%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP038^2 : 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 : n022.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 08:55:03 AM UTC 2026
% Result : Theorem 7.44s 2.34s
% Output : Refutation 7.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP038^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n022.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 08:25:06 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP038^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : Sledgehammer Coincidence problem prob_231__7211966_1
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Des21]
% 0.30/0.45 % Names : Coincidence/prob_231__7211966_1 [Des21]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 404 ( 102 unt; 80 typ; 0 def)
% 0.30/0.45 % Number of atoms : 1201 ( 241 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 16 ( 3 avg)
% 0.30/0.45 % Number of connectives : 7244 ( 57 ~; 2 |; 311 &;6415 @)
% 0.30/0.45 % ( 0 <=>; 459 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 39 ( 12 avg)
% 0.30/0.45 % Number of types : 9 ( 8 usr)
% 0.30/0.45 % Number of type conns : 314 ( 314 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 75 ( 72 usr; 8 con; 0-13 aty)
% 0.30/0.45 % Number of variables : 1935 ( 117 ^;1698 !; 15 ?;1935 :)
% 0.30/0.45 % ( 105 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.45 % SPC : TH1_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:23:15.294
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % Could-be-implicit typings (19)
% 0.30/0.45 thf(ty_t_Denotational__Semantics_Ointerp_Ointerp__ext,type,
% 0.30/0.45 denota1663640101rp_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Frechet__Correctness_Oids_Ogood__interp,type,
% 0.30/0.45 frechet_good_interp: $tType > $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Bounded__Linear__Function_Oblinfun,type,
% 0.30/0.45 bounde2145540817linfun: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Frechet__Correctness_Oids_Ostrm,type,
% 0.30/0.45 frechet_strm: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 0.30/0.45 finite_Cartesian_vec: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Product__Type_Ounit,type,
% 0.30/0.45 product_unit: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.45 product_prod: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Syntax_Oformula,type,
% 0.30/0.45 formula: $tType > $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Sum__Type_Osum,type,
% 0.30/0.45 sum_sum: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Syntax_Otrm,type,
% 0.30/0.45 trm: $tType > $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Real_Oreal,type,
% 0.30/0.45 real: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_List_Olist,type,
% 0.30/0.45 list: $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Set_Oset,type,
% 0.30/0.45 set: $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_tf_sz,type,
% 0.30/0.45 sz: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_tf_sf,type,
% 0.30/0.45 sf: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_tf_sc,type,
% 0.30/0.45 sc: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_tf_c,type,
% 0.30/0.45 c: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_tf_b,type,
% 0.30/0.45 b: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_tf_a,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 % Explicit typings (61)
% 0.30/0.45 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 0.30/0.45 real_V55928688vector:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Cardinality_OCARD__1,type,
% 0.30/0.45 cARD_1:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_HOL_Otype,type,
% 0.30/0.45 type:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.45 ord:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Otop,type,
% 0.30/0.45 top:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.45 order:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.30/0.45 finite_finite:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.45 linorder:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.45 preorder:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oorder__top,type,
% 0.30/0.45 order_top:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 0.30/0.45 topolo503727757_space:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Euclidean__Algorithm_Oeuclidean__ring__gcd,type,
% 0.30/0.45 euclid1678468529ng_gcd:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Euclidean__Algorithm_Onormalization__euclidean__semiring,type,
% 0.30/0.45 euclid1155270486miring:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_BNF__Def_Oeq__onp,type,
% 0.30/0.45 bNF_eq_onp:
% 0.30/0.45 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2,type,
% 0.30/0.45 bNF_Greatest_image2:
% 0.30/0.45 !>[C: $tType,A: $tType,B: $tType] : ( ( set @ C ) > ( C > A ) > ( C > B ) > ( set @ ( product_prod @ A @ B ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Bounded__Linear__Function_Oblinfun_OBlinfun,type,
% 0.30/0.45 bounde688532126linfun:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > ( bounde2145540817linfun @ A @ B ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_OIagree,type,
% 0.30/0.45 denotational_Iagree:
% 0.30/0.45 !>[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 ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_OVagree,type,
% 0.30/0.45 denotational_Vagree:
% 0.30/0.45 !>[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 ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_Odirectional__derivative,type,
% 0.30/0.45 denota2078997598vative:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) ) > real ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_Ofrechet,type,
% 0.30/0.45 denotational_frechet:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( finite_Cartesian_vec @ real @ C ) > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_Ois__interp,type,
% 0.30/0.45 denota2077489681interp:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_Osterm__sem,type,
% 0.30/0.45 denota126604975rm_sem:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Oblin__frechet,type,
% 0.30/0.45 frechet_blin_frechet:
% 0.30/0.45 !>[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 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Ocr__good__interp,type,
% 0.30/0.45 freche457001096interp:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm,type,
% 0.30/0.45 frechet_cr_strm:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( trm @ A @ B ) > ( frechet_strm @ A @ B ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Ogood__interp,type,
% 0.30/0.45 freche227871258interp:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Oraw__interp,type,
% 0.30/0.45 freche229654227interp:
% 0.30/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( frechet_good_interp @ A @ B @ C ) > ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Oraw__term,type,
% 0.30/0.45 frechet_raw_term:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( frechet_strm @ A @ C ) > ( trm @ A @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Osimple__term,type,
% 0.30/0.45 frechet_simple_term:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( frechet_strm @ A @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Ids_Oids,type,
% 0.30/0.45 ids:
% 0.30/0.45 !>[Sz: $tType,Sf: $tType,Sc: $tType] : ( Sz > Sz > Sz > Sf > Sf > Sf > Sc > Sc > Sc > Sc > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_If,type,
% 0.30/0.45 if:
% 0.30/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Lifting_OQuotient,type,
% 0.30/0.45 quotient:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > ( B > A ) > ( A > B > $o ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.45 ord_less_eq:
% 0.30/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.30/0.45 top_top:
% 0.30/0.45 !>[A: $tType] : A ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.45 product_Pair:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.45 product_rec_prod:
% 0.30/0.45 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.30/0.45 product_fst:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 0.30/0.45 product_snd:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Set_OCollect,type,
% 0.30/0.45 collect:
% 0.30/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Static__Semantics_OFVDiff,type,
% 0.30/0.45 static_FVDiff:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ ( sum_sum @ C @ C ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Static__Semantics_OFVT,type,
% 0.30/0.45 static_FVT:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ ( sum_sum @ C @ C ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Static__Semantics_OSIGT,type,
% 0.30/0.45 static_SIGT:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Sum__Type_OInl,type,
% 0.30/0.45 sum_Inl:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.30/0.45 sum_rec_sum:
% 0.30/0.45 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_OPredicational,type,
% 0.30/0.45 predicational:
% 0.30/0.45 !>[B: $tType,A: $tType,C: $tType] : ( B > ( formula @ A @ B @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Odfree,type,
% 0.30/0.45 dfree:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Oids_OP,type,
% 0.30/0.45 p:
% 0.30/0.45 !>[Sc: $tType,Sf: $tType,Sz: $tType] : ( Sc > ( formula @ Sf @ Sc @ Sz ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Oids_Oempty,type,
% 0.30/0.45 empty:
% 0.30/0.45 !>[B: $tType,A: $tType] : ( B > ( trm @ A @ B ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Oids_Of0,type,
% 0.30/0.45 f0:
% 0.30/0.45 !>[Sf: $tType,Sz: $tType] : ( Sf > ( trm @ Sf @ Sz ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Otrm_OFunction,type,
% 0.30/0.45 function:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( A > ( C > ( trm @ A @ C ) ) > ( trm @ A @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.30/0.45 plus:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( trm @ A @ C ) > ( trm @ A @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.30/0.45 times:
% 0.30/0.45 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( trm @ A @ C ) > ( trm @ A @ C ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Topological__Spaces_Ocontinuous__on,type,
% 0.30/0.45 topolo2071040574ous_on:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Typedef_Otype__definition,type,
% 0.30/0.45 type_definition:
% 0.30/0.45 !>[B: $tType,A: $tType] : ( ( B > A ) > ( A > B ) > ( set @ A ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_member,type,
% 0.30/0.45 member:
% 0.30/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_I,type,
% 0.30/0.45 i: denota1663640101rp_ext @ a @ b @ c @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_J,type,
% 0.30/0.45 j: denota1663640101rp_ext @ a @ b @ c @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060nu_062,type,
% 0.30/0.45 nu: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060nu_062_H,type,
% 0.30/0.45 nu2: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_t1____,type,
% 0.30/0.45 t1: trm @ a @ c ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_t2____,type,
% 0.30/0.45 t2: trm @ a @ c ).
% 0.30/0.45
% 0.30/0.45 % Relevant facts (256)
% 0.30/0.45 thf(fact_0_agree__plus2,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 0.30/0.45 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( plus @ B @ A @ T1 @ T2 ) ) )
% 0.30/0.45 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_plus2
% 0.30/0.45 thf(fact_1_agree,axiom,
% 0.30/0.45 denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree
% 0.30/0.45 thf(fact_2_agree1,axiom,
% 0.30/0.45 denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t1 ) ).
% 0.30/0.45
% 0.30/0.45 % agree1
% 0.30/0.45 thf(fact_3_dfree2,axiom,
% 0.30/0.45 dfree @ a @ c @ t2 ).
% 0.30/0.45
% 0.30/0.45 % dfree2
% 0.30/0.45 thf(fact_4_agree__plus1,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 0.30/0.45 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( plus @ B @ A @ T1 @ T2 ) ) )
% 0.30/0.45 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_plus1
% 0.30/0.45 thf(fact_5_agree__comm,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [A2: 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 )] :
% 0.30/0.45 ( ( denotational_Vagree @ A @ A2 @ B2 @ V )
% 0.30/0.45 => ( denotational_Vagree @ A @ B2 @ A2 @ V ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_comm
% 0.30/0.45 thf(fact_6_agree__refl,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),A2: set @ ( sum_sum @ A @ A )] : ( denotational_Vagree @ A @ Nu @ Nu @ A2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_refl
% 0.30/0.45 thf(fact_7_dfree1,axiom,
% 0.30/0.45 dfree @ a @ c @ t1 ).
% 0.30/0.45
% 0.30/0.45 % dfree1
% 0.30/0.45 thf(fact_8_raw__interp__inject,axiom,
% 0.30/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.45 ( ( ( finite_finite @ A )
% 0.30/0.45 & ( finite_finite @ B )
% 0.30/0.45 & ( finite_finite @ C ) )
% 0.30/0.45 => ! [X: frechet_good_interp @ A @ B @ C,Y: frechet_good_interp @ A @ B @ C] :
% 0.30/0.45 ( ( ( freche229654227interp @ A @ B @ C @ X )
% 0.30/0.45 = ( freche229654227interp @ A @ B @ C @ Y ) )
% 0.30/0.45 = ( X = Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % raw_interp_inject
% 0.30/0.45 thf(fact_9_raw__term__inject,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C,Y: frechet_strm @ A @ C] :
% 0.30/0.45 ( ( ( frechet_raw_term @ A @ C @ X )
% 0.30/0.45 = ( frechet_raw_term @ A @ C @ Y ) )
% 0.30/0.45 = ( X = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 % raw_term_inject
% 0.30/0.45 thf(fact_10_agree__times1,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 0.30/0.45 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( times @ B @ A @ T1 @ T2 ) ) )
% 0.30/0.45 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_times1
% 0.30/0.45 thf(fact_11_agree__times2,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 0.30/0.45 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( times @ B @ A @ T1 @ T2 ) ) )
% 0.30/0.45 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_times2
% 0.30/0.45 thf(fact_12_agree__func,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( finite_finite @ A )
% 0.30/0.45 => ! [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 ),Var: B,Args: A > ( trm @ B @ A ),I: A] :
% 0.30/0.45 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( function @ B @ A @ Var @ Args ) ) )
% 0.30/0.45 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( Args @ I ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % agree_func
% 0.30/0.45 thf(fact_13_P__def,axiom,
% 0.30/0.45 ( ( p @ sc @ sf @ sz )
% 0.30/0.45 = ( predicational @ sc @ sf @ sz ) ) ).
% 0.30/0.45
% 0.30/0.45 % P_def
% 0.30/0.45 thf(fact_14_IH2,axiom,
% 0.30/0.45 ( ( denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t2 ) )
% 0.30/0.45 => ( ( denotational_Iagree @ a @ b @ c @ i @ j
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t2 ) ) ) ) )
% 0.30/0.45 => ( ( denotational_frechet @ a @ b @ c @ i @ t2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) )
% 0.30/0.45 = ( denotational_frechet @ a @ b @ c @ j @ t2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % IH2
% 0.30/0.45 thf(fact_15_seq__sem_Ocases,axiom,
% 0.30/0.45 ! [X: product_prod @ ( denota1663640101rp_ext @ sf @ sc @ sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ sf @ sc @ sz ) ) @ ( list @ ( formula @ sf @ sc @ sz ) ) )] :
% 0.30/0.45 ~ ! [I2: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,S: product_prod @ ( list @ ( formula @ sf @ sc @ sz ) ) @ ( list @ ( formula @ sf @ sc @ sz ) )] :
% 0.30/0.45 ( X
% 0.30/0.45 != ( product_Pair @ ( denota1663640101rp_ext @ sf @ sc @ sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ sf @ sc @ sz ) ) @ ( list @ ( formula @ sf @ sc @ sz ) ) ) @ I2 @ S ) ) ).
% 0.30/0.45
% 0.30/0.45 % seq_sem.cases
% 0.30/0.45 thf(fact_16_raw__term,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C] : ( member @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C @ X ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % raw_term
% 0.30/0.45 thf(fact_17_raw__term__cases,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 0.30/0.45 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.45 => ~ ! [X3: frechet_strm @ A @ C] :
% 0.30/0.45 ( Y
% 0.30/0.45 != ( frechet_raw_term @ A @ C @ X3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % raw_term_cases
% 0.30/0.45 thf(fact_18_raw__term__induct,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,Y: trm @ A @ C,P: ( trm @ A @ C ) > $o] :
% 0.30/0.45 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.45 => ( ! [X3: frechet_strm @ A @ C] : ( P @ ( frechet_raw_term @ A @ C @ X3 ) )
% 0.30/0.45 => ( P @ Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % raw_term_induct
% 0.30/0.45 thf(fact_19_coincidence__frechet,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType,C: $tType] :
% 0.30/0.45 ( ( ( finite_finite @ C )
% 0.30/0.45 & ( finite_finite @ A )
% 0.30/0.45 & ( finite_finite @ B ) )
% 0.30/0.45 => ! [Theta: trm @ A @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),I3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.45 ( ( dfree @ A @ C @ Theta )
% 0.30/0.45 => ( ( denotational_Vagree @ C @ Nu @ Nu2 @ ( static_FVDiff @ A @ C @ Theta ) )
% 0.30/0.45 => ( ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 0.30/0.45 = ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % coincidence_frechet
% 0.30/0.45 thf(fact_20_IA,axiom,
% 0.30/0.45 ( denotational_Iagree @ a @ b @ c @ i @ j
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % IA
% 0.30/0.45 thf(fact_21_IA1,axiom,
% 0.30/0.45 ( denotational_Iagree @ a @ b @ c @ i @ j
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % IA1
% 0.30/0.45 thf(fact_22_IA2,axiom,
% 0.30/0.45 ( denotational_Iagree @ a @ b @ c @ i @ j
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % IA2
% 0.30/0.45 thf(fact_23_IH1,axiom,
% 0.30/0.45 ( ( denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t1 ) )
% 0.30/0.45 => ( ( denotational_Iagree @ a @ b @ c @ i @ j
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t1 ) ) ) ) )
% 0.30/0.45 => ( ( denotational_frechet @ a @ b @ c @ i @ t1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) )
% 0.30/0.45 = ( denotational_frechet @ a @ b @ c @ j @ t1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % IH1
% 0.30/0.45 thf(fact_24_Iagree__comm,axiom,
% 0.30/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.45 ( ( ( finite_finite @ A )
% 0.30/0.45 & ( finite_finite @ B )
% 0.30/0.45 & ( finite_finite @ C ) )
% 0.30/0.45 => ! [A2: denota1663640101rp_ext @ A @ B @ C @ product_unit,B2: denota1663640101rp_ext @ A @ B @ C @ product_unit,V: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] :
% 0.30/0.45 ( ( denotational_Iagree @ A @ B @ C @ A2 @ B2 @ V )
% 0.30/0.45 => ( denotational_Iagree @ A @ B @ C @ B2 @ A2 @ V ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Iagree_comm
% 0.30/0.45 thf(fact_25_Iagree__refl,axiom,
% 0.30/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.45 ( ( ( finite_finite @ A )
% 0.30/0.45 & ( finite_finite @ B )
% 0.30/0.45 & ( finite_finite @ C ) )
% 0.30/0.45 => ! [I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,A2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] : ( denotational_Iagree @ A @ B @ C @ I3 @ I3 @ A2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % Iagree_refl
% 0.30/0.45 thf(fact_26_FunctionFrechet_Ocases,axiom,
% 0.30/0.45 ! [B: $tType,C: $tType,A: $tType] :
% 0.30/0.45 ( ( ( finite_finite @ A )
% 0.30/0.45 & ( finite_finite @ C )
% 0.30/0.45 & ( finite_finite @ B ) )
% 0.30/0.45 => ! [X: product_prod @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ A] :
% 0.30/0.45 ~ ! [I2: denota1663640101rp_ext @ A @ B @ C @ product_unit,I4: A] :
% 0.30/0.45 ( X
% 0.30/0.45 != ( product_Pair @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ A @ I2 @ I4 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % FunctionFrechet.cases
% 0.30/0.45 thf(fact_27_subs_I2_J,axiom,
% 0.30/0.45 ! [E: $tType] :
% 0.30/0.45 ( ord_less_eq @ ( set @ ( sum_sum @ a @ E ) )
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ E )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ E] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ E @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t2 ) ) ) )
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ E )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ E] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ E @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % subs(2)
% 0.30/0.45 thf(fact_28_subs_I1_J,axiom,
% 0.30/0.45 ! [D: $tType] :
% 0.30/0.45 ( ord_less_eq @ ( set @ ( sum_sum @ a @ D ) )
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ D )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ D] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ D @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t1 ) ) ) )
% 0.30/0.45 @ ( collect @ ( sum_sum @ a @ D )
% 0.30/0.45 @ ^ [Uu: sum_sum @ a @ D] :
% 0.30/0.45 ? [X2: a] :
% 0.30/0.45 ( ( Uu
% 0.30/0.45 = ( sum_Inl @ a @ D @ X2 ) )
% 0.30/0.45 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % subs(1)
% 0.30/0.45 thf(fact_29_simple__term__inverse,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 0.30/0.45 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.45 => ( ( frechet_raw_term @ A @ C @ ( frechet_simple_term @ A @ C @ Y ) )
% 0.30/0.45 = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 % simple_term_inverse
% 0.30/0.45 thf(fact_30_prod_Ocollapse,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.30/0.45 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 0.30/0.45 = Prod ) ).
