %%% Generated on Tue Feb 24 08:23:56 EST 2026
% 2.84/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.84/1.53 %%% Logic specification used:
% 2.84/1.53 %%% thf(spec, logic, $$dhol).
% 2.84/1.53
% 2.84/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2DTF19346.p
% 2.84/1.53 thf(ty_t_Denotational__Semantics_Ointerp_Ointerp__ext, type, denota1663640101rp_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.84/1.53 thf(ty_t_Frechet__Correctness_Oids_Ogood__interp, type, frechet_good_interp: ($tType > ($tType > ($tType > $tType)))).
% 2.84/1.53 thf(ty_t_Bounded__Linear__Function_Oblinfun, type, bounde2145540817linfun: ($tType > ($tType > $tType))).
% 2.84/1.53 thf(ty_t_Frechet__Correctness_Oids_Ostrm, type, frechet_strm: ($tType > ($tType > $tType))).
% 2.84/1.53 thf(ty_t_Finite__Cartesian__Product_Ovec, type, finite_Cartesian_vec: ($tType > ($tType > $tType))).
% 2.84/1.53 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.84/1.53 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.84/1.53 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.84/1.53 thf(ty_t_Syntax_Otrm, type, trm: ($tType > ($tType > $tType))).
% 2.84/1.53 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.84/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.84/1.53 thf(ty_tf_sz, type, sz: $tType).
% 2.84/1.53 thf(ty_tf_sf, type, sf: $tType).
% 2.84/1.53 thf(ty_tf_sc, type, sc: $tType).
% 2.84/1.53 thf(ty_tf_c, type, c: $tType).
% 2.84/1.53 thf(ty_tf_b, type, b: $tType).
% 2.84/1.53 thf(ty_tf_a, type, a: $tType).
% 2.84/1.53 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector, type, real_V55928688vector: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Cardinality_OCARD__1, type, cARD_1: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space, type, ordere890947078_space: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Lattices_Osup, type, sup: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Topological__Spaces_Odiscrete__topology, type, topolo2133971006pology: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_cl_Topological__Spaces_Otopological__space, type, topolo503727757_space: (!> [A:$tType]: ($o))).
% 2.84/1.53 thf(sy_c_BNF__Def_Orel__fun, type, bNF_rel_fun: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > ((A > B) > ((C > D) > $o))))))).
% 2.84/1.53 thf(sy_c_Denotational__Semantics_OIagree, type, denotational_Iagree: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > ((set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))) > $o)))))).
% 2.84/1.53 thf(sy_c_Denotational__Semantics_OVagree, type, denotational_Vagree: (!> [C:$tType]: ((((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) > (((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) > ((set @ ((sum_sum @ C) @ C)) > $o)))))).
% 2.84/1.53 thf(sy_c_Denotational__Semantics_Ointerp_OFunctions, type, denota593628964ctions: (!> [A:$tType,B:$tType,C:$tType,Z:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ Z) > (A > (((finite_Cartesian_vec @ real) @ C) > real)))))).
% 2.84/1.53 thf(sy_c_Denotational__Semantics_Ois__interp, type, denota2077489681interp: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > $o)))).
% 2.84/1.53 thf(sy_c_Denotational__Semantics_Osterm__sem, type, denota126604975rm_sem: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((trm @ A) @ C) > (((finite_Cartesian_vec @ real) @ C) > real)))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Oblin__frechet, type, frechet_blin_frechet: (!> [Sf:$tType,Sc:$tType,Sz:$tType]: (((((frechet_good_interp @ Sf) @ Sc) @ Sz) > (((frechet_strm @ Sf) @ Sz) > (((finite_Cartesian_vec @ real) @ Sz) > ((bounde2145540817linfun @ ((finite_Cartesian_vec @ real) @ Sz)) @ real))))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Ocr__good__interp, type, freche457001096interp: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > ((((frechet_good_interp @ A) @ B) @ C) > $o))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm, type, frechet_cr_strm: (!> [A:$tType,B:$tType]: ((((trm @ A) @ B) > (((frechet_strm @ A) @ B) > $o))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Ogood__interp, type, freche227871258interp: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((frechet_good_interp @ A) @ B) @ C))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Oraw__interp, type, freche229654227interp: (!> [A:$tType,B:$tType,C:$tType]: (((((frechet_good_interp @ A) @ B) @ C) > ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Oraw__term, type, frechet_raw_term: (!> [A:$tType,C:$tType]: ((((frechet_strm @ A) @ C) > ((trm @ A) @ C))))).
% 2.84/1.53 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Osimple__term, type, frechet_simple_term: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > ((frechet_strm @ A) @ C))))).
% 2.84/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.84/1.53 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.84/1.53 thf(sy_c_Lifting_Orel__pred__comp, type, rel_pred_comp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((B > $o) > (A > $o)))))).
% 2.84/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.84/1.53 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.84/1.53 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 2.84/1.53 thf(sy_c_Relation_ODomainp, type, domainp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > (A > $o))))).
% 2.84/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.84/1.53 thf(sy_c_Static__Semantics_OFVT, type, static_FVT: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (set @ ((sum_sum @ C) @ C)))))).
% 2.84/1.53 thf(sy_c_Static__Semantics_OSIGT, type, static_SIGT: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (set @ A))))).
% 2.84/1.53 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 2.84/1.53 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 2.84/1.53 thf(sy_c_Syntax_Odfree, type, dfree: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > $o)))).
% 2.84/1.53 thf(sy_c_Syntax_Otrm_OTimes, type, times: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (((trm @ A) @ C) > ((trm @ A) @ C)))))).
% 2.84/1.53 thf(sy_c_Topological__Spaces_Ocontinuous__on, type, topolo2071040574ous_on: (!> [A:$tType,B:$tType]: (((set @ A) > ((A > B) > $o))))).
% 2.84/1.53 thf(sy_c_Typedef_Otype__definition, type, type_definition: (!> [B:$tType,A:$tType]: (((B > A) > ((A > B) > ((set @ A) > $o)))))).
% 2.84/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.84/1.53 thf(sy_v_I, type, i: ((((denota1663640101rp_ext @ a) @ c) @ b) @ product_unit)).
% 2.84/1.53 thf(sy_v_J, type, j: ((((denota1663640101rp_ext @ a) @ c) @ b) @ product_unit)).
% 2.84/1.53 thf(sy_v__092_060nu_062, type, nu: ((product_prod @ ((finite_Cartesian_vec @ real) @ b)) @ ((finite_Cartesian_vec @ real) @ b))).
% 2.84/1.53 thf(sy_v__092_060nu_062_H, type, nu2: ((product_prod @ ((finite_Cartesian_vec @ real) @ b)) @ ((finite_Cartesian_vec @ real) @ b))).
% 2.84/1.53 thf(sy_v__092_060theta_062_092_060_094sub_0621____, type, theta_1: ((trm @ a) @ b)).
% 2.84/1.53 thf(sy_v__092_060theta_062_092_060_094sub_0622____, type, theta_2: ((trm @ a) @ b)).
% 2.84/1.53 thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062, axiom, (! [C:$tType,B:$tType]: ((((finite_finite @ B) & (finite_finite @ C)) => (! [I:((((denota1663640101rp_ext @ a) @ B) @ C) @ product_unit),J:((((denota1663640101rp_ext @ a) @ B) @ C) @ product_unit)]: ((((((((denotational_Iagree @ a) @ B) @ C) @ I) @ J) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ B) @ C))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ B) @ C))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ B) @ C)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ ((((times @ a) @ b) @ theta_1) @ theta_2)))))))))) => ((((((denotational_Iagree @ a) @ B) @ C) @ I) @ J) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ B) @ C))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ B) @ C))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ B) @ C)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_1)))))))))))))))).
% 2.84/1.53 thf(fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062, axiom, (! [C:$tType,B:$tType]: ((((finite_finite @ B) & (finite_finite @ C)) => (! [I:((((denota1663640101rp_ext @ a) @ B) @ C) @ product_unit),J:((((denota1663640101rp_ext @ a) @ B) @ C) @ product_unit)]: ((((((((denotational_Iagree @ a) @ B) @ C) @ I) @ J) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ B) @ C))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ B) @ C))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ B) @ C)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ ((((times @ a) @ b) @ theta_1) @ theta_2)))))))))) => ((((((denotational_Iagree @ a) @ B) @ C) @ I) @ J) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ B) @ C))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ B) @ C))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ B) @ C)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_2)))))))))))))))).
% 2.84/1.53 thf(fact_2_IA, axiom, ((((((denotational_Iagree @ a) @ c) @ b) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ c) @ b))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ c) @ b))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ c) @ b)) @ X)) & ((((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_1)) | (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_2))))))))))).
% 2.84/1.53 thf(fact_3_dfree__Times_Oprems_I2_J, axiom, ((((((denotational_Iagree @ a) @ c) @ b) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ c) @ b))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ c) @ b))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ c) @ b)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ ((((times @ a) @ b) @ theta_1) @ theta_2))))))))))).
% 2.84/1.53 thf(fact_4_dfree__Times_Ohyps_I1_J, axiom, (((dfree @ a) @ b) @ theta_1)).
% 2.84/1.53 thf(fact_5_sum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,X1:A,Y1:A]: ((((((sum_Inl @ A) @ B) @ X1) = (((sum_Inl @ A) @ B) @ Y1)) = (X1 = Y1))))).
% 2.84/1.53 thf(fact_6_old_Osum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,A2:A,A3:A]: ((((((sum_Inl @ A) @ B) @ A2) = (((sum_Inl @ A) @ B) @ A3)) = (A2 = A3))))).
% 2.84/1.53 thf(fact_7_Isubs_I2_J, axiom, (! [E:$tType]: ((((ord_less_eq @ (set @ ((sum_sum @ a) @ E))) @ ((collect @ ((sum_sum @ a) @ E)) @ (^ [Uu:((sum_sum @ a) @ E)]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ E) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_2))))))))) @ ((collect @ ((sum_sum @ a) @ E)) @ (^ [Uu:((sum_sum @ a) @ E)]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ E) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ ((((times @ a) @ b) @ theta_1) @ theta_2))))))))))))).
% 2.84/1.53 thf(fact_8_Isubs_I1_J, axiom, (! [D2:$tType]: ((((ord_less_eq @ (set @ ((sum_sum @ a) @ D2))) @ ((collect @ ((sum_sum @ a) @ D2)) @ (^ [Uu:((sum_sum @ a) @ D2)]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ D2) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_1))))))))) @ ((collect @ ((sum_sum @ a) @ D2)) @ (^ [Uu:((sum_sum @ a) @ D2)]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ D2) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ ((((times @ a) @ b) @ theta_1) @ theta_2))))))))))))).
% 2.84/1.53 thf(fact_9_Iagree__comm, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [A4:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),B2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),V:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C)))]: ((((((((denotational_Iagree @ A) @ B) @ C) @ A4) @ B2) @ V) => ((((((denotational_Iagree @ A) @ B) @ C) @ B2) @ A4) @ V)))))))).
% 2.84/1.53 thf(fact_10_Iagree__refl, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [I:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),A4:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C)))]: (((((((denotational_Iagree @ A) @ B) @ C) @ I) @ I) @ A4))))))).
% 2.84/1.53 thf(fact_11_Inl__inject, axiom, (! [B:$tType,A:$tType,X2:A,Y:A]: ((((((sum_Inl @ A) @ B) @ X2) = (((sum_Inl @ A) @ B) @ Y)) => (X2 = Y))))).
% 2.84/1.53 thf(fact_12_IH1, axiom, (((((denotational_Vagree @ b) @ nu) @ nu2) @ (((static_FVT @ a) @ b) @ theta_1)) => (((((((denotational_Iagree @ a) @ c) @ b) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ c) @ b))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ c) @ b))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ c) @ b)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_1))))))))) => (((((((denota126604975rm_sem @ a) @ c) @ b) @ i) @ theta_1) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ b)) @ ((finite_Cartesian_vec @ real) @ b)) @ nu)) = ((((((denota126604975rm_sem @ a) @ c) @ b) @ j) @ theta_1) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ b)) @ ((finite_Cartesian_vec @ real) @ b)) @ nu2)))))).
% 2.84/1.53 thf(fact_13_rel__pred__comp__def, axiom, (! [B:$tType,A:$tType]: ((((rel_pred_comp @ A) @ B) = (^ [R:(A > (B > $o)),P:(B > $o),X:A]: ((? [Y2:B]: ((((R @ X) @ Y2) & (P @ Y2)))))))))).
% 2.84/1.53 thf(fact_14_IH2, axiom, (((((denotational_Vagree @ b) @ nu) @ nu2) @ (((static_FVT @ a) @ b) @ theta_2)) => (((((((denotational_Iagree @ a) @ c) @ b) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ c) @ b))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ c) @ b))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ c) @ b)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_2))))))))) => (((((((denota126604975rm_sem @ a) @ c) @ b) @ i) @ theta_2) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ b)) @ ((finite_Cartesian_vec @ real) @ b)) @ nu)) = ((((((denota126604975rm_sem @ a) @ c) @ b) @ j) @ theta_2) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ b)) @ ((finite_Cartesian_vec @ real) @ b)) @ nu2)))))).
% 2.84/1.53 thf(fact_15_Iagree__Func, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [I:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),J:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),V:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))),F:A]: ((((((((denotational_Iagree @ A) @ B) @ C) @ I) @ J) @ V) => ((((member @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))) @ (((sum_Inl @ A) @ ((sum_sum @ B) @ C)) @ F)) @ V) => (((((((denota593628964ctions @ A) @ B) @ C) @ product_unit) @ I) @ F) = ((((((denota593628964ctions @ A) @ B) @ C) @ product_unit) @ J) @ F)))))))))).
% 2.84/1.53 thf(fact_16_raw__interp__inject, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X2:(((frechet_good_interp @ A) @ B) @ C),Y:(((frechet_good_interp @ A) @ B) @ C)]: (((((((freche229654227interp @ A) @ B) @ C) @ X2) = ((((freche229654227interp @ A) @ B) @ C) @ Y)) = (X2 = Y)))))))).
% 2.84/1.53 thf(fact_17_dfree__Times_Ohyps_I2_J, axiom, (((dfree @ a) @ b) @ theta_2)).
% 2.84/1.53 thf(fact_18_coincidence__sterm, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Theta:((trm @ B) @ A),I:((((denota1663640101rp_ext @ B) @ C) @ A) @ product_unit)]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVT @ B) @ A) @ Theta)) => (((((((denota126604975rm_sem @ B) @ C) @ A) @ I) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ Nu)) = ((((((denota126604975rm_sem @ B) @ C) @ A) @ I) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ Nu2)))))))))).
% 2.84/1.53 thf(fact_19_dfree__Times_Oprems_I1_J, axiom, ((((denotational_Vagree @ b) @ nu) @ nu2) @ (((static_FVT @ a) @ b) @ ((((times @ a) @ b) @ theta_1) @ theta_2)))).
% 2.84/1.53 thf(fact_20_VAs_I2_J, axiom, ((((denotational_Vagree @ b) @ nu) @ nu2) @ (((static_FVT @ a) @ b) @ theta_2))).
% 2.84/1.53 thf(fact_21_VAs_I1_J, axiom, ((((denotational_Vagree @ b) @ nu) @ nu2) @ (((static_FVT @ a) @ b) @ theta_1))).
% 2.84/1.53 thf(fact_22_VA, axiom, ((((denotational_Vagree @ b) @ nu) @ nu2) @ (((sup_sup @ (set @ ((sum_sum @ b) @ b))) @ (((static_FVT @ a) @ b) @ theta_1)) @ (((static_FVT @ a) @ b) @ theta_2)))).
% 2.84/1.53 thf(fact_23_agree__sub, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A4:(set @ ((sum_sum @ A) @ A)),B2:(set @ ((sum_sum @ A) @ A)),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Omega:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A))]: (((((ord_less_eq @ (set @ ((sum_sum @ A) @ A))) @ A4) @ B2) => (((((denotational_Vagree @ A) @ Nu) @ Omega) @ B2) => ((((denotational_Vagree @ A) @ Nu) @ Omega) @ A4))))))))).
% 2.84/1.53 thf(fact_24_agree__comm, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A4:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),B2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),V:(set @ ((sum_sum @ A) @ A))]: ((((((denotational_Vagree @ A) @ A4) @ B2) @ V) => ((((denotational_Vagree @ A) @ B2) @ A4) @ V)))))))).
% 2.84/1.54 thf(fact_25_agree__refl, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),A4:(set @ ((sum_sum @ A) @ A))]: (((((denotational_Vagree @ A) @ Nu) @ Nu) @ A4))))))).
% 2.84/1.54 thf(fact_26_agree__supset, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [B2:(set @ ((sum_sum @ A) @ A)),A4:(set @ ((sum_sum @ A) @ A)),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A))]: (((((ord_less_eq @ (set @ ((sum_sum @ A) @ A))) @ B2) @ A4) => (((((denotational_Vagree @ A) @ Nu) @ Nu2) @ A4) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ B2))))))))).
% 2.84/1.54 thf(fact_27_cr__good__interp__def, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => ((((freche457001096interp @ A) @ B) @ C) = (^ [X:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Y2:(((frechet_good_interp @ A) @ B) @ C)]: ((X = ((((freche229654227interp @ A) @ B) @ C) @ Y2))))))))).
% 2.84/1.54 thf(fact_28_dfree__Times__simps, axiom, (! [B:$tType,A:$tType,A2:((trm @ A) @ B),B3:((trm @ A) @ B)]: (((((dfree @ A) @ B) @ ((((times @ A) @ B) @ A2) @ B3)) = ((((dfree @ A) @ B) @ A2) & (((dfree @ A) @ B) @ B3)))))).
% 2.84/1.54 thf(fact_29_simple__term__inject, axiom, (! [C:$tType,A:$tType,X2:((trm @ A) @ C),Y:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ X2) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (((((frechet_simple_term @ A) @ C) @ X2) = (((frechet_simple_term @ A) @ C) @ Y)) = (X2 = Y))))))).
% 2.84/1.54 thf(fact_30_simple__term__induct, axiom, (! [C:$tType,A:$tType,P2:(((frechet_strm @ A) @ C) > $o),X2:((frechet_strm @ A) @ C)]: (((! [Y3:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ Y3) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (P2 @ (((frechet_simple_term @ A) @ C) @ Y3))))) => (P2 @ X2))))).
% 2.84/1.54 thf(fact_31_simple__term__cases, axiom, (! [C:$tType,A:$tType,X2:((frechet_strm @ A) @ C)]: ((~ ((! [Y3:((trm @ A) @ C)]: (((X2 = (((frechet_simple_term @ A) @ C) @ Y3)) => (~ ((((member @ ((trm @ A) @ C)) @ Y3) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))))))))))))).
% 2.84/1.54 thf(fact_32_raw__interp__inverse, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X2:(((frechet_good_interp @ A) @ B) @ C)]: ((((((freche227871258interp @ A) @ B) @ C) @ ((((freche229654227interp @ A) @ B) @ C) @ X2)) = X2))))))).
% 2.84/1.54 thf(fact_33_raw__term__induct, axiom, (! [C:$tType,A:$tType,Y:((trm @ A) @ C),P2:(((trm @ A) @ C) > $o)]: (((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((! [X3:((frechet_strm @ A) @ C)]: ((P2 @ (((frechet_raw_term @ A) @ C) @ X3)))) => (P2 @ Y)))))).
% 2.84/1.54 thf(fact_34_raw__term__cases, axiom, (! [C:$tType,A:$tType,Y:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (~ ((! [X3:((frechet_strm @ A) @ C)]: ((Y != (((frechet_raw_term @ A) @ C) @ X3)))))))))).
% 2.84/1.54 thf(fact_35_raw__term, axiom, (! [C:$tType,A:$tType,X2:((frechet_strm @ A) @ C)]: ((((member @ ((trm @ A) @ C)) @ (((frechet_raw_term @ A) @ C) @ X2)) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C)))))).
% 2.84/1.54 thf(fact_36_trm_Oinject_I5_J, axiom, (! [C:$tType,A:$tType,X51:((trm @ A) @ C),X52:((trm @ A) @ C),Y51:((trm @ A) @ C),Y52:((trm @ A) @ C)]: (((((((times @ A) @ C) @ X51) @ X52) = ((((times @ A) @ C) @ Y51) @ Y52)) = ((X51 = Y51) & (X52 = Y52)))))).
% 2.84/1.54 thf(fact_37_raw__term__inject, axiom, (! [C:$tType,A:$tType,X2:((frechet_strm @ A) @ C),Y:((frechet_strm @ A) @ C)]: ((((((frechet_raw_term @ A) @ C) @ X2) = (((frechet_raw_term @ A) @ C) @ Y)) = (X2 = Y))))).
% 2.84/1.54 thf(fact_38_raw__term__inverse, axiom, (! [C:$tType,A:$tType,X2:((frechet_strm @ A) @ C)]: (((((frechet_simple_term @ A) @ C) @ (((frechet_raw_term @ A) @ C) @ X2)) = X2)))).
% 2.84/1.54 thf(fact_39_simple__term__inverse, axiom, (! [C:$tType,A:$tType,Y:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((((frechet_raw_term @ A) @ C) @ (((frechet_simple_term @ A) @ C) @ Y)) = Y))))).
% 2.84/1.54 thf(fact_40_agree__union, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Omega:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),A4:(set @ ((sum_sum @ A) @ A)),B2:(set @ ((sum_sum @ A) @ A))]: ((((((denotational_Vagree @ A) @ Nu) @ Omega) @ A4) => (((((denotational_Vagree @ A) @ Nu) @ Omega) @ B2) => ((((denotational_Vagree @ A) @ Nu) @ Omega) @ (((sup_sup @ (set @ ((sum_sum @ A) @ A))) @ A4) @ B2)))))))))).
% 2.84/1.54 thf(fact_41_Iagree__sub, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [A4:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))),B2:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))),I:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),J:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((ord_less_eq @ (set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C)))) @ A4) @ B2) => (((((((denotational_Iagree @ A) @ B) @ C) @ I) @ J) @ B2) => ((((((denotational_Iagree @ A) @ B) @ C) @ I) @ J) @ A4))))))))).
% 2.84/1.54 thf(fact_42_dfree_Odfree__Times, axiom, (! [C:$tType,A:$tType,Theta_1:((trm @ A) @ C),Theta_2:((trm @ A) @ C)]: (((((dfree @ A) @ C) @ Theta_1) => ((((dfree @ A) @ C) @ Theta_2) => (((dfree @ A) @ C) @ ((((times @ A) @ C) @ Theta_1) @ Theta_2))))))).
% 2.84/1.54 thf(fact_43_cr__strm__def, axiom, (! [B:$tType,A:$tType]: ((((frechet_cr_strm @ A) @ B) = (^ [X:((trm @ A) @ B),Y2:((frechet_strm @ A) @ B)]: ((X = (((frechet_raw_term @ A) @ B) @ Y2)))))))).
% 2.84/1.54 thf(fact_44_fst__sup, axiom, (! [B:$tType,A:$tType]: ((((sup @ A) & (sup @ B)) => (! [X2:((product_prod @ A) @ B),Y:((product_prod @ A) @ B)]: (((((product_fst @ A) @ B) @ (((sup_sup @ ((product_prod @ A) @ B)) @ X2) @ Y)) = (((sup_sup @ A) @ (((product_fst @ A) @ B) @ X2)) @ (((product_fst @ A) @ B) @ Y))))))))).
% 2.84/1.54 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.84/1.54 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 2.84/1.54 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.84/1.54 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.84/1.54 thf(fact_49_Un__subset__iff, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) @ C2) = ((((ord_less_eq @ (set @ A)) @ A4) @ C2) & (((ord_less_eq @ (set @ A)) @ B2) @ C2)))))).
% 2.84/1.54 thf(fact_50_sup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,C3:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C3)) @ A2) = ((((ord_less_eq @ A) @ B3) @ A2) & (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 2.84/1.54 thf(fact_51_le__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X2) @ Y)) @ Z2) = ((((ord_less_eq @ A) @ X2) @ Z2) & (((ord_less_eq @ A) @ Y) @ Z2))))))))).
% 2.84/1.54 thf(fact_52_FVT_Osimps_I5_J, axiom, (! [C:$tType,A:$tType,F:((trm @ A) @ C),G:((trm @ A) @ C)]: (((((static_FVT @ A) @ C) @ ((((times @ A) @ C) @ F) @ G)) = (((sup_sup @ (set @ ((sum_sum @ C) @ C))) @ (((static_FVT @ A) @ C) @ F)) @ (((static_FVT @ A) @ C) @ G)))))).
% 2.84/1.54 thf(fact_53_SIGT_Osimps_I5_J, axiom, (! [C:$tType,A:$tType,T1:((trm @ A) @ C),T2:((trm @ A) @ C)]: (((((static_SIGT @ A) @ C) @ ((((times @ A) @ C) @ T1) @ T2)) = (((sup_sup @ (set @ A)) @ (((static_SIGT @ A) @ C) @ T1)) @ (((static_SIGT @ A) @ C) @ T2)))))).
% 2.84/1.54 thf(fact_54_type__definition__strm, axiom, (! [C:$tType,A:$tType]: ((((((type_definition @ ((frechet_strm @ A) @ C)) @ ((trm @ A) @ C)) @ ((frechet_raw_term @ A) @ C)) @ ((frechet_simple_term @ A) @ C)) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C)))))).
% 2.84/1.54 thf(fact_55_good__interp__inverse, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (((((freche229654227interp @ A) @ B) @ C) @ ((((freche227871258interp @ A) @ B) @ C) @ Y)) = Y)))))))).
% 2.84/1.54 thf(fact_56_raw__interp__induct, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),P2:(((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > $o)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((! [X3:(((frechet_good_interp @ A) @ B) @ C)]: ((P2 @ ((((freche229654227interp @ A) @ B) @ C) @ X3)))) => (P2 @ Y))))))))).
% 2.84/1.54 thf(fact_57_raw__interp__cases, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (~ ((! [X3:(((frechet_good_interp @ A) @ B) @ C)]: ((Y != ((((freche229654227interp @ A) @ B) @ C) @ X3))))))))))))).
% 2.84/1.54 thf(fact_58_raw__interp, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X2:(((frechet_good_interp @ A) @ B) @ C)]: ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ ((((freche229654227interp @ A) @ B) @ C) @ X2)) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))))))))).
% 2.84/1.54 thf(fact_59_good__interp__inject, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ X2) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((((((freche227871258interp @ A) @ B) @ C) @ X2) = ((((freche227871258interp @ A) @ B) @ C) @ Y)) = (X2 = Y)))))))))).
% 2.84/1.54 thf(fact_60_good__interp__induct, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [P2:((((frechet_good_interp @ A) @ B) @ C) > $o),X2:(((frechet_good_interp @ A) @ B) @ C)]: (((! [Y3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y3) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (P2 @ ((((freche227871258interp @ A) @ B) @ C) @ Y3))))) => (P2 @ X2)))))))).
% 2.84/1.54 thf(fact_61_good__interp__cases, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X2:(((frechet_good_interp @ A) @ B) @ C)]: ((~ ((! [Y3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((X2 = ((((freche227871258interp @ A) @ B) @ C) @ Y3)) => (~ ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y3) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C)))))))))))))))).
% 2.84/1.54 thf(fact_62_subsetI, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B2))))).
% 2.84/1.54 thf(fact_63_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A4) => (A4 = B2)))))).
% 2.84/1.54 thf(fact_64_sup__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X:A]: ((((sup_sup @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 2.84/1.54 thf(fact_65_sup_Oidem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 2.84/1.54 thf(fact_66_sup__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A]: (((((sup_sup @ A) @ X2) @ X2) = X2))))))).
% 2.84/1.54 thf(fact_67_sup_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B3)) = (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.84/1.54 thf(fact_68_sup__left__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y)) = (((sup_sup @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_69_sup_Oright__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ B3) = (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.84/1.54 thf(fact_70_UnCI, axiom, (! [A:$tType,C3:A,B2:(set @ A),A4:(set @ A)]: ((((~ ((((member @ A) @ C3) @ B2))) => (((member @ A) @ C3) @ A4)) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B2)))))).
% 2.84/1.54 thf(fact_71_Un__iff, axiom, (! [A:$tType,C3:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) = ((((member @ A) @ C3) @ A4) | (((member @ A) @ C3) @ B2)))))).
% 2.84/1.54 thf(fact_72_sup__set__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: (((collect @ A) @ (((sup_sup @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) @ (^ [X:A]: ((((member @ A) @ X) @ B4))))))))))).
% 2.84/1.54 thf(fact_73_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) @ (^ [X:A]: ((((member @ A) @ X) @ B4)))))))))).
% 2.84/1.54 thf(fact_74_in__mono, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B2)))))).
% 2.84/1.54 thf(fact_75_subsetD, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B2)))))).
% 2.84/1.54 thf(fact_76_equalityE, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((A4 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A4)))))))))).
% 2.84/1.54 thf(fact_77_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A5) => (((member @ A) @ X) @ B4)))))))))).
% 2.84/1.54 thf(fact_78_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((A4 = B2) => (((ord_less_eq @ (set @ A)) @ A4) @ B2))))).
% 2.84/1.54 thf(fact_79_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((A4 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A4))))).
% 2.84/1.54 thf(fact_80_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A5) => (((member @ A) @ T3) @ B4)))))))))).
% 2.84/1.54 thf(fact_81_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.84/1.54 thf(fact_82_Collect__mono, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)))))).
% 2.84/1.54 thf(fact_83_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C2) => (((ord_less_eq @ (set @ A)) @ A4) @ C2)))))).
% 2.84/1.54 thf(fact_84_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z3:(set @ A)]: ((Y4 = Z3))) = (^ [A5:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B4) & (((ord_less_eq @ (set @ A)) @ B4) @ A5)))))))).
% 2.84/1.54 thf(fact_85_Collect__mono__iff, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)) = (! [X:A]: (((P2 @ X) => (Q @ X)))))))).
% 2.84/1.54 thf(fact_86_inf__sup__aci_I8_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y)) = (((sup_sup @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_87_inf__sup__aci_I7_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y:A,Z2:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y) @ Z2)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X2) @ Z2))))))))).
% 2.84/1.54 thf(fact_88_inf__sup__aci_I6_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y:A,Z2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X2) @ Y)) @ Z2) = (((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y) @ Z2))))))))).
% 2.84/1.54 thf(fact_89_inf__sup__aci_I5_J, axiom, (! [A:$tType]: (((lattice @ A) => ((sup_sup @ A) = (^ [X:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X)))))))).
% 2.84/1.54 thf(fact_90_sup__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X:A]: ((((sup_sup @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 2.84/1.54 thf(fact_91_boolean__algebra__cancel_Osup1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A4:A,K:A,A2:A,B3:A]: (((A4 = (((sup_sup @ A) @ K) @ A2)) => ((((sup_sup @ A) @ A4) @ B3) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A2) @ B3)))))))))).
% 2.84/1.54 thf(fact_92_boolean__algebra__cancel_Osup2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,K:A,B3:A,A2:A]: (((B2 = (((sup_sup @ A) @ K) @ B3)) => ((((sup_sup @ A) @ A2) @ B2) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A2) @ B3)))))))))).
% 2.84/1.54 thf(fact_93_sup_Oassoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A,C3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ C3) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B3) @ C3))))))))).
% 2.84/1.54 thf(fact_94_sup__assoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y:A,Z2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X2) @ Y)) @ Z2) = (((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y) @ Z2))))))))).
% 2.84/1.54 thf(fact_95_sup_Ocommute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [A6:A,B5:A]: ((((sup_sup @ A) @ B5) @ A6)))))))).
% 2.84/1.54 thf(fact_96_sup__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [X:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X)))))))).
% 2.84/1.54 thf(fact_97_sup_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A2:A,C3:A]: (((((sup_sup @ A) @ B3) @ (((sup_sup @ A) @ A2) @ C3)) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B3) @ C3))))))))).
% 2.84/1.54 thf(fact_98_sup__left__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y:A,Z2:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y) @ Z2)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X2) @ Z2))))))))).
% 2.84/1.54 thf(fact_99_UnE, axiom, (! [A:$tType,C3:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) => ((~ ((((member @ A) @ C3) @ A4))) => (((member @ A) @ C3) @ B2)))))).
% 2.84/1.54 thf(fact_100_UnI1, axiom, (! [A:$tType,C3:A,A4:(set @ A),B2:(set @ A)]: (((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B2)))))).
% 2.84/1.54 thf(fact_101_UnI2, axiom, (! [A:$tType,C3:A,B2:(set @ A),A4:(set @ A)]: (((((member @ A) @ C3) @ B2) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B2)))))).
% 2.84/1.54 thf(fact_102_bex__Un, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),P2:(A > $o)]: (((? [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) & (P2 @ X)))) = ((? [X:A]: (((((member @ A) @ X) @ A4) & (P2 @ X)))) | (? [X:A]: (((((member @ A) @ X) @ B2) & (P2 @ X))))))))).
% 2.84/1.54 thf(fact_103_ball__Un, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),P2:(A > $o)]: (((! [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) => (P2 @ X)))) = ((! [X:A]: (((((member @ A) @ X) @ A4) => (P2 @ X)))) & (! [X:A]: (((((member @ A) @ X) @ B2) => (P2 @ X))))))))).
% 2.84/1.54 thf(fact_104_Un__assoc, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) @ C2) = (((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B2) @ C2)))))).
% 2.84/1.54 thf(fact_105_Un__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ A4) = A4)))).
% 2.84/1.54 thf(fact_106_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: ((((sup_sup @ (set @ A)) @ B4) @ A5))))))).
% 2.84/1.54 thf(fact_107_Un__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) = (((sup_sup @ (set @ A)) @ A4) @ B2))))).
% 2.84/1.54 thf(fact_108_Un__left__commute, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B2) @ C2)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A4) @ C2)))))).
% 2.84/1.54 thf(fact_109_Collect__subset, axiom, (! [A:$tType,A4:(set @ A),P2:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A4) & (P2 @ X)))))) @ A4)))).
% 2.84/1.54 thf(fact_110_Un__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A5) | (((member @ A) @ X) @ B4))))))))))).
% 2.84/1.54 thf(fact_111_Collect__disj__eq, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((P2 @ X) | (Q @ X))))) = (((sup_sup @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)))))).
% 2.84/1.54 thf(fact_112_inf__sup__ord_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [Y:A,X2:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_113_inf__sup__ord_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y:A]: ((((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_114_le__supE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A,X2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ X2) => (~ (((((ord_less_eq @ A) @ A2) @ X2) => (~ ((((ord_less_eq @ A) @ B3) @ X2))))))))))))).
% 2.84/1.54 thf(fact_115_le__supI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,X2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ X2) => ((((ord_less_eq @ A) @ B3) @ X2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ X2))))))))).
% 2.84/1.54 thf(fact_116_sup__ge1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y:A]: ((((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_117_sup__ge2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y:A,X2:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_118_le__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,A2:A,B3:A]: (((((ord_less_eq @ A) @ X2) @ A2) => (((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.84/1.54 thf(fact_119_le__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,B3:A,A2:A]: (((((ord_less_eq @ A) @ X2) @ B3) => (((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.84/1.54 thf(fact_120_sup_Omono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C3:A,A2:A,D3:A,B3:A]: (((((ord_less_eq @ A) @ C3) @ A2) => ((((ord_less_eq @ A) @ D3) @ B3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C3) @ D3)) @ (((sup_sup @ A) @ A2) @ B3)))))))))).
% 2.84/1.54 thf(fact_121_sup__mono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,C3:A,B3:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ C3) => ((((ord_less_eq @ A) @ B3) @ D3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ (((sup_sup @ A) @ C3) @ D3)))))))))).
% 2.84/1.54 thf(fact_122_sup__least, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y:A,X2:A,Z2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => ((((ord_less_eq @ A) @ Z2) @ X2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y) @ Z2)) @ X2))))))))).
% 2.84/1.54 thf(fact_123_le__iff__sup, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [X:A,Y2:A]: (((((sup_sup @ A) @ X) @ Y2) = Y2)))))))).
% 2.84/1.54 thf(fact_124_sup_OorderE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => (A2 = (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.84/1.54 thf(fact_125_sup_OorderI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: (((A2 = (((sup_sup @ A) @ A2) @ B3)) => (((ord_less_eq @ A) @ B3) @ A2)))))))).
% 2.84/1.54 thf(fact_126_sup__unique, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [F:(A > (A > A)),X2:A,Y:A]: (((! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ X3) @ ((F @ X3) @ Y3)))) => ((! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ Y3) @ ((F @ X3) @ Y3)))) => ((! [X3:A,Y3:A,Z4:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((ord_less_eq @ A) @ Z4) @ X3) => (((ord_less_eq @ A) @ ((F @ Y3) @ Z4)) @ X3))))) => ((((sup_sup @ A) @ X2) @ Y) = ((F @ X2) @ Y))))))))))).
% 2.84/1.54 thf(fact_127_sup_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((sup_sup @ A) @ A2) @ B3) = A2)))))))).
% 2.84/1.54 thf(fact_128_sup_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((sup_sup @ A) @ A2) @ B3) = B3)))))))).
% 2.84/1.54 thf(fact_129_sup__absorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y:A,X2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => ((((sup_sup @ A) @ X2) @ Y) = X2)))))))).
% 2.84/1.54 thf(fact_130_sup__absorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((sup_sup @ A) @ X2) @ Y) = Y)))))))).
% 2.84/1.54 thf(fact_131_sup_OboundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,C3:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C3)) @ A2) => (~ (((((ord_less_eq @ A) @ B3) @ A2) => (~ ((((ord_less_eq @ A) @ C3) @ A2))))))))))))).
% 2.84/1.54 thf(fact_132_sup_OboundedI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C3) @ A2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C3)) @ A2))))))))).
% 2.84/1.54 thf(fact_133_sup_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A6:A]: ((A6 = (((sup_sup @ A) @ A6) @ B5))))))))).
% 2.84/1.54 thf(fact_134_sup_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: ((((ord_less_eq @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.84/1.54 thf(fact_135_sup_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A2:A]: ((((ord_less_eq @ A) @ B3) @ (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.84/1.54 thf(fact_136_sup_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A6:A]: (((((sup_sup @ A) @ A6) @ B5) = A6)))))))).
% 2.84/1.54 thf(fact_137_sup_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [A6:A,B5:A]: (((((sup_sup @ A) @ A6) @ B5) = B5)))))))).
% 2.84/1.54 thf(fact_138_sup_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C3:A,A2:A,B3:A]: (((((ord_less_eq @ A) @ C3) @ A2) => (((ord_less_eq @ A) @ C3) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.84/1.54 thf(fact_139_sup_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C3:A,B3:A,A2:A]: (((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.84/1.54 thf(fact_140_fst__mono, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (ord @ B)) => (! [X2:((product_prod @ A) @ B),Y:((product_prod @ A) @ B)]: (((((ord_less_eq @ ((product_prod @ A) @ B)) @ X2) @ Y) => (((ord_less_eq @ A) @ (((product_fst @ A) @ B) @ X2)) @ (((product_fst @ A) @ B) @ Y))))))))).
% 2.84/1.54 thf(fact_141_Un__mono, axiom, (! [A:$tType,A4:(set @ A),C2:(set @ A),B2:(set @ A),D4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C2) => ((((ord_less_eq @ (set @ A)) @ B2) @ D4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) @ (((sup_sup @ (set @ A)) @ C2) @ D4))))))).
% 2.84/1.54 thf(fact_142_Un__least, axiom, (! [A:$tType,A4:(set @ A),C2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C2) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) @ C2)))))).
% 2.84/1.54 thf(fact_143_Un__upper1, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B2))))).
% 2.84/1.54 thf(fact_144_Un__upper2, axiom, (! [A:$tType,B2:(set @ A),A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A4) @ B2))))).
% 2.84/1.54 thf(fact_145_Un__absorb1, axiom, (! [A:$tType,A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B2) => ((((sup_sup @ (set @ A)) @ A4) @ B2) = B2))))).
% 2.84/1.54 thf(fact_146_Un__absorb2, axiom, (! [A:$tType,B2:(set @ A),A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A4) => ((((sup_sup @ (set @ A)) @ A4) @ B2) = A4))))).
% 2.84/1.54 thf(fact_147_subset__UnE, axiom, (! [A:$tType,C2:(set @ A),A4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B2)) => (~ ((! [A7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ A4) => (! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ B2) => (C2 != (((sup_sup @ (set @ A)) @ A7) @ B6)))))))))))))).
% 2.84/1.54 thf(fact_148_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ B4) = B4))))))).
% 2.84/1.54 thf(fact_149_type__definition__good__interp, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (((((type_definition @ (((frechet_good_interp @ A) @ B) @ C)) @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((freche229654227interp @ A) @ B) @ C)) @ (((freche227871258interp @ A) @ B) @ C)) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))))))).
% 2.84/1.54 thf(fact_150_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 2.84/1.54 thf(fact_151_sterm__continuous_H, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [I:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Theta:((trm @ A) @ C),S:(set @ ((finite_Cartesian_vec @ real) @ C))]: ((((((denota2077489681interp @ A) @ B) @ C) @ I) => ((((dfree @ A) @ C) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ C)) @ real) @ S) @ (((((denota126604975rm_sem @ A) @ B) @ C) @ I) @ Theta)))))))))).
% 2.84/1.54 thf(fact_152_old_Osum_Osimps_I7_J, axiom, (! [B:$tType,T:$tType,A:$tType,F1:(A > T),F22:(B > T),A2:A]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ A2)) = (F1 @ A2))))).
% 2.84/1.54 thf(fact_153_strm_Orep__transfer, axiom, (! [C:$tType,A:$tType]: (((((((((bNF_rel_fun @ ((trm @ A) @ C)) @ ((frechet_strm @ A) @ C)) @ ((trm @ A) @ C)) @ ((trm @ A) @ C)) @ ((frechet_cr_strm @ A) @ C)) @ (^ [Y4:((trm @ A) @ C),Z3:((trm @ A) @ C)]: ((Y4 = Z3)))) @ (^ [X:((trm @ A) @ C)]: (X))) @ ((frechet_raw_term @ A) @ C))))).
% 2.84/1.54 thf(fact_154_good__interp_Orep__transfer, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => ((((((((bNF_rel_fun @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((frechet_good_interp @ A) @ B) @ C)) @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((freche457001096interp @ A) @ B) @ C)) @ (^ [Y4:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Z3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: ((Y4 = Z3)))) @ (^ [X:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (X))) @ (((freche229654227interp @ A) @ B) @ C)))))).
% 2.84/1.54 thf(fact_155_good__interp_Odomain, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => ((((domainp @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((frechet_good_interp @ A) @ B) @ C)) @ (((freche457001096interp @ A) @ B) @ C)) = (((denota2077489681interp @ A) @ B) @ C)))))).
% 2.84/1.54 thf(fact_156_strm_Odomain, axiom, (! [C:$tType,A:$tType]: (((((domainp @ ((trm @ A) @ C)) @ ((frechet_strm @ A) @ C)) @ ((frechet_cr_strm @ A) @ C)) = ((dfree @ A) @ C))))).
% 2.84/1.54 thf(fact_157_predicate1I, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) => (Q @ X3)))) => (((ord_less_eq @ (A > $o)) @ P2) @ Q))))).
% 2.84/1.54 thf(fact_158_sup1CI, axiom, (! [A:$tType,B2:(A > $o),X2:A,A4:(A > $o)]: ((((~ ((B2 @ X2))) => (A4 @ X2)) => ((((sup_sup @ (A > $o)) @ A4) @ B2) @ X2))))).
% 2.84/1.54 thf(fact_159_fun__mono, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,C2:(A > (B > $o)),A4:(A > (B > $o)),B2:(C > (D > $o)),D4:(C > (D > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ C2) @ A4) => ((((ord_less_eq @ (C > (D > $o))) @ B2) @ D4) => (((ord_less_eq @ ((A > C) > ((B > D) > $o))) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B2)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ C2) @ D4))))))).
% 2.84/1.54 thf(fact_160_predicate1D, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o),X2:A]: (((((ord_less_eq @ (A > $o)) @ P2) @ Q) => ((P2 @ X2) => (Q @ X2)))))).
% 2.84/1.54 thf(fact_161_rev__predicate1D, axiom, (! [A:$tType,P2:(A > $o),X2:A,Q:(A > $o)]: (((P2 @ X2) => ((((ord_less_eq @ (A > $o)) @ P2) @ Q) => (Q @ X2)))))).
% 2.84/1.54 thf(fact_162_sup1I2, axiom, (! [A:$tType,B2:(A > $o),X2:A,A4:(A > $o)]: (((B2 @ X2) => ((((sup_sup @ (A > $o)) @ A4) @ B2) @ X2))))).
% 2.84/1.54 thf(fact_163_sup1I1, axiom, (! [A:$tType,A4:(A > $o),X2:A,B2:(A > $o)]: (((A4 @ X2) => ((((sup_sup @ (A > $o)) @ A4) @ B2) @ X2))))).
% 2.84/1.54 thf(fact_164_sup1E, axiom, (! [A:$tType,A4:(A > $o),B2:(A > $o),X2:A]: ((((((sup_sup @ (A > $o)) @ A4) @ B2) @ X2) => ((~ ((A4 @ X2))) => (B2 @ X2)))))).
% 2.84/1.54 thf(fact_165_apply__rsp_H, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (B > $o)),R2:(C > (D > $o)),F:(A > C),G:(B > D),X2:A,Y:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ R1) @ R2) @ F) @ G) => (((R1 @ X2) @ Y) => ((R2 @ (F @ X2)) @ (G @ Y))))))).
% 2.84/1.54 thf(fact_166_typedef__rep__transfer, axiom, (! [A:$tType,B:$tType,Rep:(B > A),Abs:(A > B),A4:(set @ A),T4:(A > (B > $o))]: (((((((type_definition @ B) @ A) @ Rep) @ Abs) @ A4) => ((T4 = (^ [X:A,Y2:B]: ((X = (Rep @ Y2))))) => ((((((((bNF_rel_fun @ A) @ B) @ A) @ A) @ T4) @ (^ [Y4:A,Z3:A]: ((Y4 = Z3)))) @ (^ [X:A]: (X))) @ Rep)))))).
% 2.84/1.54 thf(fact_167_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ A2) @ B3) => (A2 = B3))))))))).
% 2.84/1.54 thf(fact_168_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A6:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A6) & (((ord_less_eq @ A) @ A6) @ B5))))))))).
% 2.84/1.54 thf(fact_169_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 2.84/1.54 thf(fact_170_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:(A > (A > $o)),A2:A,B3:A]: (((! [A8:A,B7:A]: (((((ord_less_eq @ A) @ A8) @ B7) => ((P2 @ A8) @ B7)))) => ((! [A8:A,B7:A]: ((((P2 @ B7) @ A8) => ((P2 @ A8) @ B7)))) => ((P2 @ A2) @ B3))))))))).
% 2.84/1.54 thf(fact_171_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.84/1.54 thf(fact_172_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X2) @ Z2))))))))).
% 2.84/1.54 thf(fact_173_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ A2) => (A2 = B3))))))))).
% 2.84/1.54 thf(fact_174_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((B3 = C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.84/1.54 thf(fact_175_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C3:A]: (((A2 = B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.84/1.54 thf(fact_176_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A6:A,B5:A]: (((((ord_less_eq @ A) @ A6) @ B5) & (((ord_less_eq @ A) @ B5) @ A6))))))))).
% 2.84/1.54 thf(fact_177_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y) = (X2 = Y))))))))).
% 2.84/1.54 thf(fact_178_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z2)))) => (((((ord_less_eq @ A) @ X2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X2)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y))))))))))))))))).
% 2.84/1.54 thf(fact_179_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.84/1.54 thf(fact_180_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y))) => (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 2.84/1.54 thf(fact_181_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((X2 = Y) => (((ord_less_eq @ A) @ X2) @ Y)))))))).
% 2.84/1.54 thf(fact_182_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) | (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 2.84/1.54 thf(fact_183_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ X2) => (X2 = Y))))))))).
% 2.84/1.54 thf(fact_184_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) & (((ord_less_eq @ A) @ Y2) @ X))))))))).
% 2.84/1.54 thf(fact_185_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B3:A,F:(A > B),C3:B]: (((((ord_less_eq @ A) @ A2) @ B3) => (((F @ B3) = C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C3)))))))))).
% 2.84/1.54 thf(fact_186_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((A2 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C3))))))))))).
% 2.84/1.54 thf(fact_187_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B3:A,F:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C3)))))))))).
% 2.84/1.54 thf(fact_188_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C3))))))))))).
% 2.84/1.54 thf(fact_189_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))))).
% 2.84/1.54 thf(fact_190_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.84/1.54 thf(fact_191_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 2.84/1.54 thf(fact_192_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 2.84/1.54 thf(fact_193_sterm__continuous, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [I:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Theta:((trm @ A) @ C)]: ((((((denota2077489681interp @ A) @ B) @ C) @ I) => ((((dfree @ A) @ C) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ C)) @ real) @ (top_top @ (set @ ((finite_Cartesian_vec @ real) @ C)))) @ (((((denota126604975rm_sem @ A) @ B) @ C) @ I) @ Theta)))))))))).
% 2.84/1.54 thf(fact_194_sup__Un__eq, axiom, (! [A:$tType,R3:(set @ A),S:(set @ A)]: (((((sup_sup @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R3)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (^ [X:A]: ((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ R3) @ S)))))))).
% 2.84/1.54 thf(fact_195_pred__subset__eq, axiom, (! [A:$tType,R3:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R3)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (((ord_less_eq @ (set @ A)) @ R3) @ S))))).
% 2.84/1.54 thf(fact_196_top__apply, axiom, (! [C:$tType,D:$tType]: (((top @ C) => ((top_top @ (D > C)) = (^ [X:D]: ((top_top @ C)))))))).
% 2.84/1.54 thf(fact_197_UNIV__I, axiom, (! [A:$tType,X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))).
% 2.84/1.54 thf(fact_198_predicate2I, axiom, (! [B:$tType,A:$tType,P2:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X3:A,Y3:B]: ((((P2 @ X3) @ Y3) => ((Q @ X3) @ Y3)))) => (((ord_less_eq @ (A > (B > $o))) @ P2) @ Q))))).
% 2.84/1.54 thf(fact_199_sup__top__right, axiom, (! [A:$tType]: (((bounded_lattice_top @ A) => (! [X2:A]: (((((sup_sup @ A) @ X2) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.84/1.54 thf(fact_200_sup__top__left, axiom, (! [A:$tType]: (((bounded_lattice_top @ A) => (! [X2:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X2) = (top_top @ A)))))))).
% 2.84/1.54 thf(fact_201_fst__top, axiom, (! [B:$tType,A:$tType]: ((((top @ A) & (top @ B)) => ((((product_fst @ A) @ B) @ (top_top @ ((product_prod @ A) @ B))) = (top_top @ A)))))).
% 2.84/1.54 thf(fact_202_predicate2D, axiom, (! [A:$tType,B:$tType,P2:(A > (B > $o)),Q:(A > (B > $o)),X2:A,Y:B]: (((((ord_less_eq @ (A > (B > $o))) @ P2) @ Q) => (((P2 @ X2) @ Y) => ((Q @ X2) @ Y)))))).
% 2.84/1.54 thf(fact_203_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P2:(A > (B > $o)),X2:A,Y:B,Q:(A > (B > $o))]: ((((P2 @ X2) @ Y) => ((((ord_less_eq @ (A > (B > $o))) @ P2) @ Q) => ((Q @ X2) @ Y)))))).
% 2.84/1.54 thf(fact_204_top_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_top @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A2) => (A2 = (top_top @ A))))))))).
% 2.84/1.54 thf(fact_205_top_Oextremum__unique, axiom, (! [A:$tType]: (((order_top @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A2) = (A2 = (top_top @ A))))))))).
% 2.84/1.54 thf(fact_206_top__greatest, axiom, (! [A:$tType]: (((order_top @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ (top_top @ A)))))))).
% 2.84/1.54 thf(fact_207_subset__UNIV, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ (top_top @ (set @ A)))))).
% 2.84/1.54 thf(fact_208_Un__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = (top_top @ (set @ A)))))).
% 2.84/1.54 thf(fact_209_Un__UNIV__right, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.84/1.54 thf(fact_210_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.84/1.54 thf(fact_211_UNIV__eq__I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A4))) => ((top_top @ (set @ A)) = A4))))).
% 2.84/1.54 thf(fact_212_UNIV__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (^ [X:A]: ($true))))))).
% 2.84/1.54 thf(fact_213_DomainpE, axiom, (! [A:$tType,B:$tType,R4:(A > (B > $o)),A2:A]: ((((((domainp @ A) @ B) @ R4) @ A2) => (~ ((! [B7:B]: ((~ (((R4 @ A2) @ B7))))))))))).
% 2.84/1.54 thf(fact_214_Domainp_Ocases, axiom, (! [A:$tType,B:$tType,R4:(A > (B > $o)),A2:A]: ((((((domainp @ A) @ B) @ R4) @ A2) => (~ ((! [B7:B]: ((~ (((R4 @ A2) @ B7))))))))))).
% 2.84/1.54 thf(fact_215_Domainp_Osimps, axiom, (! [B:$tType,A:$tType]: ((((domainp @ A) @ B) = (^ [R5:(A > (B > $o)),A6:A]: ((? [B5:A,C4:B]: (((A6 = B5) & ((R5 @ B5) @ C4)))))))))).
% 2.84/1.54 thf(fact_216_Domainp_ODomainI, axiom, (! [B:$tType,A:$tType,R4:(A > (B > $o)),A2:A,B3:B]: ((((R4 @ A2) @ B3) => ((((domainp @ A) @ B) @ R4) @ A2))))).
% 2.84/1.54 thf(fact_217_Domainp_Oinducts, axiom, (! [B:$tType,A:$tType,R4:(A > (B > $o)),X2:A,P2:(A > $o)]: ((((((domainp @ A) @ B) @ R4) @ X2) => ((! [A8:A,B7:B]: ((((R4 @ A8) @ B7) => (P2 @ A8)))) => (P2 @ X2)))))).
% 2.84/1.54 thf(fact_218_fun_Orel__mono, axiom, (! [D:$tType,B:$tType,A:$tType,R3:(A > (B > $o)),Ra:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ R3) @ Ra) => (((ord_less_eq @ ((D > A) > ((D > B) > $o))) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))) @ R3)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))) @ Ra)))))).
% 2.84/1.54 thf(fact_219_continuous__on__cases__le, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S2:(set @ A),H:(A > real),A2:real,F:(A > B),G:(A > B)]: ((((((topolo2071040574ous_on @ A) @ B) @ ((collect @ A) @ (^ [T3:A]: (((((member @ A) @ T3) @ S2) & (((ord_less_eq @ real) @ (H @ T3)) @ A2)))))) @ F) => (((((topolo2071040574ous_on @ A) @ B) @ ((collect @ A) @ (^ [T3:A]: (((((member @ A) @ T3) @ S2) & (((ord_less_eq @ real) @ A2) @ (H @ T3))))))) @ G) => (((((topolo2071040574ous_on @ A) @ real) @ S2) @ H) => ((! [T5:A]: (((((member @ A) @ T5) @ S2) => (((H @ T5) = A2) => ((F @ T5) = (G @ T5)))))) => ((((topolo2071040574ous_on @ A) @ B) @ S2) @ (^ [T3:A]: (((((if @ B) @ (((ord_less_eq @ real) @ (H @ T3)) @ A2)) @ (F @ T3)) @ (G @ T3))))))))))))))).
% 2.84/1.54 thf(fact_220_continuous__on__cases__1, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => (! [S2:(set @ real),A2:real,F:(real > A),G:(real > A)]: ((((((topolo2071040574ous_on @ real) @ A) @ ((collect @ real) @ (^ [T3:real]: (((((member @ real) @ T3) @ S2) & (((ord_less_eq @ real) @ T3) @ A2)))))) @ F) => (((((topolo2071040574ous_on @ real) @ A) @ ((collect @ real) @ (^ [T3:real]: (((((member @ real) @ T3) @ S2) & (((ord_less_eq @ real) @ A2) @ T3)))))) @ G) => (((((member @ real) @ A2) @ S2) => ((F @ A2) = (G @ A2))) => ((((topolo2071040574ous_on @ real) @ A) @ S2) @ (^ [T3:real]: (((((if @ A) @ (((ord_less_eq @ real) @ T3) @ A2)) @ (F @ T3)) @ (G @ T3)))))))))))))).
% 2.84/1.54 thf(fact_221_agree__UNIV__eq, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Omega:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A))]: ((((((denotational_Vagree @ A) @ Nu) @ Omega) @ (top_top @ (set @ ((sum_sum @ A) @ A)))) => (Nu = Omega)))))))).
% 2.84/1.54 thf(fact_222_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A))))))))).
% 2.84/1.54 thf(fact_223_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.84/1.54 thf(fact_224_fun_Orel__transfer, axiom, (! [B:$tType,A:$tType,C:$tType,E2:$tType,D:$tType,Sa:(A > (C > $o)),Sc2:(B > (E2 > $o))]: (((((((((bNF_rel_fun @ (A > (B > $o))) @ (C > (E2 > $o))) @ ((D > A) > ((D > B) > $o))) @ ((D > C) > ((D > E2) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ (B > $o)) @ (E2 > $o)) @ Sa) @ ((((((bNF_rel_fun @ B) @ E2) @ $o) @ $o) @ Sc2) @ (^ [Y4:$o,Z3:$o]: ((Y4 = Z3)))))) @ ((((((bNF_rel_fun @ (D > A)) @ (D > C)) @ ((D > B) > $o)) @ ((D > E2) > $o)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ C) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))) @ Sa)) @ ((((((bNF_rel_fun @ (D > B)) @ (D > E2)) @ $o) @ $o) @ ((((((bNF_rel_fun @ D) @ D) @ B) @ E2) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))) @ Sc2)) @ (^ [Y4:$o,Z3:$o]: ((Y4 = Z3)))))) @ (((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3))))) @ (((((bNF_rel_fun @ D) @ D) @ C) @ E2) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))))))).
% 2.84/1.54 thf(fact_225_fun_Orel__refl, axiom, (! [B:$tType,D:$tType,Ra:(B > (B > $o)),X2:(D > B)]: (((! [X3:B]: (((Ra @ X3) @ X3))) => ((((((((bNF_rel_fun @ D) @ D) @ B) @ B) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))) @ Ra) @ X2) @ X2))))).
% 2.84/1.54 thf(fact_226_fun_Orel__eq, axiom, (! [A:$tType,D:$tType]: ((((((((bNF_rel_fun @ D) @ D) @ A) @ A) @ (^ [Y4:D,Z3:D]: ((Y4 = Z3)))) @ (^ [Y4:A,Z3:A]: ((Y4 = Z3)))) = (^ [Y4:(D > A),Z3:(D > A)]: ((Y4 = Z3))))))).
% 2.84/1.54 thf(fact_227_frechet__continuous, axiom, (! [I:((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit),Theta:((trm @ sf) @ sz)]: ((((((denota2077489681interp @ sf) @ sc) @ sz) @ I) => ((((dfree @ sf) @ sz) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ sz)) @ ((bounde2145540817linfun @ ((finite_Cartesian_vec @ real) @ sz)) @ real)) @ (top_top @ (set @ ((finite_Cartesian_vec @ real) @ sz)))) @ (((((frechet_blin_frechet @ sf) @ sc) @ sz) @ ((((freche227871258interp @ sf) @ sc) @ sz) @ I)) @ (((frechet_simple_term @ sf) @ sz) @ Theta)))))))).
% 2.84/1.54 thf(fact_228_rel__funI, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D)]: (((! [X3:A,Y3:B]: ((((A4 @ X3) @ Y3) => ((B2 @ (F @ X3)) @ (G @ Y3))))) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B2) @ F) @ G))))).
% 2.84/1.54 thf(fact_229_top1I, axiom, (! [A:$tType,X2:A]: (((top_top @ (A > $o)) @ X2)))).
% 2.84/1.54 thf(fact_230_rel__funD, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D),X2:A,Y:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B2) @ F) @ G) => (((A4 @ X2) @ Y) => ((B2 @ (F @ X2)) @ (G @ Y))))))).
% 2.84/1.54 thf(fact_231_rel__fun__mono, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,X4:(A > (B > $o)),A4:(C > (D > $o)),F:(A > C),G:(B > D),Y5:(A > (B > $o)),B2:(C > (D > $o))]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ X4) @ A4) @ F) @ G) => ((! [X3:A,Y3:B]: ((((Y5 @ X3) @ Y3) => ((X4 @ X3) @ Y3)))) => ((! [X3:C,Y3:D]: ((((A4 @ X3) @ Y3) => ((B2 @ X3) @ Y3)))) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ Y5) @ B2) @ F) @ G))))))).
% 2.84/1.54 thf(fact_232_rel__fun__mono_H, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,Y5:(A > (B > $o)),X4:(A > (B > $o)),A4:(C > (D > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D)]: (((! [X3:A,Y3:B]: ((((Y5 @ X3) @ Y3) => ((X4 @ X3) @ Y3)))) => ((! [X3:C,Y3:D]: ((((A4 @ X3) @ Y3) => ((B2 @ X3) @ Y3)))) => (((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ X4) @ A4) @ F) @ G) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ Y5) @ B2) @ F) @ G))))))).
% 2.84/1.54 thf(fact_233_ge__eq__refl, axiom, (! [A:$tType,R3:(A > (A > $o)),X2:A]: (((((ord_less_eq @ (A > (A > $o))) @ (^ [Y4:A,Z3:A]: ((Y4 = Z3)))) @ R3) => ((R3 @ X2) @ X2))))).
% 2.84/1.54 thf(fact_234_refl__ge__eq, axiom, (! [A:$tType,R3:(A > (A > $o))]: (((! [X3:A]: (((R3 @ X3) @ X3))) => (((ord_less_eq @ (A > (A > $o))) @ (^ [Y4:A,Z3:A]: ((Y4 = Z3)))) @ R3))))).
% 2.84/1.54 thf(fact_235_let__rsp, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (B > $o)),R2:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((A > C) > C)) @ ((B > D) > D)) @ R1) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ C) @ D) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ R1) @ R2)) @ R2)) @ (^ [S3:A,F2:(A > C)]: ((F2 @ S3)))) @ (^ [S3:B,F2:(B > D)]: ((F2 @ S3))))))).
% 2.84/1.54 thf(fact_236_Let__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B2:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((A > C) > C)) @ ((B > D) > D)) @ A4) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ C) @ D) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B2)) @ B2)) @ (^ [S3:A,F2:(A > C)]: ((F2 @ S3)))) @ (^ [S3:B,F2:(B > D)]: ((F2 @ S3))))))).
% 2.84/1.54 thf(fact_237_rel__funD2, axiom, (! [B:$tType,C:$tType,A:$tType,A4:(A > (A > $o)),B2:(B > (C > $o)),F:(A > B),G:(A > C),X2:A]: ((((((((((bNF_rel_fun @ A) @ A) @ B) @ C) @ A4) @ B2) @ F) @ G) => (((A4 @ X2) @ X2) => ((B2 @ (F @ X2)) @ (G @ X2))))))).
% 2.84/1.54 thf(fact_238_rel__funE, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D),X2:A,Y:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B2) @ F) @ G) => (((A4 @ X2) @ Y) => ((B2 @ (F @ X2)) @ (G @ Y))))))).