% 0.30/0.45
% 0.30/0.45 % prod.collapse
% 0.30/0.45 thf(fact_31_cr__good__interp__def,axiom,
% 0.30/0.45 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.45 ( ( ( finite_finite @ A )
% 0.30/0.45 & ( finite_finite @ B )
% 0.30/0.45 & ( finite_finite @ C ) )
% 0.30/0.45 => ( ( freche457001096interp @ A @ B @ C )
% 0.30/0.45 = ( ^ [X2: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y2: frechet_good_interp @ A @ B @ C] :
% 0.30/0.45 ( X2
% 0.30/0.45 = ( freche229654227interp @ A @ B @ C @ Y2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % cr_good_interp_def
% 0.30/0.45 thf(fact_32_cr__strm__def,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( frechet_cr_strm @ A @ B )
% 0.30/0.45 = ( ^ [X2: trm @ A @ B,Y2: frechet_strm @ A @ B] :
% 0.30/0.45 ( X2
% 0.30/0.45 = ( frechet_raw_term @ A @ B @ Y2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % cr_strm_def
% 0.30/0.45 thf(fact_33_dfree__Times__simps,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType,A3: trm @ A @ B,B3: trm @ A @ B] :
% 0.30/0.45 ( ( dfree @ A @ B @ ( times @ A @ B @ A3 @ B3 ) )
% 0.30/0.45 = ( ( dfree @ A @ B @ A3 )
% 0.30/0.45 & ( dfree @ A @ B @ B3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % dfree_Times_simps
% 0.30/0.45 thf(fact_34_dfree__Plus__simps,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType,A3: trm @ A @ B,B3: trm @ A @ B] :
% 0.30/0.45 ( ( dfree @ A @ B @ ( plus @ A @ B @ A3 @ B3 ) )
% 0.30/0.45 = ( ( dfree @ A @ B @ A3 )
% 0.30/0.45 & ( dfree @ A @ B @ B3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % dfree_Plus_simps
% 0.30/0.45 thf(fact_35_dfree__Fun__simps,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,I: A,Args: B > ( trm @ A @ B )] :
% 0.30/0.45 ( ( dfree @ A @ B @ ( function @ A @ B @ I @ Args ) )
% 0.30/0.45 = ( ! [X2: B] : ( dfree @ A @ B @ ( Args @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % dfree_Fun_simps
% 0.30/0.45 thf(fact_36_simple__term__cases,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C] :
% 0.30/0.45 ~ ! [Y3: trm @ A @ C] :
% 0.30/0.45 ( ( X
% 0.30/0.45 = ( frechet_simple_term @ A @ C @ Y3 ) )
% 0.30/0.45 => ~ ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % simple_term_cases
% 0.30/0.45 thf(fact_37_raw__term__inverse,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C] :
% 0.30/0.45 ( ( frechet_simple_term @ A @ C @ ( frechet_raw_term @ A @ C @ X ) )
% 0.30/0.45 = X ) ).
% 0.30/0.45
% 0.30/0.45 % raw_term_inverse
% 0.30/0.45 thf(fact_38_simple__term__inject,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X: trm @ A @ C,Y: trm @ A @ C] :
% 0.30/0.45 ( ( member @ ( trm @ A @ C ) @ X @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.45 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.45 => ( ( ( frechet_simple_term @ A @ C @ X )
% 0.30/0.45 = ( frechet_simple_term @ A @ C @ Y ) )
% 0.30/0.45 = ( X = Y ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % simple_term_inject
% 0.30/0.45 thf(fact_39_simple__term__induct,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,P: ( frechet_strm @ A @ C ) > $o,X: frechet_strm @ A @ C] :
% 0.30/0.45 ( ! [Y3: trm @ A @ C] :
% 0.30/0.45 ( ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.45 => ( P @ ( frechet_simple_term @ A @ C @ Y3 ) ) )
% 0.30/0.45 => ( P @ X ) ) ).
% 0.30/0.45
% 0.30/0.45 % simple_term_induct
% 0.30/0.45 thf(fact_40_old_Oprod_Oinject,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,A3: A,B3: B,A4: A,B4: B] :
% 0.30/0.45 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.30/0.45 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.30/0.45 = ( ( A3 = A4 )
% 0.30/0.45 & ( B3 = B4 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % old.prod.inject
% 0.30/0.45 thf(fact_41_prod_Oinject,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 0.30/0.45 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.30/0.45 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.30/0.45 = ( ( X1 = Y1 )
% 0.30/0.45 & ( X22 = Y22 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod.inject
% 0.30/0.45 thf(fact_42_trm_Oinject_I3_J,axiom,
% 0.30/0.45 ! [A: $tType,C: $tType,X31: A,X32: C > ( trm @ A @ C ),Y31: A,Y32: C > ( trm @ A @ C )] :
% 0.30/0.45 ( ( ( function @ A @ C @ X31 @ X32 )
% 0.30/0.45 = ( function @ A @ C @ Y31 @ Y32 ) )
% 0.30/0.45 = ( ( X31 = Y31 )
% 0.30/0.45 & ( X32 = Y32 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % trm.inject(3)
% 0.30/0.45 thf(fact_43_trm_Oinject_I4_J,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X41: trm @ A @ C,X42: trm @ A @ C,Y41: trm @ A @ C,Y42: trm @ A @ C] :
% 0.30/0.45 ( ( ( plus @ A @ C @ X41 @ X42 )
% 0.30/0.45 = ( plus @ A @ C @ Y41 @ Y42 ) )
% 0.30/0.45 = ( ( X41 = Y41 )
% 0.30/0.45 & ( X42 = Y42 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % trm.inject(4)
% 0.30/0.45 thf(fact_44_trm_Oinject_I5_J,axiom,
% 0.30/0.45 ! [C: $tType,A: $tType,X51: trm @ A @ C,X52: trm @ A @ C,Y51: trm @ A @ C,Y52: trm @ A @ C] :
% 0.30/0.46 ( ( ( times @ A @ C @ X51 @ X52 )
% 0.30/0.46 = ( times @ A @ C @ Y51 @ Y52 ) )
% 0.30/0.46 = ( ( X51 = Y51 )
% 0.30/0.46 & ( X52 = Y52 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(5)
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 = ( Q @ X3 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( F @ X3 )
% 0.30/0.46 = ( G @ X3 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_agree__sub,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( finite_finite @ A )
% 0.30/0.46 => ! [A2: 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 )] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ A2 @ B2 )
% 0.30/0.46 => ( ( denotational_Vagree @ A @ Nu @ Omega @ B2 )
% 0.30/0.46 => ( denotational_Vagree @ A @ Nu @ Omega @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_sub
% 0.30/0.46 thf(fact_50_agree__supset,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( finite_finite @ A )
% 0.30/0.46 => ! [B2: set @ ( sum_sum @ A @ A ),A2: 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 )] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ B2 @ A2 )
% 0.30/0.46 => ( ( denotational_Vagree @ A @ Nu @ Nu2 @ A2 )
% 0.30/0.46 => ( denotational_Vagree @ A @ Nu @ Nu2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_supset
% 0.30/0.46 thf(fact_51_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.30/0.46 ~ ! [A5: A,B5: B] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ B @ A5 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_53_Pair__inject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A3: A,B3: B,A4: A,B4: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.30/0.46 => ~ ( ( A3 = A4 )
% 0.30/0.46 => ( B3 != B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_54_prod__cases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_55_surj__pair,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.30/0.46 ? [X3: A,Y3: B] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_56_prod__induct7,axiom,
% 0.30/0.46 ! [G2: $tType,F2: $tType,E2: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) @ D3 @ ( product_Pair @ E2 @ ( product_prod @ F2 @ G2 ) @ E3 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct7
% 0.30/0.46 thf(fact_57_prod__induct6,axiom,
% 0.30/0.46 ! [F2: $tType,E2: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ F2 ) @ D3 @ ( product_Pair @ E2 @ F2 @ E3 @ F3 ) ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct6
% 0.30/0.46 thf(fact_58_prod__induct5,axiom,
% 0.30/0.46 ! [E2: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C2: C,D3: D2,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E2 ) @ C2 @ ( product_Pair @ D2 @ E2 @ D3 @ E3 ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct5
% 0.30/0.46 thf(fact_59_prod__induct4,axiom,
% 0.30/0.46 ! [D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C2: C,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct4
% 0.30/0.46 thf(fact_60_prod__induct3,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct3
% 0.30/0.46 thf(fact_61_prod__cases7,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E2: $tType,F2: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2,G3: G2] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) @ D3 @ ( product_Pair @ E2 @ ( product_prod @ F2 @ G2 ) @ E3 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases7
% 0.30/0.46 thf(fact_62_prod__cases6,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E2: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ F2 ) @ D3 @ ( product_Pair @ E2 @ F2 @ E3 @ F3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases6
% 0.30/0.46 thf(fact_63_prod__cases5,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C2: C,D3: D2,E3: E2] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E2 ) @ C2 @ ( product_Pair @ D2 @ E2 @ D3 @ E3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases5
% 0.30/0.46 thf(fact_64_prod__cases4,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C2: C,D3: D2] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases4
% 0.30/0.46 thf(fact_65_prod__cases3,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C2: C] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases3
% 0.30/0.46 thf(fact_66_fst__conv,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X1: A,X22: B] :
% 0.30/0.46 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X22 ) )
% 0.30/0.46 = X1 ) ).
% 0.30/0.46
% 0.30/0.46 % fst_conv
% 0.30/0.46 thf(fact_67_fst__eqD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: A,Y: B,A3: A] :
% 0.30/0.46 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y ) )
% 0.30/0.46 = A3 )
% 0.30/0.46 => ( X = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_eqD
% 0.30/0.46 thf(fact_68_snd__conv,axiom,
% 0.30/0.46 ! [Aa: $tType,A: $tType,X1: Aa,X22: A] :
% 0.30/0.46 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X1 @ X22 ) )
% 0.30/0.46 = X22 ) ).
% 0.30/0.46
% 0.30/0.46 % snd_conv
% 0.30/0.46 thf(fact_69_snd__eqD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: B,Y: A,A3: A] :
% 0.30/0.46 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 0.30/0.46 = A3 )
% 0.30/0.46 => ( Y = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % snd_eqD
% 0.30/0.46 thf(fact_70_prod__eq__iff,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ^ [Y4: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y4 = Z ) )
% 0.30/0.46 = ( ^ [S2: product_prod @ A @ B,T3: product_prod @ A @ B] :
% 0.30/0.46 ( ( ( product_fst @ A @ B @ S2 )
% 0.30/0.46 = ( product_fst @ A @ B @ T3 ) )
% 0.30/0.46 & ( ( product_snd @ A @ B @ S2 )
% 0.30/0.46 = ( product_snd @ A @ B @ T3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eq_iff
% 0.30/0.46 thf(fact_71_prod_Oexpand,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 0.30/0.46 ( ( ( ( product_fst @ A @ B @ Prod )
% 0.30/0.46 = ( product_fst @ A @ B @ Prod2 ) )
% 0.30/0.46 & ( ( product_snd @ A @ B @ Prod )
% 0.30/0.46 = ( product_snd @ A @ B @ Prod2 ) ) )
% 0.30/0.46 => ( Prod = Prod2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.expand
% 0.30/0.46 thf(fact_72_prod__eqI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: product_prod @ A @ B,Q2: product_prod @ A @ B] :
% 0.30/0.46 ( ( ( product_fst @ A @ B @ P2 )
% 0.30/0.46 = ( product_fst @ A @ B @ Q2 ) )
% 0.30/0.46 => ( ( ( product_snd @ A @ B @ P2 )
% 0.30/0.46 = ( product_snd @ A @ B @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_73_dfree__Fun,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,Args: C > ( trm @ A @ C ),I: A] :
% 0.30/0.46 ( ! [I4: C] : ( dfree @ A @ C @ ( Args @ I4 ) )
% 0.30/0.46 => ( dfree @ A @ C @ ( function @ A @ C @ I @ Args ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Fun
% 0.30/0.46 thf(fact_74_dfree_Odfree__Plus,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,Theta_1: trm @ A @ C,Theta_2: trm @ A @ C] :
% 0.30/0.46 ( ( dfree @ A @ C @ Theta_1 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta_2 )
% 0.30/0.46 => ( dfree @ A @ C @ ( plus @ A @ C @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.dfree_Plus
% 0.30/0.46 thf(fact_75_dfree__Times,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,Theta_1: trm @ A @ C,Theta_2: trm @ A @ C] :
% 0.30/0.46 ( ( dfree @ A @ C @ Theta_1 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta_2 )
% 0.30/0.46 => ( dfree @ A @ C @ ( times @ A @ C @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Times
% 0.30/0.46 thf(fact_76_trm_Odistinct_I23_J,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,X31: A,X32: C > ( trm @ A @ C ),X41: trm @ A @ C,X42: trm @ A @ C] :
% 0.30/0.46 ( ( function @ A @ C @ X31 @ X32 )
% 0.30/0.46 != ( plus @ A @ C @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(23)
% 0.30/0.46 thf(fact_77_trm_Odistinct_I25_J,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,X31: A,X32: C > ( trm @ A @ C ),X51: trm @ A @ C,X52: trm @ A @ C] :
% 0.30/0.46 ( ( function @ A @ C @ X31 @ X32 )
% 0.30/0.46 != ( times @ A @ C @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(25)
% 0.30/0.46 thf(fact_78_trm_Odistinct_I31_J,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,X41: trm @ A @ C,X42: trm @ A @ C,X51: trm @ A @ C,X52: trm @ A @ C] :
% 0.30/0.46 ( ( plus @ A @ C @ X41 @ X42 )
% 0.30/0.46 != ( times @ A @ C @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(31)
% 0.30/0.46 thf(fact_79_surjective__pairing,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,T4: product_prod @ A @ B] :
% 0.30/0.46 ( T4
% 0.30/0.46 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T4 ) @ ( product_snd @ A @ B @ T4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % surjective_pairing
% 0.30/0.46 thf(fact_80_prod_Oexhaust__sel,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( Prod
% 0.30/0.46 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.exhaust_sel
% 0.30/0.46 thf(fact_81_Pair__le,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A3: A,B3: B,C3: A,D4: B] :
% 0.30/0.46 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ C3 @ D4 ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ A3 @ C3 )
% 0.30/0.46 & ( ord_less_eq @ B @ B3 @ D4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_le
% 0.30/0.46 thf(fact_82_directional__derivative__def,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ( ( denota2078997598vative @ A @ B @ C )
% 0.30/0.46 = ( ^ [I5: denota1663640101rp_ext @ A @ B @ C @ product_unit,T3: trm @ A @ C,V2: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C )] : ( denotational_frechet @ A @ B @ C @ I5 @ T3 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ V2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ V2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % directional_derivative_def
% 0.30/0.46 thf(fact_83_raw__interp__inverse,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ( freche227871258interp @ A @ B @ C @ ( freche229654227interp @ A @ B @ C @ X ) )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % raw_interp_inverse
% 0.30/0.46 thf(fact_84_old_Oprod_Orec,axiom,
% 0.30/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A3: A,B3: B] :
% 0.30/0.46 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.46 = ( F1 @ A3 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.rec
% 0.30/0.46 thf(fact_85_type__definition__strm,axiom,
% 0.30/0.46 ! [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 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_definition_strm
% 0.30/0.46 thf(fact_86_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: A > B > $o,X: A,Y: B,A3: product_prod @ A @ B] :
% 0.30/0.46 ( ( P @ X @ Y )
% 0.30/0.46 => ( ( A3
% 0.30/0.46 = ( product_Pair @ A @ B @ X @ Y ) )
% 0.30/0.46 => ( P @ ( product_fst @ A @ B @ A3 ) @ ( product_snd @ A @ B @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % BNF_Greatest_Fixpoint.subst_Pair
% 0.30/0.46 thf(fact_87_conjI__realizer,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: A > $o,P2: A,Q: B > $o,Q2: B] :
% 0.30/0.46 ( ( P @ P2 )
% 0.30/0.46 => ( ( Q @ Q2 )
% 0.30/0.46 => ( ( P @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) )
% 0.30/0.46 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conjI_realizer
% 0.30/0.46 thf(fact_88_exI__realizer,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: A > B > $o,Y: A,X: B] :
% 0.30/0.46 ( ( P @ Y @ X )
% 0.30/0.46 => ( P @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exI_realizer
% 0.30/0.46 thf(fact_89_less__eq__prod__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( ord @ A )
% 0.30/0.46 & ( ord @ B ) )
% 0.30/0.46 => ( ( ord_less_eq @ ( product_prod @ A @ B ) )
% 0.30/0.46 = ( ^ [X2: product_prod @ A @ B,Y2: product_prod @ A @ B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( product_fst @ A @ B @ X2 ) @ ( product_fst @ A @ B @ Y2 ) )
% 0.30/0.46 & ( ord_less_eq @ B @ ( product_snd @ A @ B @ X2 ) @ ( product_snd @ A @ B @ Y2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_prod_def
% 0.30/0.46 thf(fact_90_Iagree__sub,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [A2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),B2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,J: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) ) @ A2 @ B2 )
% 0.30/0.46 => ( ( denotational_Iagree @ A @ B @ C @ I3 @ J @ B2 )
% 0.30/0.46 => ( denotational_Iagree @ A @ B @ C @ I3 @ J @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Iagree_sub
% 0.30/0.46 thf(fact_91_subset__Collect__iff,axiom,
% 0.30/0.46 ! [A: $tType,B2: set @ A,A2: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A2 )
% 0.30/0.46 & ( P @ X2 ) ) ) )
% 0.30/0.46 = ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ B2 )
% 0.30/0.46 => ( P @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Collect_iff
% 0.30/0.46 thf(fact_92_subset__CollectI,axiom,
% 0.30/0.46 ! [A: $tType,B2: set @ A,A2: set @ A,Q: A > $o,P: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ B2 )
% 0.30/0.46 => ( ( Q @ X3 )
% 0.30/0.46 => ( P @ X3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ B2 )
% 0.30/0.46 & ( Q @ X2 ) ) )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A2 )
% 0.30/0.46 & ( P @ X2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_CollectI
% 0.30/0.46 thf(fact_93_Pair__mono,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [X: A,X4: A,Y: B,Y5: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ X4 )
% 0.30/0.46 => ( ( ord_less_eq @ B @ Y @ Y5 )
% 0.30/0.46 => ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( product_Pair @ A @ B @ X4 @ Y5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_mono
% 0.30/0.46 thf(fact_94_fst__mono,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( ord @ A )
% 0.30/0.46 & ( ord @ B ) )
% 0.30/0.46 => ! [X: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 0.30/0.46 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ ( product_fst @ A @ B @ X ) @ ( product_fst @ A @ B @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_mono
% 0.30/0.46 thf(fact_95_snd__mono,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( ord @ A )
% 0.30/0.46 & ( ord @ B ) )
% 0.30/0.46 => ! [X: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 0.30/0.46 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ B @ ( product_snd @ A @ B @ X ) @ ( product_snd @ A @ B @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % snd_mono
% 0.30/0.46 thf(fact_96_exE__realizer_H,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: A > B > $o,P2: product_prod @ B @ A] :
% 0.30/0.46 ( ( P @ ( product_snd @ B @ A @ P2 ) @ ( product_fst @ B @ A @ P2 ) )
% 0.30/0.46 => ~ ! [X3: B,Y3: A] :
% 0.30/0.46 ~ ( P @ Y3 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exE_realizer'
% 0.30/0.46 thf(fact_97_euclid__ext__aux_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid1678468529ng_gcd @ A )
% 0.30/0.46 => ! [X: product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) ) )] :
% 0.30/0.46 ~ ! [S3: A,S4: A,T5: A,T6: A,R: A,R2: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) ) ) @ S3 @ ( product_Pair @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) ) @ S4 @ ( product_Pair @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) @ T5 @ ( product_Pair @ A @ ( product_prod @ A @ A ) @ T6 @ ( product_Pair @ A @ A @ R @ R2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % euclid_ext_aux.cases
% 0.30/0.46 thf(fact_98_sum_Oinject_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.30/0.46 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.30/0.46 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sum.inject(1)
% 0.30/0.46 thf(fact_99_old_Osum_Oinject_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A3: A,A4: A] :
% 0.30/0.46 ( ( ( sum_Inl @ A @ B @ A3 )
% 0.30/0.46 = ( sum_Inl @ A @ B @ A4 ) )
% 0.30/0.46 = ( A3 = A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.inject(1)
% 0.30/0.46 thf(fact_100_good__interp__inverse,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ( freche229654227interp @ A @ B @ C @ ( freche227871258interp @ A @ B @ C @ Y ) )
% 0.30/0.46 = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % good_interp_inverse
% 0.30/0.46 thf(fact_101_f0__def,axiom,
% 0.30/0.46 ( ( f0 @ sf @ sz )
% 0.30/0.46 = ( ^ [F4: sf] : ( function @ sf @ sz @ F4 @ ( empty @ sz @ sf ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f0_def
% 0.30/0.46 thf(fact_102_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A2 )
% 0.30/0.46 => ( member @ A @ X3 @ B2 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_103_raw__interp__induct,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit,P: ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o] :
% 0.30/0.46 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ! [X3: frechet_good_interp @ A @ B @ C] : ( P @ ( freche229654227interp @ A @ B @ C @ X3 ) )
% 0.30/0.46 => ( P @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % raw_interp_induct
% 0.30/0.46 thf(fact_104_raw__interp__cases,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ~ ! [X3: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( freche229654227interp @ A @ B @ C @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % raw_interp_cases
% 0.30/0.46 thf(fact_105_raw__interp,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [X: frechet_good_interp @ A @ B @ C] : ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C @ X ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % raw_interp
% 0.30/0.46 thf(fact_106_good__interp__cases,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ~ ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( X
% 0.30/0.46 = ( freche227871258interp @ A @ B @ C @ Y3 ) )
% 0.30/0.46 => ~ ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % good_interp_cases
% 0.30/0.46 thf(fact_107_good__interp__induct,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [P: ( frechet_good_interp @ A @ B @ C ) > $o,X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( P @ ( freche227871258interp @ A @ B @ C @ Y3 ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % good_interp_induct
% 0.30/0.46 thf(fact_108_good__interp__inject,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ! [X: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ X @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ( ( freche227871258interp @ A @ B @ C @ X )
% 0.30/0.46 = ( freche227871258interp @ A @ B @ C @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % good_interp_inject
% 0.30/0.46 thf(fact_109_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_110_gcd_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid1155270486miring @ A )
% 0.30/0.46 => ! [X: product_prod @ A @ A] :
% 0.30/0.46 ~ ! [A5: A,B5: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ A @ A @ A5 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gcd.cases
% 0.30/0.46 thf(fact_111_Collect__mono__iff,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.30/0.46 = ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( Q @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_112_set__eq__subset,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_113_subset__trans,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_114_Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_115_subset__refl,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_116_subset__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ! [T3: A] :
% 0.30/0.46 ( ( member @ A @ T3 @ A6 )
% 0.30/0.46 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_117_equalityD2,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_118_equalityD1,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_119_subset__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A6 )
% 0.30/0.46 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_120_equalityE,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_121_subsetD,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.46 => ( ( member @ A @ C3 @ A2 )
% 0.30/0.46 => ( member @ A @ C3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_122_in__mono,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.46 => ( ( member @ A @ X @ A2 )
% 0.30/0.46 => ( member @ A @ X @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_123_Inl__inject,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( ( sum_Inl @ A @ B @ X )
% 0.30/0.46 = ( sum_Inl @ A @ B @ Y ) )
% 0.30/0.46 => ( X = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_inject
% 0.30/0.46 thf(fact_124_Collect__subset,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,P: A > $o] :
% 0.30/0.46 ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A2 )
% 0.30/0.46 & ( P @ X2 ) ) )
% 0.30/0.46 @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_subset
% 0.30/0.46 thf(fact_125_less__eq__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( ord_less_eq @ ( A > $o )
% 0.30/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ A6 )
% 0.30/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_set_def
% 0.30/0.46 thf(fact_126_sterm__determines__frechet,axiom,
% 0.30/0.46 ! [A1: $tType,B1: $tType,B22: $tType,A22: $tType,C: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ A22 )
% 0.30/0.46 & ( finite_finite @ B22 )
% 0.30/0.46 & ( finite_finite @ B1 )
% 0.30/0.46 & ( finite_finite @ A1 ) )
% 0.30/0.46 => ! [I3: denota1663640101rp_ext @ A1 @ B1 @ C @ product_unit,J: denota1663640101rp_ext @ A22 @ B22 @ C @ product_unit,Theta_12: trm @ A1 @ C,Theta_22: trm @ A22 @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C )] :
% 0.30/0.46 ( ( denota2077489681interp @ A1 @ B1 @ C @ I3 )
% 0.30/0.46 => ( ( denota2077489681interp @ A22 @ B22 @ C @ J )
% 0.30/0.46 => ( ( dfree @ A1 @ C @ Theta_12 )
% 0.30/0.46 => ( ( dfree @ A22 @ C @ Theta_22 )
% 0.30/0.46 => ( ( ( denota126604975rm_sem @ A1 @ B1 @ C @ I3 @ Theta_12 )
% 0.30/0.46 = ( denota126604975rm_sem @ A22 @ B22 @ C @ J @ Theta_22 ) )
% 0.30/0.46 => ( ( denotational_frechet @ A1 @ B1 @ C @ I3 @ Theta_12 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 0.30/0.46 = ( denotational_frechet @ A22 @ B22 @ C @ J @ Theta_22 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sterm_determines_frechet
% 0.30/0.46 thf(fact_127_type__definition__good__interp,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ( 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 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_definition_good_interp
% 0.30/0.46 thf(fact_128_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_129_old_Osum_Osimps_I7_J,axiom,
% 0.30/0.46 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A3: A] :
% 0.30/0.46 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A3 ) )
% 0.30/0.46 = ( F1 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.simps(7)
% 0.30/0.46 thf(fact_130_image2__def,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType] :
% 0.30/0.46 ( ( bNF_Greatest_image2 @ C @ A @ B )
% 0.30/0.46 = ( ^ [A6: set @ C,F4: C > A,G4: C > B] :
% 0.30/0.46 ( collect @ ( product_prod @ A @ B )
% 0.30/0.46 @ ^ [Uu: product_prod @ A @ B] :
% 0.30/0.46 ? [A7: C] :
% 0.30/0.46 ( ( Uu
% 0.30/0.46 = ( product_Pair @ A @ B @ ( F4 @ A7 ) @ ( G4 @ A7 ) ) )
% 0.30/0.46 & ( member @ C @ A7 @ A6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % image2_def
% 0.30/0.46 thf(fact_131_predicate1I,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate1I
% 0.30/0.46 thf(fact_132_rev__predicate1D,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,X: A,Q: A > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.30/0.46 => ( Q @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_predicate1D
% 0.30/0.46 thf(fact_133_predicate1D,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.30/0.46 => ( ( P @ X )
% 0.30/0.46 => ( Q @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate1D
% 0.30/0.46 thf(fact_134_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_135_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_136_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_137_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F4: A > B,G4: A > B] :
% 0.30/0.46 ! [X2: A] : ( ord_less_eq @ B @ ( F4 @ X2 ) @ ( G4 @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_138_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.30/0.46 => ( ! [X3: B,Y3: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_139_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A3: A,B3: A,F: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 0.30/0.46 => ( ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_140_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( F @ B3 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.30/0.46 => ( ! [X3: B,Y3: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_141_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A3: A,B3: A,F: A > B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 => ( ( ( F @ B3 )
% 0.30/0.46 = C3 )
% 0.30/0.46 => ( ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_142_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.30/0.46 = ( ^ [X2: A,Y2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.30/0.46 & ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_143_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_144_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_145_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_146_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_147_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A,B3: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_148_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_149_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_150_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.30/0.46 = ( ^ [A7: A,B7: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A7 @ B7 )
% 0.30/0.46 & ( ord_less_eq @ A @ B7 @ A7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_151_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A3: A,B3: A,C3: A] :
% 0.30/0.46 ( ( A3 = B3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_152_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A3: A,B3: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 => ( ( B3 = C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_153_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.30/0.46 => ( A3 = B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_154_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_155_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_156_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A3: A,B3: A] :
% 0.30/0.46 ( ! [A5: A,B5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.30/0.46 => ( P @ A5 @ B5 ) )
% 0.30/0.46 => ( ! [A5: A,B5: A] :
% 0.30/0.46 ( ( P @ B5 @ A5 )
% 0.30/0.46 => ( P @ A5 @ B5 ) )
% 0.30/0.46 => ( P @ A3 @ B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_157_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B3: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.30/0.46 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_158_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.30/0.46 = ( ^ [A7: A,B7: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B7 @ A7 )
% 0.30/0.46 & ( ord_less_eq @ A @ A7 @ B7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_159_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B3: A,A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 => ( A3 = B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_160_image2__eqI,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,B3: A,F: B > A,X: B,C3: C,G: B > C,A2: set @ B] :
% 0.30/0.46 ( ( B3
% 0.30/0.46 = ( F @ X ) )
% 0.30/0.46 => ( ( C3
% 0.30/0.46 = ( G @ X ) )
% 0.30/0.46 => ( ( member @ B @ X @ A2 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ B3 @ C3 ) @ ( bNF_Greatest_image2 @ B @ A @ C @ A2 @ F @ G ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % image2_eqI
% 0.30/0.46 thf(fact_161_coincidence__sterm_H,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ A ) )
% 0.30/0.46 => ! [Theta: trm @ A @ B,Nu: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),I3: denota1663640101rp_ext @ A @ C @ B @ product_unit,J: denota1663640101rp_ext @ A @ C @ B @ product_unit] :
% 0.30/0.46 ( ( dfree @ A @ B @ Theta )
% 0.30/0.46 => ( ( denotational_Vagree @ B @ Nu @ Nu2 @ ( static_FVT @ A @ B @ Theta ) )
% 0.30/0.46 => ( ( denotational_Iagree @ A @ C @ B @ I3 @ J
% 0.30/0.46 @ ( collect @ ( sum_sum @ A @ ( sum_sum @ C @ B ) )
% 0.30/0.46 @ ^ [Uu: sum_sum @ A @ ( sum_sum @ C @ B )] :
% 0.30/0.46 ? [X2: A] :
% 0.30/0.46 ( ( Uu
% 0.30/0.46 = ( sum_Inl @ A @ ( sum_sum @ C @ B ) @ X2 ) )
% 0.30/0.46 & ( member @ A @ X2 @ ( static_SIGT @ A @ B @ Theta ) ) ) ) )
% 0.30/0.46 => ( ( denota126604975rm_sem @ A @ C @ B @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu ) )
% 0.30/0.46 = ( denota126604975rm_sem @ A @ C @ B @ J @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % coincidence_sterm'
% 0.30/0.46 thf(fact_162_coincidence__sterm,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ B ) )
% 0.30/0.46 => ! [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,I3: denota1663640101rp_ext @ B @ C @ A @ product_unit] :
% 0.30/0.46 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ Theta ) )
% 0.30/0.46 => ( ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu ) )
% 0.30/0.46 = ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % coincidence_sterm
% 0.30/0.46 thf(fact_163_pred__subset__eq,axiom,
% 0.30/0.46 ! [A: $tType,R3: set @ A,S5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > $o )
% 0.30/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ R3 )
% 0.30/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ S5 ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ A ) @ R3 @ S5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq
% 0.30/0.46 thf(fact_164_sterm__continuous_H,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ B ) )
% 0.30/0.46 => ! [I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C,S5: set @ ( finite_Cartesian_vec @ real @ C )] :
% 0.30/0.46 ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.30/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ S5 @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sterm_continuous'
% 0.30/0.46 thf(fact_165_agree__func__fvt,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( finite_finite @ A )
% 0.30/0.46 => ! [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 ),F: B,Args: A > ( trm @ B @ A ),I: A] :
% 0.30/0.46 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ ( function @ B @ A @ F @ Args ) ) )
% 0.30/0.46 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ ( Args @ I ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_func_fvt
% 0.30/0.46 thf(fact_166_subrelI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S6: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ! [X3: A,Y3: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R4 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S6 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R4 @ S6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subrelI
% 0.30/0.46 thf(fact_167_FVDiff__sub,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: trm @ B @ A] : ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ ( static_FVT @ B @ A @ F ) @ ( static_FVDiff @ B @ A @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % FVDiff_sub
% 0.30/0.46 thf(fact_168_pred__equals__eq2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S5: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( ( ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ R3 ) )
% 0.30/0.46 = ( ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ S5 ) ) )
% 0.30/0.46 = ( R3 = S5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_equals_eq2
% 0.30/0.46 thf(fact_169_pred__subset__eq2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S5: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B > $o )
% 0.30/0.46 @ ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ R3 )
% 0.30/0.46 @ ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ S5 ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq2
% 0.30/0.46 thf(fact_170_sterm__continuous,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ B ) )
% 0.30/0.46 => ! [I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C] :
% 0.30/0.46 ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.30/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ C ) ) ) @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sterm_continuous
% 0.30/0.46 thf(fact_171_ids_Ocoincidence__sterm_H,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,A: $tType,C: $tType,B: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Theta: trm @ A @ B,Nu: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),I3: denota1663640101rp_ext @ A @ C @ B @ product_unit,J: denota1663640101rp_ext @ A @ C @ B @ product_unit] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( dfree @ A @ B @ Theta )
% 0.30/0.46 => ( ( denotational_Vagree @ B @ Nu @ Nu2 @ ( static_FVT @ A @ B @ Theta ) )
% 0.30/0.46 => ( ( denotational_Iagree @ A @ C @ B @ I3 @ J
% 0.30/0.46 @ ( collect @ ( sum_sum @ A @ ( sum_sum @ C @ B ) )
% 0.30/0.46 @ ^ [Uu: sum_sum @ A @ ( sum_sum @ C @ B )] :
% 0.30/0.46 ? [X2: A] :
% 0.30/0.46 ( ( Uu
% 0.30/0.46 = ( sum_Inl @ A @ ( sum_sum @ C @ B ) @ X2 ) )
% 0.30/0.46 & ( member @ A @ X2 @ ( static_SIGT @ A @ B @ Theta ) ) ) ) )
% 0.30/0.46 => ( ( denota126604975rm_sem @ A @ C @ B @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu ) )
% 0.30/0.46 = ( denota126604975rm_sem @ A @ C @ B @ J @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu2 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.coincidence_sterm'
% 0.30/0.46 thf(fact_172_continuous__on__cases__le,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ B ) )
% 0.30/0.46 => ! [S6: set @ A,H: A > real,A3: real,F: A > B,G: A > B] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ B
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [T3: A] :
% 0.30/0.46 ( ( member @ A @ T3 @ S6 )
% 0.30/0.46 & ( ord_less_eq @ real @ ( H @ T3 ) @ A3 ) ) )
% 0.30/0.46 @ F )
% 0.30/0.46 => ( ( topolo2071040574ous_on @ A @ B
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [T3: A] :
% 0.30/0.46 ( ( member @ A @ T3 @ S6 )
% 0.30/0.46 & ( ord_less_eq @ real @ A3 @ ( H @ T3 ) ) ) )
% 0.30/0.46 @ G )
% 0.30/0.46 => ( ( topolo2071040574ous_on @ A @ real @ S6 @ H )
% 0.30/0.46 => ( ! [T6: A] :
% 0.30/0.46 ( ( member @ A @ T6 @ S6 )
% 0.30/0.46 => ( ( ( H @ T6 )
% 0.30/0.46 = A3 )
% 0.30/0.46 => ( ( F @ T6 )
% 0.30/0.46 = ( G @ T6 ) ) ) )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ B @ S6
% 0.30/0.46 @ ^ [T3: A] : ( if @ B @ ( ord_less_eq @ real @ ( H @ T3 ) @ A3 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_cases_le
% 0.30/0.46 thf(fact_173_top__apply,axiom,
% 0.30/0.46 ! [C: $tType,D2: $tType] :
% 0.30/0.46 ( ( top @ C )
% 0.30/0.46 => ( ( top_top @ ( D2 > C ) )
% 0.30/0.46 = ( ^ [X2: D2] : ( top_top @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_apply
% 0.30/0.46 thf(fact_174_UNIV__I,axiom,
% 0.30/0.46 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_I