% 2.84/1.54 thf(fact_239_Domainp__refl, axiom, (! [B:$tType,A:$tType]: ((((domainp @ A) @ B) = ((domainp @ A) @ B))))).
% 2.84/1.54 thf(fact_240_Domainp__iff, axiom, (! [B:$tType,A:$tType]: ((((domainp @ A) @ B) = (^ [T6:(A > (B > $o)),X:A]: ((? [X5:B]: (((T6 @ X) @ X5))))))))).
% 2.84/1.54 thf(fact_241_Domain__eq__top, axiom, (! [A:$tType]: (((((domainp @ A) @ A) @ (^ [Y4:A,Z3:A]: ((Y4 = Z3)))) = (top_top @ (A > $o)))))).
% 2.84/1.54 thf(fact_242_iso__tuple__UNIV__I, axiom, (! [A:$tType,X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))).
% 2.84/1.54 thf(fact_243_continuous__on__fst, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((topolo503727757_space @ A) & ((topolo503727757_space @ B) & (topolo503727757_space @ C))) => (! [S2:(set @ A),F:(A > ((product_prod @ B) @ C))]: ((((((topolo2071040574ous_on @ A) @ ((product_prod @ B) @ C)) @ S2) @ F) => ((((topolo2071040574ous_on @ A) @ B) @ S2) @ (^ [X:A]: ((((product_fst @ B) @ C) @ (F @ X)))))))))))).
% 2.84/1.54 thf(fact_244_continuous__on__cong, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S2:(set @ A),T7:(set @ A),F:(A > B),G:(A > B)]: (((S2 = T7) => ((! [X3:A]: (((((member @ A) @ X3) @ T7) => ((F @ X3) = (G @ X3))))) => (((((topolo2071040574ous_on @ A) @ B) @ S2) @ F) = ((((topolo2071040574ous_on @ A) @ B) @ T7) @ G)))))))))).
% 2.84/1.54 thf(fact_245_continuous__on__discrete, axiom, (! [B:$tType,A:$tType]: ((((topolo2133971006pology @ A) & (topolo503727757_space @ B)) => (! [A4:(set @ A),F:(A > B)]: (((((topolo2071040574ous_on @ A) @ B) @ A4) @ F))))))).
% 2.84/1.54 thf(fact_246_continuous__on__id, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => (! [S2:(set @ A)]: (((((topolo2071040574ous_on @ A) @ A) @ S2) @ (^ [X:A]: (X))))))))).
% 2.84/1.54 thf(fact_247_continuous__on__const, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S2:(set @ A),C3:B]: (((((topolo2071040574ous_on @ A) @ B) @ S2) @ (^ [X:A]: (C3))))))))).
% 2.84/1.54 thf(fact_248_continuous__on__subset, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S2:(set @ A),F:(A > B),T7:(set @ A)]: ((((((topolo2071040574ous_on @ A) @ B) @ S2) @ F) => ((((ord_less_eq @ (set @ A)) @ T7) @ S2) => ((((topolo2071040574ous_on @ A) @ B) @ T7) @ F))))))))).
% 2.84/1.54 thf(fact_249_continuous__on__product__then__coordinatewise__UNIV, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ C)) => (! [F:(A > (B > C)),I2:B]: ((((((topolo2071040574ous_on @ A) @ (B > C)) @ (top_top @ (set @ A))) @ F) => ((((topolo2071040574ous_on @ A) @ C) @ (top_top @ (set @ A))) @ (^ [X:A]: (((F @ X) @ I2))))))))))).
% 2.84/1.54 thf(fact_250_type__copy__ex__RepI, axiom, (! [B:$tType,A:$tType,Rep:(A > B),Abs:(B > A),F3:(B > $o)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((? [X5:B]: ((F3 @ X5))) = (? [B5:A]: ((F3 @ (Rep @ B5))))))))).
% 2.84/1.54 thf(fact_251_conj__subset__def, axiom, (! [A:$tType,A4:(set @ A),P2:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ (^ [X:A]: (((P2 @ X) & (Q @ X)))))) = ((((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ P2)) & (((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ Q))))))).
% 2.84/1.54 thf(fact_252_continuous__on__product__then__coordinatewise, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ C)) => (! [S:(set @ A),F:(A > (B > C)),I2:B]: ((((((topolo2071040574ous_on @ A) @ (B > C)) @ S) @ F) => ((((topolo2071040574ous_on @ A) @ C) @ S) @ (^ [X:A]: (((F @ X) @ I2))))))))))).
% 2.84/1.54 thf(fact_253_continuous__on__coordinatewise__then__product, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ C)) => (! [S:(set @ A),F:(A > (B > C))]: (((! [I3:B]: (((((topolo2071040574ous_on @ A) @ C) @ S) @ (^ [X:A]: (((F @ X) @ I3)))))) => ((((topolo2071040574ous_on @ A) @ (B > C)) @ S) @ F)))))))).
% 2.84/1.54 thf(fact_254_type__copy__obj__one__point__absE, axiom, (! [A:$tType,B:$tType,Rep:(A > B),Abs:(B > A),S2:A]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => (~ ((! [X3:B]: ((S2 != (Abs @ X3)))))))))).
% 2.84/1.54 thf(fact_255_rel__fun__def__butlast, axiom, (! [B:$tType,D:$tType,C:$tType,E2:$tType,F4:$tType,A:$tType,R3:(A > (B > $o)),S:(C > (E2 > $o)),T4:(D > (F4 > $o)),F:(A > (C > D)),G:(B > (E2 > F4))]: ((((((((((bNF_rel_fun @ A) @ B) @ (C > D)) @ (E2 > F4)) @ R3) @ ((((((bNF_rel_fun @ C) @ E2) @ D) @ F4) @ S) @ T4)) @ F) @ G) = (! [X:A,Y2:B]: ((((R3 @ X) @ Y2) => ((((((((bNF_rel_fun @ C) @ E2) @ D) @ F4) @ S) @ T4) @ (F @ X)) @ (G @ Y2))))))))).
% 2.84/1.54 thf(subcl_Finite__Set_Ofinite___HOL_Otype, axiom, (! [A:$tType]: (((finite_finite @ A) => (type @ A))))).
% 2.84/1.54 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.84/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 2.84/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: (((linorder @ A) => (order @ A))))).
% 2.84/1.54 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: (((linorder @ A) => (preorder @ A))))).
% 2.84/1.54 thf(tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector, axiom, (! [A9:$tType,A10:$tType]: ((((real_V55928688vector @ A9) & (real_V55928688vector @ A10)) => (real_V55928688vector @ ((bounde2145540817linfun @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (ordere890947078_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1, axiom, (! [A9:$tType,A10:$tType]: ((((real_V55928688vector @ A9) & (finite_finite @ A10)) => (real_V55928688vector @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice, axiom, (bounded_lattice @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Lattices_Obounded__lattice_2, axiom, (! [A9:$tType,A10:$tType]: ((((bounded_lattice @ A9) & (bounded_lattice @ A10)) => (bounded_lattice @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space_3, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (ordere890947078_space @ A10)) => (ordere890947078_space @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_4, axiom, (! [A9:$tType,A10:$tType]: ((((real_V55928688vector @ A9) & (real_V55928688vector @ A10)) => (real_V55928688vector @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_5, axiom, (ordere890947078_space @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_6, axiom, (real_V55928688vector @ real)).
% 2.84/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_7, axiom, (bounded_lattice @ $o)).
% 2.84/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice_8, axiom, (! [A9:$tType]: ((bounded_lattice @ (set @ A9))))).
% 2.84/1.54 thf(tcon_fun___Lattices_Obounded__lattice_9, axiom, (! [A9:$tType,A10:$tType]: (((bounded_lattice @ A10) => (bounded_lattice @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Topological__Spaces_Otopological__space, axiom, (! [A9:$tType,A10:$tType]: (((topolo503727757_space @ A10) => (topolo503727757_space @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A9:$tType,A10:$tType]: (((bounded_lattice @ A10) => (bounded_lattice_top @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A9:$tType,A10:$tType]: (((semilattice_sup @ A10) => (semilattice_sup @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A9:$tType,A10:$tType]: (((order_top @ A10) => (order_top @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A9:$tType,A10:$tType]: (((preorder @ A10) => (preorder @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Lattices_Olattice, axiom, (! [A9:$tType,A10:$tType]: (((lattice @ A10) => (lattice @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: (((order @ A10) => (order @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Orderings_Otop, axiom, (! [A9:$tType,A10:$tType]: (((top @ A10) => (top @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Orderings_Oord, axiom, (! [A9:$tType,A10:$tType]: (((ord @ A10) => (ord @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_fun___Lattices_Osup, axiom, (! [A9:$tType,A10:$tType]: (((semilattice_sup @ A10) => (sup @ (A9 > A10)))))).
% 2.84/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_10, axiom, (! [A9:$tType]: ((bounded_lattice_top @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_11, axiom, (! [A9:$tType]: ((semilattice_sup @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Orderings_Oorder__top_12, axiom, (! [A9:$tType]: ((order_top @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Orderings_Opreorder_13, axiom, (! [A9:$tType]: ((preorder @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Finite__Set_Ofinite_14, axiom, (! [A9:$tType]: (((finite_finite @ A9) => (finite_finite @ (set @ A9)))))).
% 2.84/1.54 thf(tcon_Set_Oset___Lattices_Olattice_15, axiom, (! [A9:$tType]: ((lattice @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Orderings_Oorder_16, axiom, (! [A9:$tType]: ((order @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Orderings_Otop_17, axiom, (! [A9:$tType]: ((top @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Orderings_Oord_18, axiom, (! [A9:$tType]: ((ord @ (set @ A9))))).
% 2.84/1.54 thf(tcon_Set_Oset___Lattices_Osup_19, axiom, (! [A9:$tType]: ((sup @ (set @ A9))))).
% 2.84/1.54 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_20, axiom, (topolo503727757_space @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology, axiom, (topolo2133971006pology @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_21, axiom, (bounded_lattice_top @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_22, axiom, (semilattice_sup @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Orderings_Oorder__top_23, axiom, (order_top @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Orderings_Opreorder_24, axiom, (preorder @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Finite__Set_Ofinite_25, axiom, (finite_finite @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Lattices_Olattice_26, axiom, (lattice @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_27, axiom, (order @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Orderings_Otop_28, axiom, (top @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Orderings_Oord_29, axiom, (ord @ $o)).
% 2.84/1.54 thf(tcon_HOL_Obool___Lattices_Osup_30, axiom, (sup @ $o)).
% 2.84/1.54 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_31, axiom, (topolo503727757_space @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Lattices_Osemilattice__sup_32, axiom, (semilattice_sup @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Orderings_Opreorder_33, axiom, (preorder @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Orderings_Olinorder_34, axiom, (linorder @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Lattices_Olattice_35, axiom, (lattice @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Orderings_Oorder_36, axiom, (order @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Orderings_Oord_37, axiom, (ord @ real)).
% 2.84/1.54 thf(tcon_Real_Oreal___Lattices_Osup_38, axiom, (sup @ real)).
% 2.84/1.54 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_39, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ ((sum_sum @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_40, axiom, (! [A9:$tType,A10:$tType]: ((((topolo503727757_space @ A9) & (topolo503727757_space @ A10)) => (topolo503727757_space @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Lattices_Obounded__lattice__top_41, axiom, (! [A9:$tType,A10:$tType]: ((((bounded_lattice @ A9) & (bounded_lattice @ A10)) => (bounded_lattice_top @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_42, axiom, (! [A9:$tType,A10:$tType]: ((((semilattice_sup @ A9) & (semilattice_sup @ A10)) => (semilattice_sup @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Orderings_Oorder__top_43, axiom, (! [A9:$tType,A10:$tType]: ((((order_top @ A9) & (order_top @ A10)) => (order_top @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_44, axiom, (! [A9:$tType,A10:$tType]: ((((preorder @ A9) & (preorder @ A10)) => (preorder @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_45, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Lattices_Olattice_46, axiom, (! [A9:$tType,A10:$tType]: ((((lattice @ A9) & (lattice @ A10)) => (lattice @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Orderings_Oorder_47, axiom, (! [A9:$tType,A10:$tType]: ((((order @ A9) & (order @ A10)) => (order @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Orderings_Otop_48, axiom, (! [A9:$tType,A10:$tType]: ((((top @ A9) & (top @ A10)) => (top @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Orderings_Oord_49, axiom, (! [A9:$tType,A10:$tType]: ((((ord @ A9) & (ord @ A10)) => (ord @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Oprod___Lattices_Osup_50, axiom, (! [A9:$tType,A10:$tType]: ((((sup @ A9) & (sup @ A10)) => (sup @ ((product_prod @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_51, axiom, (bounded_lattice_top @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_52, axiom, (semilattice_sup @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_53, axiom, (order_top @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_54, axiom, (preorder @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_55, axiom, (linorder @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Finite__Set_Ofinite_56, axiom, (finite_finite @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Lattices_Olattice_57, axiom, (lattice @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Orderings_Oorder_58, axiom, (order @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Orderings_Otop_59, axiom, (top @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Orderings_Oord_60, axiom, (ord @ product_unit)).
% 2.84/1.54 thf(tcon_Product__Type_Ounit___Lattices_Osup_61, axiom, (sup @ product_unit)).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_62, axiom, (! [A9:$tType,A10:$tType]: ((((topolo503727757_space @ A9) & (finite_finite @ A10)) => (topolo503727757_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__sup_63, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (semilattice_sup @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_64, axiom, (! [A9:$tType,A10:$tType]: ((((order @ A9) & (finite_finite @ A10)) => (preorder @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_65, axiom, (! [A9:$tType,A10:$tType]: ((((linorder @ A9) & (cARD_1 @ A10)) => (linorder @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_66, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_67, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (lattice @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_68, axiom, (! [A9:$tType,A10:$tType]: ((((order @ A9) & (finite_finite @ A10)) => (order @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_69, axiom, (! [A9:$tType,A10:$tType]: ((((ord @ A9) & (finite_finite @ A10)) => (ord @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osup_70, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (sup @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.84/1.54 thf(tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_71, axiom, (! [A9:$tType,A10:$tType]: ((((real_V55928688vector @ A9) & (real_V55928688vector @ A10)) => (topolo503727757_space @ ((bounde2145540817linfun @ A9) @ A10)))))).
% 2.84/1.54 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.84/1.54 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 2.84/1.54 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 2.84/1.54 thf(tfree_0, hypothesis, (finite_finite @ b)).
% 2.84/1.54 thf(tfree_1, hypothesis, (finite_finite @ a)).
% 2.84/1.54 thf(tfree_2, hypothesis, (finite_finite @ c)).
% 2.84/1.54 thf(tfree_3, hypothesis, (finite_finite @ sc)).
% 2.84/1.54 thf(tfree_4, hypothesis, (finite_finite @ sz)).
% 2.84/1.54 thf(tfree_5, hypothesis, (linorder @ sz)).
% 2.84/1.54 thf(tfree_6, hypothesis, (finite_finite @ sf)).
% 2.84/1.54 thf(conj_0, conjecture, ((((((denotational_Iagree @ a) @ c) @ b) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ c) @ b))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ c) @ b))]: ((? [X:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ c) @ b)) @ X)) & (((member @ a) @ X) @ (((static_SIGT @ a) @ b) @ theta_1)))))))))).
% 2.84/1.54 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2DTF19346.p
% 2.84/1.54 ------------------------
% 2.91/1.61 ---- Cleaned THF ---
% 2.91/1.61 thf(ty_t_Denotational__Semantics_Ointerp_Ointerp__ext,type,
% 2.91/1.61 denota1663640101rp_ext: $tType > $tType > $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Frechet__Correctness_Oids_Ogood__interp,type,
% 2.91/1.61 frechet_good_interp: $tType > $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Bounded__Linear__Function_Oblinfun,type,
% 2.91/1.61 bounde2145540817linfun: $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Frechet__Correctness_Oids_Ostrm,type,
% 2.91/1.61 frechet_strm: $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 2.91/1.61 finite_Cartesian_vec: $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Product__Type_Ounit,type,
% 2.91/1.61 product_unit: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Product__Type_Oprod,type,
% 2.91/1.61 product_prod: $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Sum__Type_Osum,type,
% 2.91/1.61 sum_sum: $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Syntax_Otrm,type,
% 2.91/1.61 trm: $tType > $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Real_Oreal,type,
% 2.91/1.61 real: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_t_Set_Oset,type,
% 2.91/1.61 set: $tType > $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_tf_sz,type,
% 2.91/1.61 sz: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_tf_sf,type,
% 2.91/1.61 sf: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_tf_sc,type,
% 2.91/1.61 sc: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_tf_c,type,
% 2.91/1.61 c: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_tf_b,type,
% 2.91/1.61 b: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(ty_tf_a,type,
% 2.91/1.61 a: $tType ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 2.91/1.61 real_V55928688vector:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Cardinality_OCARD__1,type,
% 2.91/1.61 cARD_1:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 2.91/1.61 ordere890947078_space:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.91/1.61 bounded_lattice:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_HOL_Otype,type,
% 2.91/1.61 type:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Lattices_Osup,type,
% 2.91/1.61 sup:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Orderings_Oord,type,
% 2.91/1.61 ord:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Orderings_Otop,type,
% 2.91/1.61 top:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Orderings_Oorder,type,
% 2.91/1.61 order:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Lattices_Olattice,type,
% 2.91/1.61 lattice:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Finite__Set_Ofinite,type,
% 2.91/1.61 finite_finite:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Orderings_Olinorder,type,
% 2.91/1.61 linorder:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Orderings_Opreorder,type,
% 2.91/1.61 preorder:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Orderings_Oorder__top,type,
% 2.91/1.61 order_top:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.91/1.61 semilattice_sup:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.91/1.61 bounded_lattice_top:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Topological__Spaces_Odiscrete__topology,type,
% 2.91/1.61 topolo2133971006pology:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 2.91/1.61 topolo503727757_space:
% 2.91/1.61 !>[A: $tType] : $o ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_BNF__Def_Orel__fun,type,
% 2.91/1.61 bNF_rel_fun:
% 2.91/1.61 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Denotational__Semantics_OIagree,type,
% 2.91/1.61 denotational_Iagree:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Denotational__Semantics_OVagree,type,
% 2.91/1.61 denotational_Vagree:
% 2.91/1.61 !>[C: $tType] : ( ( product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) ) > ( product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) ) > ( set @ ( sum_sum @ C @ C ) ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Denotational__Semantics_Ointerp_OFunctions,type,
% 2.91/1.61 denota593628964ctions:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType,Z: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ Z ) > A > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Denotational__Semantics_Ois__interp,type,
% 2.91/1.61 denota2077489681interp:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Denotational__Semantics_Osterm__sem,type,
% 2.91/1.61 denota126604975rm_sem:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Oblin__frechet,type,
% 2.91/1.61 frechet_blin_frechet:
% 2.91/1.61 !>[Sf: $tType,Sc: $tType,Sz: $tType] : ( ( frechet_good_interp @ Sf @ Sc @ Sz ) > ( frechet_strm @ Sf @ Sz ) > ( finite_Cartesian_vec @ real @ Sz ) > ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ Sz ) @ real ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Ocr__good__interp,type,
% 2.91/1.61 freche457001096interp:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm,type,
% 2.91/1.61 frechet_cr_strm:
% 2.91/1.61 !>[A: $tType,B: $tType] : ( ( trm @ A @ B ) > ( frechet_strm @ A @ B ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Ogood__interp,type,
% 2.91/1.61 freche227871258interp:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Oraw__interp,type,
% 2.91/1.61 freche229654227interp:
% 2.91/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( frechet_good_interp @ A @ B @ C ) > ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Oraw__term,type,
% 2.91/1.61 frechet_raw_term:
% 2.91/1.61 !>[A: $tType,C: $tType] : ( ( frechet_strm @ A @ C ) > ( trm @ A @ C ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Osimple__term,type,
% 2.91/1.61 frechet_simple_term:
% 2.91/1.61 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( frechet_strm @ A @ C ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_If,type,
% 2.91/1.61 if:
% 2.91/1.61 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.91/1.61 sup_sup:
% 2.91/1.61 !>[A: $tType] : ( A > A > A ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Lifting_Orel__pred__comp,type,
% 2.91/1.61 rel_pred_comp:
% 2.91/1.61 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( B > $o ) > A > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.91/1.61 ord_less_eq:
% 2.91/1.61 !>[A: $tType] : ( A > A > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.91/1.61 top_top:
% 2.91/1.61 !>[A: $tType] : A ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 2.91/1.61 product_fst:
% 2.91/1.61 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Relation_ODomainp,type,
% 2.91/1.61 domainp:
% 2.91/1.61 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > A > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Set_OCollect,type,
% 2.91/1.61 collect:
% 2.91/1.61 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Static__Semantics_OFVT,type,
% 2.91/1.61 static_FVT:
% 2.91/1.61 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ ( sum_sum @ C @ C ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Static__Semantics_OSIGT,type,
% 2.91/1.61 static_SIGT:
% 2.91/1.61 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Sum__Type_OInl,type,
% 2.91/1.61 sum_Inl:
% 2.91/1.61 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 2.91/1.61 sum_rec_sum:
% 2.91/1.61 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Syntax_Odfree,type,
% 2.91/1.61 dfree:
% 2.91/1.61 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Syntax_Otrm_OTimes,type,
% 2.91/1.61 times:
% 2.91/1.61 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( trm @ A @ C ) > ( trm @ A @ C ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Topological__Spaces_Ocontinuous__on,type,
% 2.91/1.61 topolo2071040574ous_on:
% 2.91/1.61 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_Typedef_Otype__definition,type,
% 2.91/1.61 type_definition:
% 2.91/1.61 !>[B: $tType,A: $tType] : ( ( B > A ) > ( A > B ) > ( set @ A ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_c_member,type,
% 2.91/1.61 member:
% 2.91/1.61 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_v_I,type,
% 2.91/1.61 i: denota1663640101rp_ext @ a @ c @ b @ product_unit ).
% 2.91/1.61
% 2.91/1.61 thf(sy_v_J,type,
% 2.91/1.61 j: denota1663640101rp_ext @ a @ c @ b @ product_unit ).
% 2.91/1.61
% 2.91/1.61 thf(sy_v__092_060nu_062,type,
% 2.91/1.61 nu: product_prod @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_v__092_060nu_062_H,type,
% 2.91/1.61 nu2: product_prod @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) ).
% 2.91/1.61
% 2.91/1.61 thf(sy_v__092_060theta_062_092_060_094sub_0621____,type,
% 2.91/1.61 theta_1: trm @ a @ b ).
% 2.91/1.61
% 2.91/1.61 thf(sy_v__092_060theta_062_092_060_094sub_0622____,type,
% 2.91/1.61 theta_2: trm @ a @ b ).
% 2.91/1.61
% 2.91/1.61 thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [I: denota1663640101rp_ext @ a @ B @ C @ product_unit,J: denota1663640101rp_ext @ a @ B @ C @ product_unit] :
% 2.91/1.61 ( ( denotational_Iagree @ a @ B @ C @ I @ J
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
% 2.91/1.61 => ( denotational_Iagree @ a @ B @ C @ I @ J
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [I: denota1663640101rp_ext @ a @ B @ C @ product_unit,J: denota1663640101rp_ext @ a @ B @ C @ product_unit] :
% 2.91/1.61 ( ( denotational_Iagree @ a @ B @ C @ I @ J
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
% 2.91/1.61 => ( denotational_Iagree @ a @ B @ C @ I @ J
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ B @ C ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ B @ C )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ B @ C ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_2_IA,axiom,
% 2.91/1.61 ( denotational_Iagree @ a @ c @ b @ i @ j
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 2.91/1.61 & ( ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) )
% 2.91/1.61 | ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_3_dfree__Times_Oprems_I2_J,axiom,
% 2.91/1.61 ( denotational_Iagree @ a @ c @ b @ i @ j
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_4_dfree__Times_Ohyps_I1_J,axiom,
% 2.91/1.61 dfree @ a @ b @ theta_1 ).
% 2.91/1.61
% 2.91/1.61 thf(fact_5_sum_Oinject_I1_J,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 2.91/1.61 ( ( ( sum_Inl @ A @ B @ X1 )
% 2.91/1.61 = ( sum_Inl @ A @ B @ Y1 ) )
% 2.91/1.61 = ( X1 = Y1 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_6_old_Osum_Oinject_I1_J,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,A2: A,A3: A] :
% 2.91/1.61 ( ( ( sum_Inl @ A @ B @ A2 )
% 2.91/1.61 = ( sum_Inl @ A @ B @ A3 ) )
% 2.91/1.61 = ( A2 = A3 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_7_Isubs_I2_J,axiom,
% 2.91/1.61 ! [E: $tType] :
% 2.91/1.61 ( ord_less_eq @ ( set @ ( sum_sum @ a @ E ) )
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ E )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ E] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ E @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) )
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ E )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ E] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ E @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_8_Isubs_I1_J,axiom,
% 2.91/1.61 ! [D2: $tType] :
% 2.91/1.61 ( ord_less_eq @ ( set @ ( sum_sum @ a @ D2 ) )
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ D2 )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ D2] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ D2 @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) )
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ D2 )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ D2] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ D2 @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_9_Iagree__comm,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [A4: denota1663640101rp_ext @ A @ B @ C @ product_unit,B2: denota1663640101rp_ext @ A @ B @ C @ product_unit,V: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] :
% 2.91/1.61 ( ( denotational_Iagree @ A @ B @ C @ A4 @ B2 @ V )
% 2.91/1.61 => ( denotational_Iagree @ A @ B @ C @ B2 @ A4 @ V ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_10_Iagree__refl,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,A4: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] : ( denotational_Iagree @ A @ B @ C @ I @ I @ A4 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_11_Inl__inject,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 2.91/1.61 ( ( ( sum_Inl @ A @ B @ X2 )
% 2.91/1.61 = ( sum_Inl @ A @ B @ Y ) )
% 2.91/1.61 => ( X2 = Y ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_12_IH1,axiom,
% 2.91/1.61 ( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ) )
% 2.91/1.61 => ( ( denotational_Iagree @ a @ c @ b @ i @ j
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) )
% 2.91/1.61 => ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
% 2.91/1.61 = ( denota126604975rm_sem @ a @ c @ b @ j @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_13_rel__pred__comp__def,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( rel_pred_comp @ A @ B )
% 2.91/1.61 = ( ^ [R: A > B > $o,P: B > $o,X: A] :
% 2.91/1.61 ? [Y2: B] :
% 2.91/1.61 ( ( R @ X @ Y2 )
% 2.91/1.61 & ( P @ Y2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_14_IH2,axiom,
% 2.91/1.61 ( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ) )
% 2.91/1.61 => ( ( denotational_Iagree @ a @ c @ b @ i @ j
% 2.91/1.61 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 2.91/1.61 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 2.91/1.61 ? [X: a] :
% 2.91/1.61 ( ( Uu
% 2.91/1.61 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 2.91/1.61 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) )
% 2.91/1.61 => ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
% 2.91/1.61 = ( denota126604975rm_sem @ a @ c @ b @ j @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_15_Iagree__Func,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ C )
% 2.91/1.61 & ( finite_finite @ B ) )
% 2.91/1.61 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,J: denota1663640101rp_ext @ A @ B @ C @ product_unit,V: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),F: A] :
% 2.91/1.61 ( ( denotational_Iagree @ A @ B @ C @ I @ J @ V )
% 2.91/1.61 => ( ( member @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) @ ( sum_Inl @ A @ ( sum_sum @ B @ C ) @ F ) @ V )
% 2.91/1.61 => ( ( denota593628964ctions @ A @ B @ C @ product_unit @ I @ F )
% 2.91/1.61 = ( denota593628964ctions @ A @ B @ C @ product_unit @ J @ F ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_16_raw__interp__inject,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [X2: frechet_good_interp @ A @ B @ C,Y: frechet_good_interp @ A @ B @ C] :
% 2.91/1.61 ( ( ( freche229654227interp @ A @ B @ C @ X2 )
% 2.91/1.61 = ( freche229654227interp @ A @ B @ C @ Y ) )
% 2.91/1.61 = ( X2 = Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_17_dfree__Times_Ohyps_I2_J,axiom,
% 2.91/1.61 dfree @ a @ b @ theta_2 ).
% 2.91/1.61
% 2.91/1.61 thf(fact_18_coincidence__sterm,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ C )
% 2.91/1.61 & ( finite_finite @ B ) )
% 2.91/1.61 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Theta: trm @ B @ A,I: denota1663640101rp_ext @ B @ C @ A @ product_unit] :
% 2.91/1.61 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ Theta ) )
% 2.91/1.61 => ( ( denota126604975rm_sem @ B @ C @ A @ I @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu ) )
% 2.91/1.61 = ( denota126604975rm_sem @ B @ C @ A @ I @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu2 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_19_dfree__Times_Oprems_I1_J,axiom,
% 2.91/1.61 denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_20_VAs_I2_J,axiom,
% 2.91/1.61 denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_21_VAs_I1_J,axiom,
% 2.91/1.61 denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_22_VA,axiom,
% 2.91/1.61 denotational_Vagree @ b @ nu @ nu2 @ ( sup_sup @ ( set @ ( sum_sum @ b @ b ) ) @ ( static_FVT @ a @ b @ theta_1 ) @ ( static_FVT @ a @ b @ theta_2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_23_agree__sub,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ! [A4: set @ ( sum_sum @ A @ A ),B2: set @ ( sum_sum @ A @ A ),Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Omega: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A )] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ A4 @ B2 )
% 2.91/1.61 => ( ( denotational_Vagree @ A @ Nu @ Omega @ B2 )
% 2.91/1.61 => ( denotational_Vagree @ A @ Nu @ Omega @ A4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_24_agree__comm,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ! [A4: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),B2: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),V: set @ ( sum_sum @ A @ A )] :
% 2.91/1.61 ( ( denotational_Vagree @ A @ A4 @ B2 @ V )
% 2.91/1.61 => ( denotational_Vagree @ A @ B2 @ A4 @ V ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_25_agree__refl,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),A4: set @ ( sum_sum @ A @ A )] : ( denotational_Vagree @ A @ Nu @ Nu @ A4 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_26_agree__supset,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ! [B2: set @ ( sum_sum @ A @ A ),A4: set @ ( sum_sum @ A @ A ),Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A )] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ B2 @ A4 )
% 2.91/1.61 => ( ( denotational_Vagree @ A @ Nu @ Nu2 @ A4 )
% 2.91/1.61 => ( denotational_Vagree @ A @ Nu @ Nu2 @ B2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_27_cr__good__interp__def,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ( ( freche457001096interp @ A @ B @ C )
% 2.91/1.61 = ( ^ [X: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y2: frechet_good_interp @ A @ B @ C] :
% 2.91/1.61 ( X
% 2.91/1.61 = ( freche229654227interp @ A @ B @ C @ Y2 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_28_dfree__Times__simps,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,A2: trm @ A @ B,B3: trm @ A @ B] :
% 2.91/1.61 ( ( dfree @ A @ B @ ( times @ A @ B @ A2 @ B3 ) )
% 2.91/1.61 = ( ( dfree @ A @ B @ A2 )
% 2.91/1.61 & ( dfree @ A @ B @ B3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_29_simple__term__inject,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,X2: trm @ A @ C,Y: trm @ A @ C] :
% 2.91/1.61 ( ( member @ ( trm @ A @ C ) @ X2 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 2.91/1.61 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 2.91/1.61 => ( ( ( frechet_simple_term @ A @ C @ X2 )
% 2.91/1.61 = ( frechet_simple_term @ A @ C @ Y ) )
% 2.91/1.61 = ( X2 = Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_30_simple__term__induct,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,P2: ( frechet_strm @ A @ C ) > $o,X2: frechet_strm @ A @ C] :
% 2.91/1.61 ( ! [Y3: trm @ A @ C] :
% 2.91/1.61 ( ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 2.91/1.61 => ( P2 @ ( frechet_simple_term @ A @ C @ Y3 ) ) )
% 2.91/1.61 => ( P2 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_31_simple__term__cases,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C] :
% 2.91/1.61 ~ ! [Y3: trm @ A @ C] :
% 2.91/1.61 ( ( X2
% 2.91/1.61 = ( frechet_simple_term @ A @ C @ Y3 ) )
% 2.91/1.61 => ~ ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_32_raw__interp__inverse,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [X2: frechet_good_interp @ A @ B @ C] :
% 2.91/1.61 ( ( freche227871258interp @ A @ B @ C @ ( freche229654227interp @ A @ B @ C @ X2 ) )
% 2.91/1.61 = X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_33_raw__term__induct,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,Y: trm @ A @ C,P2: ( trm @ A @ C ) > $o] :
% 2.91/1.61 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 2.91/1.61 => ( ! [X3: frechet_strm @ A @ C] : ( P2 @ ( frechet_raw_term @ A @ C @ X3 ) )
% 2.91/1.61 => ( P2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_34_raw__term__cases,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 2.91/1.61 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 2.91/1.61 => ~ ! [X3: frechet_strm @ A @ C] :
% 2.91/1.61 ( Y
% 2.91/1.61 != ( frechet_raw_term @ A @ C @ X3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_35_raw__term,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C] : ( member @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C @ X2 ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_36_trm_Oinject_I5_J,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,X51: trm @ A @ C,X52: trm @ A @ C,Y51: trm @ A @ C,Y52: trm @ A @ C] :
% 2.91/1.61 ( ( ( times @ A @ C @ X51 @ X52 )
% 2.91/1.61 = ( times @ A @ C @ Y51 @ Y52 ) )
% 2.91/1.61 = ( ( X51 = Y51 )
% 2.91/1.61 & ( X52 = Y52 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_37_raw__term__inject,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C,Y: frechet_strm @ A @ C] :
% 2.91/1.61 ( ( ( frechet_raw_term @ A @ C @ X2 )
% 2.91/1.61 = ( frechet_raw_term @ A @ C @ Y ) )
% 2.91/1.61 = ( X2 = Y ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_38_raw__term__inverse,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,X2: frechet_strm @ A @ C] :
% 2.91/1.61 ( ( frechet_simple_term @ A @ C @ ( frechet_raw_term @ A @ C @ X2 ) )
% 2.91/1.61 = X2 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_39_simple__term__inverse,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 2.91/1.61 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 2.91/1.61 => ( ( frechet_raw_term @ A @ C @ ( frechet_simple_term @ A @ C @ Y ) )
% 2.91/1.61 = Y ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_40_agree__union,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Omega: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),A4: set @ ( sum_sum @ A @ A ),B2: set @ ( sum_sum @ A @ A )] :
% 2.91/1.61 ( ( denotational_Vagree @ A @ Nu @ Omega @ A4 )
% 2.91/1.61 => ( ( denotational_Vagree @ A @ Nu @ Omega @ B2 )
% 2.91/1.61 => ( denotational_Vagree @ A @ Nu @ Omega @ ( sup_sup @ ( set @ ( sum_sum @ A @ A ) ) @ A4 @ B2 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_41_Iagree__sub,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [A4: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),B2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),I: denota1663640101rp_ext @ A @ B @ C @ product_unit,J: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) ) @ A4 @ B2 )
% 2.91/1.61 => ( ( denotational_Iagree @ A @ B @ C @ I @ J @ B2 )
% 2.91/1.61 => ( denotational_Iagree @ A @ B @ C @ I @ J @ A4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_42_dfree_Odfree__Times,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,Theta_1: trm @ A @ C,Theta_2: trm @ A @ C] :
% 2.91/1.61 ( ( dfree @ A @ C @ Theta_1 )
% 2.91/1.61 => ( ( dfree @ A @ C @ Theta_2 )
% 2.91/1.61 => ( dfree @ A @ C @ ( times @ A @ C @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_43_cr__strm__def,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( frechet_cr_strm @ A @ B )
% 2.91/1.61 = ( ^ [X: trm @ A @ B,Y2: frechet_strm @ A @ B] :
% 2.91/1.61 ( X
% 2.91/1.61 = ( frechet_raw_term @ A @ B @ Y2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_44_fst__sup,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( sup @ A )
% 2.91/1.61 & ( sup @ B ) )
% 2.91/1.61 => ! [X2: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 2.91/1.61 ( ( product_fst @ A @ B @ ( sup_sup @ ( product_prod @ A @ B ) @ X2 @ Y ) )
% 2.91/1.61 = ( sup_sup @ A @ ( product_fst @ A @ B @ X2 ) @ ( product_fst @ A @ B @ Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_45_mem__Collect__eq,axiom,
% 2.91/1.61 ! [A: $tType,A2: A,P2: A > $o] :
% 2.91/1.61 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 2.91/1.61 = ( P2 @ A2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_46_Collect__mem__eq,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A] :
% 2.91/1.61 ( ( collect @ A
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 2.91/1.61 = A4 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_47_Collect__cong,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.91/1.61 ( ! [X3: A] :
% 2.91/1.61 ( ( P2 @ X3 )
% 2.91/1.61 = ( Q @ X3 ) )
% 2.91/1.61 => ( ( collect @ A @ P2 )
% 2.91/1.61 = ( collect @ A @ Q ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_48_ext,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.91/1.61 ( ! [X3: A] :
% 2.91/1.61 ( ( F @ X3 )
% 2.91/1.61 = ( G @ X3 ) )
% 2.91/1.61 => ( F = G ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_49_Un__subset__iff,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ C2 )
% 2.91/1.61 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 2.91/1.61 & ( ord_less_eq @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_50_sup_Obounded__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,C3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A2 )
% 2.91/1.61 = ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 & ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_51_le__sup__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X2 @ Y ) @ Z2 )
% 2.91/1.61 = ( ( ord_less_eq @ A @ X2 @ Z2 )
% 2.91/1.61 & ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_52_FVT_Osimps_I5_J,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,F: trm @ A @ C,G: trm @ A @ C] :
% 2.91/1.61 ( ( static_FVT @ A @ C @ ( times @ A @ C @ F @ G ) )
% 2.91/1.61 = ( sup_sup @ ( set @ ( sum_sum @ C @ C ) ) @ ( static_FVT @ A @ C @ F ) @ ( static_FVT @ A @ C @ G ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_53_SIGT_Osimps_I5_J,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType,T1: trm @ A @ C,T2: trm @ A @ C] :
% 2.91/1.61 ( ( static_SIGT @ A @ C @ ( times @ A @ C @ T1 @ T2 ) )
% 2.91/1.61 = ( sup_sup @ ( set @ A ) @ ( static_SIGT @ A @ C @ T1 ) @ ( static_SIGT @ A @ C @ T2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_54_type__definition__strm,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType] : ( type_definition @ ( frechet_strm @ A @ C ) @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C ) @ ( frechet_simple_term @ A @ C ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_55_good__interp__inverse,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 2.91/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 2.91/1.61 => ( ( freche229654227interp @ A @ B @ C @ ( freche227871258interp @ A @ B @ C @ Y ) )
% 2.91/1.61 = Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_56_raw__interp__induct,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit,P2: ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o] :
% 2.91/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 2.91/1.61 => ( ! [X3: frechet_good_interp @ A @ B @ C] : ( P2 @ ( freche229654227interp @ A @ B @ C @ X3 ) )
% 2.91/1.61 => ( P2 @ Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_57_raw__interp__cases,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 2.91/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 2.91/1.61 => ~ ! [X3: frechet_good_interp @ A @ B @ C] :
% 2.91/1.61 ( Y
% 2.91/1.61 != ( freche229654227interp @ A @ B @ C @ X3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_58_raw__interp,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [X2: frechet_good_interp @ A @ B @ C] : ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C @ X2 ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_59_good__interp__inject,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [X2: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 2.91/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ X2 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 2.91/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 2.91/1.61 => ( ( ( freche227871258interp @ A @ B @ C @ X2 )
% 2.91/1.61 = ( freche227871258interp @ A @ B @ C @ Y ) )
% 2.91/1.61 = ( X2 = Y ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_60_good__interp__induct,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [P2: ( frechet_good_interp @ A @ B @ C ) > $o,X2: frechet_good_interp @ A @ B @ C] :
% 2.91/1.61 ( ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 2.91/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 2.91/1.61 => ( P2 @ ( freche227871258interp @ A @ B @ C @ Y3 ) ) )
% 2.91/1.61 => ( P2 @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_61_good__interp__cases,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ! [X2: frechet_good_interp @ A @ B @ C] :
% 2.91/1.61 ~ ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 2.91/1.61 ( ( X2
% 2.91/1.61 = ( freche227871258interp @ A @ B @ C @ Y3 ) )
% 2.91/1.61 => ~ ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_62_subsetI,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ! [X3: A] :
% 2.91/1.61 ( ( member @ A @ X3 @ A4 )
% 2.91/1.61 => ( member @ A @ X3 @ B2 ) )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_63_subset__antisym,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A4 )
% 2.91/1.61 => ( A4 = B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_64_sup__apply,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ B )
% 2.91/1.61 => ( ( sup_sup @ ( A > B ) )
% 2.91/1.61 = ( ^ [F2: A > B,G2: A > B,X: A] : ( sup_sup @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_65_sup_Oidem,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ A2 @ A2 )
% 2.91/1.61 = A2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_66_sup__idem,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X2 @ X2 )
% 2.91/1.61 = X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_67_sup_Oleft__idem,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A] :
% 2.91/1.61 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) )
% 2.91/1.61 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_68_sup__left__idem,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) )
% 2.91/1.61 = ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_69_sup_Oright__idem,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A] :
% 2.91/1.61 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ B3 )
% 2.91/1.61 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_70_UnCI,axiom,
% 2.91/1.61 ! [A: $tType,C3: A,B2: set @ A,A4: set @ A] :
% 2.91/1.61 ( ( ~ ( member @ A @ C3 @ B2 )
% 2.91/1.61 => ( member @ A @ C3 @ A4 ) )
% 2.91/1.61 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_71_Un__iff,axiom,
% 2.91/1.61 ! [A: $tType,C3: A,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 2.91/1.61 = ( ( member @ A @ C3 @ A4 )
% 2.91/1.61 | ( member @ A @ C3 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_72_sup__set__def,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ( collect @ A
% 2.91/1.61 @ ( sup_sup @ ( A > $o )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ A5 )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_73_less__eq__set__def,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ( ord_less_eq @ ( A > $o )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ A5 )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_74_in__mono,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 => ( ( member @ A @ X2 @ A4 )
% 2.91/1.61 => ( member @ A @ X2 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_75_subsetD,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,C3: A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 => ( ( member @ A @ C3 @ A4 )
% 2.91/1.61 => ( member @ A @ C3 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_76_equalityE,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( A4 = B2 )
% 2.91/1.61 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_77_subset__eq,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ! [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ A5 )
% 2.91/1.61 => ( member @ A @ X @ B4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_78_equalityD1,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( A4 = B2 )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ A4 @ B2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_79_equalityD2,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( A4 = B2 )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ B2 @ A4 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_80_subset__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ! [T3: A] :
% 2.91/1.61 ( ( member @ A @ T3 @ A5 )
% 2.91/1.61 => ( member @ A @ T3 @ B4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_81_subset__refl,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_82_Collect__mono,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.91/1.61 ( ! [X3: A] :
% 2.91/1.61 ( ( P2 @ X3 )
% 2.91/1.61 => ( Q @ X3 ) )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_83_subset__trans,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_84_set__eq__subset,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B4 )
% 2.91/1.61 & ( ord_less_eq @ ( set @ A ) @ B4 @ A5 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_85_Collect__mono__iff,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 2.91/1.61 = ( ! [X: A] :
% 2.91/1.61 ( ( P2 @ X )
% 2.91/1.61 => ( Q @ X ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_86_inf__sup__aci_I8_J,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( lattice @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) )
% 2.91/1.61 = ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_87_inf__sup__aci_I7_J,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( lattice @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) )
% 2.91/1.61 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X2 @ Z2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_88_inf__sup__aci_I6_J,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( lattice @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y ) @ Z2 )
% 2.91/1.61 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_89_inf__sup__aci_I5_J,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( lattice @ A )
% 2.91/1.61 => ( ( sup_sup @ A )
% 2.91/1.61 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_90_sup__fun__def,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ B )
% 2.91/1.61 => ( ( sup_sup @ ( A > B ) )
% 2.91/1.61 = ( ^ [F2: A > B,G2: A > B,X: A] : ( sup_sup @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_91_boolean__algebra__cancel_Osup1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A4: A,K: A,A2: A,B3: A] :
% 2.91/1.61 ( ( A4
% 2.91/1.61 = ( sup_sup @ A @ K @ A2 ) )
% 2.91/1.61 => ( ( sup_sup @ A @ A4 @ B3 )
% 2.91/1.61 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_92_boolean__algebra__cancel_Osup2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B2: A,K: A,B3: A,A2: A] :
% 2.91/1.61 ( ( B2
% 2.91/1.61 = ( sup_sup @ A @ K @ B3 ) )
% 2.91/1.61 => ( ( sup_sup @ A @ A2 @ B2 )
% 2.91/1.61 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_93_sup_Oassoc,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.61 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ C3 )
% 2.91/1.61 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_94_sup__assoc,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y ) @ Z2 )
% 2.91/1.61 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_95_sup_Ocommute,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ( ( sup_sup @ A )
% 2.91/1.61 = ( ^ [A6: A,B5: A] : ( sup_sup @ A @ B5 @ A6 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_96_sup__commute,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ( ( sup_sup @ A )
% 2.91/1.61 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_97_sup_Oleft__commute,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.61 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A2 @ C3 ) )
% 2.91/1.61 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_98_sup__left__commute,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y @ Z2 ) )
% 2.91/1.61 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X2 @ Z2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_99_UnE,axiom,
% 2.91/1.61 ! [A: $tType,C3: A,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 2.91/1.61 => ( ~ ( member @ A @ C3 @ A4 )
% 2.91/1.61 => ( member @ A @ C3 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_100_UnI1,axiom,
% 2.91/1.61 ! [A: $tType,C3: A,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( member @ A @ C3 @ A4 )
% 2.91/1.61 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_101_UnI2,axiom,
% 2.91/1.61 ! [A: $tType,C3: A,B2: set @ A,A4: set @ A] :
% 2.91/1.61 ( ( member @ A @ C3 @ B2 )
% 2.91/1.61 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_102_bex__Un,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,P2: A > $o] :
% 2.91/1.61 ( ( ? [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 2.91/1.61 & ( P2 @ X ) ) )
% 2.91/1.61 = ( ? [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ A4 )
% 2.91/1.61 & ( P2 @ X ) )
% 2.91/1.61 | ? [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ B2 )
% 2.91/1.61 & ( P2 @ X ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_103_ball__Un,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,P2: A > $o] :
% 2.91/1.61 ( ( ! [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 2.91/1.61 => ( P2 @ X ) ) )
% 2.91/1.61 = ( ! [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ A4 )
% 2.91/1.61 => ( P2 @ X ) )
% 2.91/1.61 & ! [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ B2 )
% 2.91/1.61 => ( P2 @ X ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_104_Un__assoc,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ C2 )
% 2.91/1.61 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_105_Un__absorb,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 2.91/1.61 = A4 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_106_Un__commute,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A5 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_107_Un__left__absorb,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 2.91/1.61 = ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_108_Un__left__commute,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A,C2: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) )
% 2.91/1.61 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_109_Collect__subset,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,P2: A > $o] :
% 2.91/1.61 ( ord_less_eq @ ( set @ A )
% 2.91/1.61 @ ( collect @ A
% 2.91/1.61 @ ^ [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ A4 )
% 2.91/1.61 & ( P2 @ X ) ) )
% 2.91/1.61 @ A4 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_110_Un__def,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ( collect @ A
% 2.91/1.61 @ ^ [X: A] :
% 2.91/1.61 ( ( member @ A @ X @ A5 )
% 2.91/1.61 | ( member @ A @ X @ B4 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_111_Collect__disj__eq,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.91/1.61 ( ( collect @ A
% 2.91/1.61 @ ^ [X: A] :
% 2.91/1.61 ( ( P2 @ X )
% 2.91/1.61 | ( Q @ X ) ) )
% 2.91/1.61 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_112_inf__sup__ord_I4_J,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( lattice @ A )
% 2.91/1.61 => ! [Y: A,X2: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_113_inf__sup__ord_I3_J,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( lattice @ A )
% 2.91/1.61 => ! [X2: A,Y: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_114_le__supE,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X2 )
% 2.91/1.61 => ~ ( ( ord_less_eq @ A @ A2 @ X2 )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ B3 @ X2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_115_le__supI,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,X2: A,B3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ X2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ B3 @ X2 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_116_sup__ge1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,Y: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_117_sup__ge2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [Y: A,X2: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_118_le__supI1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,A2: A,B3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X2 @ A2 )
% 2.91/1.61 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_119_le__supI2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,B3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X2 @ B3 )
% 2.91/1.61 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_120_sup_Omono,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [C3: A,A2: A,D3: A,B3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ C3 @ A2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ D3 @ B3 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( sup_sup @ A @ C3 @ D3 ) @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_121_sup__mono,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,C3: A,B3: A,D3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ C3 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ B3 @ D3 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ ( sup_sup @ A @ C3 @ D3 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_122_sup__least,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [Y: A,X2: A,Z2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ Y @ X2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ Z2 @ X2 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z2 ) @ X2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_123_le__iff__sup,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ( ( ord_less_eq @ A )
% 2.91/1.61 = ( ^ [X: A,Y2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X @ Y2 )
% 2.91/1.61 = Y2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_124_sup_OorderE,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ( A2
% 2.91/1.61 = ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_125_sup_OorderI,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A] :
% 2.91/1.61 ( ( A2
% 2.91/1.61 = ( sup_sup @ A @ A2 @ B3 ) )
% 2.91/1.61 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_126_sup__unique,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [F: A > A > A,X2: A,Y: A] :
% 2.91/1.61 ( ! [X3: A,Y3: A] : ( ord_less_eq @ A @ X3 @ ( F @ X3 @ Y3 ) )
% 2.91/1.61 => ( ! [X3: A,Y3: A] : ( ord_less_eq @ A @ Y3 @ ( F @ X3 @ Y3 ) )
% 2.91/1.61 => ( ! [X3: A,Y3: A,Z4: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ Z4 @ X3 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( F @ Y3 @ Z4 ) @ X3 ) ) )
% 2.91/1.61 => ( ( sup_sup @ A @ X2 @ Y )
% 2.91/1.61 = ( F @ X2 @ Y ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_127_sup_Oabsorb1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ( ( sup_sup @ A @ A2 @ B3 )
% 2.91/1.61 = A2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_128_sup_Oabsorb2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( ( sup_sup @ A @ A2 @ B3 )
% 2.91/1.61 = B3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_129_sup__absorb1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [Y: A,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ Y @ X2 )
% 2.91/1.61 => ( ( sup_sup @ A @ X2 @ Y )
% 2.91/1.61 = X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_130_sup__absorb2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 => ( ( sup_sup @ A @ X2 @ Y )
% 2.91/1.61 = Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_131_sup_OboundedE,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,C3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A2 )
% 2.91/1.61 => ~ ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_132_sup_OboundedI,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ C3 @ A2 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_133_sup_Oorder__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ( ( ord_less_eq @ A )
% 2.91/1.61 = ( ^ [B5: A,A6: A] :
% 2.91/1.61 ( A6
% 2.91/1.61 = ( sup_sup @ A @ A6 @ B5 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_134_sup_Ocobounded1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_135_sup_Ocobounded2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [B3: A,A2: A] : ( ord_less_eq @ A @ B3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_136_sup_Oabsorb__iff1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ( ( ord_less_eq @ A )
% 2.91/1.61 = ( ^ [B5: A,A6: A] :
% 2.91/1.61 ( ( sup_sup @ A @ A6 @ B5 )
% 2.91/1.61 = A6 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_137_sup_Oabsorb__iff2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ( ( ord_less_eq @ A )
% 2.91/1.61 = ( ^ [A6: A,B5: A] :
% 2.91/1.61 ( ( sup_sup @ A @ A6 @ B5 )
% 2.91/1.61 = B5 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_138_sup_OcoboundedI1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [C3: A,A2: A,B3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ C3 @ A2 )
% 2.91/1.61 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_139_sup_OcoboundedI2,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( semilattice_sup @ A )
% 2.91/1.61 => ! [C3: A,B3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ C3 @ B3 )
% 2.91/1.61 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_140_fst__mono,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( ord @ A )
% 2.91/1.61 & ( ord @ B ) )
% 2.91/1.61 => ! [X2: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 2.91/1.61 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X2 @ Y )
% 2.91/1.61 => ( ord_less_eq @ A @ ( product_fst @ A @ B @ X2 ) @ ( product_fst @ A @ B @ Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_141_Un__mono,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,C2: set @ A,B2: set @ A,D4: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 2.91/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D4 )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C2 @ D4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_142_Un__least,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,C2: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 2.91/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 2.91/1.61 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) @ C2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_143_Un__upper1,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_144_Un__upper2,axiom,
% 2.91/1.61 ! [A: $tType,B2: set @ A,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_145_Un__absorb1,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 => ( ( sup_sup @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 = B2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_146_Un__absorb2,axiom,
% 2.91/1.61 ! [A: $tType,B2: set @ A,A4: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A4 )
% 2.91/1.61 => ( ( sup_sup @ ( set @ A ) @ A4 @ B2 )
% 2.91/1.61 = A4 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_147_subset__UnE,axiom,
% 2.91/1.61 ! [A: $tType,C2: set @ A,A4: set @ A,B2: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B2 ) )
% 2.91/1.61 => ~ ! [A7: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A7 @ A4 )
% 2.91/1.61 => ! [B6: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B2 )
% 2.91/1.61 => ( C2
% 2.91/1.61 != ( sup_sup @ ( set @ A ) @ A7 @ B6 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_148_subset__Un__eq,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 2.91/1.61 = ( ^ [A5: set @ A,B4: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 2.91/1.61 = B4 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_149_type__definition__good__interp,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ( type_definition @ ( frechet_good_interp @ A @ B @ C ) @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C ) @ ( freche227871258interp @ A @ B @ C ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_150_order__refl,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( preorder @ A )
% 2.91/1.61 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_151_sterm__continuous_H,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ C )
% 2.91/1.61 & ( finite_finite @ B ) )
% 2.91/1.61 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C,S: set @ ( finite_Cartesian_vec @ real @ C )] :
% 2.91/1.61 ( ( denota2077489681interp @ A @ B @ C @ I )
% 2.91/1.61 => ( ( dfree @ A @ C @ Theta )
% 2.91/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ S @ ( denota126604975rm_sem @ A @ B @ C @ I @ Theta ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_152_old_Osum_Osimps_I7_J,axiom,
% 2.91/1.61 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A2: A] :
% 2.91/1.61 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A2 ) )
% 2.91/1.61 = ( F1 @ A2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_153_strm_Orep__transfer,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType] :
% 2.91/1.61 ( bNF_rel_fun @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( trm @ A @ C ) @ ( trm @ A @ C ) @ ( frechet_cr_strm @ A @ C )
% 2.91/1.61 @ ^ [Y4: trm @ A @ C,Z3: trm @ A @ C] : ( Y4 = Z3 )
% 2.91/1.61 @ ^ [X: trm @ A @ C] : X
% 2.91/1.61 @ ( frechet_raw_term @ A @ C ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_154_good__interp_Orep__transfer,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ( bNF_rel_fun @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche457001096interp @ A @ B @ C )
% 2.91/1.61 @ ^ [Y4: denota1663640101rp_ext @ A @ B @ C @ product_unit,Z3: denota1663640101rp_ext @ A @ B @ C @ product_unit] : ( Y4 = Z3 )
% 2.91/1.61 @ ^ [X: denota1663640101rp_ext @ A @ B @ C @ product_unit] : X
% 2.91/1.61 @ ( freche229654227interp @ A @ B @ C ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_155_good__interp_Odomain,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ B )
% 2.91/1.61 & ( finite_finite @ C ) )
% 2.91/1.61 => ( ( domainp @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( freche457001096interp @ A @ B @ C ) )
% 2.91/1.61 = ( denota2077489681interp @ A @ B @ C ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_156_strm_Odomain,axiom,
% 2.91/1.61 ! [C: $tType,A: $tType] :
% 2.91/1.61 ( ( domainp @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( frechet_cr_strm @ A @ C ) )
% 2.91/1.61 = ( dfree @ A @ C ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_157_predicate1I,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.91/1.61 ( ! [X3: A] :
% 2.91/1.61 ( ( P2 @ X3 )
% 2.91/1.61 => ( Q @ X3 ) )
% 2.91/1.61 => ( ord_less_eq @ ( A > $o ) @ P2 @ Q ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_158_sup1CI,axiom,
% 2.91/1.61 ! [A: $tType,B2: A > $o,X2: A,A4: A > $o] :
% 2.91/1.61 ( ( ~ ( B2 @ X2 )
% 2.91/1.61 => ( A4 @ X2 ) )
% 2.91/1.61 => ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_159_fun__mono,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,D: $tType,C: $tType,C2: A > B > $o,A4: A > B > $o,B2: C > D > $o,D4: C > D > $o] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > B > $o ) @ C2 @ A4 )
% 2.91/1.61 => ( ( ord_less_eq @ ( C > D > $o ) @ B2 @ D4 )
% 2.91/1.61 => ( ord_less_eq @ ( ( A > C ) > ( B > D ) > $o ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 ) @ ( bNF_rel_fun @ A @ B @ C @ D @ C2 @ D4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_160_predicate1D,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,Q: A > $o,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > $o ) @ P2 @ Q )
% 2.91/1.61 => ( ( P2 @ X2 )
% 2.91/1.61 => ( Q @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_161_rev__predicate1D,axiom,
% 2.91/1.61 ! [A: $tType,P2: A > $o,X2: A,Q: A > $o] :
% 2.91/1.61 ( ( P2 @ X2 )
% 2.91/1.61 => ( ( ord_less_eq @ ( A > $o ) @ P2 @ Q )
% 2.91/1.61 => ( Q @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_162_sup1I2,axiom,
% 2.91/1.61 ! [A: $tType,B2: A > $o,X2: A,A4: A > $o] :
% 2.91/1.61 ( ( B2 @ X2 )
% 2.91/1.61 => ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_163_sup1I1,axiom,
% 2.91/1.61 ! [A: $tType,A4: A > $o,X2: A,B2: A > $o] :
% 2.91/1.61 ( ( A4 @ X2 )
% 2.91/1.61 => ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_164_sup1E,axiom,
% 2.91/1.61 ! [A: $tType,A4: A > $o,B2: A > $o,X2: A] :
% 2.91/1.61 ( ( sup_sup @ ( A > $o ) @ A4 @ B2 @ X2 )
% 2.91/1.61 => ( ~ ( A4 @ X2 )
% 2.91/1.61 => ( B2 @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_165_apply__rsp_H,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o,F: A > C,G: B > D,X2: A,Y: B] :
% 2.91/1.61 ( ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 @ F @ G )
% 2.91/1.61 => ( ( R1 @ X2 @ Y )
% 2.91/1.61 => ( R2 @ ( F @ X2 ) @ ( G @ Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_166_typedef__rep__transfer,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,Rep: B > A,Abs: A > B,A4: set @ A,T4: A > B > $o] :
% 2.91/1.61 ( ( type_definition @ B @ A @ Rep @ Abs @ A4 )
% 2.91/1.61 => ( ( T4
% 2.91/1.61 = ( ^ [X: A,Y2: B] :
% 2.91/1.61 ( X
% 2.91/1.61 = ( Rep @ Y2 ) ) ) )
% 2.91/1.61 => ( bNF_rel_fun @ A @ B @ A @ A @ T4
% 2.91/1.61 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 )
% 2.91/1.61 @ ^ [X: A] : X
% 2.91/1.61 @ Rep ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_167_dual__order_Oantisym,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [B3: A,A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( A2 = B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_168_dual__order_Oeq__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.91/1.61 = ( ^ [A6: A,B5: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ B5 @ A6 )
% 2.91/1.61 & ( ord_less_eq @ A @ A6 @ B5 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_169_dual__order_Otrans,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 2.91/1.61 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_170_linorder__wlog,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ! [P2: A > A > $o,A2: A,B3: A] :
% 2.91/1.61 ( ! [A8: A,B7: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A8 @ B7 )
% 2.91/1.61 => ( P2 @ A8 @ B7 ) )
% 2.91/1.61 => ( ! [A8: A,B7: A] :
% 2.91/1.61 ( ( P2 @ B7 @ A8 )
% 2.91/1.61 => ( P2 @ A8 @ B7 ) )
% 2.91/1.61 => ( P2 @ A2 @ B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_171_dual__order_Orefl,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_172_order__trans,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( preorder @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.91/1.61 => ( ord_less_eq @ A @ X2 @ Z2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_173_order__class_Oorder_Oantisym,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [A2: A,B3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.61 => ( A2 = B3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_174_ord__le__eq__trans,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ord @ A )
% 2.91/1.61 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( ( B3 = C3 )