% 0.30/0.46 thf(fact_175_predicate2I,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.30/0.46 ( ! [X3: A,Y3: B] :
% 0.30/0.46 ( ( P @ X3 @ Y3 )
% 0.30/0.46 => ( Q @ X3 @ Y3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate2I
% 0.30/0.46 thf(fact_176_fst__top,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( top @ A )
% 0.30/0.46 & ( top @ B ) )
% 0.30/0.46 => ( ( product_fst @ A @ B @ ( top_top @ ( product_prod @ A @ B ) ) )
% 0.30/0.46 = ( top_top @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_top
% 0.30/0.46 thf(fact_177_snd__top,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( top @ A )
% 0.30/0.46 & ( top @ B ) )
% 0.30/0.46 => ( ( product_snd @ B @ A @ ( top_top @ ( product_prod @ B @ A ) ) )
% 0.30/0.46 = ( top_top @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % snd_top
% 0.30/0.46 thf(fact_178_continuous__on__cases__1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( topolo503727757_space @ A )
% 0.30/0.46 => ! [S6: set @ real,A3: real,F: real > A,G: real > A] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ real @ A
% 0.30/0.46 @ ( collect @ real
% 0.30/0.46 @ ^ [T3: real] :
% 0.30/0.46 ( ( member @ real @ T3 @ S6 )
% 0.30/0.46 & ( ord_less_eq @ real @ T3 @ A3 ) ) )
% 0.30/0.46 @ F )
% 0.30/0.46 => ( ( topolo2071040574ous_on @ real @ A
% 0.30/0.46 @ ( collect @ real
% 0.30/0.46 @ ^ [T3: real] :
% 0.30/0.46 ( ( member @ real @ T3 @ S6 )
% 0.30/0.46 & ( ord_less_eq @ real @ A3 @ T3 ) ) )
% 0.30/0.46 @ G )
% 0.30/0.46 => ( ( ( member @ real @ A3 @ S6 )
% 0.30/0.46 => ( ( F @ A3 )
% 0.30/0.46 = ( G @ A3 ) ) )
% 0.30/0.46 => ( topolo2071040574ous_on @ real @ A @ S6
% 0.30/0.46 @ ^ [T3: real] : ( if @ A @ ( ord_less_eq @ real @ T3 @ A3 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_cases_1
% 0.30/0.46 thf(fact_179_top_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_top @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( top_top @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top.extremum_uniqueI
% 0.30/0.46 thf(fact_180_top_Oextremum__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_top @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 0.30/0.46 = ( A3
% 0.30/0.46 = ( top_top @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top.extremum_unique
% 0.30/0.46 thf(fact_181_top__greatest,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_top @ A )
% 0.30/0.46 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ ( top_top @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_greatest
% 0.30/0.46 thf(fact_182_rev__predicate2D,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 0.30/0.46 ( ( P @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.30/0.46 => ( Q @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_predicate2D
% 0.30/0.46 thf(fact_183_predicate2D,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.30/0.46 => ( ( P @ X @ Y )
% 0.30/0.46 => ( Q @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate2D
% 0.30/0.46 thf(fact_184_subset__UNIV,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_UNIV
% 0.30/0.46 thf(fact_185_ids_Oseq__sem_Ocases,axiom,
% 0.30/0.46 ! [Sz: $tType,Sc: $tType,Sf: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: product_prod @ ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) )] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ~ ! [I2: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,S: product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) )] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) ) @ I2 @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.seq_sem.cases
% 0.30/0.46 thf(fact_186_UNIV__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( top_top @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A
% 0.30/0.46 @ ^ [X2: A] : $true ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_def
% 0.30/0.46 thf(fact_187_UNIV__witness,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_witness
% 0.30/0.46 thf(fact_188_UNIV__eq__I,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A] :
% 0.30/0.46 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.30/0.46 => ( ( top_top @ ( set @ A ) )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_eq_I
% 0.30/0.46 thf(fact_189_ids_Osingleton_Oinduct,axiom,
% 0.30/0.46 ! [Sf: $tType,Sc: $tType,A: $tType,Sz: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( trm @ A @ Sz ) > Sz > $o,A0: trm @ A @ Sz,A12: Sz] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ! [T6: trm @ A @ Sz,X_1: Sz] : ( P @ T6 @ X_1 )
% 0.30/0.46 => ( P @ A0 @ A12 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.singleton.induct
% 0.30/0.46 thf(fact_190_ids_Oseq__sem_Oinduct,axiom,
% 0.30/0.46 ! [Sz: $tType,Sc: $tType,Sf: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) > ( product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) ) > $o,A0: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,A12: product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) )] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ! [I2: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,X_1: product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) )] : ( P @ I2 @ X_1 )
% 0.30/0.46 => ( P @ A0 @ A12 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.seq_sem.induct
% 0.30/0.46 thf(fact_191_ids_Osingleton_Ocases,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,A: $tType,Sz: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: product_prod @ ( trm @ A @ Sz ) @ Sz] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ~ ! [T6: trm @ A @ Sz,I4: Sz] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( product_Pair @ ( trm @ A @ Sz ) @ Sz @ T6 @ I4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.singleton.cases
% 0.30/0.46 thf(fact_192_top__prod__def,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( top @ B )
% 0.30/0.46 & ( top @ A ) )
% 0.30/0.46 => ( ( top_top @ ( product_prod @ A @ B ) )
% 0.30/0.46 = ( product_Pair @ A @ B @ ( top_top @ A ) @ ( top_top @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_prod_def
% 0.30/0.46 thf(fact_193_ids_OP__def,axiom,
% 0.30/0.46 ! [Sf: $tType,Sz: $tType,Sc: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P2: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( p @ Sc @ Sf @ Sz @ P2 )
% 0.30/0.46 = ( predicational @ Sc @ Sf @ Sz @ P2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.P_def
% 0.30/0.46 thf(fact_194_ids_Ocoincidence__sterm,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,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,I3: denota1663640101rp_ext @ B @ C @ A @ product_unit] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ Theta ) )
% 0.30/0.46 => ( ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu ) )
% 0.30/0.46 = ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.coincidence_sterm
% 0.30/0.46 thf(fact_195_ids_Of0__def,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,F: Sf] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( f0 @ Sf @ Sz @ F )
% 0.30/0.46 = ( function @ Sf @ Sz @ F @ ( empty @ Sz @ Sf ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.f0_def
% 0.30/0.46 thf(fact_196_ids_Ocoincidence__frechet,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Theta: trm @ A @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),I3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.30/0.46 => ( ( denotational_Vagree @ C @ Nu @ Nu2 @ ( static_FVDiff @ A @ C @ Theta ) )
% 0.30/0.46 => ( ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 0.30/0.46 = ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.coincidence_frechet
% 0.30/0.46 thf(fact_197_frechet__continuous,axiom,
% 0.30/0.46 ! [I3: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Theta: trm @ sf @ sz] :
% 0.30/0.46 ( ( denota2077489681interp @ sf @ sc @ sz @ I3 )
% 0.30/0.46 => ( ( dfree @ sf @ sz @ Theta )
% 0.30/0.46 => ( 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 @ I3 ) @ ( frechet_simple_term @ sf @ sz @ Theta ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % frechet_continuous
% 0.30/0.46 thf(fact_198_ids_Osterm__determines__frechet,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,A1: $tType,B1: $tType,B22: $tType,A22: $tType,C: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ A22 )
% 0.30/0.46 & ( finite_finite @ B22 )
% 0.30/0.46 & ( finite_finite @ B1 )
% 0.30/0.46 & ( finite_finite @ A1 )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ A1 @ B1 @ C @ product_unit,J: denota1663640101rp_ext @ A22 @ B22 @ C @ product_unit,Theta_12: trm @ A1 @ C,Theta_22: trm @ A22 @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C )] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( denota2077489681interp @ A1 @ B1 @ C @ I3 )
% 0.30/0.46 => ( ( denota2077489681interp @ A22 @ B22 @ C @ J )
% 0.30/0.46 => ( ( dfree @ A1 @ C @ Theta_12 )
% 0.30/0.46 => ( ( dfree @ A22 @ C @ Theta_22 )
% 0.30/0.46 => ( ( ( denota126604975rm_sem @ A1 @ B1 @ C @ I3 @ Theta_12 )
% 0.30/0.46 = ( denota126604975rm_sem @ A22 @ B22 @ C @ J @ Theta_22 ) )
% 0.30/0.46 => ( ( denotational_frechet @ A1 @ B1 @ C @ I3 @ Theta_12 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 0.30/0.46 = ( denotational_frechet @ A22 @ B22 @ C @ J @ Theta_22 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.sterm_determines_frechet
% 0.30/0.46 thf(fact_199_ids_Osterm__continuous,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.30/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ C ) ) ) @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.sterm_continuous
% 0.30/0.46 thf(fact_200_top__empty__eq2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( top_top @ ( A > B > $o ) )
% 0.30/0.46 = ( ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_empty_eq2
% 0.30/0.46 thf(fact_201_top__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( top_top @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_set_def
% 0.30/0.46 thf(fact_202_Vagree__univ,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( finite_finite @ A )
% 0.30/0.46 => ! [A3: finite_Cartesian_vec @ real @ A,B3: finite_Cartesian_vec @ real @ A,C3: finite_Cartesian_vec @ real @ A,D4: finite_Cartesian_vec @ real @ A] :
% 0.30/0.46 ( ( denotational_Vagree @ A @ ( product_Pair @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ A3 @ B3 ) @ ( product_Pair @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ C3 @ D4 ) @ ( top_top @ ( set @ ( sum_sum @ A @ A ) ) ) )
% 0.30/0.46 => ( ( A3 = C3 )
% 0.30/0.46 & ( B3 = D4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Vagree_univ
% 0.30/0.46 thf(fact_203_agree__UNIV__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( finite_finite @ A )
% 0.30/0.46 => ! [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 )] :
% 0.30/0.46 ( ( denotational_Vagree @ A @ Nu @ Omega @ ( top_top @ ( set @ ( sum_sum @ A @ A ) ) ) )
% 0.30/0.46 => ( Nu = Omega ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_UNIV_eq
% 0.30/0.46 thf(fact_204_ids_Oraw__term__inject,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C,Y: frechet_strm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( ( frechet_raw_term @ A @ C @ X )
% 0.30/0.46 = ( frechet_raw_term @ A @ C @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_term_inject
% 0.30/0.46 thf(fact_205_ids_Oraw__interp__inject,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C,Y: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( ( freche229654227interp @ A @ B @ C @ X )
% 0.30/0.46 = ( freche229654227interp @ A @ B @ C @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_interp_inject
% 0.30/0.46 thf(fact_206_ids_Ofrechet__continuous,axiom,
% 0.30/0.46 ! [Sc: $tType,Sz: $tType,Sf: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,Theta: trm @ Sf @ Sz] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( denota2077489681interp @ Sf @ Sc @ Sz @ I3 )
% 0.30/0.46 => ( ( dfree @ Sf @ Sz @ Theta )
% 0.30/0.46 => ( 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 @ I3 ) @ ( frechet_simple_term @ Sf @ Sz @ Theta ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.frechet_continuous
% 0.30/0.46 thf(fact_207_ids_Oraw__interp__inverse,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( freche227871258interp @ A @ B @ C @ ( freche229654227interp @ A @ B @ C @ X ) )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_interp_inverse
% 0.30/0.46 thf(fact_208_ids_Oraw__term__inverse,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( frechet_simple_term @ A @ C @ ( frechet_raw_term @ A @ C @ X ) )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_term_inverse
% 0.30/0.46 thf(fact_209_ids_Oraw__term,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( member @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C @ X ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_term
% 0.30/0.46 thf(fact_210_ids_Oraw__term__cases,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: trm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.46 => ~ ! [X3: frechet_strm @ A @ C] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( frechet_raw_term @ A @ C @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_term_cases
% 0.30/0.46 thf(fact_211_ids_Oraw__term__induct,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: trm @ A @ C,P: ( trm @ A @ C ) > $o] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.46 => ( ! [X3: frechet_strm @ A @ C] : ( P @ ( frechet_raw_term @ A @ C @ X3 ) )
% 0.30/0.46 => ( P @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_term_induct
% 0.30/0.46 thf(fact_212_ids_Osimple__term__cases,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ~ ! [Y3: trm @ A @ C] :
% 0.30/0.46 ( ( X
% 0.30/0.46 = ( frechet_simple_term @ A @ C @ Y3 ) )
% 0.30/0.46 => ~ ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.simple_term_cases
% 0.30/0.46 thf(fact_213_ids_Osimple__term__induct,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( frechet_strm @ A @ C ) > $o,X: frechet_strm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ! [Y3: trm @ A @ C] :
% 0.30/0.46 ( ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.46 => ( P @ ( frechet_simple_term @ A @ C @ Y3 ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.simple_term_induct
% 0.30/0.46 thf(fact_214_ids_Osimple__term__inject,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: trm @ A @ C,Y: trm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( trm @ A @ C ) @ X @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.46 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.46 => ( ( ( frechet_simple_term @ A @ C @ X )
% 0.30/0.46 = ( frechet_simple_term @ A @ C @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.simple_term_inject
% 0.30/0.46 thf(fact_215_ids_Oraw__interp__induct,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit,P: ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ! [X3: frechet_good_interp @ A @ B @ C] : ( P @ ( freche229654227interp @ A @ B @ C @ X3 ) )
% 0.30/0.46 => ( P @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_interp_induct
% 0.30/0.46 thf(fact_216_ids_Oraw__interp__cases,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ~ ! [X3: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( freche229654227interp @ A @ B @ C @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_interp_cases
% 0.30/0.46 thf(fact_217_ids_Oraw__interp,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C @ X ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.raw_interp
% 0.30/0.46 thf(fact_218_ids_Ogood__interp__cases,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ~ ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( X
% 0.30/0.46 = ( freche227871258interp @ A @ B @ C @ Y3 ) )
% 0.30/0.46 => ~ ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.good_interp_cases
% 0.30/0.46 thf(fact_219_ids_Ogood__interp__induct,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( frechet_good_interp @ A @ B @ C ) > $o,X: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( P @ ( freche227871258interp @ A @ B @ C @ Y3 ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.good_interp_induct
% 0.30/0.46 thf(fact_220_ids_Ogood__interp__inject,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ X @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ( ( freche227871258interp @ A @ B @ C @ X )
% 0.30/0.46 = ( freche227871258interp @ A @ B @ C @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.good_interp_inject
% 0.30/0.46 thf(fact_221_ids_Ocr__strm__def,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( frechet_cr_strm @ A @ B )
% 0.30/0.46 = ( ^ [X2: trm @ A @ B,Y2: frechet_strm @ A @ B] :
% 0.30/0.46 ( X2
% 0.30/0.46 = ( frechet_raw_term @ A @ B @ Y2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.cr_strm_def
% 0.30/0.46 thf(fact_222_ids_Ocr__good__interp__def,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( freche457001096interp @ A @ B @ C )
% 0.30/0.46 = ( ^ [X2: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y2: frechet_good_interp @ A @ B @ C] :
% 0.30/0.46 ( X2
% 0.30/0.46 = ( freche229654227interp @ A @ B @ C @ Y2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.cr_good_interp_def
% 0.30/0.46 thf(fact_223_ids_Osimple__term__inverse,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: trm @ A @ C] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 0.30/0.46 => ( ( frechet_raw_term @ A @ C @ ( frechet_simple_term @ A @ C @ Y ) )
% 0.30/0.46 = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.simple_term_inverse
% 0.30/0.46 thf(fact_224_ids_Ogood__interp__inverse,axiom,
% 0.30/0.46 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 0.30/0.46 => ( ( freche229654227interp @ A @ B @ C @ ( freche227871258interp @ A @ B @ C @ Y ) )
% 0.30/0.46 = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.good_interp_inverse
% 0.30/0.46 thf(fact_225_ids_Osterm__continuous_H,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C,S5: set @ ( finite_Cartesian_vec @ real @ C )] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 0.30/0.46 => ( ( dfree @ A @ C @ Theta )
% 0.30/0.46 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ S5 @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.sterm_continuous'
% 0.30/0.46 thf(fact_226_ids_Otype__definition__strm,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( 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 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.type_definition_strm
% 0.30/0.46 thf(fact_227_ids_Otype__definition__good__interp,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( 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 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.type_definition_good_interp
% 0.30/0.46 thf(fact_228_frechet__blin,axiom,
% 0.30/0.46 ! [I3: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Theta: trm @ sf @ sz] :
% 0.30/0.46 ( ( denota2077489681interp @ sf @ sc @ sz @ I3 )
% 0.30/0.46 => ( ( dfree @ sf @ sz @ Theta )
% 0.30/0.46 => ( ( ^ [V2: finite_Cartesian_vec @ real @ sz] : ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real @ ( denotational_frechet @ sf @ sc @ sz @ I3 @ Theta @ V2 ) ) )
% 0.30/0.46 = ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ I3 ) @ ( frechet_simple_term @ sf @ sz @ Theta ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % frechet_blin
% 0.30/0.46 thf(fact_229_continuous__on__snd,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ B )
% 0.30/0.46 & ( topolo503727757_space @ C ) )
% 0.30/0.46 => ! [S6: set @ A,F: A > ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S6 @ F )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ C @ S6
% 0.30/0.46 @ ^ [X2: A] : ( product_snd @ B @ C @ ( F @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_snd
% 0.30/0.46 thf(fact_230_top1I,axiom,
% 0.30/0.46 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.30/0.46
% 0.30/0.46 % top1I
% 0.30/0.46 thf(fact_231_top2I,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: A,Y: B] : ( top_top @ ( A > B > $o ) @ X @ Y ) ).