% 2.91/1.61 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_175_ord__eq__le__trans,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( ord @ A )
% 2.91/1.61 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.61 ( ( A2 = B3 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.91/1.61 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_176_order__class_Oorder_Oeq__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.91/1.61 = ( ^ [A6: A,B5: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A6 @ B5 )
% 2.91/1.61 & ( ord_less_eq @ A @ B5 @ A6 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_177_antisym__conv,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [Y: A,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ Y @ X2 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 = ( X2 = Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_178_le__cases3,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ! [X2: A,Y: A,Z2: A] :
% 2.91/1.61 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.91/1.61 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ X2 @ Z2 ) )
% 2.91/1.61 => ( ( ( ord_less_eq @ A @ X2 @ Z2 )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.91/1.61 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 2.91/1.61 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ Z2 @ X2 ) )
% 2.91/1.61 => ~ ( ( ord_less_eq @ A @ Z2 @ X2 )
% 2.91/1.61 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_179_order_Otrans,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.91/1.61 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_180_le__cases,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_181_eq__refl,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( preorder @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ( X2 = Y )
% 2.91/1.61 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_182_linear,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_183_antisym,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ! [X2: A,Y: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.61 => ( ( ord_less_eq @ A @ Y @ X2 )
% 2.91/1.61 => ( X2 = Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_184_eq__iff,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order @ A )
% 2.91/1.61 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.91/1.61 = ( ^ [X: A,Y2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.61 & ( ord_less_eq @ A @ Y2 @ X ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_185_ord__le__eq__subst,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType] :
% 2.91/1.61 ( ( ( ord @ B )
% 2.91/1.61 & ( ord @ A ) )
% 2.91/1.61 => ! [A2: A,B3: A,F: A > B,C3: B] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( ( ( F @ B3 )
% 2.91/1.61 = C3 )
% 2.91/1.61 => ( ! [X3: A,Y3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.91/1.61 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.61 => ( ord_less_eq @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_186_ord__eq__le__subst,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType] :
% 2.91/1.61 ( ( ( ord @ B )
% 2.91/1.61 & ( ord @ A ) )
% 2.91/1.61 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.61 ( ( A2
% 2.91/1.61 = ( F @ B3 ) )
% 2.91/1.61 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.91/1.61 => ( ! [X3: B,Y3: B] :
% 2.91/1.61 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.61 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_187_order__subst2,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType] :
% 2.91/1.61 ( ( ( order @ C )
% 2.91/1.61 & ( order @ A ) )
% 2.91/1.61 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.61 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 2.91/1.61 => ( ! [X3: A,Y3: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.91/1.61 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.61 => ( ord_less_eq @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_188_order__subst1,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType] :
% 2.91/1.61 ( ( ( order @ B )
% 2.91/1.61 & ( order @ A ) )
% 2.91/1.61 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.61 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 2.91/1.61 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.91/1.61 => ( ! [X3: B,Y3: B] :
% 2.91/1.61 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.91/1.61 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.61 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_189_le__fun__def,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ord @ B )
% 2.91/1.61 => ( ( ord_less_eq @ ( A > B ) )
% 2.91/1.61 = ( ^ [F2: A > B,G2: A > B] :
% 2.91/1.61 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_190_le__funI,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ord @ B )
% 2.91/1.61 => ! [F: A > B,G: A > B] :
% 2.91/1.61 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 2.91/1.61 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_191_le__funE,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ord @ B )
% 2.91/1.61 => ! [F: A > B,G: A > B,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.91/1.61 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_192_le__funD,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ord @ B )
% 2.91/1.61 => ! [F: A > B,G: A > B,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.91/1.61 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_193_sterm__continuous,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.61 ( ( ( finite_finite @ A )
% 2.91/1.61 & ( finite_finite @ C )
% 2.91/1.61 & ( finite_finite @ B ) )
% 2.91/1.61 => ! [I: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C] :
% 2.91/1.61 ( ( denota2077489681interp @ A @ B @ C @ I )
% 2.91/1.61 => ( ( dfree @ A @ C @ Theta )
% 2.91/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ C ) ) ) @ ( denota126604975rm_sem @ A @ B @ C @ I @ Theta ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_194_sup__Un__eq,axiom,
% 2.91/1.61 ! [A: $tType,R3: set @ A,S: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( A > $o )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ R3 )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 2.91/1.61 = ( ^ [X: A] : ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ R3 @ S ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_195_pred__subset__eq,axiom,
% 2.91/1.61 ! [A: $tType,R3: set @ A,S: set @ A] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > $o )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ R3 )
% 2.91/1.61 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 2.91/1.61 = ( ord_less_eq @ ( set @ A ) @ R3 @ S ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_196_top__apply,axiom,
% 2.91/1.61 ! [C: $tType,D: $tType] :
% 2.91/1.61 ( ( top @ C )
% 2.91/1.61 => ( ( top_top @ ( D > C ) )
% 2.91/1.61 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_197_UNIV__I,axiom,
% 2.91/1.61 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_198_predicate2I,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,P2: A > B > $o,Q: A > B > $o] :
% 2.91/1.61 ( ! [X3: A,Y3: B] :
% 2.91/1.61 ( ( P2 @ X3 @ Y3 )
% 2.91/1.61 => ( Q @ X3 @ Y3 ) )
% 2.91/1.61 => ( ord_less_eq @ ( A > B > $o ) @ P2 @ Q ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_199_sup__top__right,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( bounded_lattice_top @ A )
% 2.91/1.61 => ! [X2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ X2 @ ( top_top @ A ) )
% 2.91/1.61 = ( top_top @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_200_sup__top__left,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( bounded_lattice_top @ A )
% 2.91/1.61 => ! [X2: A] :
% 2.91/1.61 ( ( sup_sup @ A @ ( top_top @ A ) @ X2 )
% 2.91/1.61 = ( top_top @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_201_fst__top,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( top @ A )
% 2.91/1.61 & ( top @ B ) )
% 2.91/1.61 => ( ( product_fst @ A @ B @ ( top_top @ ( product_prod @ A @ B ) ) )
% 2.91/1.61 = ( top_top @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_202_predicate2D,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,P2: A > B > $o,Q: A > B > $o,X2: A,Y: B] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > B > $o ) @ P2 @ Q )
% 2.91/1.61 => ( ( P2 @ X2 @ Y )
% 2.91/1.61 => ( Q @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_203_rev__predicate2D,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,P2: A > B > $o,X2: A,Y: B,Q: A > B > $o] :
% 2.91/1.61 ( ( P2 @ X2 @ Y )
% 2.91/1.61 => ( ( ord_less_eq @ ( A > B > $o ) @ P2 @ Q )
% 2.91/1.61 => ( Q @ X2 @ Y ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_204_top_Oextremum__uniqueI,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order_top @ A )
% 2.91/1.61 => ! [A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 2.91/1.61 => ( A2
% 2.91/1.61 = ( top_top @ A ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_205_top_Oextremum__unique,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order_top @ A )
% 2.91/1.61 => ! [A2: A] :
% 2.91/1.61 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 2.91/1.61 = ( A2
% 2.91/1.61 = ( top_top @ A ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_206_top__greatest,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( order_top @ A )
% 2.91/1.61 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( top_top @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_207_subset__UNIV,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( top_top @ ( set @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_208_Un__UNIV__left,axiom,
% 2.91/1.61 ! [A: $tType,B2: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 2.91/1.61 = ( top_top @ ( set @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_209_Un__UNIV__right,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A] :
% 2.91/1.61 ( ( sup_sup @ ( set @ A ) @ A4 @ ( top_top @ ( set @ A ) ) )
% 2.91/1.61 = ( top_top @ ( set @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_210_UNIV__witness,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_211_UNIV__eq__I,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A] :
% 2.91/1.61 ( ! [X3: A] : ( member @ A @ X3 @ A4 )
% 2.91/1.61 => ( ( top_top @ ( set @ A ) )
% 2.91/1.61 = A4 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_212_UNIV__def,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( top_top @ ( set @ A ) )
% 2.91/1.61 = ( collect @ A
% 2.91/1.61 @ ^ [X: A] : $true ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_213_DomainpE,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,R4: A > B > $o,A2: A] :
% 2.91/1.61 ( ( domainp @ A @ B @ R4 @ A2 )
% 2.91/1.61 => ~ ! [B7: B] :
% 2.91/1.61 ~ ( R4 @ A2 @ B7 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_214_Domainp_Ocases,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,R4: A > B > $o,A2: A] :
% 2.91/1.61 ( ( domainp @ A @ B @ R4 @ A2 )
% 2.91/1.61 => ~ ! [B7: B] :
% 2.91/1.61 ~ ( R4 @ A2 @ B7 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_215_Domainp_Osimps,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( domainp @ A @ B )
% 2.91/1.61 = ( ^ [R5: A > B > $o,A6: A] :
% 2.91/1.61 ? [B5: A,C4: B] :
% 2.91/1.61 ( ( A6 = B5 )
% 2.91/1.61 & ( R5 @ B5 @ C4 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_216_Domainp_ODomainI,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,R4: A > B > $o,A2: A,B3: B] :
% 2.91/1.61 ( ( R4 @ A2 @ B3 )
% 2.91/1.61 => ( domainp @ A @ B @ R4 @ A2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_217_Domainp_Oinducts,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,R4: A > B > $o,X2: A,P2: A > $o] :
% 2.91/1.61 ( ( domainp @ A @ B @ R4 @ X2 )
% 2.91/1.61 => ( ! [A8: A,B7: B] :
% 2.91/1.61 ( ( R4 @ A8 @ B7 )
% 2.91/1.61 => ( P2 @ A8 ) )
% 2.91/1.61 => ( P2 @ X2 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_218_fun_Orel__mono,axiom,
% 2.91/1.61 ! [D: $tType,B: $tType,A: $tType,R3: A > B > $o,Ra: A > B > $o] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > B > $o ) @ R3 @ Ra )
% 2.91/1.61 => ( ord_less_eq @ ( ( D > A ) > ( D > B ) > $o )
% 2.91/1.61 @ ( bNF_rel_fun @ D @ D @ A @ B
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 2.91/1.61 @ R3 )
% 2.91/1.61 @ ( bNF_rel_fun @ D @ D @ A @ B
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 2.91/1.61 @ Ra ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_219_continuous__on__cases__le,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ B ) )
% 2.91/1.61 => ! [S2: set @ A,H: A > real,A2: real,F: A > B,G: A > B] :
% 2.91/1.61 ( ( topolo2071040574ous_on @ A @ B
% 2.91/1.61 @ ( collect @ A
% 2.91/1.61 @ ^ [T3: A] :
% 2.91/1.61 ( ( member @ A @ T3 @ S2 )
% 2.91/1.61 & ( ord_less_eq @ real @ ( H @ T3 ) @ A2 ) ) )
% 2.91/1.61 @ F )
% 2.91/1.61 => ( ( topolo2071040574ous_on @ A @ B
% 2.91/1.61 @ ( collect @ A
% 2.91/1.61 @ ^ [T3: A] :
% 2.91/1.61 ( ( member @ A @ T3 @ S2 )
% 2.91/1.61 & ( ord_less_eq @ real @ A2 @ ( H @ T3 ) ) ) )
% 2.91/1.61 @ G )
% 2.91/1.61 => ( ( topolo2071040574ous_on @ A @ real @ S2 @ H )
% 2.91/1.61 => ( ! [T5: A] :
% 2.91/1.61 ( ( member @ A @ T5 @ S2 )
% 2.91/1.61 => ( ( ( H @ T5 )
% 2.91/1.61 = A2 )
% 2.91/1.61 => ( ( F @ T5 )
% 2.91/1.61 = ( G @ T5 ) ) ) )
% 2.91/1.61 => ( topolo2071040574ous_on @ A @ B @ S2
% 2.91/1.61 @ ^ [T3: A] : ( if @ B @ ( ord_less_eq @ real @ ( H @ T3 ) @ A2 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_220_continuous__on__cases__1,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( topolo503727757_space @ A )
% 2.91/1.61 => ! [S2: set @ real,A2: real,F: real > A,G: real > A] :
% 2.91/1.61 ( ( topolo2071040574ous_on @ real @ A
% 2.91/1.61 @ ( collect @ real
% 2.91/1.61 @ ^ [T3: real] :
% 2.91/1.61 ( ( member @ real @ T3 @ S2 )
% 2.91/1.61 & ( ord_less_eq @ real @ T3 @ A2 ) ) )
% 2.91/1.61 @ F )
% 2.91/1.61 => ( ( topolo2071040574ous_on @ real @ A
% 2.91/1.61 @ ( collect @ real
% 2.91/1.61 @ ^ [T3: real] :
% 2.91/1.61 ( ( member @ real @ T3 @ S2 )
% 2.91/1.61 & ( ord_less_eq @ real @ A2 @ T3 ) ) )
% 2.91/1.61 @ G )
% 2.91/1.61 => ( ( ( member @ real @ A2 @ S2 )
% 2.91/1.61 => ( ( F @ A2 )
% 2.91/1.61 = ( G @ A2 ) ) )
% 2.91/1.61 => ( topolo2071040574ous_on @ real @ A @ S2
% 2.91/1.61 @ ^ [T3: real] : ( if @ A @ ( ord_less_eq @ real @ T3 @ A2 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_221_agree__UNIV__eq,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),Omega: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A )] :
% 2.91/1.61 ( ( denotational_Vagree @ A @ Nu @ Omega @ ( top_top @ ( set @ ( sum_sum @ A @ A ) ) ) )
% 2.91/1.61 => ( Nu = Omega ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_222_top__empty__eq,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( top_top @ ( A > $o ) )
% 2.91/1.61 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_223_top__set__def,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( top_top @ ( set @ A ) )
% 2.91/1.61 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_224_fun_Orel__transfer,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,C: $tType,E2: $tType,D: $tType,Sa: A > C > $o,Sc2: B > E2 > $o] :
% 2.91/1.61 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > E2 > $o ) @ ( ( D > A ) > ( D > B ) > $o ) @ ( ( D > C ) > ( D > E2 ) > $o )
% 2.91/1.61 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( E2 > $o ) @ Sa
% 2.91/1.61 @ ( bNF_rel_fun @ B @ E2 @ $o @ $o @ Sc2
% 2.91/1.61 @ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
% 2.91/1.61 @ ( bNF_rel_fun @ ( D > A ) @ ( D > C ) @ ( ( D > B ) > $o ) @ ( ( D > E2 ) > $o )
% 2.91/1.61 @ ( bNF_rel_fun @ D @ D @ A @ C
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 2.91/1.61 @ Sa )
% 2.91/1.61 @ ( bNF_rel_fun @ ( D > B ) @ ( D > E2 ) @ $o @ $o
% 2.91/1.61 @ ( bNF_rel_fun @ D @ D @ B @ E2
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 2.91/1.61 @ Sc2 )
% 2.91/1.61 @ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
% 2.91/1.61 @ ( bNF_rel_fun @ D @ D @ A @ B
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 ) )
% 2.91/1.61 @ ( bNF_rel_fun @ D @ D @ C @ E2
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_225_fun_Orel__refl,axiom,
% 2.91/1.61 ! [B: $tType,D: $tType,Ra: B > B > $o,X2: D > B] :
% 2.91/1.61 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 2.91/1.61 => ( bNF_rel_fun @ D @ D @ B @ B
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 2.91/1.61 @ Ra
% 2.91/1.61 @ X2
% 2.91/1.61 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_226_fun_Orel__eq,axiom,
% 2.91/1.61 ! [A: $tType,D: $tType] :
% 2.91/1.61 ( ( bNF_rel_fun @ D @ D @ A @ A
% 2.91/1.61 @ ^ [Y4: D,Z3: D] : ( Y4 = Z3 )
% 2.91/1.61 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.91/1.61 = ( ^ [Y4: D > A,Z3: D > A] : ( Y4 = Z3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_227_frechet__continuous,axiom,
% 2.91/1.61 ! [I: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Theta: trm @ sf @ sz] :
% 2.91/1.61 ( ( denota2077489681interp @ sf @ sc @ sz @ I )
% 2.91/1.61 => ( ( dfree @ sf @ sz @ Theta )
% 2.91/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ sz ) @ ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real ) @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ sz ) ) ) @ ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ I ) @ ( frechet_simple_term @ sf @ sz @ Theta ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_228_rel__funI,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 2.91/1.61 ( ! [X3: A,Y3: B] :
% 2.91/1.61 ( ( A4 @ X3 @ Y3 )
% 2.91/1.61 => ( B2 @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 2.91/1.61 => ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 @ F @ G ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_229_top1I,axiom,
% 2.91/1.61 ! [A: $tType,X2: A] : ( top_top @ ( A > $o ) @ X2 ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_230_rel__funD,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y: B] :
% 2.91/1.61 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 @ F @ G )
% 2.91/1.61 => ( ( A4 @ X2 @ Y )
% 2.91/1.61 => ( B2 @ ( F @ X2 ) @ ( G @ Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_231_rel__fun__mono,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,X4: A > B > $o,A4: C > D > $o,F: A > C,G: B > D,Y5: A > B > $o,B2: C > D > $o] :
% 2.91/1.61 ( ( bNF_rel_fun @ A @ B @ C @ D @ X4 @ A4 @ F @ G )
% 2.91/1.61 => ( ! [X3: A,Y3: B] :
% 2.91/1.61 ( ( Y5 @ X3 @ Y3 )
% 2.91/1.61 => ( X4 @ X3 @ Y3 ) )
% 2.91/1.61 => ( ! [X3: C,Y3: D] :
% 2.91/1.61 ( ( A4 @ X3 @ Y3 )
% 2.91/1.61 => ( B2 @ X3 @ Y3 ) )
% 2.91/1.61 => ( bNF_rel_fun @ A @ B @ C @ D @ Y5 @ B2 @ F @ G ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_232_rel__fun__mono_H,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,Y5: A > B > $o,X4: A > B > $o,A4: C > D > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 2.91/1.61 ( ! [X3: A,Y3: B] :
% 2.91/1.61 ( ( Y5 @ X3 @ Y3 )
% 2.91/1.61 => ( X4 @ X3 @ Y3 ) )
% 2.91/1.61 => ( ! [X3: C,Y3: D] :
% 2.91/1.61 ( ( A4 @ X3 @ Y3 )
% 2.91/1.61 => ( B2 @ X3 @ Y3 ) )
% 2.91/1.61 => ( ( bNF_rel_fun @ A @ B @ C @ D @ X4 @ A4 @ F @ G )
% 2.91/1.61 => ( bNF_rel_fun @ A @ B @ C @ D @ Y5 @ B2 @ F @ G ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_233_ge__eq__refl,axiom,
% 2.91/1.61 ! [A: $tType,R3: A > A > $o,X2: A] :
% 2.91/1.61 ( ( ord_less_eq @ ( A > A > $o )
% 2.91/1.61 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 )
% 2.91/1.61 @ R3 )
% 2.91/1.61 => ( R3 @ X2 @ X2 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_234_refl__ge__eq,axiom,
% 2.91/1.61 ! [A: $tType,R3: A > A > $o] :
% 2.91/1.61 ( ! [X3: A] : ( R3 @ X3 @ X3 )
% 2.91/1.61 => ( ord_less_eq @ ( A > A > $o )
% 2.91/1.61 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 )
% 2.91/1.61 @ R3 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_235_let__rsp,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o] :
% 2.91/1.61 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 ) @ R2 )
% 2.91/1.61 @ ^ [S3: A,F2: A > C] : ( F2 @ S3 )
% 2.91/1.61 @ ^ [S3: B,F2: B > D] : ( F2 @ S3 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_236_Let__transfer,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o] :
% 2.91/1.61 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ A4 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 ) @ B2 )
% 2.91/1.61 @ ^ [S3: A,F2: A > C] : ( F2 @ S3 )
% 2.91/1.61 @ ^ [S3: B,F2: B > D] : ( F2 @ S3 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_237_rel__funD2,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType,A4: A > A > $o,B2: B > C > $o,F: A > B,G: A > C,X2: A] :
% 2.91/1.61 ( ( bNF_rel_fun @ A @ A @ B @ C @ A4 @ B2 @ F @ G )
% 2.91/1.61 => ( ( A4 @ X2 @ X2 )
% 2.91/1.61 => ( B2 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_238_rel__funE,axiom,
% 2.91/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y: B] :
% 2.91/1.61 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B2 @ F @ G )
% 2.91/1.61 => ( ( A4 @ X2 @ Y )
% 2.91/1.61 => ( B2 @ ( F @ X2 ) @ ( G @ Y ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_239_Domainp__refl,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( domainp @ A @ B )
% 2.91/1.61 = ( domainp @ A @ B ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_240_Domainp__iff,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( domainp @ A @ B )
% 2.91/1.61 = ( ^ [T6: A > B > $o,X: A] :
% 2.91/1.61 ? [X5: B] : ( T6 @ X @ X5 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_241_Domain__eq__top,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( domainp @ A @ A
% 2.91/1.61 @ ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.91/1.61 = ( top_top @ ( A > $o ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_242_iso__tuple__UNIV__I,axiom,
% 2.91/1.61 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_243_continuous__on__fst,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ B )
% 2.91/1.61 & ( topolo503727757_space @ C ) )
% 2.91/1.61 => ! [S2: set @ A,F: A > ( product_prod @ B @ C )] :
% 2.91/1.61 ( ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S2 @ F )
% 2.91/1.61 => ( topolo2071040574ous_on @ A @ B @ S2
% 2.91/1.61 @ ^ [X: A] : ( product_fst @ B @ C @ ( F @ X ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_244_continuous__on__cong,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ B ) )
% 2.91/1.61 => ! [S2: set @ A,T7: set @ A,F: A > B,G: A > B] :
% 2.91/1.61 ( ( S2 = T7 )
% 2.91/1.61 => ( ! [X3: A] :
% 2.91/1.61 ( ( member @ A @ X3 @ T7 )
% 2.91/1.61 => ( ( F @ X3 )
% 2.91/1.61 = ( G @ X3 ) ) )
% 2.91/1.61 => ( ( topolo2071040574ous_on @ A @ B @ S2 @ F )
% 2.91/1.61 = ( topolo2071040574ous_on @ A @ B @ T7 @ G ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_245_continuous__on__discrete,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo2133971006pology @ A )
% 2.91/1.61 & ( topolo503727757_space @ B ) )
% 2.91/1.61 => ! [A4: set @ A,F: A > B] : ( topolo2071040574ous_on @ A @ B @ A4 @ F ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_246_continuous__on__id,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( topolo503727757_space @ A )
% 2.91/1.61 => ! [S2: set @ A] :
% 2.91/1.61 ( topolo2071040574ous_on @ A @ A @ S2
% 2.91/1.61 @ ^ [X: A] : X ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_247_continuous__on__const,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ B ) )
% 2.91/1.61 => ! [S2: set @ A,C3: B] :
% 2.91/1.61 ( topolo2071040574ous_on @ A @ B @ S2
% 2.91/1.61 @ ^ [X: A] : C3 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_248_continuous__on__subset,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ B ) )
% 2.91/1.61 => ! [S2: set @ A,F: A > B,T7: set @ A] :
% 2.91/1.61 ( ( topolo2071040574ous_on @ A @ B @ S2 @ F )
% 2.91/1.61 => ( ( ord_less_eq @ ( set @ A ) @ T7 @ S2 )
% 2.91/1.61 => ( topolo2071040574ous_on @ A @ B @ T7 @ F ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_249_continuous__on__product__then__coordinatewise__UNIV,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ C ) )
% 2.91/1.61 => ! [F: A > B > C,I2: B] :
% 2.91/1.61 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ ( top_top @ ( set @ A ) ) @ F )
% 2.91/1.61 => ( topolo2071040574ous_on @ A @ C @ ( top_top @ ( set @ A ) )
% 2.91/1.61 @ ^ [X: A] : ( F @ X @ I2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_250_type__copy__ex__RepI,axiom,
% 2.91/1.61 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A,F3: B > $o] :
% 2.91/1.61 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 2.91/1.61 => ( ( ? [X5: B] : ( F3 @ X5 ) )
% 2.91/1.61 = ( ? [B5: A] : ( F3 @ ( Rep @ B5 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_251_conj__subset__def,axiom,
% 2.91/1.61 ! [A: $tType,A4: set @ A,P2: A > $o,Q: A > $o] :
% 2.91/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4
% 2.91/1.61 @ ( collect @ A
% 2.91/1.61 @ ^ [X: A] :
% 2.91/1.61 ( ( P2 @ X )
% 2.91/1.61 & ( Q @ X ) ) ) )
% 2.91/1.61 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ P2 ) )
% 2.91/1.61 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ Q ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_252_continuous__on__product__then__coordinatewise,axiom,
% 2.91/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ C ) )
% 2.91/1.61 => ! [S: set @ A,F: A > B > C,I2: B] :
% 2.91/1.61 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ S @ F )
% 2.91/1.61 => ( topolo2071040574ous_on @ A @ C @ S
% 2.91/1.61 @ ^ [X: A] : ( F @ X @ I2 ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_253_continuous__on__coordinatewise__then__product,axiom,
% 2.91/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 2.91/1.61 ( ( ( topolo503727757_space @ A )
% 2.91/1.61 & ( topolo503727757_space @ C ) )
% 2.91/1.61 => ! [S: set @ A,F: A > B > C] :
% 2.91/1.61 ( ! [I3: B] :
% 2.91/1.61 ( topolo2071040574ous_on @ A @ C @ S
% 2.91/1.61 @ ^ [X: A] : ( F @ X @ I3 ) )
% 2.91/1.61 => ( topolo2071040574ous_on @ A @ ( B > C ) @ S @ F ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_254_type__copy__obj__one__point__absE,axiom,
% 2.91/1.61 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,S2: A] :
% 2.91/1.61 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 2.91/1.61 => ~ ! [X3: B] :
% 2.91/1.61 ( S2
% 2.91/1.61 != ( Abs @ X3 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(fact_255_rel__fun__def__butlast,axiom,
% 2.91/1.61 ! [B: $tType,D: $tType,C: $tType,E2: $tType,F4: $tType,A: $tType,R3: A > B > $o,S: C > E2 > $o,T4: D > F4 > $o,F: A > C > D,G: B > E2 > F4] :
% 2.91/1.61 ( ( bNF_rel_fun @ A @ B @ ( C > D ) @ ( E2 > F4 ) @ R3 @ ( bNF_rel_fun @ C @ E2 @ D @ F4 @ S @ T4 ) @ F @ G )
% 2.91/1.61 = ( ! [X: A,Y2: B] :
% 2.91/1.61 ( ( R3 @ X @ Y2 )
% 2.91/1.61 => ( bNF_rel_fun @ C @ E2 @ D @ F4 @ S @ T4 @ ( F @ X ) @ ( G @ Y2 ) ) ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( finite_finite @ A )
% 2.91/1.61 => ( type @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ( type @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ( ord @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ( order @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.91/1.61 ! [A: $tType] :
% 2.91/1.61 ( ( linorder @ A )
% 2.91/1.61 => ( preorder @ A ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 2.91/1.61 ! [A9: $tType,A10: $tType] :
% 2.91/1.61 ( ( ( real_V55928688vector @ A9 )
% 2.91/1.61 & ( real_V55928688vector @ A10 ) )
% 2.91/1.61 => ( real_V55928688vector @ ( bounde2145540817linfun @ A9 @ A10 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 2.91/1.61 ! [A9: $tType,A10: $tType] :
% 2.91/1.61 ( ( ( ordere890947078_space @ A9 )
% 2.91/1.61 & ( finite_finite @ A10 ) )
% 2.91/1.61 => ( ordere890947078_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1,axiom,
% 2.91/1.61 ! [A9: $tType,A10: $tType] :
% 2.91/1.61 ( ( ( real_V55928688vector @ A9 )
% 2.91/1.61 & ( finite_finite @ A10 ) )
% 2.91/1.61 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice,axiom,
% 2.91/1.61 bounded_lattice @ product_unit ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Product__Type_Oprod___Lattices_Obounded__lattice_2,axiom,
% 2.91/1.61 ! [A9: $tType,A10: $tType] :
% 2.91/1.61 ( ( ( bounded_lattice @ A9 )
% 2.91/1.61 & ( bounded_lattice @ A10 ) )
% 2.91/1.61 => ( bounded_lattice @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space_3,axiom,
% 2.91/1.61 ! [A9: $tType,A10: $tType] :
% 2.91/1.61 ( ( ( ordere890947078_space @ A9 )
% 2.91/1.61 & ( ordere890947078_space @ A10 ) )
% 2.91/1.61 => ( ordere890947078_space @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_4,axiom,
% 2.91/1.61 ! [A9: $tType,A10: $tType] :
% 2.91/1.61 ( ( ( real_V55928688vector @ A9 )
% 2.91/1.61 & ( real_V55928688vector @ A10 ) )
% 2.91/1.61 => ( real_V55928688vector @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_5,axiom,
% 2.91/1.61 ordere890947078_space @ real ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_6,axiom,
% 2.91/1.61 real_V55928688vector @ real ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_7,axiom,
% 2.91/1.61 bounded_lattice @ $o ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_Set_Oset___Lattices_Obounded__lattice_8,axiom,
% 2.91/1.61 ! [A9: $tType] : ( bounded_lattice @ ( set @ A9 ) ) ).
% 2.91/1.61
% 2.91/1.61 thf(tcon_fun___Lattices_Obounded__lattice_9,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( bounded_lattice @ A10 )
% 2.91/1.62 => ( bounded_lattice @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( topolo503727757_space @ A10 )
% 2.91/1.62 => ( topolo503727757_space @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( bounded_lattice @ A10 )
% 2.91/1.62 => ( bounded_lattice_top @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( semilattice_sup @ A10 )
% 2.91/1.62 => ( semilattice_sup @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( order_top @ A10 )
% 2.91/1.62 => ( order_top @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( preorder @ A10 )
% 2.91/1.62 => ( preorder @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( finite_finite @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( lattice @ A10 )
% 2.91/1.62 => ( lattice @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( order @ A10 )
% 2.91/1.62 => ( order @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Orderings_Otop,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( top @ A10 )
% 2.91/1.62 => ( top @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Orderings_Oord,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ord @ A10 )
% 2.91/1.62 => ( ord @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_fun___Lattices_Osup,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( semilattice_sup @ A10 )
% 2.91/1.62 => ( sup @ ( A9 > A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_10,axiom,
% 2.91/1.62 ! [A9: $tType] : ( bounded_lattice_top @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_11,axiom,
% 2.91/1.62 ! [A9: $tType] : ( semilattice_sup @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Orderings_Oorder__top_12,axiom,
% 2.91/1.62 ! [A9: $tType] : ( order_top @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Orderings_Opreorder_13,axiom,
% 2.91/1.62 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Finite__Set_Ofinite_14,axiom,
% 2.91/1.62 ! [A9: $tType] :
% 2.91/1.62 ( ( finite_finite @ A9 )
% 2.91/1.62 => ( finite_finite @ ( set @ A9 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Lattices_Olattice_15,axiom,
% 2.91/1.62 ! [A9: $tType] : ( lattice @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Orderings_Oorder_16,axiom,
% 2.91/1.62 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Orderings_Otop_17,axiom,
% 2.91/1.62 ! [A9: $tType] : ( top @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Orderings_Oord_18,axiom,
% 2.91/1.62 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Set_Oset___Lattices_Osup_19,axiom,
% 2.91/1.62 ! [A9: $tType] : ( sup @ ( set @ A9 ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_20,axiom,
% 2.91/1.62 topolo503727757_space @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology,axiom,
% 2.91/1.62 topolo2133971006pology @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_21,axiom,
% 2.91/1.62 bounded_lattice_top @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_22,axiom,
% 2.91/1.62 semilattice_sup @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Orderings_Oorder__top_23,axiom,
% 2.91/1.62 order_top @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Orderings_Opreorder_24,axiom,
% 2.91/1.62 preorder @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.91/1.62 linorder @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Finite__Set_Ofinite_25,axiom,
% 2.91/1.62 finite_finite @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Lattices_Olattice_26,axiom,
% 2.91/1.62 lattice @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Orderings_Oorder_27,axiom,
% 2.91/1.62 order @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Orderings_Otop_28,axiom,
% 2.91/1.62 top @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Orderings_Oord_29,axiom,
% 2.91/1.62 ord @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_HOL_Obool___Lattices_Osup_30,axiom,
% 2.91/1.62 sup @ $o ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_31,axiom,
% 2.91/1.62 topolo503727757_space @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Lattices_Osemilattice__sup_32,axiom,
% 2.91/1.62 semilattice_sup @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Orderings_Opreorder_33,axiom,
% 2.91/1.62 preorder @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Orderings_Olinorder_34,axiom,
% 2.91/1.62 linorder @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Lattices_Olattice_35,axiom,
% 2.91/1.62 lattice @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Orderings_Oorder_36,axiom,
% 2.91/1.62 order @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Orderings_Oord_37,axiom,
% 2.91/1.62 ord @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Real_Oreal___Lattices_Osup_38,axiom,
% 2.91/1.62 sup @ real ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_39,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( finite_finite @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( finite_finite @ ( sum_sum @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_40,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( topolo503727757_space @ A9 )
% 2.91/1.62 & ( topolo503727757_space @ A10 ) )
% 2.91/1.62 => ( topolo503727757_space @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Lattices_Obounded__lattice__top_41,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( bounded_lattice @ A9 )
% 2.91/1.62 & ( bounded_lattice @ A10 ) )
% 2.91/1.62 => ( bounded_lattice_top @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_42,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( semilattice_sup @ A9 )
% 2.91/1.62 & ( semilattice_sup @ A10 ) )
% 2.91/1.62 => ( semilattice_sup @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Orderings_Oorder__top_43,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( order_top @ A9 )
% 2.91/1.62 & ( order_top @ A10 ) )
% 2.91/1.62 => ( order_top @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_44,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( preorder @ A9 )
% 2.91/1.62 & ( preorder @ A10 ) )
% 2.91/1.62 => ( preorder @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_45,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( finite_finite @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( finite_finite @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Lattices_Olattice_46,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( lattice @ A9 )
% 2.91/1.62 & ( lattice @ A10 ) )
% 2.91/1.62 => ( lattice @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Orderings_Oorder_47,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( order @ A9 )
% 2.91/1.62 & ( order @ A10 ) )
% 2.91/1.62 => ( order @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Orderings_Otop_48,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( top @ A9 )
% 2.91/1.62 & ( top @ A10 ) )
% 2.91/1.62 => ( top @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Orderings_Oord_49,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( ord @ A9 )
% 2.91/1.62 & ( ord @ A10 ) )
% 2.91/1.62 => ( ord @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Oprod___Lattices_Osup_50,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( sup @ A9 )
% 2.91/1.62 & ( sup @ A10 ) )
% 2.91/1.62 => ( sup @ ( product_prod @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_51,axiom,
% 2.91/1.62 bounded_lattice_top @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_52,axiom,
% 2.91/1.62 semilattice_sup @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_53,axiom,
% 2.91/1.62 order_top @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_54,axiom,
% 2.91/1.62 preorder @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_55,axiom,
% 2.91/1.62 linorder @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Finite__Set_Ofinite_56,axiom,
% 2.91/1.62 finite_finite @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Lattices_Olattice_57,axiom,
% 2.91/1.62 lattice @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Orderings_Oorder_58,axiom,
% 2.91/1.62 order @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Orderings_Otop_59,axiom,
% 2.91/1.62 top @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Orderings_Oord_60,axiom,
% 2.91/1.62 ord @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Product__Type_Ounit___Lattices_Osup_61,axiom,
% 2.91/1.62 sup @ product_unit ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_62,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( topolo503727757_space @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( topolo503727757_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__sup_63,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( ordere890947078_space @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( semilattice_sup @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_64,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( order @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( preorder @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_65,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( linorder @ A9 )
% 2.91/1.62 & ( cARD_1 @ A10 ) )
% 2.91/1.62 => ( linorder @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_66,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( finite_finite @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( finite_finite @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_67,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( ordere890947078_space @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( lattice @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_68,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( order @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( order @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_69,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( ord @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( ord @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osup_70,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( ordere890947078_space @ A9 )
% 2.91/1.62 & ( finite_finite @ A10 ) )
% 2.91/1.62 => ( sup @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_71,axiom,
% 2.91/1.62 ! [A9: $tType,A10: $tType] :
% 2.91/1.62 ( ( ( real_V55928688vector @ A9 )
% 2.91/1.62 & ( real_V55928688vector @ A10 ) )
% 2.91/1.62 => ( topolo503727757_space @ ( bounde2145540817linfun @ A9 @ A10 ) ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(help_If_3_1_T,axiom,
% 2.91/1.62 ! [P2: $o] :
% 2.91/1.62 ( ( P2 = $true )
% 2.91/1.62 | ( P2 = $false ) ) ).