% 0.30/0.46
% 0.30/0.46 % top2I
% 0.30/0.46 thf(fact_232_continuous__on__const,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ B ) )
% 0.30/0.46 => ! [S6: set @ A,C3: B] :
% 0.30/0.46 ( topolo2071040574ous_on @ A @ B @ S6
% 0.30/0.46 @ ^ [X2: A] : C3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_const
% 0.30/0.46 thf(fact_233_continuous__on__id,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( topolo503727757_space @ A )
% 0.30/0.46 => ! [S6: set @ A] :
% 0.30/0.46 ( topolo2071040574ous_on @ A @ A @ S6
% 0.30/0.46 @ ^ [X2: A] : X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_id
% 0.30/0.46 thf(fact_234_continuous__on__subset,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ B ) )
% 0.30/0.46 => ! [S6: set @ A,F: A > B,T4: set @ A] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ B @ S6 @ F )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ T4 @ S6 )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ B @ T4 @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_subset
% 0.30/0.46 thf(fact_235_continuous__on__Pair,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ B )
% 0.30/0.46 & ( topolo503727757_space @ C ) )
% 0.30/0.46 => ! [S6: set @ A,F: A > B,G: A > C] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ B @ S6 @ F )
% 0.30/0.46 => ( ( topolo2071040574ous_on @ A @ C @ S6 @ G )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S6
% 0.30/0.46 @ ^ [X2: A] : ( product_Pair @ B @ C @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_Pair
% 0.30/0.46 thf(fact_236_ids_Ofrechet__blin,axiom,
% 0.30/0.46 ! [Sc: $tType,Sz: $tType,Sf: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,Theta: trm @ Sf @ Sz] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( denota2077489681interp @ Sf @ Sc @ Sz @ I3 )
% 0.30/0.46 => ( ( dfree @ Sf @ Sz @ Theta )
% 0.30/0.46 => ( ( ^ [V2: finite_Cartesian_vec @ real @ Sz] : ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ Sz ) @ real @ ( denotational_frechet @ Sf @ Sc @ Sz @ I3 @ Theta @ V2 ) ) )
% 0.30/0.46 = ( frechet_blin_frechet @ Sf @ Sc @ Sz @ ( freche227871258interp @ Sf @ Sc @ Sz @ I3 ) @ ( frechet_simple_term @ Sf @ Sz @ Theta ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.frechet_blin
% 0.30/0.46 thf(fact_237_continuous__on__fst,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ B )
% 0.30/0.46 & ( topolo503727757_space @ C ) )
% 0.30/0.46 => ! [S6: set @ A,F: A > ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S6 @ F )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ B @ S6
% 0.30/0.46 @ ^ [X2: A] : ( product_fst @ B @ C @ ( F @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_fst
% 0.30/0.46 thf(fact_238_continuous__on__product__then__coordinatewise__UNIV,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ C ) )
% 0.30/0.46 => ! [F: A > B > C,I: B] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ ( top_top @ ( set @ A ) ) @ F )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ C @ ( top_top @ ( set @ A ) )
% 0.30/0.46 @ ^ [X2: A] : ( F @ X2 @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_product_then_coordinatewise_UNIV
% 0.30/0.46 thf(fact_239_blin__frechet_Oabs__eq,axiom,
% 0.30/0.46 ! [Xb: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Xa: trm @ sf @ sz,X: finite_Cartesian_vec @ real @ sz] :
% 0.30/0.46 ( ( bNF_eq_onp @ ( denota1663640101rp_ext @ sf @ sc @ sz @ product_unit ) @ ( denota2077489681interp @ sf @ sc @ sz ) @ Xb @ Xb )
% 0.30/0.46 => ( ( bNF_eq_onp @ ( trm @ sf @ sz ) @ ( dfree @ sf @ sz ) @ Xa @ Xa )
% 0.30/0.46 => ( ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ Xb ) @ ( frechet_simple_term @ sf @ sz @ Xa ) @ X )
% 0.30/0.46 = ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real @ ( denotational_frechet @ sf @ sc @ sz @ Xb @ Xa @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % blin_frechet.abs_eq
% 0.30/0.46 thf(fact_240_ids_Oblin__frechet_Oabs__eq,axiom,
% 0.30/0.46 ! [Sf: $tType,Sc: $tType,Sz: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sc )
% 0.30/0.46 & ( finite_finite @ Sf ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Xb: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,Xa: trm @ Sf @ Sz,X: finite_Cartesian_vec @ real @ Sz] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( ( bNF_eq_onp @ ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) @ ( denota2077489681interp @ Sf @ Sc @ Sz ) @ Xb @ Xb )
% 0.30/0.46 => ( ( bNF_eq_onp @ ( trm @ Sf @ Sz ) @ ( dfree @ Sf @ Sz ) @ Xa @ Xa )
% 0.30/0.46 => ( ( frechet_blin_frechet @ Sf @ Sc @ Sz @ ( freche227871258interp @ Sf @ Sc @ Sz @ Xb ) @ ( frechet_simple_term @ Sf @ Sz @ Xa ) @ X )
% 0.30/0.46 = ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ Sz ) @ real @ ( denotational_frechet @ Sf @ Sc @ Sz @ Xb @ Xa @ X ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.blin_frechet.abs_eq
% 0.30/0.46 thf(fact_241_continuous__on__coordinatewise__then__product,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ C ) )
% 0.30/0.46 => ! [S5: set @ A,F: A > B > C] :
% 0.30/0.46 ( ! [I4: B] :
% 0.30/0.46 ( topolo2071040574ous_on @ A @ C @ S5
% 0.30/0.46 @ ^ [X2: A] : ( F @ X2 @ I4 ) )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ ( B > C ) @ S5 @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_coordinatewise_then_product
% 0.30/0.46 thf(fact_242_continuous__on__product__then__coordinatewise,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A )
% 0.30/0.46 & ( topolo503727757_space @ C ) )
% 0.30/0.46 => ! [S5: set @ A,F: A > B > C,I: B] :
% 0.30/0.46 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ S5 @ F )
% 0.30/0.46 => ( topolo2071040574ous_on @ A @ C @ S5
% 0.30/0.46 @ ^ [X2: A] : ( F @ X2 @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % continuous_on_product_then_coordinatewise
% 0.30/0.46 thf(fact_243_Quotient__good__interp,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C ) )
% 0.30/0.46 => ( quotient @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( bNF_eq_onp @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) @ ( freche227871258interp @ A @ B @ C ) @ ( freche229654227interp @ A @ B @ C ) @ ( freche457001096interp @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Quotient_good_interp
% 0.30/0.46 thf(fact_244_Quotient__strm,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType] : ( quotient @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( bNF_eq_onp @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) @ ( frechet_simple_term @ A @ C ) @ ( frechet_raw_term @ A @ C ) @ ( frechet_cr_strm @ A @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % Quotient_strm
% 0.30/0.46 thf(fact_245_ids_OQuotient__strm,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( quotient @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( bNF_eq_onp @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) @ ( frechet_simple_term @ A @ C ) @ ( frechet_raw_term @ A @ C ) @ ( frechet_cr_strm @ A @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.Quotient_strm
% 0.30/0.46 thf(fact_246_ids_OQuotient__good__interp,axiom,
% 0.30/0.46 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A )
% 0.30/0.46 & ( finite_finite @ B )
% 0.30/0.46 & ( finite_finite @ C )
% 0.30/0.46 & ( finite_finite @ Sz )
% 0.30/0.46 & ( linorder @ Sz )
% 0.30/0.46 & ( finite_finite @ Sf )
% 0.30/0.46 & ( finite_finite @ Sc ) )
% 0.30/0.46 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 0.30/0.46 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.46 => ( quotient @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( bNF_eq_onp @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) @ ( freche227871258interp @ A @ B @ C ) @ ( freche229654227interp @ A @ B @ C ) @ ( freche457001096interp @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ids.Quotient_good_interp
% 0.30/0.46 thf(fact_247_typedef__to__Quotient,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,S5: set @ B,T7: B > A > $o] :
% 0.30/0.46 ( ( type_definition @ A @ B @ Rep @ Abs @ S5 )
% 0.30/0.46 => ( ( T7
% 0.30/0.46 = ( ^ [X2: B,Y2: A] :
% 0.30/0.46 ( X2
% 0.30/0.46 = ( Rep @ Y2 ) ) ) )
% 0.30/0.46 => ( quotient @ B @ A
% 0.30/0.46 @ ( bNF_eq_onp @ B
% 0.30/0.46 @ ^ [X2: B] : ( member @ B @ X2 @ S5 ) )
% 0.30/0.46 @ Abs
% 0.30/0.46 @ Rep
% 0.30/0.46 @ T7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % typedef_to_Quotient
% 0.30/0.46 thf(fact_248_open__typedef__to__Quotient,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,P: B > $o,T7: B > A > $o] :
% 0.30/0.46 ( ( type_definition @ A @ B @ Rep @ Abs @ ( collect @ B @ P ) )
% 0.30/0.46 => ( ( T7
% 0.30/0.46 = ( ^ [X2: B,Y2: A] :
% 0.30/0.46 ( X2
% 0.30/0.46 = ( Rep @ Y2 ) ) ) )
% 0.30/0.46 => ( quotient @ B @ A @ ( bNF_eq_onp @ B @ P ) @ Abs @ Rep @ T7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % open_typedef_to_Quotient
% 0.30/0.46 thf(fact_249_QuotientI,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Abs: B > A,Rep: A > B,R3: B > B > $o,T7: B > A > $o] :
% 0.30/0.46 ( ! [A5: A] :
% 0.30/0.46 ( ( Abs @ ( Rep @ A5 ) )
% 0.30/0.46 = A5 )
% 0.30/0.46 => ( ! [A5: A] : ( R3 @ ( Rep @ A5 ) @ ( Rep @ A5 ) )
% 0.30/0.46 => ( ! [R2: B,S4: B] :
% 0.30/0.46 ( ( R3 @ R2 @ S4 )
% 0.30/0.46 = ( ( R3 @ R2 @ R2 )
% 0.30/0.46 & ( R3 @ S4 @ S4 )
% 0.30/0.46 & ( ( Abs @ R2 )
% 0.30/0.46 = ( Abs @ S4 ) ) ) )
% 0.30/0.46 => ( ( T7
% 0.30/0.46 = ( ^ [X2: B,Y2: A] :
% 0.30/0.46 ( ( R3 @ X2 @ X2 )
% 0.30/0.46 & ( ( Abs @ X2 )
% 0.30/0.46 = Y2 ) ) ) )
% 0.30/0.46 => ( quotient @ B @ A @ R3 @ Abs @ Rep @ T7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % QuotientI
% 0.30/0.46 thf(fact_250_Quotient__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( quotient @ A @ B )
% 0.30/0.46 = ( ^ [R5: A > A > $o,Abs2: A > B,Rep2: B > A,T8: A > B > $o] :
% 0.30/0.46 ( ! [A7: B] :
% 0.30/0.46 ( ( Abs2 @ ( Rep2 @ A7 ) )
% 0.30/0.46 = A7 )
% 0.30/0.46 & ! [A7: B] : ( R5 @ ( Rep2 @ A7 ) @ ( Rep2 @ A7 ) )
% 0.30/0.46 & ! [R6: A,S2: A] :
% 0.30/0.46 ( ( R5 @ R6 @ S2 )
% 0.30/0.46 = ( ( R5 @ R6 @ R6 )
% 0.30/0.46 & ( R5 @ S2 @ S2 )
% 0.30/0.46 & ( ( Abs2 @ R6 )
% 0.30/0.46 = ( Abs2 @ S2 ) ) ) )
% 0.30/0.46 & ( T8
% 0.30/0.46 = ( ^ [X2: A,Y2: B] :
% 0.30/0.46 ( ( R5 @ X2 @ X2 )
% 0.30/0.46 & ( ( Abs2 @ X2 )
% 0.30/0.46 = Y2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Quotient_def
% 0.30/0.46 thf(fact_251_Quotient__cr__rel,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R3: A > A > $o,Abs: A > B,Rep: B > A,T7: A > B > $o] :
% 0.30/0.46 ( ( quotient @ A @ B @ R3 @ Abs @ Rep @ T7 )
% 0.30/0.46 => ( T7
% 0.30/0.46 = ( ^ [X2: A,Y2: B] :
% 0.30/0.46 ( ( R3 @ X2 @ X2 )
% 0.30/0.46 & ( ( Abs @ X2 )
% 0.30/0.46 = Y2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Quotient_cr_rel
% 0.30/0.46 thf(fact_252_eq__onp__le__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ord_less_eq @ ( A > A > $o ) @ ( bNF_eq_onp @ A @ P )
% 0.30/0.46 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_onp_le_eq
% 0.30/0.46 thf(fact_253_Quotient__rep__abs__eq,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R3: A > A > $o,Abs: A > B,Rep: B > A,T7: A > B > $o,T4: A] :
% 0.30/0.46 ( ( quotient @ A @ B @ R3 @ Abs @ Rep @ T7 )
% 0.30/0.46 => ( ( R3 @ T4 @ T4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > A > $o ) @ R3
% 0.30/0.46 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.30/0.46 => ( ( Rep @ ( Abs @ T4 ) )
% 0.30/0.46 = T4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Quotient_rep_abs_eq
% 0.30/0.46 thf(fact_254_UNIV__typedef__to__Quotient,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,T7: B > A > $o] :
% 0.30/0.46 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.30/0.46 => ( ( T7
% 0.30/0.46 = ( ^ [X2: B,Y2: A] :
% 0.30/0.46 ( X2
% 0.30/0.46 = ( Rep @ Y2 ) ) ) )
% 0.30/0.46 => ( quotient @ B @ A
% 0.30/0.46 @ ^ [Y4: B,Z: B] : ( Y4 = Z )
% 0.30/0.46 @ Abs
% 0.30/0.46 @ Rep
% 0.30/0.46 @ T7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_typedef_to_Quotient
% 0.30/0.46 thf(fact_255_Quotient__eq__onp__typedef,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: A > $o,Abs: A > B,Rep: B > A,Cr: A > B > $o] :
% 0.30/0.46 ( ( quotient @ A @ B @ ( bNF_eq_onp @ A @ P ) @ Abs @ Rep @ Cr )
% 0.30/0.46 => ( type_definition @ B @ A @ Rep @ Abs @ ( collect @ A @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Quotient_eq_onp_typedef
% 0.30/0.46
% 0.30/0.46 % Subclasses (5)
% 0.30/0.46 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( finite_finite @ A )
% 0.30/0.46 => ( type @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( type @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ord @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( order @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( preorder @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % Type constructors (52)
% 0.30/0.46 thf(tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( real_V55928688vector @ A8 )
% 0.30/0.46 & ( real_V55928688vector @ A9 ) )
% 0.30/0.46 => ( real_V55928688vector @ ( bounde2145540817linfun @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( real_V55928688vector @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_2,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( real_V55928688vector @ A8 )
% 0.30/0.46 & ( real_V55928688vector @ A9 ) )
% 0.30/0.46 => ( real_V55928688vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_3,axiom,
% 0.30/0.46 real_V55928688vector @ real ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( topolo503727757_space @ A9 )
% 0.30/0.46 => ( topolo503727757_space @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( order_top @ A9 )
% 0.30/0.46 => ( order_top @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( preorder @ A9 )
% 0.30/0.46 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( finite_finite @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( order @ A9 )
% 0.30/0.46 => ( order @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Otop,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( top @ A9 )
% 0.30/0.46 => ( top @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ord @ A9 )
% 0.30/0.46 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder__top_4,axiom,
% 0.30/0.46 ! [A8: $tType] : ( order_top @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.30/0.46 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Finite__Set_Ofinite_6,axiom,
% 0.30/0.46 ! [A8: $tType] :
% 0.30/0.46 ( ( finite_finite @ A8 )
% 0.30/0.46 => ( finite_finite @ ( set @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder_7,axiom,
% 0.30/0.46 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Otop_8,axiom,
% 0.30/0.46 ! [A8: $tType] : ( top @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.30/0.46 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_10,axiom,
% 0.30/0.46 topolo503727757_space @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__top_11,axiom,
% 0.30/0.46 order_top @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 0.30/0.46 preorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Finite__Set_Ofinite_13,axiom,
% 0.30/0.46 finite_finite @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Otop_15,axiom,
% 0.30/0.46 top @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_17,axiom,
% 0.30/0.46 topolo503727757_space @ real ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Real_Oreal___Orderings_Opreorder_18,axiom,
% 0.30/0.46 preorder @ real ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Real_Oreal___Orderings_Olinorder_19,axiom,
% 0.30/0.46 linorder @ real ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Real_Oreal___Orderings_Oorder_20,axiom,
% 0.30/0.46 order @ real ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Real_Oreal___Orderings_Oord_21,axiom,
% 0.30/0.46 ord @ real ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_22,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( finite_finite @ ( sum_sum @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_23,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A8 )
% 0.30/0.46 & ( topolo503727757_space @ A9 ) )
% 0.30/0.46 => ( topolo503727757_space @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oorder__top_24,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( order_top @ A8 )
% 0.30/0.46 & ( order_top @ A9 ) )
% 0.30/0.46 => ( order_top @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_25,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( preorder @ A8 )
% 0.30/0.46 & ( preorder @ A9 ) )
% 0.30/0.46 => ( preorder @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_26,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( finite_finite @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oorder_27,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( order @ A8 )
% 0.30/0.46 & ( order @ A9 ) )
% 0.30/0.46 => ( order @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Otop_28,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( top @ A8 )
% 0.30/0.46 & ( top @ A9 ) )
% 0.30/0.46 => ( top @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oord_29,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( ord @ A8 )
% 0.30/0.46 & ( ord @ A9 ) )
% 0.30/0.46 => ( ord @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_30,axiom,
% 0.30/0.46 order_top @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31,axiom,
% 0.30/0.46 preorder @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32,axiom,
% 0.30/0.46 linorder @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Finite__Set_Ofinite_33,axiom,
% 0.30/0.46 finite_finite @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder_34,axiom,
% 0.30/0.46 order @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Otop_35,axiom,
% 0.30/0.46 top @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oord_36,axiom,
% 0.30/0.46 ord @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_37,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( topolo503727757_space @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( topolo503727757_space @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_38,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( order @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( preorder @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_39,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( linorder @ A8 )
% 0.30/0.46 & ( cARD_1 @ A9 ) )
% 0.30/0.46 => ( linorder @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_40,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( finite_finite @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( finite_finite @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_41,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( order @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( order @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_42,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( ord @ A8 )
% 0.30/0.46 & ( finite_finite @ A9 ) )
% 0.30/0.46 => ( ord @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_43,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ( real_V55928688vector @ A8 )
% 0.30/0.46 & ( real_V55928688vector @ A9 ) )
% 0.30/0.46 => ( topolo503727757_space @ ( bounde2145540817linfun @ A8 @ A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Helper facts (3)
% 0.30/0.46 thf(help_If_3_1_T,axiom,
% 0.30/0.46 ! [P: $o] :
% 0.30/0.46 ( ( P = $true )
% 0.30/0.46 | ( P = $false ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_2_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $false @ X @ Y )
% 0.30/0.46 = Y ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_1_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $true @ X @ Y )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % Free types (7)
% 0.30/0.46 thf(tfree_0,hypothesis,
% 0.30/0.46 finite_finite @ c ).
% 0.30/0.46
% 0.30/0.46 thf(tfree_1,hypothesis,
% 0.30/0.46 finite_finite @ a ).
% 0.30/0.46
% 0.30/0.46 thf(tfree_2,hypothesis,
% 0.30/0.46 finite_finite @ sz ).
% 0.30/0.46
% 0.30/0.46 thf(tfree_3,hypothesis,
% 0.30/0.46 linorder @ sz ).
% 0.30/0.46
% 0.30/0.46 thf(tfree_4,hypothesis,
% 0.30/0.46 finite_finite @ sf ).
% 0.30/0.46
% 0.30/0.46 thf(tfree_5,hypothesis,
% 0.30/0.46 finite_finite @ sc ).
% 0.30/0.46
% 0.30/0.46 thf(tfree_6,hypothesis,
% 0.30/0.46 finite_finite @ b ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t2 ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.94/1.56 ---- Embedded in THF ---
% 2.94/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.94/1.56 %%% Generated on Tue Feb 24 08:25:07 EST 2026
% 2.94/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.94/1.56 %%% Logic specification used:
% 2.94/1.56 %%% thf(spec, logic, $$dhol).
% 2.94/1.56
% 2.94/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EGxl0yY1Vf/DTF2DTF18030.p
% 2.94/1.56 thf(ty_t_Denotational__Semantics_Ointerp_Ointerp__ext, type, denota1663640101rp_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.94/1.56 thf(ty_t_Frechet__Correctness_Oids_Ogood__interp, type, frechet_good_interp: ($tType > ($tType > ($tType > $tType)))).
% 2.94/1.56 thf(ty_t_Bounded__Linear__Function_Oblinfun, type, bounde2145540817linfun: ($tType > ($tType > $tType))).
% 2.94/1.56 thf(ty_t_Frechet__Correctness_Oids_Ostrm, type, frechet_strm: ($tType > ($tType > $tType))).
% 2.94/1.56 thf(ty_t_Finite__Cartesian__Product_Ovec, type, finite_Cartesian_vec: ($tType > ($tType > $tType))).
% 2.94/1.56 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.94/1.56 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.94/1.56 thf(ty_t_Syntax_Oformula, type, formula: ($tType > ($tType > ($tType > $tType)))).
% 2.94/1.56 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.94/1.56 thf(ty_t_Syntax_Otrm, type, trm: ($tType > ($tType > $tType))).
% 2.94/1.56 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.94/1.56 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.94/1.56 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.94/1.56 thf(ty_tf_sz, type, sz: $tType).
% 2.94/1.56 thf(ty_tf_sf, type, sf: $tType).
% 2.94/1.56 thf(ty_tf_sc, type, sc: $tType).
% 2.94/1.56 thf(ty_tf_c, type, c: $tType).
% 2.94/1.56 thf(ty_tf_b, type, b: $tType).
% 2.94/1.56 thf(ty_tf_a, type, a: $tType).
% 2.94/1.56 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector, type, real_V55928688vector: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Cardinality_OCARD__1, type, cARD_1: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Topological__Spaces_Otopological__space, type, topolo503727757_space: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Euclidean__Algorithm_Oeuclidean__ring__gcd, type, euclid1678468529ng_gcd: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_cl_Euclidean__Algorithm_Onormalization__euclidean__semiring, type, euclid1155270486miring: (!> [A:$tType]: ($o))).
% 2.94/1.56 thf(sy_c_BNF__Def_Oeq__onp, type, bNF_eq_onp: (!> [A:$tType]: (((A > $o) > (A > (A > $o)))))).
% 2.94/1.56 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2, type, bNF_Greatest_image2: (!> [C:$tType,A:$tType,B:$tType]: (((set @ C) > ((C > A) > ((C > B) > (set @ ((product_prod @ A) @ B)))))))).
% 2.94/1.56 thf(sy_c_Bounded__Linear__Function_Oblinfun_OBlinfun, type, bounde688532126linfun: (!> [A:$tType,B:$tType]: (((A > B) > ((bounde2145540817linfun @ A) @ B))))).
% 2.94/1.56 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))) > $o)))))).
% 2.94/1.56 thf(sy_c_Denotational__Semantics_OVagree, type, denotational_Vagree: (!> [C:$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)) > $o)))))).
% 2.94/1.56 thf(sy_c_Denotational__Semantics_Odirectional__derivative, type, denota2078997598vative: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((trm @ A) @ C) > (((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) > real)))))).
% 2.94/1.56 thf(sy_c_Denotational__Semantics_Ofrechet, type, denotational_frechet: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((trm @ A) @ C) > (((finite_Cartesian_vec @ real) @ C) > (((finite_Cartesian_vec @ real) @ C) > real))))))).
% 2.94/1.56 thf(sy_c_Denotational__Semantics_Ois__interp, type, denota2077489681interp: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > $o)))).
% 2.94/1.56 thf(sy_c_Denotational__Semantics_Osterm__sem, type, denota126604975rm_sem: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((trm @ A) @ C) > (((finite_Cartesian_vec @ real) @ C) > real)))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Oblin__frechet, type, frechet_blin_frechet: (!> [Sf:$tType,Sc:$tType,Sz:$tType]: (((((frechet_good_interp @ Sf) @ Sc) @ Sz) > (((frechet_strm @ Sf) @ Sz) > (((finite_Cartesian_vec @ real) @ Sz) > ((bounde2145540817linfun @ ((finite_Cartesian_vec @ real) @ Sz)) @ real))))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Ocr__good__interp, type, freche457001096interp: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > ((((frechet_good_interp @ A) @ B) @ C) > $o))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm, type, frechet_cr_strm: (!> [A:$tType,B:$tType]: ((((trm @ A) @ B) > (((frechet_strm @ A) @ B) > $o))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Ogood__interp, type, freche227871258interp: (!> [A:$tType,B:$tType,C:$tType]: ((((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > (((frechet_good_interp @ A) @ B) @ C))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Oraw__interp, type, freche229654227interp: (!> [A:$tType,B:$tType,C:$tType]: (((((frechet_good_interp @ A) @ B) @ C) > ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Oraw__term, type, frechet_raw_term: (!> [A:$tType,C:$tType]: ((((frechet_strm @ A) @ C) > ((trm @ A) @ C))))).