% 2.91/1.62
% 2.91/1.62 thf(help_If_2_1_T,axiom,
% 2.91/1.62 ! [A: $tType,X2: A,Y: A] :
% 2.91/1.62 ( ( if @ A @ $false @ X2 @ Y )
% 2.91/1.62 = Y ) ).
% 2.91/1.62
% 2.91/1.62 thf(help_If_1_1_T,axiom,
% 2.91/1.62 ! [A: $tType,X2: A,Y: A] :
% 2.91/1.62 ( ( if @ A @ $true @ X2 @ Y )
% 2.91/1.62 = X2 ) ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_0,hypothesis,
% 2.91/1.62 finite_finite @ b ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_1,hypothesis,
% 2.91/1.62 finite_finite @ a ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_2,hypothesis,
% 2.91/1.62 finite_finite @ c ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_3,hypothesis,
% 2.91/1.62 finite_finite @ sc ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_4,hypothesis,
% 2.91/1.62 finite_finite @ sz ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_5,hypothesis,
% 2.91/1.62 linorder @ sz ).
% 2.91/1.62
% 2.91/1.62 thf(tfree_6,hypothesis,
% 2.91/1.62 finite_finite @ sf ).
% 2.91/1.62
% 2.91/1.62 thf(conj_0,conjecture,
% 2.91/1.62 ( denotational_Iagree @ a @ c @ b @ i @ j
% 2.91/1.62 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
% 2.91/1.62 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ c @ b )] :
% 2.91/1.62 ? [X: a] :
% 2.91/1.62 ( ( Uu
% 2.91/1.62 = ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ X ) )
% 2.91/1.62 & ( member @ a @ X @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ) ).
% 2.91/1.62 ------------------------
% 2.91/1.63 % (19997)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/2Mi)
% 2.91/1.64 % (19997)Instruction limit reached!
% 2.91/1.64 % (19997)------------------------------
% 2.91/1.64 % (19997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (19997)Termination reason: Unknown
% 2.91/1.64 % (19997)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (19997)Memory used [KB]: 1535
% 2.91/1.64 % (19997)Time elapsed: 0.003 s
% 2.91/1.64 % (19997)Instructions burned: 4 (million)
% 2.91/1.64 % (19997)------------------------------
% 2.91/1.64 % (19997)------------------------------
% 2.91/1.64 % (19994)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/183Mi)
% 2.91/1.64 % (19996)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_19346 for (2999ds/27Mi)
% 2.91/1.64 % (19995)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_19346 for (2999ds/4Mi)
% 2.91/1.64 % (19998)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_19346 for (2999ds/2Mi)
% 2.91/1.64 % (20000)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_19346 for (2999ds/275Mi)
% 2.91/1.64 % (20001)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/18Mi)
% 2.91/1.64 % (19998)Instruction limit reached!
% 2.91/1.64 % (19998)------------------------------
% 2.91/1.64 % (19998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (19998)Termination reason: Unknown
% 2.91/1.64 % (19998)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (19998)Memory used [KB]: 1535
% 2.91/1.64 % (19998)Time elapsed: 0.004 s
% 2.91/1.64 % (19998)Instructions burned: 3 (million)
% 2.91/1.64 % (19998)------------------------------
% 2.91/1.64 % (19998)------------------------------
% 2.91/1.64 % (19995)Instruction limit reached!
% 2.91/1.64 % (19995)------------------------------
% 2.91/1.64 % (19995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (19995)Termination reason: Unknown
% 2.91/1.64 % (19995)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (19995)Memory used [KB]: 1535
% 2.91/1.64 % (19995)Time elapsed: 0.005 s
% 2.91/1.64 % (19995)Instructions burned: 4 (million)
% 2.91/1.64 % (19995)------------------------------
% 2.91/1.64 % (19995)------------------------------
% 2.91/1.65 % (20004)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/3Mi)
% 2.91/1.65 % (20004)Instruction limit reached!
% 2.91/1.65 % (20004)------------------------------
% 2.91/1.65 % (20004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.65 % (20004)Termination reason: Unknown
% 2.91/1.65 % (20004)Termination phase: shuffling
% 2.91/1.65
% 2.91/1.65 % (20004)Memory used [KB]: 1535
% 2.91/1.65 % (20004)Time elapsed: 0.002 s
% 2.91/1.65 % (20004)Instructions burned: 3 (million)
% 2.91/1.65 % (20004)------------------------------
% 2.91/1.65 % (20004)------------------------------
% 2.91/1.65 % (20001)Instruction limit reached!
% 2.91/1.65 % (20001)------------------------------
% 2.91/1.65 % (20001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.65 % (20001)Termination reason: Unknown
% 2.91/1.65 % (20001)Termination phase: shuffling
% 2.91/1.65
% 2.91/1.65 % (20001)Memory used [KB]: 1918
% 2.91/1.65 % (20001)Time elapsed: 0.013 s
% 2.91/1.65 % (20001)Instructions burned: 18 (million)
% 2.91/1.65 % (20001)------------------------------
% 2.91/1.65 % (20001)------------------------------
% 2.91/1.66 % (20007)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_19346 for (2999ds/3Mi)
% 2.91/1.66 % (20007)Instruction limit reached!
% 2.91/1.66 % (20007)------------------------------
% 2.91/1.66 % (20007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (20007)Termination reason: Unknown
% 2.91/1.66 % (20007)Termination phase: shuffling
% 2.91/1.66
% 2.91/1.66 % (20007)Memory used [KB]: 1535
% 2.91/1.66 % (20007)Time elapsed: 0.002 s
% 2.91/1.66 % (20007)Instructions burned: 3 (million)
% 2.91/1.66 % (20007)------------------------------
% 2.91/1.66 % (20007)------------------------------
% 2.91/1.66 % (19996)Instruction limit reached!
% 2.91/1.66 % (19996)------------------------------
% 2.91/1.66 % (19996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (19996)Termination reason: Unknown
% 2.91/1.66 % (19996)Termination phase: shuffling
% 2.91/1.66
% 2.91/1.66 % (19996)Memory used [KB]: 2046
% 2.91/1.66 % (19996)Time elapsed: 0.020 s
% 2.91/1.66 % (19996)Instructions burned: 28 (million)
% 2.91/1.66 % (19996)------------------------------
% 2.91/1.66 % (19996)------------------------------
% 2.91/1.66 % (20005)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_19346 for (2999ds/37Mi)
% 2.91/1.66 % (20006)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_19346 for (2999ds/15Mi)
% 2.91/1.67 % (20009)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/7Mi)
% 2.91/1.67 % (20009)Instruction limit reached!
% 2.91/1.67 % (20009)------------------------------
% 2.91/1.67 % (20009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.67 % (20009)Termination reason: Unknown
% 2.91/1.67 % (20009)Termination phase: shuffling
% 2.91/1.67
% 2.91/1.67 % (20009)Memory used [KB]: 1663
% 2.91/1.67 % (20009)Time elapsed: 0.004 s
% 2.91/1.67 % (20009)Instructions burned: 9 (million)
% 2.91/1.67 % (20009)------------------------------
% 2.91/1.67 % (20009)------------------------------
% 2.91/1.67 % (20008)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_19346 for (2999ds/1041Mi)
% 2.91/1.67 % (20006)Instruction limit reached!
% 2.91/1.67 % (20006)------------------------------
% 2.91/1.67 % (20006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.67 % (20006)Termination reason: Unknown
% 2.91/1.67 % (20006)Termination phase: shuffling
% 2.91/1.67
% 2.91/1.67 % (20006)Memory used [KB]: 1791
% 2.91/1.67 % (20006)Time elapsed: 0.012 s
% 2.91/1.67 % (20006)Instructions burned: 15 (million)
% 2.91/1.67 % (20006)------------------------------
% 2.91/1.67 % (20006)------------------------------
% 2.91/1.68 % (20010)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/16Mi)
% 2.91/1.68 % (20011)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_19346 for (2999ds/3Mi)
% 2.91/1.68 % (20011)Instruction limit reached!
% 2.91/1.68 % (20011)------------------------------
% 2.91/1.68 % (20011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.68 % (20011)Termination reason: Unknown
% 2.91/1.68 % (20011)Termination phase: shuffling
% 2.91/1.68
% 2.91/1.68 % (20011)Memory used [KB]: 1535
% 2.91/1.68 % (20011)Time elapsed: 0.003 s
% 2.91/1.68 % (20011)Instructions burned: 5 (million)
% 2.91/1.68 % (20011)------------------------------
% 2.91/1.68 % (20011)------------------------------
% 2.91/1.68 % (20005)Instruction limit reached!
% 2.91/1.68 % (20005)------------------------------
% 2.91/1.68 % (20005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.68 % (20005)Termination reason: Unknown
% 2.91/1.68 % (20005)Termination phase: shuffling
% 2.91/1.68
% 2.91/1.68 % (20005)Memory used [KB]: 2302
% 2.91/1.68 % (20005)Time elapsed: 0.022 s
% 2.91/1.68 % (20005)Instructions burned: 37 (million)
% 2.91/1.68 % (20005)------------------------------
% 2.91/1.68 % (20005)------------------------------
% 2.91/1.69 % (20010)Instruction limit reached!
% 2.91/1.69 % (20010)------------------------------
% 2.91/1.69 % (20010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.69 % (20010)Termination reason: Unknown
% 2.91/1.69 % (20010)Termination phase: shuffling
% 2.91/1.69
% 2.91/1.69 % (20010)Memory used [KB]: 1791
% 2.91/1.69 % (20010)Time elapsed: 0.012 s
% 2.91/1.69 % (20010)Instructions burned: 16 (million)
% 2.91/1.69 % (20010)------------------------------
% 2.91/1.69 % (20010)------------------------------
% 2.91/1.69 % (20012)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_19346 for (2999ds/3Mi)
% 2.91/1.69 % (20013)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/7Mi)
% 2.91/1.69 % (20012)Instruction limit reached!
% 2.91/1.69 % (20012)------------------------------
% 2.91/1.69 % (20012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.69 % (20012)Termination reason: Unknown
% 2.91/1.69 % (20012)Termination phase: shuffling
% 2.91/1.69
% 2.91/1.69 % (20012)Memory used [KB]: 1535
% 2.91/1.69 % (20012)Time elapsed: 0.003 s
% 2.91/1.69 % (20012)Instructions burned: 4 (million)
% 2.91/1.69 % (20012)------------------------------
% 2.91/1.69 % (20012)------------------------------
% 2.91/1.69 % (20013)Instruction limit reached!
% 2.91/1.69 % (20013)------------------------------
% 2.91/1.69 % (20013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.69 % (20013)Termination reason: Unknown
% 2.91/1.69 % (20013)Termination phase: shuffling
% 2.91/1.69
% 2.91/1.69 % (20013)Memory used [KB]: 1663
% 2.91/1.69 % (20013)Time elapsed: 0.004 s
% 2.91/1.69 % (20013)Instructions burned: 8 (million)
% 2.91/1.69 % (20013)------------------------------
% 2.91/1.69 % (20013)------------------------------
% 2.97/1.70 % (20014)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/3Mi)
% 2.97/1.70 % (20014)Instruction limit reached!
% 2.97/1.70 % (20014)------------------------------
% 2.97/1.70 % (20014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.70 % (20014)Termination reason: Unknown
% 2.97/1.70 % (20014)Termination phase: shuffling
% 2.97/1.70
% 2.97/1.70 % (20014)Memory used [KB]: 1535
% 2.97/1.70 % (20014)Time elapsed: 0.003 s
% 2.97/1.70 % (20014)Instructions burned: 3 (million)
% 2.97/1.70 % (20014)------------------------------
% 2.97/1.70 % (20014)------------------------------
% 2.97/1.70 % (20017)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/710Mi)
% 2.97/1.70 % (20016)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/18Mi)
% 2.97/1.71 % (20015)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/4Mi)
% 2.97/1.71 % (20015)Instruction limit reached!
% 2.97/1.71 % (20015)------------------------------
% 2.97/1.71 % (20015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (20015)Termination reason: Unknown
% 2.97/1.71 % (20015)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (20015)Memory used [KB]: 1535
% 2.97/1.71 % (20015)Time elapsed: 0.005 s
% 2.97/1.71 % (20015)Instructions burned: 5 (million)
% 2.97/1.71 % (20015)------------------------------
% 2.97/1.71 % (20015)------------------------------
% 2.97/1.71 % (20016)Instruction limit reached!
% 2.97/1.71 % (20016)------------------------------
% 2.97/1.71 % (20016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (20016)Termination reason: Unknown
% 2.97/1.71 % (20016)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (20016)Memory used [KB]: 1918
% 2.97/1.71 % (20016)Time elapsed: 0.008 s
% 2.97/1.71 % (20016)Instructions burned: 18 (million)
% 2.97/1.71 % (20016)------------------------------
% 2.97/1.71 % (20016)------------------------------
% 2.97/1.71 % (20018)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/6Mi)
% 2.97/1.71 % (20018)Instruction limit reached!
% 2.97/1.71 % (20018)------------------------------
% 2.97/1.71 % (20018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (20018)Termination reason: Unknown
% 2.97/1.71 % (20018)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (20018)Memory used [KB]: 1535
% 2.97/1.71 % (20018)Time elapsed: 0.004 s
% 2.97/1.71 % (20018)Instructions burned: 7 (million)
% 2.97/1.71 % (20018)------------------------------
% 2.97/1.71 % (20018)------------------------------
% 2.97/1.72 % (20020)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_19346 for (2999ds/21Mi)
% 2.97/1.72 % (19994)Instruction limit reached!
% 2.97/1.72 % (19994)------------------------------
% 2.97/1.72 % (19994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.72 % (19994)Termination reason: Unknown
% 2.97/1.72 % (19994)Termination phase: Saturation
% 2.97/1.72
% 2.97/1.72 % (19994)Memory used [KB]: 7419
% 2.97/1.72 % (19994)Time elapsed: 0.084 s
% 2.97/1.72 % (19994)Instructions burned: 184 (million)
% 2.97/1.72 % (19994)------------------------------
% 2.97/1.72 % (19994)------------------------------
% 2.97/1.72 % (20021)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19346 for (2999ds/5Mi)
% 2.97/1.73 % (20019)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_19346 for (2999ds/902Mi)
% 2.97/1.73 % (20021)Instruction limit reached!
% 2.97/1.73 % (20021)------------------------------
% 2.97/1.73 % (20021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (20021)Termination reason: Unknown
% 2.97/1.73 % (20021)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (20021)Memory used [KB]: 1663
% 2.97/1.73 % (20021)Time elapsed: 0.004 s
% 2.97/1.73 % (20021)Instructions burned: 7 (million)
% 2.97/1.73 % (20021)------------------------------
% 2.97/1.73 % (20021)------------------------------
% 2.97/1.73 % (20020)Instruction limit reached!
% 2.97/1.73 % (20020)------------------------------
% 2.97/1.73 % (20020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (20020)Termination reason: Unknown
% 2.97/1.73 % (20020)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (20020)Memory used [KB]: 2046
% 2.97/1.73 % (20020)Time elapsed: 0.010 s
% 2.97/1.73 % (20020)Instructions burned: 22 (million)
% 2.97/1.73 % (20020)------------------------------
% 2.97/1.73 % (20020)------------------------------
% 2.97/1.74 % (20024)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_19346 for (2998ds/779Mi)
% 2.97/1.74 % (20022)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_19346 for (2998ds/6Mi)
% 2.97/1.74 % (20000)Instruction limit reached!
% 2.97/1.74 % (20000)------------------------------
% 2.97/1.74 % (20000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.74 % (20000)Termination reason: Unknown
% 2.97/1.74 % (20000)Termination phase: Saturation
% 2.97/1.74
% 2.97/1.74 % (20000)Memory used [KB]: 7547
% 2.97/1.74 % (20000)Time elapsed: 0.102 s
% 2.97/1.74 % (20000)Instructions burned: 276 (million)
% 2.97/1.74 % (20000)------------------------------
% 2.97/1.74 % (20000)------------------------------
% 2.97/1.74 % (20023)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19346 for (2998ds/377Mi)
% 2.97/1.75 % (20022)Instruction limit reached!
% 2.97/1.75 % (20022)------------------------------
% 2.97/1.75 % (20022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.75 % (20022)Termination reason: Unknown
% 2.97/1.75 % (20022)Termination phase: shuffling
% 2.97/1.75
% 2.97/1.75 % (20022)Memory used [KB]: 1663
% 2.97/1.75 % (20022)Time elapsed: 0.006 s
% 2.97/1.75 % (20022)Instructions burned: 6 (million)
% 2.97/1.75 % (20022)------------------------------
% 2.97/1.75 % (20022)------------------------------
% 2.97/1.75 % (20025)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_19346 for (2998ds/19Mi)
% 2.97/1.76 % (20025)Instruction limit reached!
% 2.97/1.76 % (20025)------------------------------
% 2.97/1.76 % (20025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.76 % (20025)Termination reason: Unknown
% 2.97/1.76 % (20025)Termination phase: shuffling
% 2.97/1.76
% 2.97/1.76 % (20025)Memory used [KB]: 1918
% 2.97/1.76 % (20025)Time elapsed: 0.007 s
% 2.97/1.76 % (20025)Instructions burned: 19 (million)
% 2.97/1.76 % (20025)------------------------------
% 2.97/1.76 % (20025)------------------------------
% 2.97/1.76 % (20026)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19346 for (2998ds/879Mi)
% 2.97/1.77 % (20027)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19346 for (2998ds/17Mi)
% 2.97/1.77 % (20027)Instruction limit reached!
% 2.97/1.77 % (20027)------------------------------
% 2.97/1.77 % (20027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.77 % (20027)Termination reason: Unknown
% 2.97/1.77 % (20027)Termination phase: shuffling
% 2.97/1.77
% 2.97/1.78 % (20027)Memory used [KB]: 1918
% 2.97/1.78 % (20027)Time elapsed: 0.008 s
% 2.97/1.78 % (20027)Instructions burned: 17 (million)
% 2.97/1.78 % (20027)------------------------------
% 2.97/1.78 % (20027)------------------------------
% 2.97/1.79 % (20028)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19346 for (2998ds/3Mi)
% 2.97/1.79 % (20028)Instruction limit reached!
% 2.97/1.79 % (20028)------------------------------
% 2.97/1.79 % (20028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.79 % (20028)Termination reason: Unknown
% 2.97/1.79 % (20028)Termination phase: shuffling
% 2.97/1.79
% 2.97/1.79 % (20028)Memory used [KB]: 1535
% 2.97/1.79 % (20028)Time elapsed: 0.003 s
% 2.97/1.79 % (20028)Instructions burned: 4 (million)
% 2.97/1.79 % (20028)------------------------------
% 2.97/1.79 % (20028)------------------------------
% 2.97/1.80 % (20032)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19346 for (2998ds/30Mi)
% 2.97/1.81 % (20032)Instruction limit reached!
% 2.97/1.81 % (20032)------------------------------
% 2.97/1.81 % (20032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.81 % (20032)Termination reason: Unknown
% 2.97/1.81 % (20032)Termination phase: shuffling
% 2.97/1.81
% 2.97/1.81 % (20032)Memory used [KB]: 2174
% 2.97/1.81 % (20032)Time elapsed: 0.013 s
% 2.97/1.81 % (20032)Instructions burned: 31 (million)
% 2.97/1.81 % (20032)------------------------------
% 2.97/1.81 % (20032)------------------------------
% 2.97/1.82 % (20039)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19346 for (2998ds/127Mi)
% 2.97/1.86 % (20039)Instruction limit reached!
% 2.97/1.86 % (20039)------------------------------
% 2.97/1.86 % (20039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.86 % (20039)Termination reason: Unknown
% 2.97/1.86 % (20039)Termination phase: Saturation
% 2.97/1.86
% 2.97/1.86 % (20039)Memory used [KB]: 7164
% 2.97/1.86 % (20039)Time elapsed: 0.043 s
% 2.97/1.86 % (20039)Instructions burned: 127 (million)
% 2.97/1.86 % (20039)------------------------------
% 2.97/1.86 % (20039)------------------------------
% 2.97/1.87 % (20040)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19346 for (2997ds/100Mi)
% 2.97/1.89 % (20023)Instruction limit reached!
% 2.97/1.89 % (20023)------------------------------
% 2.97/1.89 % (20023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.89 % (20023)Termination reason: Unknown
% 2.97/1.89 % (20023)Termination phase: Saturation
% 2.97/1.89
% 2.97/1.89 % (20023)Memory used [KB]: 8571
% 2.97/1.89 % (20023)Time elapsed: 0.148 s
% 2.97/1.89 % (20023)Instructions burned: 379 (million)
% 2.97/1.89 % (20023)------------------------------
% 2.97/1.89 % (20023)------------------------------
% 2.97/1.90 % (20041)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_19346 for (2997ds/3Mi)
% 2.97/1.90 % (20041)Instruction limit reached!
% 2.97/1.90 % (20041)------------------------------
% 2.97/1.90 % (20041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.90 % (20041)Termination reason: Unknown
% 2.97/1.90 % (20041)Termination phase: shuffling
% 2.97/1.90
% 2.97/1.90 % (20041)Memory used [KB]: 1535
% 2.97/1.90 % (20041)Time elapsed: 0.003 s
% 2.97/1.90 % (20041)Instructions burned: 6 (million)
% 2.97/1.90 % (20041)------------------------------
% 2.97/1.90 % (20041)------------------------------
% 2.97/1.90 % (20040)Instruction limit reached!
% 2.97/1.90 % (20040)------------------------------
% 2.97/1.90 % (20040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.90 % (20040)Termination reason: Unknown
% 2.97/1.90 % (20040)Termination phase: Property scanning
% 2.97/1.90
% 2.97/1.90 % (20040)Memory used [KB]: 2814
% 2.97/1.90 % (20040)Time elapsed: 0.033 s
% 2.97/1.90 % (20040)Instructions burned: 102 (million)
% 2.97/1.90 % (20040)------------------------------
% 2.97/1.90 % (20040)------------------------------
% 2.97/1.91 % (20042)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_19346 for (2997ds/20Mi)
% 2.97/1.91 % (20043)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_19346 for (2997ds/86Mi)
% 2.97/1.93 % (20042)Instruction limit reached!
% 2.97/1.93 % (20042)------------------------------
% 2.97/1.93 % (20042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.93 % (20042)Termination reason: Unknown
% 2.97/1.93 % (20042)Termination phase: shuffling
% 2.97/1.93
% 2.97/1.93 % (20042)Memory used [KB]: 1918
% 2.97/1.93 % (20042)Time elapsed: 0.013 s
% 2.97/1.93 % (20042)Instructions burned: 21 (million)
% 2.97/1.93 % (20042)------------------------------
% 2.97/1.93 % (20042)------------------------------
% 2.97/1.93 % (20017)Instruction limit reached!
% 2.97/1.93 % (20017)------------------------------
% 2.97/1.93 % (20017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.93 % (20017)Termination reason: Unknown
% 2.97/1.93 % (20017)Termination phase: Saturation
% 2.97/1.93
% 2.97/1.93 % (20017)Memory used [KB]: 8571
% 2.97/1.93 % (20017)Time elapsed: 0.225 s
% 2.97/1.93 % (20017)Instructions burned: 711 (million)
% 2.97/1.93 % (20017)------------------------------
% 2.97/1.93 % (20017)------------------------------
% 2.97/1.94 % (20045)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_19346 for (2997ds/39Mi)
% 2.97/1.94 % (20043)Instruction limit reached!
% 2.97/1.94 % (20043)------------------------------
% 2.97/1.94 % (20043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.94 % (20043)Termination reason: Unknown
% 2.97/1.94 % (20043)Termination phase: Property scanning
% 2.97/1.94
% 2.97/1.94 % (20043)Memory used [KB]: 2558
% 2.97/1.94 % (20043)Time elapsed: 0.029 s
% 2.97/1.94 % (20043)Instructions burned: 87 (million)
% 2.97/1.94 % (20043)------------------------------
% 2.97/1.94 % (20043)------------------------------
% 2.97/1.94 % (20044)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_19346 for (2997ds/107Mi)
% 2.97/1.95 % (20045)Instruction limit reached!
% 2.97/1.95 % (20045)------------------------------
% 2.97/1.95 % (20045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.95 % (20045)Termination reason: Unknown
% 2.97/1.95 % (20045)Termination phase: shuffling
% 2.97/1.95
% 2.97/1.95 % (20045)Memory used [KB]: 2302
% 2.97/1.95 % (20045)Time elapsed: 0.012 s
% 2.97/1.95 % (20045)Instructions burned: 39 (million)
% 2.97/1.95 % (20045)------------------------------
% 2.97/1.95 % (20045)------------------------------
% 2.97/1.95 % (20046)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/448Mi)
% 2.97/1.96 % (20047)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/46Mi)
% 2.97/1.97 % (20047)Instruction limit reached!
% 2.97/1.97 % (20047)------------------------------
% 2.97/1.97 % (20047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.97 % (20047)Termination reason: Unknown
% 2.97/1.97 % (20047)Termination phase: SInE selection
% 2.97/1.97
% 2.97/1.97 % (20047)Memory used [KB]: 2174
% 2.97/1.97 % (20047)Time elapsed: 0.017 s
% 2.97/1.97 % (20047)Instructions burned: 48 (million)
% 2.97/1.97 % (20047)------------------------------
% 2.97/1.97 % (20047)------------------------------
% 2.97/1.98 % (20048)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/98Mi)
% 2.97/2.00 % (20024)Instruction limit reached!
% 2.97/2.00 % (20024)------------------------------
% 2.97/2.00 % (20024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.00 % (20024)Termination reason: Unknown
% 2.97/2.00 % (20024)Termination phase: Saturation
% 2.97/2.00
% 2.97/2.00 % (20024)Memory used [KB]: 9338
% 2.97/2.00 % (20024)Time elapsed: 0.263 s
% 2.97/2.00 % (20024)Instructions burned: 779 (million)
% 2.97/2.00 % (20024)------------------------------
% 2.97/2.00 % (20024)------------------------------
% 2.97/2.00 % (20044)Instruction limit reached!
% 2.97/2.00 % (20044)------------------------------
% 2.97/2.00 % (20044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.00 % (20044)Termination reason: Unknown
% 2.97/2.00 % (20044)Termination phase: Saturation
% 2.97/2.00
% 2.97/2.00 % (20044)Memory used [KB]: 7036
% 2.97/2.00 % (20044)Time elapsed: 0.061 s
% 2.97/2.00 % (20044)Instructions burned: 108 (million)
% 2.97/2.00 % (20044)------------------------------
% 2.97/2.00 % (20044)------------------------------
% 2.97/2.01 % (20008)Instruction limit reached!
% 2.97/2.01 % (20008)------------------------------
% 2.97/2.01 % (20008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.01 % (20008)Termination reason: Unknown
% 2.97/2.01 % (20008)Termination phase: Saturation
% 2.97/2.01
% 2.97/2.01 % (20008)Memory used [KB]: 10234
% 2.97/2.01 % (20008)Time elapsed: 0.336 s
% 2.97/2.01 % (20008)Instructions burned: 1043 (million)
% 2.97/2.01 % (20008)------------------------------
% 2.97/2.01 % (20008)------------------------------
% 2.97/2.01 % (20048)Instruction limit reached!
% 2.97/2.01 % (20048)------------------------------
% 2.97/2.01 % (20048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.01 % (20048)Termination reason: Unknown
% 2.97/2.01 % (20048)Termination phase: Property scanning
% 2.97/2.01
% 2.97/2.01 % (20048)Memory used [KB]: 2814
% 2.97/2.01 % (20048)Time elapsed: 0.029 s
% 2.97/2.01 % (20048)Instructions burned: 100 (million)
% 2.97/2.01 % (20048)------------------------------
% 2.97/2.01 % (20048)------------------------------
% 2.97/2.02 % (20051)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/39Mi)
% 2.97/2.02 % (20049)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/507Mi)
% 2.97/2.02 % (20050)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/149Mi)
% 2.97/2.02 % (20052)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19346 for (2996ds/6Mi)
% 5.65/2.02 % (20052)Instruction limit reached!
% 5.65/2.02 % (20052)------------------------------
% 5.65/2.02 % (20052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.02 % (20052)Termination reason: Unknown
% 5.65/2.02 % (20052)Termination phase: shuffling
% 5.65/2.02
% 5.65/2.02 % (20052)Memory used [KB]: 1663
% 5.65/2.02 % (20052)Time elapsed: 0.003 s
% 5.65/2.02 % (20052)Instructions burned: 7 (million)
% 5.65/2.02 % (20052)------------------------------
% 5.65/2.02 % (20052)------------------------------
% 5.65/2.02 % (20019)Instruction limit reached!
% 5.65/2.02 % (20019)------------------------------
% 5.65/2.02 % (20019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.02 % (20019)Termination reason: Unknown
% 5.65/2.02 % (20019)Termination phase: Saturation
% 5.65/2.02
% 5.65/2.02 % (20019)Memory used [KB]: 8443
% 5.65/2.02 % (20019)Time elapsed: 0.300 s
% 5.65/2.02 % (20019)Instructions burned: 902 (million)
% 5.65/2.02 % (20019)------------------------------
% 5.65/2.02 % (20019)------------------------------
% 5.65/2.03 % (20051)Instruction limit reached!