% 2.94/1.56 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Osimple__term, type, frechet_simple_term: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > ((frechet_strm @ A) @ C))))).
% 2.94/1.56 thf(sy_c_Ids_Oids, type, ids: (!> [Sz:$tType,Sf:$tType,Sc:$tType]: ((Sz > (Sz > (Sz > (Sf > (Sf > (Sf > (Sc > (Sc > (Sc > (Sc > $o))))))))))))).
% 2.94/1.56 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.94/1.56 thf(sy_c_Lifting_OQuotient, type, quotient: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > ((B > A) > ((A > (B > $o)) > $o))))))).
% 2.94/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.94/1.56 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.94/1.56 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.94/1.56 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.94/1.56 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 2.94/1.56 thf(sy_c_Product__Type_Oprod_Osnd, type, product_snd: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > B)))).
% 2.94/1.56 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.94/1.56 thf(sy_c_Static__Semantics_OFVDiff, type, static_FVDiff: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (set @ ((sum_sum @ C) @ C)))))).
% 2.94/1.56 thf(sy_c_Static__Semantics_OFVT, type, static_FVT: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (set @ ((sum_sum @ C) @ C)))))).
% 2.94/1.56 thf(sy_c_Static__Semantics_OSIGT, type, static_SIGT: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (set @ A))))).
% 2.94/1.56 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 2.94/1.56 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 2.94/1.56 thf(sy_c_Syntax_OPredicational, type, predicational: (!> [B:$tType,A:$tType,C:$tType]: ((B > (((formula @ A) @ B) @ C))))).
% 2.94/1.56 thf(sy_c_Syntax_Odfree, type, dfree: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > $o)))).
% 2.94/1.56 thf(sy_c_Syntax_Oids_OP, type, p: (!> [Sc:$tType,Sf:$tType,Sz:$tType]: ((Sc > (((formula @ Sf) @ Sc) @ Sz))))).
% 2.94/1.56 thf(sy_c_Syntax_Oids_Oempty, type, empty: (!> [B:$tType,A:$tType]: ((B > ((trm @ A) @ B))))).
% 2.94/1.56 thf(sy_c_Syntax_Oids_Of0, type, f0: (!> [Sf:$tType,Sz:$tType]: ((Sf > ((trm @ Sf) @ Sz))))).
% 2.94/1.56 thf(sy_c_Syntax_Otrm_OFunction, type, function: (!> [A:$tType,C:$tType]: ((A > ((C > ((trm @ A) @ C)) > ((trm @ A) @ C)))))).
% 2.94/1.56 thf(sy_c_Syntax_Otrm_OPlus, type, plus: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (((trm @ A) @ C) > ((trm @ A) @ C)))))).
% 2.94/1.56 thf(sy_c_Syntax_Otrm_OTimes, type, times: (!> [A:$tType,C:$tType]: ((((trm @ A) @ C) > (((trm @ A) @ C) > ((trm @ A) @ C)))))).
% 2.94/1.56 thf(sy_c_Topological__Spaces_Ocontinuous__on, type, topolo2071040574ous_on: (!> [A:$tType,B:$tType]: (((set @ A) > ((A > B) > $o))))).
% 2.94/1.56 thf(sy_c_Typedef_Otype__definition, type, type_definition: (!> [B:$tType,A:$tType]: (((B > A) > ((A > B) > ((set @ A) > $o)))))).
% 2.94/1.56 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.94/1.56 thf(sy_v_I, type, i: ((((denota1663640101rp_ext @ a) @ b) @ c) @ product_unit)).
% 2.94/1.56 thf(sy_v_J, type, j: ((((denota1663640101rp_ext @ a) @ b) @ c) @ product_unit)).
% 2.94/1.56 thf(sy_v__092_060nu_062, type, nu: ((product_prod @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c))).
% 2.94/1.56 thf(sy_v__092_060nu_062_H, type, nu2: ((product_prod @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c))).
% 2.94/1.56 thf(sy_v_t1____, type, t1: ((trm @ a) @ c)).
% 2.94/1.56 thf(sy_v_t2____, type, t2: ((trm @ a) @ c)).
% 2.94/1.56 thf(fact_0_agree__plus2, axiom, (! [A:$tType,B:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),T1:((trm @ B) @ A),T2:((trm @ B) @ A)]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ ((((plus @ B) @ A) @ T1) @ T2))) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ T2))))))))).
% 2.94/1.56 thf(fact_1_agree, axiom, ((((denotational_Vagree @ c) @ nu) @ nu2) @ (((static_FVDiff @ a) @ c) @ ((((plus @ a) @ c) @ t1) @ t2)))).
% 2.94/1.56 thf(fact_2_agree1, axiom, ((((denotational_Vagree @ c) @ nu) @ nu2) @ (((static_FVDiff @ a) @ c) @ t1))).
% 2.94/1.56 thf(fact_3_dfree2, axiom, (((dfree @ a) @ c) @ t2)).
% 2.94/1.56 thf(fact_4_agree__plus1, axiom, (! [A:$tType,B:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),T1:((trm @ B) @ A),T2:((trm @ B) @ A)]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ ((((plus @ B) @ A) @ T1) @ T2))) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ T1))))))))).
% 2.94/1.56 thf(fact_5_agree__comm, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A2:((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) @ A2) @ B2) @ V) => ((((denotational_Vagree @ A) @ B2) @ A2) @ V)))))))).
% 2.94/1.56 thf(fact_6_agree__refl, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),A2:(set @ ((sum_sum @ A) @ A))]: (((((denotational_Vagree @ A) @ Nu) @ Nu) @ A2))))))).
% 2.94/1.56 thf(fact_7_dfree1, axiom, (((dfree @ a) @ c) @ t1)).
% 2.94/1.56 thf(fact_8_raw__interp__inject, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X:(((frechet_good_interp @ A) @ B) @ C),Y:(((frechet_good_interp @ A) @ B) @ C)]: (((((((freche229654227interp @ A) @ B) @ C) @ X) = ((((freche229654227interp @ A) @ B) @ C) @ Y)) = (X = Y)))))))).
% 2.94/1.56 thf(fact_9_raw__term__inject, axiom, (! [C:$tType,A:$tType,X:((frechet_strm @ A) @ C),Y:((frechet_strm @ A) @ C)]: ((((((frechet_raw_term @ A) @ C) @ X) = (((frechet_raw_term @ A) @ C) @ Y)) = (X = Y))))).
% 2.94/1.56 thf(fact_10_agree__times1, axiom, (! [A:$tType,B:$tType]: (((finite_finite @ 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)),T1:((trm @ B) @ A),T2:((trm @ B) @ A)]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ ((((times @ B) @ A) @ T1) @ T2))) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ T1))))))))).
% 2.94/1.56 thf(fact_11_agree__times2, axiom, (! [A:$tType,B:$tType]: (((finite_finite @ 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)),T1:((trm @ B) @ A),T2:((trm @ B) @ A)]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ ((((times @ B) @ A) @ T1) @ T2))) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ T2))))))))).
% 2.94/1.56 thf(fact_12_agree__func, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ 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)),Var:B,Args:(A > ((trm @ B) @ A)),I:A]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ ((((function @ B) @ A) @ Var) @ Args))) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVDiff @ B) @ A) @ (Args @ I)))))))))).
% 2.94/1.56 thf(fact_13_P__def, axiom, ((((p @ sc) @ sf) @ sz) = (((predicational @ sc) @ sf) @ sz))).
% 2.94/1.56 thf(fact_14_IH2, axiom, (((((denotational_Vagree @ c) @ nu) @ nu2) @ (((static_FVDiff @ a) @ c) @ t2)) => (((((((denotational_Iagree @ a) @ b) @ c) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ b) @ c))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ b) @ c))]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ b) @ c)) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ t2))))))))) => ((((((((denotational_frechet @ a) @ b) @ c) @ i) @ t2) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu)) = (((((((denotational_frechet @ a) @ b) @ c) @ j) @ t2) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu2)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu2)))))).
% 2.94/1.56 thf(fact_15_seq__sem_Ocases, axiom, (! [X:((product_prod @ ((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit)) @ ((product_prod @ (list @ (((formula @ sf) @ sc) @ sz))) @ (list @ (((formula @ sf) @ sc) @ sz))))]: ((~ ((! [I2:((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit),S:((product_prod @ (list @ (((formula @ sf) @ sc) @ sz))) @ (list @ (((formula @ sf) @ sc) @ sz)))]: ((X != ((((product_Pair @ ((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit)) @ ((product_prod @ (list @ (((formula @ sf) @ sc) @ sz))) @ (list @ (((formula @ sf) @ sc) @ sz)))) @ I2) @ S))))))))).
% 2.94/1.56 thf(fact_16_raw__term, axiom, (! [C:$tType,A:$tType,X:((frechet_strm @ A) @ C)]: ((((member @ ((trm @ A) @ C)) @ (((frechet_raw_term @ A) @ C) @ X)) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C)))))).
% 2.94/1.56 thf(fact_17_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)))))))))).
% 2.94/1.56 thf(fact_18_raw__term__induct, axiom, (! [C:$tType,A:$tType,Y:((trm @ A) @ C),P:(((trm @ A) @ C) > $o)]: (((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((! [X3:((frechet_strm @ A) @ C)]: ((P @ (((frechet_raw_term @ A) @ C) @ X3)))) => (P @ Y)))))).
% 2.94/1.56 thf(fact_19_coincidence__frechet, axiom, (! [B:$tType,A:$tType,C:$tType]: ((((finite_finite @ C) & ((finite_finite @ A) & (finite_finite @ B))) => (! [Theta:((trm @ A) @ C),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)),I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((dfree @ A) @ C) @ Theta) => (((((denotational_Vagree @ C) @ Nu) @ Nu2) @ (((static_FVDiff @ A) @ C) @ Theta)) => ((((((((denotational_frechet @ A) @ B) @ C) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) = (((((((denotational_frechet @ A) @ B) @ C) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu2)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu2))))))))))).
% 2.94/1.56 thf(fact_20_IA, axiom, ((((((denotational_Iagree @ a) @ b) @ c) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ b) @ c))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ b) @ c))]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ b) @ c)) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ ((((plus @ a) @ c) @ t1) @ t2))))))))))).
% 2.94/1.56 thf(fact_21_IA1, axiom, ((((((denotational_Iagree @ a) @ b) @ c) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ b) @ c))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ b) @ c))]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ b) @ c)) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ t1)))))))))).
% 2.94/1.56 thf(fact_22_IA2, axiom, ((((((denotational_Iagree @ a) @ b) @ c) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ b) @ c))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ b) @ c))]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ b) @ c)) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ t2)))))))))).
% 2.94/1.56 thf(fact_23_IH1, axiom, (((((denotational_Vagree @ c) @ nu) @ nu2) @ (((static_FVDiff @ a) @ c) @ t1)) => (((((((denotational_Iagree @ a) @ b) @ c) @ i) @ j) @ ((collect @ ((sum_sum @ a) @ ((sum_sum @ b) @ c))) @ (^ [Uu:((sum_sum @ a) @ ((sum_sum @ b) @ c))]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ ((sum_sum @ b) @ c)) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ t1))))))))) => ((((((((denotational_frechet @ a) @ b) @ c) @ i) @ t1) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu)) = (((((((denotational_frechet @ a) @ b) @ c) @ j) @ t1) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu2)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ c)) @ ((finite_Cartesian_vec @ real) @ c)) @ nu2)))))).
% 2.94/1.56 thf(fact_24_Iagree__comm, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [A2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),B2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),V:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C)))]: ((((((((denotational_Iagree @ A) @ B) @ C) @ A2) @ B2) @ V) => ((((((denotational_Iagree @ A) @ B) @ C) @ B2) @ A2) @ V)))))))).
% 2.94/1.56 thf(fact_25_Iagree__refl, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),A2:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C)))]: (((((((denotational_Iagree @ A) @ B) @ C) @ I3) @ I3) @ A2))))))).
% 2.94/1.56 thf(fact_26_FunctionFrechet_Ocases, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [X:((product_prod @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ A)]: ((~ ((! [I2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),I4:A]: ((X != ((((product_Pair @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ A) @ I2) @ I4)))))))))))).
% 2.94/1.56 thf(fact_27_subs_I2_J, axiom, (! [E:$tType]: ((((ord_less_eq @ (set @ ((sum_sum @ a) @ E))) @ ((collect @ ((sum_sum @ a) @ E)) @ (^ [Uu:((sum_sum @ a) @ E)]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ E) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ t2))))))))) @ ((collect @ ((sum_sum @ a) @ E)) @ (^ [Uu:((sum_sum @ a) @ E)]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ E) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ ((((plus @ a) @ c) @ t1) @ t2))))))))))))).
% 2.94/1.56 thf(fact_28_subs_I1_J, axiom, (! [D:$tType]: ((((ord_less_eq @ (set @ ((sum_sum @ a) @ D))) @ ((collect @ ((sum_sum @ a) @ D)) @ (^ [Uu:((sum_sum @ a) @ D)]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ D) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ t1))))))))) @ ((collect @ ((sum_sum @ a) @ D)) @ (^ [Uu:((sum_sum @ a) @ D)]: ((? [X2:a]: (((Uu = (((sum_Inl @ a) @ D) @ X2)) & (((member @ a) @ X2) @ (((static_SIGT @ a) @ c) @ ((((plus @ a) @ c) @ t1) @ t2))))))))))))).
% 2.94/1.56 thf(fact_29_simple__term__inverse, axiom, (! [C:$tType,A:$tType,Y:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((((frechet_raw_term @ A) @ C) @ (((frechet_simple_term @ A) @ C) @ Y)) = Y))))).
% 2.94/1.56 thf(fact_30_prod_Ocollapse, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)) = Prod)))).
% 2.94/1.56 thf(fact_31_cr__good__interp__def, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => ((((freche457001096interp @ A) @ B) @ C) = (^ [X2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Y2:(((frechet_good_interp @ A) @ B) @ C)]: ((X2 = ((((freche229654227interp @ A) @ B) @ C) @ Y2))))))))).
% 2.94/1.56 thf(fact_32_cr__strm__def, axiom, (! [B:$tType,A:$tType]: ((((frechet_cr_strm @ A) @ B) = (^ [X2:((trm @ A) @ B),Y2:((frechet_strm @ A) @ B)]: ((X2 = (((frechet_raw_term @ A) @ B) @ Y2)))))))).
% 2.94/1.56 thf(fact_33_dfree__Times__simps, axiom, (! [B:$tType,A:$tType,A3:((trm @ A) @ B),B3:((trm @ A) @ B)]: (((((dfree @ A) @ B) @ ((((times @ A) @ B) @ A3) @ B3)) = ((((dfree @ A) @ B) @ A3) & (((dfree @ A) @ B) @ B3)))))).
% 2.94/1.56 thf(fact_34_dfree__Plus__simps, axiom, (! [B:$tType,A:$tType,A3:((trm @ A) @ B),B3:((trm @ A) @ B)]: (((((dfree @ A) @ B) @ ((((plus @ A) @ B) @ A3) @ B3)) = ((((dfree @ A) @ B) @ A3) & (((dfree @ A) @ B) @ B3)))))).
% 2.94/1.56 thf(fact_35_dfree__Fun__simps, axiom, (! [A:$tType,B:$tType,I:A,Args:(B > ((trm @ A) @ B))]: (((((dfree @ A) @ B) @ ((((function @ A) @ B) @ I) @ Args)) = (! [X2:B]: ((((dfree @ A) @ B) @ (Args @ X2)))))))).
% 2.94/1.56 thf(fact_36_simple__term__cases, axiom, (! [C:$tType,A:$tType,X:((frechet_strm @ A) @ C)]: ((~ ((! [Y3:((trm @ A) @ C)]: (((X = (((frechet_simple_term @ A) @ C) @ Y3)) => (~ ((((member @ ((trm @ A) @ C)) @ Y3) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))))))))))))).
% 2.94/1.56 thf(fact_37_raw__term__inverse, axiom, (! [C:$tType,A:$tType,X:((frechet_strm @ A) @ C)]: (((((frechet_simple_term @ A) @ C) @ (((frechet_raw_term @ A) @ C) @ X)) = X)))).
% 2.94/1.56 thf(fact_38_simple__term__inject, axiom, (! [C:$tType,A:$tType,X:((trm @ A) @ C),Y:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ X) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (((((frechet_simple_term @ A) @ C) @ X) = (((frechet_simple_term @ A) @ C) @ Y)) = (X = Y))))))).
% 2.94/1.56 thf(fact_39_simple__term__induct, axiom, (! [C:$tType,A:$tType,P:(((frechet_strm @ A) @ C) > $o),X:((frechet_strm @ A) @ C)]: (((! [Y3:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ Y3) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (P @ (((frechet_simple_term @ A) @ C) @ Y3))))) => (P @ X))))).
% 2.94/1.56 thf(fact_40_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A4:A,B4:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A4) @ B4)) = ((A3 = A4) & (B3 = B4)))))).
% 2.94/1.56 thf(fact_41_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X1 = Y1) & (X22 = Y22)))))).
% 2.94/1.56 thf(fact_42_trm_Oinject_I3_J, axiom, (! [A:$tType,C:$tType,X31:A,X32:(C > ((trm @ A) @ C)),Y31:A,Y32:(C > ((trm @ A) @ C))]: (((((((function @ A) @ C) @ X31) @ X32) = ((((function @ A) @ C) @ Y31) @ Y32)) = ((X31 = Y31) & (X32 = Y32)))))).
% 2.94/1.56 thf(fact_43_trm_Oinject_I4_J, axiom, (! [C:$tType,A:$tType,X41:((trm @ A) @ C),X42:((trm @ A) @ C),Y41:((trm @ A) @ C),Y42:((trm @ A) @ C)]: (((((((plus @ A) @ C) @ X41) @ X42) = ((((plus @ A) @ C) @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 2.94/1.56 thf(fact_44_trm_Oinject_I5_J, axiom, (! [C:$tType,A:$tType,X51:((trm @ A) @ C),X52:((trm @ A) @ C),Y51:((trm @ A) @ C),Y52:((trm @ A) @ C)]: (((((((times @ A) @ C) @ X51) @ X52) = ((((times @ A) @ C) @ Y51) @ Y52)) = ((X51 = Y51) & (X52 = Y52)))))).
% 2.94/1.56 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.94/1.56 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.94/1.56 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.94/1.56 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.94/1.56 thf(fact_49_agree__sub, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A2:(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))) @ A2) @ B2) => (((((denotational_Vagree @ A) @ Nu) @ Omega) @ B2) => ((((denotational_Vagree @ A) @ Nu) @ Omega) @ A2))))))))).
% 2.94/1.56 thf(fact_50_agree__supset, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [B2:(set @ ((sum_sum @ A) @ A)),A2:(set @ ((sum_sum @ A) @ A)),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A))]: (((((ord_less_eq @ (set @ ((sum_sum @ A) @ A))) @ B2) @ A2) => (((((denotational_Vagree @ A) @ Nu) @ Nu2) @ A2) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ B2))))))))).
% 2.94/1.56 thf(fact_51_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A5:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B5)))) => (P @ Prod))))).
% 2.94/1.56 thf(fact_52_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A5:A,B5:B]: ((Y != ((((product_Pair @ A) @ B) @ A5) @ B5))))))))).
% 2.94/1.56 thf(fact_53_Pair__inject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A4:A,B4:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A4) @ B4)) => (~ (((A3 = A4) => (B3 != B4)))))))).
% 2.94/1.56 thf(fact_54_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A5:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B5)))) => (P @ P2))))).
% 2.94/1.56 thf(fact_55_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X3:A,Y3:B]: ((P2 = ((((product_Pair @ A) @ B) @ X3) @ Y3))))))).
% 2.94/1.56 thf(fact_56_prod__induct7, axiom, (! [G2:$tType,F2:$tType,E2:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2))))))]: (((! [A5:A,B5:B,C2:C,D3:D2,E3:E2,F3:F2,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2)))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2))) @ D3) @ ((((product_Pair @ E2) @ ((product_prod @ F2) @ G2)) @ E3) @ ((((product_Pair @ F2) @ G2) @ F3) @ G3))))))))) => (P @ X))))).
% 2.94/1.56 thf(fact_57_prod__induct6, axiom, (! [F2:$tType,E2:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2)))))]: (((! [A5:A,B5:B,C2:C,D3:D2,E3:E2,F3:F2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E2) @ F2)) @ D3) @ ((((product_Pair @ E2) @ F2) @ E3) @ F3)))))))) => (P @ X))))).
% 2.94/1.56 thf(fact_58_prod__induct5, axiom, (! [E2:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2))))]: (((! [A5:A,B5:B,C2:C,D3:D2,E3:E2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ E2)) @ C2) @ ((((product_Pair @ D2) @ E2) @ D3) @ E3))))))) => (P @ X))))).
% 2.94/1.56 thf(fact_59_prod__induct4, axiom, (! [D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2)))]: (((! [A5:A,B5:B,C2:C,D3:D2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D2)) @ B5) @ ((((product_Pair @ C) @ D2) @ C2) @ D3)))))) => (P @ X))))).
% 2.94/1.56 thf(fact_60_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A5:A,B5:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B5) @ C2))))) => (P @ X))))).
% 2.94/1.56 thf(fact_61_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E2:$tType,F2:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2))))))]: ((~ ((! [A5:A,B5:B,C2:C,D3:D2,E3:E2,F3:F2,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2)))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E2) @ ((product_prod @ F2) @ G2))) @ D3) @ ((((product_Pair @ E2) @ ((product_prod @ F2) @ G2)) @ E3) @ ((((product_Pair @ F2) @ G2) @ F3) @ G3)))))))))))))).
% 2.94/1.56 thf(fact_62_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E2:$tType,F2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2)))))]: ((~ ((! [A5:A,B5:B,C2:C,D3:D2,E3:E2,F3:F2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E2) @ F2))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E2) @ F2)) @ D3) @ ((((product_Pair @ E2) @ F2) @ E3) @ F3))))))))))))).
% 2.94/1.56 thf(fact_63_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2))))]: ((~ ((! [A5:A,B5:B,C2:C,D3:D2,E3:E2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E2))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ E2)) @ C2) @ ((((product_Pair @ D2) @ E2) @ D3) @ E3)))))))))))).
% 2.94/1.56 thf(fact_64_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2)))]: ((~ ((! [A5:A,B5:B,C2:C,D3:D2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D2)) @ B5) @ ((((product_Pair @ C) @ D2) @ C2) @ D3))))))))))).
% 2.94/1.56 thf(fact_65_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A5:A,B5:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B5) @ C2)))))))))).
% 2.94/1.56 thf(fact_66_fst__conv, axiom, (! [B:$tType,A:$tType,X1:A,X22:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X1) @ X22)) = X1)))).
% 2.94/1.56 thf(fact_67_fst__eqD, axiom, (! [B:$tType,A:$tType,X:A,Y:B,A3:A]: ((((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X) @ Y)) = A3) => (X = A3))))).
% 2.94/1.56 thf(fact_68_snd__conv, axiom, (! [Aa:$tType,A:$tType,X1:Aa,X22:A]: (((((product_snd @ Aa) @ A) @ ((((product_Pair @ Aa) @ A) @ X1) @ X22)) = X22)))).
% 2.94/1.56 thf(fact_69_snd__eqD, axiom, (! [B:$tType,A:$tType,X:B,Y:A,A3:A]: ((((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y)) = A3) => (Y = A3))))).
% 2.94/1.56 thf(fact_70_prod__eq__iff, axiom, (! [B:$tType,A:$tType]: (((^ [Y4:((product_prod @ A) @ B),Z:((product_prod @ A) @ B)]: ((Y4 = Z))) = (^ [S2:((product_prod @ A) @ B),T3:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ S2) = (((product_fst @ A) @ B) @ T3)) & ((((product_snd @ A) @ B) @ S2) = (((product_snd @ A) @ B) @ T3))))))))).
% 2.94/1.56 thf(fact_71_prod_Oexpand, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B),Prod2:((product_prod @ A) @ B)]: (((((((product_fst @ A) @ B) @ Prod) = (((product_fst @ A) @ B) @ Prod2)) & ((((product_snd @ A) @ B) @ Prod) = (((product_snd @ A) @ B) @ Prod2))) => (Prod = Prod2))))).
% 2.94/1.56 thf(fact_72_prod__eqI, axiom, (! [B:$tType,A:$tType,P2:((product_prod @ A) @ B),Q2:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ P2) = (((product_fst @ A) @ B) @ Q2)) => (((((product_snd @ A) @ B) @ P2) = (((product_snd @ A) @ B) @ Q2)) => (P2 = Q2)))))).
% 2.94/1.56 thf(fact_73_dfree__Fun, axiom, (! [A:$tType,C:$tType,Args:(C > ((trm @ A) @ C)),I:A]: (((! [I4:C]: ((((dfree @ A) @ C) @ (Args @ I4)))) => (((dfree @ A) @ C) @ ((((function @ A) @ C) @ I) @ Args)))))).
% 2.94/1.56 thf(fact_74_dfree_Odfree__Plus, 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) @ ((((plus @ A) @ C) @ Theta_1) @ Theta_2))))))).
% 2.94/1.56 thf(fact_75_dfree__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))))))).
% 2.94/1.56 thf(fact_76_trm_Odistinct_I23_J, axiom, (! [C:$tType,A:$tType,X31:A,X32:(C > ((trm @ A) @ C)),X41:((trm @ A) @ C),X42:((trm @ A) @ C)]: ((((((function @ A) @ C) @ X31) @ X32) != ((((plus @ A) @ C) @ X41) @ X42))))).
% 2.94/1.56 thf(fact_77_trm_Odistinct_I25_J, axiom, (! [C:$tType,A:$tType,X31:A,X32:(C > ((trm @ A) @ C)),X51:((trm @ A) @ C),X52:((trm @ A) @ C)]: ((((((function @ A) @ C) @ X31) @ X32) != ((((times @ A) @ C) @ X51) @ X52))))).
% 2.94/1.56 thf(fact_78_trm_Odistinct_I31_J, axiom, (! [C:$tType,A:$tType,X41:((trm @ A) @ C),X42:((trm @ A) @ C),X51:((trm @ A) @ C),X52:((trm @ A) @ C)]: ((((((plus @ A) @ C) @ X41) @ X42) != ((((times @ A) @ C) @ X51) @ X52))))).
% 2.94/1.56 thf(fact_79_surjective__pairing, axiom, (! [B:$tType,A:$tType,T4:((product_prod @ A) @ B)]: ((T4 = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ T4)) @ (((product_snd @ A) @ B) @ T4)))))).
% 2.94/1.56 thf(fact_80_prod_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))).
% 2.94/1.56 thf(fact_81_Pair__le, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B3:B,C3:A,D4:B]: (((((ord_less_eq @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) @ ((((product_Pair @ A) @ B) @ C3) @ D4)) = ((((ord_less_eq @ A) @ A3) @ C3) & (((ord_less_eq @ B) @ B3) @ D4))))))))).
% 2.94/1.56 thf(fact_82_directional__derivative__def, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => ((((denota2078997598vative @ A) @ B) @ C) = (^ [I5:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),T3:((trm @ A) @ C),V2:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C))]: ((((((((denotational_frechet @ A) @ B) @ C) @ I5) @ T3) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ V2)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ V2))))))))).
% 2.94/1.56 thf(fact_83_raw__interp__inverse, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X:(((frechet_good_interp @ A) @ B) @ C)]: ((((((freche227871258interp @ A) @ B) @ C) @ ((((freche229654227interp @ A) @ B) @ C) @ X)) = X))))))).
% 2.94/1.56 thf(fact_84_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A3:A,B3:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((F1 @ A3) @ B3))))).
% 2.94/1.56 thf(fact_85_type__definition__strm, axiom, (! [C:$tType,A:$tType]: ((((((type_definition @ ((frechet_strm @ A) @ C)) @ ((trm @ A) @ C)) @ ((frechet_raw_term @ A) @ C)) @ ((frechet_simple_term @ A) @ C)) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C)))))).
% 2.94/1.56 thf(fact_86_BNF__Greatest__Fixpoint_Osubst__Pair, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),X:A,Y:B,A3:((product_prod @ A) @ B)]: ((((P @ X) @ Y) => ((A3 = ((((product_Pair @ A) @ B) @ X) @ Y)) => ((P @ (((product_fst @ A) @ B) @ A3)) @ (((product_snd @ A) @ B) @ A3))))))).
% 2.94/1.56 thf(fact_87_conjI__realizer, axiom, (! [A:$tType,B:$tType,P:(A > $o),P2:A,Q:(B > $o),Q2:B]: (((P @ P2) => ((Q @ Q2) => ((P @ (((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ P2) @ Q2))) & (Q @ (((product_snd @ A) @ B) @ ((((product_Pair @ A) @ B) @ P2) @ Q2))))))))).
% 2.94/1.56 thf(fact_88_exI__realizer, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Y:A,X:B]: ((((P @ Y) @ X) => ((P @ (((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y))) @ (((product_fst @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y))))))).
% 2.94/1.56 thf(fact_89_less__eq__prod__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (ord @ B)) => ((ord_less_eq @ ((product_prod @ A) @ B)) = (^ [X2:((product_prod @ A) @ B),Y2:((product_prod @ A) @ B)]: (((((ord_less_eq @ A) @ (((product_fst @ A) @ B) @ X2)) @ (((product_fst @ A) @ B) @ Y2)) & (((ord_less_eq @ B) @ (((product_snd @ A) @ B) @ X2)) @ (((product_snd @ A) @ B) @ Y2)))))))))).
% 2.94/1.56 thf(fact_90_Iagree__sub, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [A2:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))),B2:(set @ ((sum_sum @ A) @ ((sum_sum @ B) @ C))),I3:((((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)))) @ A2) @ B2) => (((((((denotational_Iagree @ A) @ B) @ C) @ I3) @ J) @ B2) => ((((((denotational_Iagree @ A) @ B) @ C) @ I3) @ J) @ A2))))))))).
% 2.94/1.56 thf(fact_91_subset__Collect__iff, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((((ord_less_eq @ (set @ A)) @ B2) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))))) = (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 2.94/1.56 thf(fact_92_subset__CollectI, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A),Q:(A > $o),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((! [X3:A]: (((((member @ A) @ X3) @ B2) => ((Q @ X3) => (P @ X3))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ B2) & (Q @ X2)))))) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2))))))))))).
% 2.94/1.56 thf(fact_93_Pair__mono, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [X:A,X4:A,Y:B,Y5:B]: (((((ord_less_eq @ A) @ X) @ X4) => ((((ord_less_eq @ B) @ Y) @ Y5) => (((ord_less_eq @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ ((((product_Pair @ A) @ B) @ X4) @ Y5)))))))))).
% 2.94/1.56 thf(fact_94_fst__mono, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (ord @ B)) => (! [X:((product_prod @ A) @ B),Y:((product_prod @ A) @ B)]: (((((ord_less_eq @ ((product_prod @ A) @ B)) @ X) @ Y) => (((ord_less_eq @ A) @ (((product_fst @ A) @ B) @ X)) @ (((product_fst @ A) @ B) @ Y))))))))).
% 2.94/1.56 thf(fact_95_snd__mono, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (ord @ B)) => (! [X:((product_prod @ A) @ B),Y:((product_prod @ A) @ B)]: (((((ord_less_eq @ ((product_prod @ A) @ B)) @ X) @ Y) => (((ord_less_eq @ B) @ (((product_snd @ A) @ B) @ X)) @ (((product_snd @ A) @ B) @ Y))))))))).
% 2.94/1.56 thf(fact_96_exE__realizer_H, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),P2:((product_prod @ B) @ A)]: ((((P @ (((product_snd @ B) @ A) @ P2)) @ (((product_fst @ B) @ A) @ P2)) => (~ ((! [X3:B,Y3:A]: ((~ (((P @ Y3) @ X3))))))))))).
% 2.94/1.56 thf(fact_97_euclid__ext__aux_Ocases, axiom, (! [A:$tType]: (((euclid1678468529ng_gcd @ A) => (! [X:((product_prod @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ A)))))]: ((~ ((! [S3:A,S4:A,T5:A,T6:A,R:A,R2:A]: ((X != ((((product_Pair @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ A))))) @ S3) @ ((((product_Pair @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ A)))) @ S4) @ ((((product_Pair @ A) @ ((product_prod @ A) @ ((product_prod @ A) @ A))) @ T5) @ ((((product_Pair @ A) @ ((product_prod @ A) @ A)) @ T6) @ ((((product_Pair @ A) @ A) @ R) @ R2)))))))))))))))).
% 2.94/1.56 thf(fact_98_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))))).
% 2.94/1.56 thf(fact_99_old_Osum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,A3:A,A4:A]: ((((((sum_Inl @ A) @ B) @ A3) = (((sum_Inl @ A) @ B) @ A4)) = (A3 = A4))))).
% 2.94/1.56 thf(fact_100_good__interp__inverse, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (((((freche229654227interp @ A) @ B) @ C) @ ((((freche227871258interp @ A) @ B) @ C) @ Y)) = Y)))))))).
% 2.94/1.56 thf(fact_101_f0__def, axiom, (((f0 @ sf) @ sz) = (^ [F4:sf]: (((((function @ sf) @ sz) @ F4) @ ((empty @ sz) @ sf)))))).
% 2.94/1.56 thf(fact_102_subsetI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 2.94/1.56 thf(fact_103_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),P:(((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > $o)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((! [X3:(((frechet_good_interp @ A) @ B) @ C)]: ((P @ ((((freche229654227interp @ A) @ B) @ C) @ X3)))) => (P @ Y))))))))).
% 2.94/1.56 thf(fact_104_raw__interp__cases, axiom, (! [C:$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))))))))))))).
% 2.94/1.56 thf(fact_105_raw__interp, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X:(((frechet_good_interp @ A) @ B) @ C)]: ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ ((((freche229654227interp @ A) @ B) @ C) @ X)) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))))))))).
% 2.94/1.56 thf(fact_106_good__interp__cases, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X:(((frechet_good_interp @ A) @ B) @ C)]: ((~ ((! [Y3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((X = ((((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)))))))))))))))).
% 2.94/1.56 thf(fact_107_good__interp__induct, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [P:((((frechet_good_interp @ A) @ B) @ C) > $o),X:(((frechet_good_interp @ A) @ B) @ C)]: (((! [Y3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y3) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (P @ ((((freche227871258interp @ A) @ B) @ C) @ Y3))))) => (P @ X)))))))).
% 2.94/1.56 thf(fact_108_good__interp__inject, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (! [X:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ X) @ ((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) @ X) = ((((freche227871258interp @ A) @ B) @ C) @ Y)) = (X = Y)))))))))).
% 2.94/1.56 thf(fact_109_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A2) => (A2 = B2)))))).
% 2.94/1.56 thf(fact_110_gcd_Ocases, axiom, (! [A:$tType]: (((euclid1155270486miring @ A) => (! [X:((product_prod @ A) @ A)]: ((~ ((! [A5:A,B5:A]: ((X != ((((product_Pair @ A) @ A) @ A5) @ B5)))))))))))).
% 2.94/1.56 thf(fact_111_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 2.94/1.56 thf(fact_112_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z:(set @ A)]: ((Y4 = Z))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 2.94/1.56 thf(fact_113_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C4) => (((ord_less_eq @ (set @ A)) @ A2) @ C4)))))).
% 2.94/1.56 thf(fact_114_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.94/1.56 thf(fact_115_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 2.94/1.56 thf(fact_116_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A6) => (((member @ A) @ T3) @ B6)))))))))).
% 2.94/1.56 thf(fact_117_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A2))))).
% 2.94/1.56 thf(fact_118_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 2.94/1.56 thf(fact_119_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A6) => (((member @ A) @ X2) @ B6)))))))))).
% 2.94/1.56 thf(fact_120_equalityE, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A2)))))))))).
% 2.94/1.56 thf(fact_121_subsetD, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ C3) @ A2) => (((member @ A) @ C3) @ B2)))))).
% 2.94/1.56 thf(fact_122_in__mono, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B2)))))).
% 2.94/1.56 thf(fact_123_Inl__inject, axiom, (! [B:$tType,A:$tType,X:A,Y:A]: ((((((sum_Inl @ A) @ B) @ X) = (((sum_Inl @ A) @ B) @ Y)) => (X = Y))))).
% 2.94/1.56 thf(fact_124_Collect__subset, axiom, (! [A:$tType,A2:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))))) @ A2)))).
% 2.94/1.56 thf(fact_125_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X2:A]: ((((member @ A) @ X2) @ A6)))) @ (^ [X2:A]: ((((member @ A) @ X2) @ B6)))))))))).
% 2.94/1.56 thf(fact_126_sterm__determines__frechet, axiom, (! [A1:$tType,B1:$tType,B22:$tType,A22:$tType,C:$tType]: ((((finite_finite @ C) & ((finite_finite @ A22) & ((finite_finite @ B22) & ((finite_finite @ B1) & (finite_finite @ A1))))) => (! [I3:((((denota1663640101rp_ext @ A1) @ B1) @ C) @ product_unit),J:((((denota1663640101rp_ext @ A22) @ B22) @ C) @ product_unit),Theta_12:((trm @ A1) @ C),Theta_22:((trm @ A22) @ C),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C))]: ((((((denota2077489681interp @ A1) @ B1) @ C) @ I3) => (((((denota2077489681interp @ A22) @ B22) @ C) @ J) => ((((dfree @ A1) @ C) @ Theta_12) => ((((dfree @ A22) @ C) @ Theta_22) => (((((((denota126604975rm_sem @ A1) @ B1) @ C) @ I3) @ Theta_12) = (((((denota126604975rm_sem @ A22) @ B22) @ C) @ J) @ Theta_22)) => ((((((((denotational_frechet @ A1) @ B1) @ C) @ I3) @ Theta_12) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) = (((((((denotational_frechet @ A22) @ B22) @ C) @ J) @ Theta_22) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)))))))))))))).
% 2.94/1.56 thf(fact_127_type__definition__good__interp, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => (((((type_definition @ (((frechet_good_interp @ A) @ B) @ C)) @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((freche229654227interp @ A) @ B) @ C)) @ (((freche227871258interp @ A) @ B) @ C)) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))))))).
% 2.94/1.56 thf(fact_128_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.94/1.56 thf(fact_129_old_Osum_Osimps_I7_J, axiom, (! [B:$tType,T:$tType,A:$tType,F1:(A > T),F22:(B > T),A3:A]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ A3)) = (F1 @ A3))))).