% 5.65/2.03 % (20051)------------------------------
% 5.65/2.03 % (20051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.03 % (20051)Termination reason: Unknown
% 5.65/2.03 % (20051)Termination phase: Property scanning
% 5.65/2.03
% 5.65/2.03 % (20051)Memory used [KB]: 2174
% 5.65/2.03 % (20051)Time elapsed: 0.014 s
% 5.65/2.03 % (20051)Instructions burned: 40 (million)
% 5.65/2.03 % (20051)------------------------------
% 5.65/2.03 % (20051)------------------------------
% 5.65/2.03 % (20054)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/47Mi)
% 5.65/2.04 % (20053)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/1087Mi)
% 5.65/2.04 % (20055)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/44Mi)
% 5.65/2.05 % (20054)Instruction limit reached!
% 5.65/2.05 % (20054)------------------------------
% 5.65/2.05 % (20054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.05 % (20054)Termination reason: Unknown
% 5.65/2.05 % (20054)Termination phase: Preprocessing 1
% 5.65/2.05
% 5.65/2.05 % (20054)Memory used [KB]: 2174
% 5.65/2.05 % (20054)Time elapsed: 0.017 s
% 5.65/2.05 % (20054)Instructions burned: 47 (million)
% 5.65/2.05 % (20054)------------------------------
% 5.65/2.05 % (20054)------------------------------
% 5.65/2.05 % (20055)Instruction limit reached!
% 5.65/2.05 % (20055)------------------------------
% 5.65/2.05 % (20055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.05 % (20055)Termination reason: Unknown
% 5.65/2.05 % (20055)Termination phase: Property scanning
% 5.65/2.05
% 5.65/2.05 % (20055)Memory used [KB]: 2430
% 5.65/2.05 % (20055)Time elapsed: 0.014 s
% 5.65/2.05 % (20055)Instructions burned: 46 (million)
% 5.65/2.05 % (20055)------------------------------
% 5.65/2.05 % (20055)------------------------------
% 5.65/2.06 % (20056)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/432Mi)
% 5.65/2.06 % (20057)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/62Mi)
% 5.65/2.06 % (20050)Instruction limit reached!
% 5.65/2.06 % (20050)------------------------------
% 5.65/2.06 % (20050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.06 % (20050)Termination reason: Unknown
% 5.65/2.06 % (20050)Termination phase: Saturation
% 5.65/2.06
% 5.65/2.06 % (20050)Memory used [KB]: 7291
% 5.65/2.06 % (20050)Time elapsed: 0.050 s
% 5.65/2.06 % (20050)Instructions burned: 151 (million)
% 5.65/2.06 % (20050)------------------------------
% 5.65/2.06 % (20050)------------------------------
% 5.65/2.07 % (20058)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/31Mi)
% 5.65/2.08 % (20057)Instruction limit reached!
% 5.65/2.08 % (20057)------------------------------
% 5.65/2.08 % (20057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.08 % (20057)Termination reason: Unknown
% 5.65/2.08 % (20057)Termination phase: Property scanning
% 5.65/2.08
% 5.65/2.08 % (20057)Memory used [KB]: 2430
% 5.65/2.08 % (20057)Time elapsed: 0.019 s
% 5.65/2.08 % (20057)Instructions burned: 62 (million)
% 5.65/2.08 % (20057)------------------------------
% 5.65/2.08 % (20057)------------------------------
% 5.65/2.08 % (20046)Instruction limit reached!
% 5.65/2.08 % (20046)------------------------------
% 5.65/2.08 % (20046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.08 % (20046)Termination reason: Unknown
% 5.65/2.08 % (20046)Termination phase: Saturation
% 5.65/2.08
% 5.65/2.08 % (20046)Memory used [KB]: 8443
% 5.65/2.08 % (20046)Time elapsed: 0.159 s
% 5.65/2.08 % (20046)Instructions burned: 450 (million)
% 5.65/2.08 % (20046)------------------------------
% 5.65/2.08 % (20046)------------------------------
% 5.65/2.09 % (20058)Instruction limit reached!
% 5.65/2.09 % (20058)------------------------------
% 5.65/2.09 % (20058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.09 % (20058)Termination reason: Unknown
% 5.65/2.09 % (20058)Termination phase: Property scanning
% 5.65/2.09
% 5.65/2.09 % (20058)Memory used [KB]: 2174
% 5.65/2.09 % (20058)Time elapsed: 0.012 s
% 5.65/2.09 % (20058)Instructions burned: 31 (million)
% 5.65/2.09 % (20058)------------------------------
% 5.65/2.09 % (20058)------------------------------
% 5.65/2.09 % (20059)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/96Mi)
% 5.65/2.09 % (20060)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/453Mi)
% 5.65/2.09 % (20061)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/71Mi)
% 5.65/2.12 % (20026)Refutation not found, non-redundant clauses discarded% (20026)------------------------------
% 5.65/2.12 % (20026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.12 % (20026)Termination reason: Refutation not found, non-redundant clauses discarded
% 5.65/2.12
% 5.65/2.12 % (20026)Memory used [KB]: 9083
% 5.65/2.12 % (20026)Time elapsed: 0.355 s
% 5.65/2.12 % (20026)Instructions burned: 765 (million)
% 5.65/2.12 % (20026)------------------------------
% 5.65/2.12 % (20026)------------------------------
% 5.65/2.12 % (20059)Instruction limit reached!
% 5.65/2.12 % (20059)------------------------------
% 5.65/2.12 % (20059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.12 % (20059)Termination reason: Unknown
% 5.65/2.12 % (20059)Termination phase: Property scanning
% 5.65/2.12
% 5.65/2.12 % (20059)Memory used [KB]: 2558
% 5.65/2.12 % (20059)Time elapsed: 0.030 s
% 5.65/2.12 % (20059)Instructions burned: 98 (million)
% 5.65/2.12 % (20059)------------------------------
% 5.65/2.12 % (20059)------------------------------
% 5.65/2.12 % (20061)Instruction limit reached!
% 5.65/2.12 % (20061)------------------------------
% 5.65/2.12 % (20061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.12 % (20061)Termination reason: Unknown
% 5.65/2.12 % (20061)Termination phase: Property scanning
% 5.65/2.12
% 5.65/2.12 % (20061)Memory used [KB]: 2430
% 5.65/2.12 % (20061)Time elapsed: 0.023 s
% 5.65/2.12 % (20061)Instructions burned: 72 (million)
% 5.65/2.12 % (20061)------------------------------
% 5.65/2.12 % (20061)------------------------------
% 6.09/2.13 % (20063)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/11Mi)
% 6.09/2.13 % (20062)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/83Mi)
% 6.09/2.13 % (20064)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_19346 for (2995ds/41Mi)
% 6.09/2.13 % (20063)Instruction limit reached!
% 6.09/2.13 % (20063)------------------------------
% 6.09/2.13 % (20063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.13 % (20063)Termination reason: Unknown
% 6.09/2.13 % (20063)Termination phase: shuffling
% 6.09/2.13
% 6.09/2.13 % (20063)Memory used [KB]: 1791
% 6.09/2.13 % (20063)Time elapsed: 0.004 s
% 6.09/2.13 % (20063)Instructions burned: 11 (million)
% 6.09/2.13 % (20063)------------------------------
% 6.09/2.13 % (20063)------------------------------
% 6.09/2.14 % (20065)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/6Mi)
% 6.09/2.14 % (20064)Instruction limit reached!
% 6.09/2.14 % (20064)------------------------------
% 6.09/2.14 % (20064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.14 % (20064)Termination reason: Unknown
% 6.09/2.14 % (20064)Termination phase: Property scanning
% 6.09/2.14
% 6.09/2.14 % (20064)Memory used [KB]: 2430
% 6.09/2.14 % (20064)Time elapsed: 0.013 s
% 6.09/2.14 % (20064)Instructions burned: 43 (million)
% 6.09/2.14 % (20064)------------------------------
% 6.09/2.14 % (20064)------------------------------
% 6.09/2.14 % (20065)Instruction limit reached!
% 6.09/2.14 % (20065)------------------------------
% 6.09/2.14 % (20065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.14 % (20065)Termination reason: Unknown
% 6.09/2.14 % (20065)Termination phase: shuffling
% 6.09/2.14
% 6.09/2.14 % (20065)Memory used [KB]: 1535
% 6.09/2.14 % (20065)Time elapsed: 0.003 s
% 6.09/2.14 % (20065)Instructions burned: 6 (million)
% 6.09/2.14 % (20065)------------------------------
% 6.09/2.14 % (20065)------------------------------
% 6.09/2.15 % (20066)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/150Mi)
% 6.09/2.15 % (20067)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/343Mi)
% 6.09/2.15 % (20062)Instruction limit reached!
% 6.09/2.15 % (20062)------------------------------
% 6.09/2.15 % (20062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.15 % (20062)Termination reason: Unknown
% 6.09/2.15 % (20062)Termination phase: Property scanning
% 6.09/2.15
% 6.09/2.15 % (20062)Memory used [KB]: 2430
% 6.09/2.15 % (20062)Time elapsed: 0.026 s
% 6.09/2.15 % (20062)Instructions burned: 83 (million)
% 6.09/2.15 % (20062)------------------------------
% 6.09/2.15 % (20062)------------------------------
% 6.09/2.16 % (20068)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/109Mi)
% 6.09/2.18 % (20049)Instruction limit reached!
% 6.09/2.18 % (20049)------------------------------
% 6.09/2.18 % (20049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.18 % (20049)Termination reason: Unknown
% 6.09/2.18 % (20049)Termination phase: Saturation
% 6.09/2.18
% 6.09/2.18 % (20049)Memory used [KB]: 8187
% 6.09/2.18 % (20049)Time elapsed: 0.167 s
% 6.09/2.18 % (20049)Instructions burned: 507 (million)
% 6.09/2.18 % (20049)------------------------------
% 6.09/2.18 % (20049)------------------------------
% 6.09/2.19 % (20069)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/253Mi)
% 6.09/2.19 % (20068)Instruction limit reached!
% 6.09/2.19 % (20068)------------------------------
% 6.09/2.19 % (20068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.19 % (20068)Termination reason: Unknown
% 6.09/2.19 % (20068)Termination phase: Saturation
% 6.09/2.19
% 6.09/2.19 % (20068)Memory used [KB]: 7036
% 6.09/2.19 % (20068)Time elapsed: 0.034 s
% 6.09/2.19 % (20068)Instructions burned: 110 (million)
% 6.09/2.19 % (20068)------------------------------
% 6.09/2.19 % (20068)------------------------------
% 6.09/2.19 % (20066)Instruction limit reached!
% 6.09/2.19 % (20066)------------------------------
% 6.09/2.19 % (20066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.19 % (20066)Termination reason: Unknown
% 6.09/2.19 % (20066)Termination phase: Saturation
% 6.09/2.19
% 6.09/2.19 % (20066)Memory used [KB]: 7291
% 6.09/2.19 % (20066)Time elapsed: 0.047 s
% 6.09/2.19 % (20066)Instructions burned: 152 (million)
% 6.09/2.19 % (20066)------------------------------
% 6.09/2.19 % (20066)------------------------------
% 6.09/2.20 % (20056)Instruction limit reached!
% 6.09/2.20 % (20056)------------------------------
% 6.09/2.20 % (20056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.20 % (20056)Termination reason: Unknown
% 6.09/2.20 % (20056)Termination phase: Saturation
% 6.09/2.20
% 6.09/2.20 % (20056)Memory used [KB]: 5117
% 6.09/2.20 % (20056)Time elapsed: 0.137 s
% 6.09/2.20 % (20056)Instructions burned: 434 (million)
% 6.09/2.20 % (20056)------------------------------
% 6.09/2.20 % (20056)------------------------------
% 6.45/2.20 % (20070)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/140Mi)
% 6.45/2.20 % (20071)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/614Mi)
% 6.45/2.21 % (20072)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/202Mi)
% 6.45/2.23 % (20060)Instruction limit reached!
% 6.45/2.23 % (20060)------------------------------
% 6.45/2.23 % (20060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.23 % (20060)Termination reason: Unknown
% 6.45/2.23 % (20060)Termination phase: Saturation
% 6.45/2.23
% 6.45/2.23 % (20060)Memory used [KB]: 8827
% 6.45/2.23 % (20060)Time elapsed: 0.133 s
% 6.45/2.23 % (20060)Instructions burned: 455 (million)
% 6.45/2.23 % (20060)------------------------------
% 6.45/2.23 % (20060)------------------------------
% 6.45/2.24 % (20073)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_19346 for (2994ds/339Mi)
% 6.45/2.25 % (20070)Instruction limit reached!
% 6.45/2.25 % (20070)------------------------------
% 6.45/2.25 % (20070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.25 % (20070)Termination reason: Unknown
% 6.45/2.25 % (20070)Termination phase: Saturation
% 6.45/2.25
% 6.45/2.25 % (20070)Memory used [KB]: 7419
% 6.45/2.25 % (20070)Time elapsed: 0.046 s
% 6.45/2.25 % (20070)Instructions burned: 140 (million)
% 6.45/2.25 % (20070)------------------------------
% 6.45/2.25 % (20070)------------------------------
% 6.45/2.26 % (20067)Instruction limit reached!
% 6.45/2.26 % (20067)------------------------------
% 6.45/2.26 % (20067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.26 % (20067)Termination reason: Unknown
% 6.45/2.26 % (20067)Termination phase: Saturation
% 6.45/2.26
% 6.45/2.26 % (20067)Memory used [KB]: 8059
% 6.45/2.26 % (20067)Time elapsed: 0.108 s
% 6.45/2.26 % (20067)Instructions burned: 343 (million)
% 6.45/2.26 % (20067)------------------------------
% 6.45/2.26 % (20067)------------------------------
% 6.45/2.26 % (20074)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_19346 for (2993ds/283Mi)
% 6.45/2.27 % (20075)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_19346 for (2993ds/134Mi)
% 6.45/2.27 % (20072)Instruction limit reached!
% 6.45/2.27 % (20072)------------------------------
% 6.45/2.27 % (20072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.27 % (20072)Termination reason: Unknown
% 6.45/2.27 % (20072)Termination phase: Saturation
% 6.45/2.27
% 6.45/2.27 % (20072)Memory used [KB]: 7547
% 6.45/2.27 % (20072)Time elapsed: 0.084 s
% 6.45/2.27 % (20072)Instructions burned: 203 (million)
% 6.45/2.27 % (20072)------------------------------
% 6.45/2.27 % (20072)------------------------------
% 6.45/2.28 % (20069)Instruction limit reached!
% 6.45/2.28 % (20069)------------------------------
% 6.45/2.28 % (20069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.28 % (20069)Termination reason: Unknown
% 6.45/2.28 % (20069)Termination phase: Saturation
% 6.45/2.28
% 6.45/2.28 % (20069)Memory used [KB]: 8059
% 6.45/2.28 % (20069)Time elapsed: 0.086 s
% 6.45/2.28 % (20069)Instructions burned: 253 (million)
% 6.45/2.28 % (20069)------------------------------
% 6.45/2.28 % (20069)------------------------------
% 6.45/2.28 % (20076)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_19346 for (2993ds/298Mi)
% 6.45/2.29 % (20077)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_19346 for (2993ds/192Mi)
% 7.08/2.31 % (20075)Instruction limit reached!
% 7.08/2.31 % (20075)------------------------------
% 7.08/2.31 % (20075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.31 % (20075)Termination reason: Unknown
% 7.08/2.31 % (20075)Termination phase: Saturation
% 7.08/2.31
% 7.08/2.31 % (20075)Memory used [KB]: 7164
% 7.08/2.31 % (20075)Time elapsed: 0.042 s
% 7.08/2.31 % (20075)Instructions burned: 136 (million)
% 7.08/2.31 % (20075)------------------------------
% 7.08/2.31 % (20075)------------------------------
% 7.08/2.32 % (20078)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_19346 for (2993ds/258Mi)
% 7.08/2.34 % (20073)Instruction limit reached!
% 7.08/2.34 % (20073)------------------------------
% 7.08/2.34 % (20073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.34 % (20073)Termination reason: Unknown
% 7.08/2.34 % (20073)Termination phase: Saturation
% 7.08/2.34
% 7.08/2.34 % (20073)Memory used [KB]: 7931
% 7.08/2.34 % (20073)Time elapsed: 0.128 s
% 7.08/2.34 % (20073)Instructions burned: 340 (million)
% 7.08/2.34 % (20073)------------------------------
% 7.08/2.34 % (20073)------------------------------
% 7.08/2.34 % (20074)Instruction limit reached!
% 7.08/2.34 % (20074)------------------------------
% 7.08/2.34 % (20074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.34 % (20074)Termination reason: Unknown
% 7.08/2.34 % (20074)Termination phase: Saturation
% 7.08/2.34
% 7.08/2.34 % (20074)Memory used [KB]: 8187
% 7.08/2.34 % (20074)Time elapsed: 0.086 s
% 7.08/2.34 % (20074)Instructions burned: 285 (million)
% 7.08/2.34 % (20074)------------------------------
% 7.08/2.34 % (20074)------------------------------
% 7.08/2.35 % (20079)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/90Mi)
% 7.08/2.35 % (20077)Instruction limit reached!
% 7.08/2.35 % (20077)------------------------------
% 7.08/2.35 % (20077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.35 % (20077)Termination reason: Unknown
% 7.08/2.35 % (20077)Termination phase: Saturation
% 7.08/2.35
% 7.08/2.35 % (20077)Memory used [KB]: 8315
% 7.08/2.35 % (20077)Time elapsed: 0.065 s
% 7.08/2.35 % (20077)Instructions burned: 193 (million)
% 7.08/2.35 % (20077)------------------------------
% 7.08/2.35 % (20077)------------------------------
% 7.08/2.35 % (20080)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/231Mi)
% 7.08/2.36 % (20081)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/458Mi)
% 7.08/2.36 % (20076)Instruction limit reached!
% 7.08/2.36 % (20076)------------------------------
% 7.08/2.36 % (20076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.36 % (20076)Termination reason: Unknown
% 7.08/2.36 % (20076)Termination phase: Saturation
% 7.08/2.36
% 7.08/2.36 % (20076)Memory used [KB]: 8315
% 7.08/2.36 % (20076)Time elapsed: 0.086 s
% 7.08/2.36 % (20076)Instructions burned: 299 (million)
% 7.08/2.36 % (20076)------------------------------
% 7.08/2.36 % (20076)------------------------------
% 7.08/2.37 % (20082)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/31Mi)
% 7.08/2.38 % (20079)Instruction limit reached!
% 7.08/2.38 % (20079)------------------------------
% 7.08/2.38 % (20079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.38 % (20079)Termination reason: Unknown
% 7.08/2.38 % (20079)Termination phase: Property scanning
% 7.08/2.38
% 7.08/2.38 % (20079)Memory used [KB]: 2558
% 7.08/2.38 % (20079)Time elapsed: 0.028 s
% 7.08/2.38 % (20079)Instructions burned: 90 (million)
% 7.08/2.38 % (20079)------------------------------
% 7.08/2.38 % (20079)------------------------------
% 7.08/2.38 % (20053)Instruction limit reached!
% 7.08/2.38 % (20053)------------------------------
% 7.08/2.38 % (20053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.38 % (20053)Termination reason: Unknown
% 7.08/2.38 % (20053)Termination phase: Saturation
% 7.08/2.38
% 7.08/2.38 % (20053)Memory used [KB]: 8571
% 7.08/2.38 % (20053)Time elapsed: 0.347 s
% 7.08/2.38 % (20053)Instructions burned: 1088 (million)
% 7.08/2.38 % (20053)------------------------------
% 7.08/2.38 % (20053)------------------------------
% 7.08/2.38 % (20082)Instruction limit reached!
% 7.08/2.38 % (20082)------------------------------
% 7.08/2.38 % (20082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.38 % (20082)Termination reason: Unknown
% 7.08/2.38 % (20082)Termination phase: Property scanning
% 7.08/2.38
% 7.08/2.38 % (20082)Memory used [KB]: 2174
% 7.08/2.38 % (20082)Time elapsed: 0.012 s
% 7.08/2.38 % (20082)Instructions burned: 33 (million)
% 7.08/2.38 % (20082)------------------------------
% 7.08/2.38 % (20082)------------------------------
% 7.08/2.39 % (20071)Instruction limit reached!
% 7.08/2.39 % (20071)------------------------------
% 7.08/2.39 % (20071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.39 % (20071)Termination reason: Unknown
% 7.08/2.39 % (20071)Termination phase: Saturation
% 7.08/2.39
% 7.08/2.39 % (20071)Memory used [KB]: 8827
% 7.08/2.39 % (20071)Time elapsed: 0.205 s
% 7.08/2.39 % (20071)Instructions burned: 615 (million)
% 7.08/2.39 % (20071)------------------------------
% 7.08/2.39 % (20071)------------------------------
% 7.08/2.39 % (20083)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/297Mi)
% 7.08/2.39 % (20084)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/987Mi)
% 7.08/2.39 % (20085)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/182Mi)
% 7.08/2.40 % (20078)Instruction limit reached!
% 7.08/2.40 % (20078)------------------------------
% 7.08/2.40 % (20078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.40 % (20078)Termination reason: Unknown
% 8.12/2.40 % (20078)Termination phase: Saturation
% 8.12/2.40
% 8.12/2.40 % (20078)Memory used [KB]: 8187
% 8.12/2.40 % (20078)Time elapsed: 0.080 s
% 8.12/2.40 % (20078)Instructions burned: 258 (million)
% 8.12/2.40 % (20078)------------------------------
% 8.12/2.40 % (20078)------------------------------
% 8.12/2.40 % (20086)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/182Mi)
% 8.12/2.41 % (20087)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/154Mi)
% 8.12/2.42 % (20080)Instruction limit reached!
% 8.12/2.42 % (20080)------------------------------
% 8.12/2.42 % (20080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.42 % (20080)Termination reason: Unknown
% 8.12/2.42 % (20080)Termination phase: Saturation
% 8.12/2.42
% 8.12/2.42 % (20080)Memory used [KB]: 7547
% 8.12/2.42 % (20080)Time elapsed: 0.064 s
% 8.12/2.42 % (20080)Instructions burned: 233 (million)
% 8.12/2.42 % (20080)------------------------------
% 8.12/2.42 % (20080)------------------------------
% 8.12/2.42 % (20088)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_19346 for (2992ds/79Mi)
% 8.12/2.45 % (20085)Instruction limit reached!
% 8.12/2.45 % (20085)------------------------------
% 8.12/2.45 % (20085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.45 % (20085)Termination reason: Unknown
% 8.12/2.45 % (20085)Termination phase: Saturation
% 8.12/2.45
% 8.12/2.45 % (20085)Memory used [KB]: 7547
% 8.12/2.45 % (20085)Time elapsed: 0.056 s
% 8.12/2.45 % (20085)Instructions burned: 183 (million)
% 8.12/2.45 % (20085)------------------------------
% 8.12/2.45 % (20085)------------------------------
% 8.12/2.45 % (20087)Instruction limit reached!
% 8.12/2.45 % (20087)------------------------------
% 8.12/2.45 % (20087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.45 % (20087)Termination reason: Unknown
% 8.12/2.45 % (20087)Termination phase: Saturation
% 8.12/2.45
% 8.12/2.45 % (20087)Memory used [KB]: 3198
% 8.12/2.45 % (20087)Time elapsed: 0.044 s
% 8.12/2.45 % (20087)Instructions burned: 155 (million)
% 8.12/2.45 % (20087)------------------------------
% 8.12/2.45 % (20087)------------------------------
% 8.12/2.45 % (20088)Instruction limit reached!
% 8.12/2.45 % (20088)------------------------------
% 8.12/2.45 % (20088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.45 % (20088)Termination reason: Unknown
% 8.12/2.45 % (20088)Termination phase: Function definition elimination
% 8.12/2.45
% 8.12/2.45 % (20088)Memory used [KB]: 2430
% 8.12/2.45 % (20088)Time elapsed: 0.026 s
% 8.12/2.45 % (20088)Instructions burned: 80 (million)
% 8.12/2.45 % (20088)------------------------------
% 8.12/2.45 % (20088)------------------------------
% 8.12/2.45 % (20086)Instruction limit reached!
% 8.12/2.45 % (20086)------------------------------
% 8.12/2.45 % (20086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.45 % (20086)Termination reason: Unknown
% 8.12/2.45 % (20086)Termination phase: Saturation
% 8.12/2.45
% 8.12/2.45 % (20086)Memory used [KB]: 7547
% 8.12/2.45 % (20086)Time elapsed: 0.058 s
% 8.12/2.45 % (20086)Instructions burned: 184 (million)
% 8.12/2.45 % (20086)------------------------------
% 8.12/2.45 % (20086)------------------------------
% 8.12/2.46 % (20089)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/216Mi)
% 8.12/2.46 % (20090)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/114Mi)
% 8.12/2.46 % (20091)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/922Mi)
% 8.12/2.46 % (20092)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/182Mi)
% 8.12/2.47 % (20083)Instruction limit reached!
% 8.12/2.47 % (20083)------------------------------
% 8.12/2.47 % (20083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.47 % (20083)Termination reason: Unknown
% 8.12/2.47 % (20083)Termination phase: Saturation
% 8.12/2.47
% 8.12/2.47 % (20083)Memory used [KB]: 8187
% 8.12/2.47 % (20083)Time elapsed: 0.086 s
% 8.12/2.47 % (20083)Instructions burned: 298 (million)
% 8.12/2.47 % (20083)------------------------------
% 8.12/2.47 % (20083)------------------------------
% 8.12/2.48 % (20093)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/164Mi)
% 8.12/2.49 % (20090)Instruction limit reached!
% 8.12/2.49 % (20090)------------------------------
% 8.12/2.49 % (20090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.49 % (20090)Termination reason: Unknown
% 8.12/2.49 % (20090)Termination phase: Saturation
% 8.12/2.49
% 8.12/2.49 % (20090)Memory used [KB]: 7036
% 8.12/2.49 % (20090)Time elapsed: 0.035 s
% 8.12/2.49 % (20090)Instructions burned: 115 (million)
% 8.12/2.49 % (20090)------------------------------
% 8.12/2.49 % (20090)------------------------------
% 8.64/2.50 % (20094)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/50Mi)
% 8.64/2.51 % (20081)Instruction limit reached!
% 8.64/2.51 % (20081)------------------------------
% 8.64/2.51 % (20081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.51 % (20081)Termination reason: Unknown
% 8.64/2.51 % (20081)Termination phase: Saturation
% 8.64/2.51
% 8.64/2.51 % (20081)Memory used [KB]: 8571
% 8.64/2.51 % (20081)Time elapsed: 0.146 s
% 8.64/2.51 % (20081)Instructions burned: 460 (million)
% 8.64/2.51 % (20081)------------------------------
% 8.64/2.51 % (20081)------------------------------
% 8.64/2.51 % (20092)Instruction limit reached!
% 8.64/2.51 % (20092)------------------------------
% 8.64/2.51 % (20092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.51 % (20092)Termination reason: Unknown
% 8.64/2.51 % (20092)Termination phase: Saturation
% 8.64/2.51
% 8.64/2.51 % (20092)Memory used [KB]: 7547
% 8.64/2.51 % (20092)Time elapsed: 0.052 s
% 8.64/2.51 % (20092)Instructions burned: 182 (million)
% 8.64/2.51 % (20092)------------------------------
% 8.64/2.51 % (20092)------------------------------
% 8.64/2.52 % (20096)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/368Mi)
% 8.64/2.52 % (20094)Instruction limit reached!
% 8.64/2.52 % (20094)------------------------------
% 8.64/2.52 % (20094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.52 % (20094)Termination reason: Unknown
% 8.64/2.52 % (20094)Termination phase: Property scanning
% 8.64/2.52
% 8.64/2.52 % (20094)Memory used [KB]: 2430
% 8.64/2.52 % (20094)Time elapsed: 0.016 s
% 8.64/2.52 % (20094)Instructions burned: 53 (million)
% 8.64/2.52 % (20094)------------------------------
% 8.64/2.52 % (20094)------------------------------
% 8.64/2.52 % (20089)Instruction limit reached!
% 8.64/2.52 % (20089)------------------------------
% 8.64/2.52 % (20089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.52 % (20089)Termination reason: Unknown
% 8.64/2.52 % (20089)Termination phase: Saturation
% 8.64/2.52
% 8.64/2.52 % (20089)Memory used [KB]: 7675
% 8.64/2.52 % (20089)Time elapsed: 0.062 s
% 8.64/2.52 % (20089)Instructions burned: 218 (million)
% 8.64/2.52 % (20089)------------------------------
% 8.64/2.52 % (20089)------------------------------
% 8.64/2.52 % (20097)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/1021Mi)
% 8.64/2.53 % (20098)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/267Mi)
% 8.64/2.53 % (20099)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_19346 for (2991ds/204Mi)
% 8.64/2.53 % (20093)Instruction limit reached!
% 8.64/2.53 % (20093)------------------------------
% 8.64/2.53 % (20093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.53 % (20093)Termination reason: Unknown
% 8.64/2.53 % (20093)Termination phase: Saturation
% 8.64/2.53
% 8.64/2.53 % (20093)Memory used [KB]: 2942
% 8.64/2.53 % (20093)Time elapsed: 0.047 s
% 8.64/2.53 % (20093)Instructions burned: 164 (million)
% 8.64/2.53 % (20093)------------------------------
% 8.64/2.53 % (20093)------------------------------
% 8.64/2.54 % (20100)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19346 for (2990ds/26Mi)
% 8.64/2.55 % (20100)Instruction limit reached!
% 8.64/2.55 % (20100)------------------------------
% 8.64/2.55 % (20100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.55 % (20100)Termination reason: Unknown
% 8.64/2.55 % (20100)Termination phase: shuffling
% 8.64/2.55
% 8.64/2.55 % (20100)Memory used [KB]: 2174
% 8.64/2.55 % (20100)Time elapsed: 0.009 s
% 8.64/2.55 % (20100)Instructions burned: 27 (million)
% 8.64/2.55 % (20100)------------------------------
% 8.64/2.55 % (20100)------------------------------
% 8.64/2.55 % (20101)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_19346 for (2990ds/53Mi)
% 8.64/2.57 % (20101)Instruction limit reached!
% 8.64/2.57 % (20101)------------------------------
% 8.64/2.57 % (20101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.57 % (20101)Termination reason: Unknown
% 8.64/2.57 % (20101)Termination phase: Property scanning
% 8.64/2.57
% 8.64/2.57 % (20101)Memory used [KB]: 2430
% 8.64/2.57 % (20101)Time elapsed: 0.016 s
% 8.64/2.57 % (20101)Instructions burned: 54 (million)
% 8.64/2.57 % (20101)------------------------------
% 8.64/2.57 % (20101)------------------------------
% 8.64/2.58 % (20102)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_19346 for (2990ds/4436Mi)
% 8.64/2.59 % (20099)Instruction limit reached!
% 8.64/2.59 % (20099)------------------------------
% 8.64/2.59 % (20099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.59 % (20099)Termination reason: Unknown
% 8.64/2.59 % (20099)Termination phase: Saturation
% 8.64/2.59
% 8.64/2.59 % (20099)Memory used [KB]: 7547
% 8.64/2.59 % (20099)Time elapsed: 0.064 s
% 8.64/2.59 % (20099)Instructions burned: 204 (million)
% 8.64/2.59 % (20099)------------------------------
% 8.64/2.59 % (20099)------------------------------
% 9.13/2.60 % (20103)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_19346 for (2990ds/1539Mi)
% 9.13/2.61 % (20098)Instruction limit reached!
% 9.13/2.61 % (20098)------------------------------
% 9.13/2.61 % (20098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.61 % (20098)Termination reason: Unknown
% 9.13/2.61 % (20098)Termination phase: Saturation
% 9.13/2.61
% 9.13/2.61 % (20098)Memory used [KB]: 8059
% 9.13/2.61 % (20098)Time elapsed: 0.080 s
% 9.13/2.61 % (20098)Instructions burned: 269 (million)
% 9.13/2.61 % (20098)------------------------------
% 9.13/2.61 % (20098)------------------------------
% 9.13/2.61 % (20104)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_19346 for (2990ds/408Mi)
% 9.13/2.63 % (20096)Instruction limit reached!
% 9.13/2.63 % (20096)------------------------------
% 9.13/2.63 % (20096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.63 % (20096)Termination reason: Unknown
% 9.13/2.63 % (20096)Termination phase: Saturation
% 9.13/2.63
% 9.13/2.63 % (20096)Memory used [KB]: 8827
% 9.13/2.63 % (20096)Time elapsed: 0.117 s
% 9.13/2.63 % (20096)Instructions burned: 371 (million)
% 9.13/2.63 % (20096)------------------------------
% 9.13/2.63 % (20096)------------------------------
% 9.13/2.64 % (20105)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_19346 for (2989ds/5205Mi)
% 9.33/2.71 % (20084)Instruction limit reached!
% 9.33/2.71 % (20084)------------------------------
% 9.33/2.71 % (20084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.71 % (20084)Termination reason: Unknown
% 9.33/2.71 % (20084)Termination phase: Saturation
% 9.33/2.71
% 9.33/2.71 % (20084)Memory used [KB]: 10234
% 9.33/2.71 % (20084)Time elapsed: 0.321 s
% 9.33/2.71 % (20084)Instructions burned: 988 (million)
% 9.33/2.71 % (20084)------------------------------
% 9.33/2.71 % (20084)------------------------------
% 9.33/2.72 % (20106)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_19346 for (2989ds/1913Mi)
% 9.33/2.74 % (20104)Instruction limit reached!
% 9.33/2.74 % (20104)------------------------------
% 9.33/2.74 % (20104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.74 % (20104)Termination reason: Unknown
% 9.33/2.74 % (20104)Termination phase: Saturation
% 9.33/2.74
% 9.33/2.74 % (20104)Memory used [KB]: 8699
% 9.33/2.74 % (20104)Time elapsed: 0.127 s
% 9.33/2.74 % (20104)Instructions burned: 408 (million)
% 9.33/2.74 % (20104)------------------------------
% 9.33/2.74 % (20104)------------------------------
% 9.33/2.75 % (20091)Instruction limit reached!
% 9.33/2.75 % (20091)------------------------------
% 9.33/2.75 % (20091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.75 % (20091)Termination reason: Unknown
% 9.33/2.75 % (20091)Termination phase: Saturation
% 9.33/2.75
% 9.33/2.75 % (20091)Memory used [KB]: 8827
% 9.33/2.75 % (20091)Time elapsed: 0.292 s
% 9.33/2.75 % (20091)Instructions burned: 923 (million)
% 9.33/2.75 % (20091)------------------------------
% 9.33/2.75 % (20091)------------------------------
% 9.33/2.75 % (20107)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_19346 for (2988ds/4350Mi)
% 9.33/2.76 % (20108)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_19346 for (2988ds/68Mi)
% 9.33/2.78 % (20108)Instruction limit reached!
% 9.33/2.78 % (20108)------------------------------
% 9.33/2.78 % (20108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.78 % (20108)Termination reason: Unknown
% 9.33/2.78 % (20108)Termination phase: Preprocessing 3
% 9.33/2.78
% 9.33/2.78 % (20108)Memory used [KB]: 2430
% 9.33/2.78 % (20108)Time elapsed: 0.023 s
% 9.33/2.78 % (20108)Instructions burned: 68 (million)
% 9.33/2.78 % (20108)------------------------------
% 9.33/2.78 % (20108)------------------------------
% 9.33/2.79 % (20109)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_19346 for (2988ds/358Mi)
% 10.13/2.83 % (20097)Instruction limit reached!
% 10.13/2.83 % (20097)------------------------------
% 10.13/2.83 % (20097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.83 % (20097)Termination reason: Unknown
% 10.13/2.83 % (20097)Termination phase: Saturation
% 10.13/2.83
% 10.13/2.83 % (20097)Memory used [KB]: 9466
% 10.13/2.83 % (20097)Time elapsed: 0.308 s
% 10.13/2.83 % (20097)Instructions burned: 1021 (million)
% 10.13/2.83 % (20097)------------------------------
% 10.13/2.83 % (20097)------------------------------
% 10.13/2.84 % (20127)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19346 for (2987ds/31Mi)
% 10.13/2.85 % (20127)Instruction limit reached!
% 10.13/2.85 % (20127)------------------------------
% 10.13/2.85 % (20127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.85 % (20127)Termination reason: Unknown
% 10.13/2.85 % (20127)Termination phase: Property scanning
% 10.13/2.85
% 10.13/2.85 % (20127)Memory used [KB]: 2174
% 10.13/2.85 % (20127)Time elapsed: 0.012 s
% 10.13/2.85 % (20127)Instructions burned: 31 (million)
% 10.13/2.85 % (20127)------------------------------
% 10.13/2.85 % (20127)------------------------------
% 10.13/2.86 % (20128)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_19346 for (2987ds/279Mi)
% 10.46/2.91 % (20109)Instruction limit reached!
% 10.46/2.91 % (20109)------------------------------
% 10.46/2.91 % (20109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.91 % (20109)Termination reason: Unknown
% 10.46/2.91 % (20109)Termination phase: Saturation
% 10.46/2.91
% 10.46/2.91 % (20109)Memory used [KB]: 7803
% 10.46/2.91 % (20109)Time elapsed: 0.136 s
% 10.46/2.91 % (20109)Instructions burned: 358 (million)
% 10.46/2.91 % (20109)------------------------------
% 10.46/2.91 % (20109)------------------------------
% 10.46/2.92 % (20129)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_19346 for (2987ds/258Mi)
% 10.46/2.94 % (20128)Instruction limit reached!
% 10.46/2.94 % (20128)------------------------------
% 10.46/2.94 % (20128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.94 % (20128)Termination reason: Unknown
% 10.46/2.94 % (20128)Termination phase: Saturation
% 10.46/2.94
% 10.46/2.94 % (20128)Memory used [KB]: 8315
% 10.46/2.94 % (20128)Time elapsed: 0.081 s
% 10.46/2.94 % (20128)Instructions burned: 280 (million)
% 10.46/2.94 % (20128)------------------------------
% 10.46/2.94 % (20128)------------------------------
% 10.46/2.95 % (20130)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19346 for (2986ds/26Mi)
% 10.46/2.96 % (20130)Instruction limit reached!
% 10.46/2.96 % (20130)------------------------------
% 10.46/2.96 % (20130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.96 % (20130)Termination reason: Unknown
% 10.46/2.96 % (20130)Termination phase: shuffling
% 10.46/2.96
% 10.46/2.96 % (20130)Memory used [KB]: 2174
% 10.46/2.96 % (20130)Time elapsed: 0.009 s
% 10.46/2.96 % (20130)Instructions burned: 26 (million)
% 10.46/2.96 % (20130)------------------------------
% 10.46/2.96 % (20130)------------------------------
% 10.46/2.97 % (20131)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_19346 for (2986ds/995Mi)
% 10.46/3.00 % (20129)Instruction limit reached!
% 10.46/3.00 % (20129)------------------------------
% 10.46/3.00 % (20129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/3.00 % (20129)Termination reason: Unknown
% 10.46/3.00 % (20129)Termination phase: Saturation
% 10.46/3.00
% 10.46/3.00 % (20129)Memory used [KB]: 7931
% 10.46/3.00 % (20129)Time elapsed: 0.082 s
% 10.46/3.00 % (20129)Instructions burned: 259 (million)
% 10.46/3.00 % (20129)------------------------------
% 10.46/3.00 % (20129)------------------------------
% 10.46/3.01 % (20132)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_19346 for (2986ds/373Mi)
% 12.58/3.07 % (20103)Instruction limit reached!
% 12.58/3.07 % (20103)------------------------------
% 12.58/3.07 % (20103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.58/3.07 % (20103)Termination reason: Unknown
% 12.58/3.07 % (20103)Termination phase: Saturation
% 12.58/3.07
% 12.58/3.07 % (20103)Memory used [KB]: 11385
% 12.58/3.07 % (20103)Time elapsed: 0.475 s
% 12.58/3.07 % (20103)Instructions burned: 1541 (million)
% 12.58/3.07 % (20103)------------------------------
% 12.58/3.07 % (20103)------------------------------
% 12.58/3.08 % (20133)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_19346 for (2985ds/253Mi)
% 13.17/3.12 % (20132)Instruction limit reached!
% 13.17/3.12 % (20132)------------------------------
% 13.17/3.12 % (20132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.12 % (20132)Termination reason: Unknown
% 13.17/3.12 % (20132)Termination phase: Saturation
% 13.17/3.12
% 13.17/3.12 % (20132)Memory used [KB]: 8187
% 13.17/3.12 % (20132)Time elapsed: 0.118 s
% 13.17/3.12 % (20132)Instructions burned: 374 (million)
% 13.17/3.12 % (20132)------------------------------
% 13.17/3.12 % (20132)------------------------------
% 13.17/3.13 % (20106)First to succeed.
% 13.17/3.13 % (20134)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_19346 for (2984ds/832Mi)
% 13.17/3.13 % (20106)Refutation found. Thanks to Tanya!
% 13.17/3.13 % SZS status Theorem for DTF2THF_19346
% 13.17/3.13 % SZS output start Proof for DTF2THF_19346
% 13.17/3.13 thf(type_def_6, type, product_unit: $tType).
% 13.17/3.13 thf(type_def_7, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_8, type, sum_sum: ($tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_9, type, set: ($tType) > $tType).
% 13.17/3.13 thf(type_def_10, type, real: $tType).
% 13.17/3.13 thf(type_def_11, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_13, type, trm: ($tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_14, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_15, type, frechet_strm: ($tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_16, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 13.17/3.13 thf(type_def_17, type, a: $tType).
% 13.17/3.13 thf(type_def_18, type, c: $tType).
% 13.17/3.13 thf(type_def_19, type, b: $tType).
% 13.17/3.13 thf(type_def_20, type, sf: $tType).
% 13.17/3.13 thf(type_def_21, type, sc: $tType).
% 13.17/3.13 thf(type_def_22, type, sz: $tType).
% 13.17/3.13 thf(func_def_0, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_1, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_2, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_3, type, frechet_strm: ($tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_4, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_5, type, product_unit: $tType).
% 13.17/3.13 thf(func_def_6, type, product_prod: ($tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_7, type, sum_sum: ($tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_8, type, trm: ($tType * $tType) > $tType).
% 13.17/3.13 thf(func_def_9, type, real: $tType).
% 13.17/3.13 thf(func_def_10, type, set: ($tType) > $tType).
% 13.17/3.13 thf(func_def_11, type, sz: $tType).
% 13.17/3.13 thf(func_def_12, type, sf: $tType).
% 13.17/3.13 thf(func_def_13, type, sc: $tType).
% 13.17/3.13 thf(func_def_14, type, c: $tType).
% 13.17/3.13 thf(func_def_15, type, b: $tType).
% 13.17/3.13 thf(func_def_16, type, a: $tType).
% 13.17/3.13 thf(func_def_17, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_18, type, cARD_1: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_19, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_20, type, bounded_lattice: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_21, type, type: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_22, type, sup: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_23, type, ord: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_24, type, top: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_25, type, order: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_26, type, lattice: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_27, type, finite_finite: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_28, type, linorder: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_29, type, preorder: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_30, type, order_top: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_31, type, semilattice_sup: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_32, type, bounded_lattice_top: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_33, type, topolo2133971006pology: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_34, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 13.17/3.13 thf(func_def_35, type, bNF_rel_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > (X0 > X2) > (X1 > X3) > $o)).
% 13.17/3.13 thf(func_def_36, type, denotational_Iagree: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2 > $o)).
% 13.17/3.13 thf(func_def_37, type, denotational_Vagree: !>[X0: $tType]:(product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o)).
% 13.17/3.13 thf(func_def_38, type, denota593628964ctions: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ X3 > X0 > finite_Cartesian_vec @ real @ X2 > real)).
% 13.17/3.13 thf(func_def_39, type, denota2077489681interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o)).
% 13.17/3.13 thf(func_def_40, type, denota126604975rm_sem: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > real)).
% 13.17/3.13 thf(func_def_41, type, frechet_blin_frechet: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp @ X0 @ X1 @ X2 > frechet_strm @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > bounde2145540817linfun @ finite_Cartesian_vec @ real @ X2 @ real)).
% 13.17/3.13 thf(func_def_42, type, freche457001096interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2 > $o)).
% 13.17/3.13 thf(func_def_43, type, frechet_cr_strm: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > frechet_strm @ X0 @ X1 > $o)).
% 13.17/3.13 thf(func_def_44, type, freche227871258interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2)).
% 13.17/3.13 thf(func_def_45, type, freche229654227interp: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit)).
% 13.17/3.13 thf(func_def_46, type, frechet_raw_term: !>[X0: $tType, X1: $tType]:(frechet_strm @ X0 @ X1 > trm @ X0 @ X1)).
% 13.17/3.13 thf(func_def_47, type, frechet_simple_term: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > frechet_strm @ X0 @ X1)).
% 13.17/3.13 thf(func_def_48, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 13.17/3.13 thf(func_def_49, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 13.17/3.13 thf(func_def_50, type, rel_pred_comp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X1 > $o) > X0 > $o)).
% 13.17/3.13 thf(func_def_51, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 13.17/3.13 thf(func_def_52, type, top_top: !>[X0: $tType]:(X0)).
% 13.17/3.13 thf(func_def_53, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 13.17/3.13 thf(func_def_54, type, domainp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > $o)).
% 13.17/3.13 thf(func_def_55, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 13.17/3.13 thf(func_def_56, type, static_FVT: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > set @ sum_sum @ X1 @ X1)).
% 13.17/3.13 thf(func_def_57, type, static_SIGT: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > set @ X0)).
% 13.17/3.13 thf(func_def_58, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 13.17/3.13 thf(func_def_59, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 13.17/3.13 thf(func_def_60, type, dfree: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > $o)).
% 13.17/3.13 thf(func_def_61, type, times: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1)).
% 13.17/3.13 thf(func_def_62, type, topolo2071040574ous_on: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > X1) > $o)).
% 13.17/3.13 thf(func_def_63, type, type_definition: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > set @ X1 > $o)).
% 13.17/3.13 thf(func_def_64, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 13.17/3.13 thf(func_def_65, type, i: denota1663640101rp_ext @ a @ c @ b @ product_unit).
% 13.17/3.13 thf(func_def_66, type, j: denota1663640101rp_ext @ a @ c @ b @ product_unit).
% 13.17/3.13 thf(func_def_67, type, nu: product_prod @ finite_Cartesian_vec @ real @ b @ finite_Cartesian_vec @ real @ b).
% 13.17/3.13 thf(func_def_68, type, nu2: product_prod @ finite_Cartesian_vec @ real @ b @ finite_Cartesian_vec @ real @ b).
% 13.17/3.13 thf(func_def_69, type, theta_1: trm @ a @ b).
% 13.17/3.13 thf(func_def_70, type, theta_2: trm @ a @ b).
% 13.17/3.13 thf(func_def_85, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 13.17/3.13 thf(func_def_86, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 13.17/3.13 thf(func_def_87, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 13.17/3.13 thf(func_def_88, type, sK3: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_89, type, sK4: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 13.17/3.13 thf(func_def_90, type, sK5: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 13.17/3.13 thf(func_def_91, type, sK6: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 13.17/3.13 thf(func_def_92, type, sK7: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 13.17/3.13 thf(func_def_93, type, sK8: !>[X0: $tType]:(X0)).
% 13.17/3.13 thf(func_def_94, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > $o) > frechet_good_interp @ X2 @ X1 @ X0)).
% 13.17/3.13 thf(func_def_95, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit)).
% 13.17/3.13 thf(func_def_96, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 13.17/3.13 thf(func_def_97, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_98, type, sK13: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 13.17/3.13 thf(func_def_99, type, sK14: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 13.17/3.13 thf(func_def_100, type, sK15: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > $o) > X1)).
% 13.17/3.13 thf(func_def_101, type, sK16: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_102, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_103, type, sK18: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_104, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X3 > X2) > (X0 > X1) > (X1 > X2 > $o) > (X0 > X3 > $o) > X0)).
% 13.17/3.13 thf(func_def_105, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X3 > X2) > (X0 > X1) > (X1 > X2 > $o) > (X0 > X3 > $o) > X3)).
% 13.17/3.13 thf(func_def_106, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > frechet_good_interp @ X2 @ X1 @ X0)).
% 13.17/3.13 thf(func_def_107, type, sK22: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 13.17/3.13 thf(func_def_108, type, sK23: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 13.17/3.13 thf(func_def_109, type, sK24: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 13.17/3.13 thf(func_def_110, type, sK25: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 13.17/3.13 thf(func_def_111, type, sK26: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 13.17/3.13 thf(func_def_112, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0 > $o) > X1)).
% 13.17/3.13 thf(func_def_113, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_114, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > real > (X1 > real) > set @ X1 > X1)).
% 13.17/3.13 thf(func_def_115, type, sK30: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > $o) > X1)).
% 13.17/3.13 thf(func_def_116, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > set @ X2 > X1)).
% 13.17/3.13 thf(func_def_117, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 13.17/3.13 thf(func_def_118, type, sK33: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 13.17/3.13 thf(func_def_119, type, sK34: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 13.17/3.13 thf(func_def_120, type, sK35: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 13.17/3.13 thf(func_def_121, type, sK36: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_122, type, sK37: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_123, type, sK38: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_124, type, sK39: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_125, type, sK40: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_126, type, sK41: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_127, type, sK42: !>[X0: $tType]:(set @ X0 > X0)).
% 13.17/3.13 thf(func_def_128, type, sK43: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > frechet_strm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_129, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X2 @ X1 @ X0 > $o) > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit)).
% 13.17/3.13 thf(func_def_130, type, sK45: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_131, type, sK46: !>[X0: $tType, X1: $tType]:((frechet_strm @ X1 @ X0 > $o) > trm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_132, type, sK47: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_133, type, sK48: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_134, type, sK49: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_135, type, sK50: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_136, type, sK51: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_137, type, sK52: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_138, type, sK53: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_139, type, sK54: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 13.17/3.13 thf(func_def_140, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_141, type, sK56: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_142, type, sK57: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_143, type, sK58: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_144, type, sK59: !>[X0: $tType, X1: $tType]:(frechet_strm @ X1 @ X0 > trm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_145, type, sK60: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 13.17/3.13 thf(func_def_146, type, sK61: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_147, type, sK62: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > frechet_strm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_148, type, sK63: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > trm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_149, type, sK64: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > frechet_strm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_150, type, sK65: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > trm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_151, type, sK66: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_152, type, sK67: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > trm @ X1 @ X0 > trm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_153, type, sK68: frechet_strm @ a @ b).
% 13.17/3.13 thf(func_def_154, type, sK69: trm @ a @ b).
% 13.17/3.13 thf(func_def_155, type, sK70: !>[X0: $tType, X1: $tType]:(X1 > (X1 > X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_156, type, sK71: !>[X0: $tType, X1: $tType]:(X1 > (X1 > X0 > $o) > X1)).
% 13.17/3.13 thf(func_def_157, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((X0 > X1 > $o) > (X5 > X0 > X3) > (X5 > X2 > $o) > (X3 > X4 > $o) > (X2 > X1 > X4) > X2)).
% 13.17/3.13 thf(func_def_158, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((X0 > X1 > $o) > (X5 > X0 > X3) > (X5 > X2 > $o) > (X3 > X4 > $o) > (X2 > X1 > X4) > X5)).
% 13.17/3.13 thf(func_def_159, type, sK74: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_160, type, sK75: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > trm @ X1 @ X0 > trm @ X1 @ X0)).
% 13.17/3.13 thf(func_def_161, type, sK76: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > X1)).
% 13.17/3.13 thf(func_def_162, type, sK77: !>[X0: $tType]:((X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_163, type, sK78: frechet_strm @ a @ b).
% 13.17/3.13 thf(func_def_164, type, sK79: trm @ a @ b).
% 13.17/3.13 thf(func_def_165, type, sK80: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 13.17/3.13 thf(func_def_166, type, sK81: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_167, type, sK82: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 13.17/3.13 thf(func_def_168, type, sK83: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 13.17/3.13 thf(func_def_169, type, sK84: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 13.17/3.13 thf(func_def_170, type, ph85: !>[X0: $tType]:(X0)).
% 13.17/3.13 thf(f9637,plain,(
% 13.17/3.13 $false),
% 13.17/3.13 inference(subsumption_resolution,[status(thm)],[f9636,f1705])).
% 13.17/3.13 thf(f1705,plain,(
% 13.17/3.13 (finite_finite @ c = $true)),
% 13.17/3.13 inference(cnf_transformation,[status(thm)],[f371])).
% 13.17/3.13 thf(f371,plain,(
% 13.17/3.13 (finite_finite @ c = $true)),
% 13.17/3.13 inference(fool_elimination,[status(thm)],[f370])).
% 13.17/3.13 thf(f370,plain,(
% 13.17/3.13 finite_finite @ c),
% 13.17/3.13 inference(rectify,[status(thm)],[f354])).
% 13.17/3.13 thf(f354,axiom,(
% 13.17/3.13 finite_finite @ c),
% 13.17/3.13 file('/export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2THF_19346.p',tfree_2)).
% 13.17/3.13 thf(f9636,plain,(
% 13.17/3.13 (finite_finite @ c != $true)),
% 13.17/3.13 inference(subsumption_resolution,[status(thm)],[f9635,f1871])).
% 13.17/3.13 thf(f1871,plain,(
% 13.17/3.13 ($true != (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1)))))))))),
% 13.17/3.13 inference(cnf_transformation,[status(thm)],[f1046])).
% 13.17/3.13 thf(f1046,plain,(
% 13.17/3.13 ($true != (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1)))))))))),
% 13.17/3.13 inference(flattening,[status(thm)],[f869])).
% 13.17/3.13 thf(f869,plain,(
% 13.17/3.13 ~($true = (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1)))))))))),
% 13.17/3.13 inference(fool_elimination,[status(thm)],[f868])).
% 13.17/3.13 thf(f868,plain,(
% 13.17/3.13 ~(denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[X0 : sum_sum @ a @ sum_sum @ c @ b] : (? [X1 : a] : ((member @ a @ X1 @ (static_SIGT @ a @ b @ theta_1)) & ((sum_Inl @ a @ sum_sum @ c @ b @ X1) = X0))))))),
% 13.17/3.13 inference(rectify,[status(thm)],[f360])).
% 13.17/3.13 thf(f360,negated_conjecture,(
% 13.17/3.13 ~(denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[X11 : sum_sum @ a @ sum_sum @ c @ b] : (? [X12 : a] : ((member @ a @ X12 @ (static_SIGT @ a @ b @ theta_1)) & ((sum_Inl @ a @ sum_sum @ c @ b @ X12) = X11))))))),
% 13.17/3.13 inference(negated_conjecture,[status(cth)],[f359])).
% 13.17/3.13 thf(f359,conjecture,(
% 13.17/3.13 (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[X11 : sum_sum @ a @ sum_sum @ c @ b] : (? [X12 : a] : ((member @ a @ X12 @ (static_SIGT @ a @ b @ theta_1)) & ((sum_Inl @ a @ sum_sum @ c @ b @ X12) = X11))))))),
% 13.17/3.13 file('/export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2THF_19346.p',conj_0)).
% 13.17/3.13 thf(f9635,plain,(
% 13.17/3.13 ($true = (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1))))))))) | (finite_finite @ c != $true)),
% 13.17/3.13 inference(subsumption_resolution,[status(thm)],[f9634,f1666])).
% 13.17/3.13 thf(f1666,plain,(
% 13.17/3.13 (finite_finite @ b = $true)),
% 13.17/3.13 inference(cnf_transformation,[status(thm)],[f757])).
% 13.17/3.13 thf(f757,plain,(
% 13.17/3.13 (finite_finite @ b = $true)),
% 13.17/3.13 inference(fool_elimination,[status(thm)],[f756])).
% 13.17/3.13 thf(f756,plain,(
% 13.17/3.13 finite_finite @ b),
% 13.17/3.13 inference(rectify,[status(thm)],[f352])).
% 13.17/3.13 thf(f352,axiom,(
% 13.17/3.13 finite_finite @ b),
% 13.17/3.13 file('/export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2THF_19346.p',tfree_0)).
% 13.17/3.13 thf(f9634,plain,(
% 13.17/3.13 (finite_finite @ b != $true) | ($true = (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1))))))))) | (finite_finite @ c != $true)),
% 13.17/3.13 inference(trivial_inequality_removal,[status(thm)],[f9633])).
% 13.17/3.13 thf(f9633,plain,(
% 13.17/3.13 (finite_finite @ c != $true) | (finite_finite @ b != $true) | ($true != $true) | ($true = (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1)))))))))),
% 13.17/3.13 inference(superposition,[status(thm)],[f1525,f1697])).
% 13.17/3.13 thf(f1697,plain,(
% 13.17/3.13 ($true = (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))) & ((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0))))))))),
% 13.17/3.13 inference(cnf_transformation,[status(thm)],[f1013])).
% 13.17/3.13 thf(f1013,plain,(
% 13.17/3.13 ($true = (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[Y0 : sum_sum @ a @ sum_sum @ c @ b]: (?? @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))) & ((sum_Inl @ a @ sum_sum @ c @ b @ Y1) = Y0))))))))),
% 13.17/3.13 inference(fool_elimination,[status(thm)],[f1012])).
% 13.17/3.13 thf(f1012,plain,(
% 13.17/3.13 (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[X0 : sum_sum @ a @ sum_sum @ c @ b] : (? [X1 : a] : (((sum_Inl @ a @ sum_sum @ c @ b @ X1) = X0) & (member @ a @ X1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))))))))),
% 13.17/3.13 inference(rectify,[status(thm)],[f4])).
% 13.17/3.13 thf(f4,axiom,(
% 13.17/3.13 (denotational_Iagree @ a @ c @ b @ i @ j @ (collect @ sum_sum @ a @ sum_sum @ c @ b @ (^[X11 : sum_sum @ a @ sum_sum @ c @ b] : (? [X12 : a] : (((sum_Inl @ a @ sum_sum @ c @ b @ X12) = X11) & (member @ a @ X12 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))))))))),
% 13.17/3.13 file('/export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2THF_19346.p',fact_3_dfree__Times_Oprems_I2_J)).
% 13.17/3.13 thf(f1525,plain,(
% 13.17/3.13 ( ! [X1 : $tType,X0 : $tType,X2 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit,X3 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit] : (($true != (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))) & ((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0)))))))) | (finite_finite @ X0 != $true) | ($true = (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1))))))))) | (finite_finite @ X1 != $true)) )),
% 13.17/3.13 inference(cnf_transformation,[status(thm)],[f1239])).
% 13.17/3.13 thf(f1239,plain,(
% 13.17/3.13 ! [X0 : $tType,X1 : $tType] : ((finite_finite @ X0 != $true) | (finite_finite @ X1 != $true) | ! [X2 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit,X3 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit] : (($true = (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1))))))))) | ($true != (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))) & ((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0))))))))))),
% 13.17/3.13 inference(flattening,[status(thm)],[f1238])).
% 13.17/3.13 thf(f1238,plain,(
% 13.17/3.13 ! [X0 : $tType,X1 : $tType] : (! [X2 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit,X3 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit] : (($true = (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1))))))))) | ($true != (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))) & ((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0))))))))) | ((finite_finite @ X1 != $true) | (finite_finite @ X0 != $true)))),
% 13.17/3.13 inference(ennf_transformation,[status(thm)],[f947])).
% 13.17/3.13 thf(f947,plain,(
% 13.17/3.13 ! [X0 : $tType,X1 : $tType] : (((finite_finite @ X1 = $true) & (finite_finite @ X0 = $true)) => ! [X2 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit,X3 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit] : (($true = (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2))) & ((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0)))))))) => ($true = (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[Y0 : sum_sum @ a @ sum_sum @ X1 @ X0]: (?? @ a @ (^[Y1 : a]: (((sum_Inl @ a @ sum_sum @ X1 @ X0 @ Y1) = Y0) & (member @ a @ Y1 @ (static_SIGT @ a @ b @ theta_1)))))))))))),
% 13.17/3.13 inference(fool_elimination,[status(thm)],[f946])).
% 13.17/3.13 thf(f946,plain,(
% 13.17/3.13 ! [X0 : $tType,X1 : $tType] : ((finite_finite @ X0 & finite_finite @ X1) => ! [X2 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit,X3 : denota1663640101rp_ext @ a @ X1 @ X0 @ product_unit] : ((denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[X4 : sum_sum @ a @ sum_sum @ X1 @ X0] : (? [X5 : a] : (((sum_Inl @ a @ sum_sum @ X1 @ X0 @ X5) = X4) & (member @ a @ X5 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2)))))))) => (denotational_Iagree @ a @ X1 @ X0 @ X2 @ X3 @ (collect @ sum_sum @ a @ sum_sum @ X1 @ X0 @ (^[X6 : sum_sum @ a @ sum_sum @ X1 @ X0] : (? [X7 : a] : ((member @ a @ X7 @ (static_SIGT @ a @ b @ theta_1)) & ((sum_Inl @ a @ sum_sum @ X1 @ X0 @ X7) = X6))))))))),
% 13.17/3.13 inference(rectify,[status(thm)],[f1])).
% 13.17/3.13 thf(f1,axiom,(
% 13.17/3.13 ! [X1 : $tType,X2 : $tType] : ((finite_finite @ X1 & finite_finite @ X2) => ! [X9 : denota1663640101rp_ext @ a @ X2 @ X1 @ product_unit,X10 : denota1663640101rp_ext @ a @ X2 @ X1 @ product_unit] : ((denotational_Iagree @ a @ X2 @ X1 @ X9 @ X10 @ (collect @ sum_sum @ a @ sum_sum @ X2 @ X1 @ (^[X11 : sum_sum @ a @ sum_sum @ X2 @ X1] : (? [X12 : a] : (((sum_Inl @ a @ sum_sum @ X2 @ X1 @ X12) = X11) & (member @ a @ X12 @ (static_SIGT @ a @ b @ (times @ a @ b @ theta_1 @ theta_2)))))))) => (denotational_Iagree @ a @ X2 @ X1 @ X9 @ X10 @ (collect @ sum_sum @ a @ sum_sum @ X2 @ X1 @ (^[X11 : sum_sum @ a @ sum_sum @ X2 @ X1] : (? [X12 : a] : ((member @ a @ X12 @ (static_SIGT @ a @ b @ theta_1)) & ((sum_Inl @ a @ sum_sum @ X2 @ X1 @ X12) = X11))))))))),
% 13.17/3.13 file('/export/starexec/sandbox2/tmp/tmp.URX9kSdnnW/DTF2THF_19346.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062)).
% 13.17/3.13 % SZS output end Proof for DTF2THF_19346
% 13.17/3.13 % (20106)------------------------------
% 13.17/3.13 % (20106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.13 % (20106)Termination reason: Refutation
% 13.17/3.13
% 13.17/3.13 % (20106)Memory used [KB]: 6780
% 13.17/3.13 % (20106)Time elapsed: 0.432 s
% 13.17/3.13 % (20106)Instructions burned: 1293 (million)
% 13.17/3.13 % (20106)------------------------------
% 13.17/3.13 % (20106)------------------------------
% 13.17/3.13 % (19990)Success in time 1.522 s
%------------------------------------------------------------------------------