% 2.94/1.56 thf(fact_130_image2__def, axiom, (! [A:$tType,B:$tType,C:$tType]: (((((bNF_Greatest_image2 @ C) @ A) @ B) = (^ [A6:(set @ C),F4:(C > A),G4:(C > B)]: (((collect @ ((product_prod @ A) @ B)) @ (^ [Uu:((product_prod @ A) @ B)]: ((? [A7:C]: (((Uu = ((((product_Pair @ A) @ B) @ (F4 @ A7)) @ (G4 @ A7))) & (((member @ C) @ A7) @ A6))))))))))))).
% 2.94/1.56 thf(fact_131_predicate1I, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (A > $o)) @ P) @ Q))))).
% 2.94/1.56 thf(fact_132_rev__predicate1D, axiom, (! [A:$tType,P:(A > $o),X:A,Q:(A > $o)]: (((P @ X) => ((((ord_less_eq @ (A > $o)) @ P) @ Q) => (Q @ X)))))).
% 2.94/1.56 thf(fact_133_predicate1D, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),X:A]: (((((ord_less_eq @ (A > $o)) @ P) @ Q) => ((P @ X) => (Q @ X)))))).
% 2.94/1.56 thf(fact_134_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.94/1.56 thf(fact_135_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.94/1.56 thf(fact_136_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.94/1.56 thf(fact_137_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F4:(A > B),G4:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F4 @ X2)) @ (G4 @ X2))))))))))).
% 2.94/1.56 thf(fact_138_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B3:B,C3:B]: (((((ord_less_eq @ A) @ A3) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A3) @ (F @ C3))))))))))).
% 2.94/1.56 thf(fact_139_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A3:A,B3:A,F:(A > C),C3:C]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ C) @ (F @ A3)) @ C3)))))))))).
% 2.94/1.56 thf(fact_140_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F:(B > A),B3:B,C3:B]: (((A3 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A3) @ (F @ C3))))))))))).
% 2.94/1.56 thf(fact_141_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B3:A,F:(A > B),C3:B]: (((((ord_less_eq @ A) @ A3) @ B3) => (((F @ B3) = C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A3)) @ C3)))))))))).
% 2.94/1.56 thf(fact_142_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) & (((ord_less_eq @ A) @ Y2) @ X2))))))))).
% 2.94/1.56 thf(fact_143_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.94/1.56 thf(fact_144_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.94/1.56 thf(fact_145_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.94/1.56 thf(fact_146_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.94/1.56 thf(fact_147_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.94/1.56 thf(fact_148_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.94/1.56 thf(fact_149_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.94/1.56 thf(fact_150_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A7:A,B7:A]: (((((ord_less_eq @ A) @ A7) @ B7) & (((ord_less_eq @ A) @ B7) @ A7))))))))).
% 2.94/1.56 thf(fact_151_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C3:A]: (((A3 = B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.94/1.56 thf(fact_152_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((B3 = C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.94/1.56 thf(fact_153_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ A3) => (A3 = B3))))))))).
% 2.94/1.56 thf(fact_154_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.94/1.56 thf(fact_155_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.94/1.56 thf(fact_156_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B3:A]: (((! [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) => ((P @ A5) @ B5)))) => ((! [A5:A,B5:A]: ((((P @ B5) @ A5) => ((P @ A5) @ B5)))) => ((P @ A3) @ B3))))))))).
% 2.94/1.56 thf(fact_157_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ A3))))))))).
% 2.94/1.56 thf(fact_158_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A7:A,B7:A]: (((((ord_less_eq @ A) @ B7) @ A7) & (((ord_less_eq @ A) @ A7) @ B7))))))))).
% 2.94/1.56 thf(fact_159_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ A3) @ B3) => (A3 = B3))))))))).
% 2.94/1.56 thf(fact_160_image2__eqI, axiom, (! [A:$tType,C:$tType,B:$tType,B3:A,F:(B > A),X:B,C3:C,G:(B > C),A2:(set @ B)]: (((B3 = (F @ X)) => ((C3 = (G @ X)) => ((((member @ B) @ X) @ A2) => (((member @ ((product_prod @ A) @ C)) @ ((((product_Pair @ A) @ C) @ B3) @ C3)) @ ((((((bNF_Greatest_image2 @ B) @ A) @ C) @ A2) @ F) @ G)))))))).
% 2.94/1.56 thf(fact_161_coincidence__sterm_H, axiom, (! [A:$tType,C:$tType,B:$tType]: ((((finite_finite @ B) & ((finite_finite @ C) & (finite_finite @ A))) => (! [Theta:((trm @ A) @ B),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)),I3:((((denota1663640101rp_ext @ A) @ C) @ B) @ product_unit),J:((((denota1663640101rp_ext @ A) @ C) @ B) @ product_unit)]: (((((dfree @ A) @ B) @ Theta) => (((((denotational_Vagree @ B) @ Nu) @ Nu2) @ (((static_FVT @ A) @ B) @ Theta)) => (((((((denotational_Iagree @ A) @ C) @ B) @ I3) @ J) @ ((collect @ ((sum_sum @ A) @ ((sum_sum @ C) @ B))) @ (^ [Uu:((sum_sum @ A) @ ((sum_sum @ C) @ B))]: ((? [X2:A]: (((Uu = (((sum_Inl @ A) @ ((sum_sum @ C) @ B)) @ X2)) & (((member @ A) @ X2) @ (((static_SIGT @ A) @ B) @ Theta))))))))) => (((((((denota126604975rm_sem @ A) @ C) @ B) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)) @ Nu)) = ((((((denota126604975rm_sem @ A) @ C) @ B) @ J) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)) @ Nu2)))))))))))).
% 2.94/1.56 thf(fact_162_coincidence__sterm, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Theta:((trm @ B) @ A),I3:((((denota1663640101rp_ext @ B) @ C) @ A) @ product_unit)]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVT @ B) @ A) @ Theta)) => (((((((denota126604975rm_sem @ B) @ C) @ A) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ Nu)) = ((((((denota126604975rm_sem @ B) @ C) @ A) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ Nu2)))))))))).
% 2.94/1.56 thf(fact_163_pred__subset__eq, axiom, (! [A:$tType,R3:(set @ A),S5:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X2:A]: ((((member @ A) @ X2) @ R3)))) @ (^ [X2:A]: ((((member @ A) @ X2) @ S5)))) = (((ord_less_eq @ (set @ A)) @ R3) @ S5))))).
% 2.94/1.56 thf(fact_164_sterm__continuous_H, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Theta:((trm @ A) @ C),S5:(set @ ((finite_Cartesian_vec @ real) @ C))]: ((((((denota2077489681interp @ A) @ B) @ C) @ I3) => ((((dfree @ A) @ C) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ C)) @ real) @ S5) @ (((((denota126604975rm_sem @ A) @ B) @ C) @ I3) @ Theta)))))))))).
% 2.94/1.56 thf(fact_165_agree__func__fvt, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ 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)),F:B,Args:(A > ((trm @ B) @ A)),I:A]: ((((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVT @ B) @ A) @ ((((function @ B) @ A) @ F) @ Args))) => ((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVT @ B) @ A) @ (Args @ I)))))))))).
% 2.94/1.56 thf(fact_166_subrelI, axiom, (! [B:$tType,A:$tType,R4:(set @ ((product_prod @ A) @ B)),S6:(set @ ((product_prod @ A) @ B))]: (((! [X3:A,Y3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R4) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ S6)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R4) @ S6))))).
% 2.94/1.56 thf(fact_167_FVDiff__sub, axiom, (! [A:$tType,B:$tType,F:((trm @ B) @ A)]: ((((ord_less_eq @ (set @ ((sum_sum @ A) @ A))) @ (((static_FVT @ B) @ A) @ F)) @ (((static_FVDiff @ B) @ A) @ F))))).
% 2.94/1.56 thf(fact_168_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S5:(set @ ((product_prod @ A) @ B))]: ((((^ [X2:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) @ R3))) = (^ [X2:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) @ S5)))) = (R3 = S5))))).
% 2.94/1.56 thf(fact_169_pred__subset__eq2, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S5:(set @ ((product_prod @ A) @ B))]: (((((ord_less_eq @ (A > (B > $o))) @ (^ [X2:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) @ R3)))) @ (^ [X2:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) @ S5)))) = (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ S5))))).
% 2.94/1.56 thf(fact_170_sterm__continuous, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & (finite_finite @ B))) => (! [I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Theta:((trm @ A) @ C)]: ((((((denota2077489681interp @ A) @ B) @ C) @ I3) => ((((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) @ I3) @ Theta)))))))))).
% 2.94/1.56 thf(fact_171_ids_Ocoincidence__sterm_H, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,A:$tType,C:$tType,B:$tType]: ((((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ A) & ((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Theta:((trm @ A) @ B),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)),I3:((((denota1663640101rp_ext @ A) @ C) @ B) @ product_unit),J:((((denota1663640101rp_ext @ A) @ C) @ B) @ product_unit)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((dfree @ A) @ B) @ Theta) => (((((denotational_Vagree @ B) @ Nu) @ Nu2) @ (((static_FVT @ A) @ B) @ Theta)) => (((((((denotational_Iagree @ A) @ C) @ B) @ I3) @ J) @ ((collect @ ((sum_sum @ A) @ ((sum_sum @ C) @ B))) @ (^ [Uu:((sum_sum @ A) @ ((sum_sum @ C) @ B))]: ((? [X2:A]: (((Uu = (((sum_Inl @ A) @ ((sum_sum @ C) @ B)) @ X2)) & (((member @ A) @ X2) @ (((static_SIGT @ A) @ B) @ Theta))))))))) => (((((((denota126604975rm_sem @ A) @ C) @ B) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)) @ Nu)) = ((((((denota126604975rm_sem @ A) @ C) @ B) @ J) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ B)) @ ((finite_Cartesian_vec @ real) @ B)) @ Nu2))))))))))))).
% 2.94/1.56 thf(fact_172_continuous__on__cases__le, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S6:(set @ A),H:(A > real),A3:real,F:(A > B),G:(A > B)]: ((((((topolo2071040574ous_on @ A) @ B) @ ((collect @ A) @ (^ [T3:A]: (((((member @ A) @ T3) @ S6) & (((ord_less_eq @ real) @ (H @ T3)) @ A3)))))) @ F) => (((((topolo2071040574ous_on @ A) @ B) @ ((collect @ A) @ (^ [T3:A]: (((((member @ A) @ T3) @ S6) & (((ord_less_eq @ real) @ A3) @ (H @ T3))))))) @ G) => (((((topolo2071040574ous_on @ A) @ real) @ S6) @ H) => ((! [T6:A]: (((((member @ A) @ T6) @ S6) => (((H @ T6) = A3) => ((F @ T6) = (G @ T6)))))) => ((((topolo2071040574ous_on @ A) @ B) @ S6) @ (^ [T3:A]: (((((if @ B) @ (((ord_less_eq @ real) @ (H @ T3)) @ A3)) @ (F @ T3)) @ (G @ T3))))))))))))))).
% 2.94/1.56 thf(fact_173_top__apply, axiom, (! [C:$tType,D2:$tType]: (((top @ C) => ((top_top @ (D2 > C)) = (^ [X2:D2]: ((top_top @ C)))))))).
% 2.94/1.56 thf(fact_174_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.94/1.56 thf(fact_175_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X3:A,Y3:B]: ((((P @ X3) @ Y3) => ((Q @ X3) @ Y3)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 2.94/1.56 thf(fact_176_fst__top, axiom, (! [B:$tType,A:$tType]: ((((top @ A) & (top @ B)) => ((((product_fst @ A) @ B) @ (top_top @ ((product_prod @ A) @ B))) = (top_top @ A)))))).
% 2.94/1.56 thf(fact_177_snd__top, axiom, (! [B:$tType,A:$tType]: ((((top @ A) & (top @ B)) => ((((product_snd @ B) @ A) @ (top_top @ ((product_prod @ B) @ A))) = (top_top @ A)))))).
% 2.94/1.56 thf(fact_178_continuous__on__cases__1, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => (! [S6:(set @ real),A3:real,F:(real > A),G:(real > A)]: ((((((topolo2071040574ous_on @ real) @ A) @ ((collect @ real) @ (^ [T3:real]: (((((member @ real) @ T3) @ S6) & (((ord_less_eq @ real) @ T3) @ A3)))))) @ F) => (((((topolo2071040574ous_on @ real) @ A) @ ((collect @ real) @ (^ [T3:real]: (((((member @ real) @ T3) @ S6) & (((ord_less_eq @ real) @ A3) @ T3)))))) @ G) => (((((member @ real) @ A3) @ S6) => ((F @ A3) = (G @ A3))) => ((((topolo2071040574ous_on @ real) @ A) @ S6) @ (^ [T3:real]: (((((if @ A) @ (((ord_less_eq @ real) @ T3) @ A3)) @ (F @ T3)) @ (G @ T3)))))))))))))).
% 2.94/1.56 thf(fact_179_top_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_top @ A) => (! [A3:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A3) => (A3 = (top_top @ A))))))))).
% 2.94/1.56 thf(fact_180_top_Oextremum__unique, axiom, (! [A:$tType]: (((order_top @ A) => (! [A3:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A3) = (A3 = (top_top @ A))))))))).
% 2.94/1.56 thf(fact_181_top__greatest, axiom, (! [A:$tType]: (((order_top @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ (top_top @ A)))))))).
% 2.94/1.56 thf(fact_182_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Y:B,Q:(A > (B > $o))]: ((((P @ X) @ Y) => ((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => ((Q @ X) @ Y)))))).
% 2.94/1.56 thf(fact_183_predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),X:A,Y:B]: (((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => (((P @ X) @ Y) => ((Q @ X) @ Y)))))).
% 2.94/1.56 thf(fact_184_subset__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (top_top @ (set @ A)))))).
% 2.94/1.56 thf(fact_185_ids_Oseq__sem_Ocases, axiom, (! [Sz:$tType,Sc:$tType,Sf:$tType]: ((((finite_finite @ Sf) & ((finite_finite @ Sc) & ((finite_finite @ Sz) & (linorder @ Sz)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((product_prod @ ((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit)) @ ((product_prod @ (list @ (((formula @ Sf) @ Sc) @ Sz))) @ (list @ (((formula @ Sf) @ Sc) @ Sz))))]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (~ ((! [I2:((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit),S:((product_prod @ (list @ (((formula @ Sf) @ Sc) @ Sz))) @ (list @ (((formula @ Sf) @ Sc) @ Sz)))]: ((X != ((((product_Pair @ ((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit)) @ ((product_prod @ (list @ (((formula @ Sf) @ Sc) @ Sz))) @ (list @ (((formula @ Sf) @ Sc) @ Sz)))) @ I2) @ S))))))))))))).
% 2.94/1.56 thf(fact_186_UNIV__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (^ [X2:A]: ($true))))))).
% 2.94/1.56 thf(fact_187_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.94/1.56 thf(fact_188_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.94/1.56 thf(fact_189_ids_Osingleton_Oinduct, axiom, (! [Sf:$tType,Sc:$tType,A:$tType,Sz:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sc) & (finite_finite @ Sf)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,P:(((trm @ A) @ Sz) > (Sz > $o)),A0:((trm @ A) @ Sz),A12:Sz]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((! [T6:((trm @ A) @ Sz),X_1:Sz]: (((P @ T6) @ X_1))) => ((P @ A0) @ A12))))))))).
% 2.94/1.56 thf(fact_190_ids_Oseq__sem_Oinduct, axiom, (! [Sz:$tType,Sc:$tType,Sf:$tType]: ((((finite_finite @ Sf) & ((finite_finite @ Sc) & ((finite_finite @ Sz) & (linorder @ Sz)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,P:(((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit) > (((product_prod @ (list @ (((formula @ Sf) @ Sc) @ Sz))) @ (list @ (((formula @ Sf) @ Sc) @ Sz))) > $o)),A0:((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit),A12:((product_prod @ (list @ (((formula @ Sf) @ Sc) @ Sz))) @ (list @ (((formula @ Sf) @ Sc) @ Sz)))]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((! [I2:((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit),X_1:((product_prod @ (list @ (((formula @ Sf) @ Sc) @ Sz))) @ (list @ (((formula @ Sf) @ Sc) @ Sz)))]: (((P @ I2) @ X_1))) => ((P @ A0) @ A12))))))))).
% 2.94/1.56 thf(fact_191_ids_Osingleton_Ocases, axiom, (! [Sc:$tType,Sf:$tType,A:$tType,Sz:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((product_prod @ ((trm @ A) @ Sz)) @ Sz)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (~ ((! [T6:((trm @ A) @ Sz),I4:Sz]: ((X != ((((product_Pair @ ((trm @ A) @ Sz)) @ Sz) @ T6) @ I4))))))))))))).
% 2.94/1.56 thf(fact_192_top__prod__def, axiom, (! [A:$tType,B:$tType]: ((((top @ B) & (top @ A)) => ((top_top @ ((product_prod @ A) @ B)) = ((((product_Pair @ A) @ B) @ (top_top @ A)) @ (top_top @ B))))))).
% 2.94/1.56 thf(fact_193_ids_OP__def, axiom, (! [Sf:$tType,Sz:$tType,Sc:$tType]: ((((finite_finite @ Sc) & ((finite_finite @ Sz) & ((linorder @ Sz) & (finite_finite @ Sf)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,P2:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((p @ Sc) @ Sf) @ Sz) @ P2) = ((((predicational @ Sc) @ Sf) @ Sz) @ P2))))))))).
% 2.94/1.56 thf(fact_194_ids_Ocoincidence__sterm, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & ((finite_finite @ B) & ((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,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),I3:((((denota1663640101rp_ext @ B) @ C) @ A) @ product_unit)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((denotational_Vagree @ A) @ Nu) @ Nu2) @ (((static_FVT @ B) @ A) @ Theta)) => (((((((denota126604975rm_sem @ B) @ C) @ A) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ Nu)) = ((((((denota126604975rm_sem @ B) @ C) @ A) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ Nu2))))))))))).
% 2.94/1.56 thf(fact_195_ids_Of0__def, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,F:Sf]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((f0 @ Sf) @ Sz) @ F) = ((((function @ Sf) @ Sz) @ F) @ ((empty @ Sz) @ Sf)))))))))).
% 2.94/1.56 thf(fact_196_ids_Ocoincidence__frechet, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,B:$tType,A:$tType,C:$tType]: ((((finite_finite @ C) & ((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Theta:((trm @ A) @ C),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)),Nu2:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)),I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((dfree @ A) @ C) @ Theta) => (((((denotational_Vagree @ C) @ Nu) @ Nu2) @ (((static_FVDiff @ A) @ C) @ Theta)) => ((((((((denotational_frechet @ A) @ B) @ C) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) = (((((((denotational_frechet @ A) @ B) @ C) @ I3) @ Theta) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu2)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu2)))))))))))).
% 2.94/1.56 thf(fact_197_frechet__continuous, axiom, (! [I3:((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit),Theta:((trm @ sf) @ sz)]: ((((((denota2077489681interp @ sf) @ sc) @ sz) @ I3) => ((((dfree @ sf) @ sz) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ sz)) @ ((bounde2145540817linfun @ ((finite_Cartesian_vec @ real) @ sz)) @ real)) @ (top_top @ (set @ ((finite_Cartesian_vec @ real) @ sz)))) @ (((((frechet_blin_frechet @ sf) @ sc) @ sz) @ ((((freche227871258interp @ sf) @ sc) @ sz) @ I3)) @ (((frechet_simple_term @ sf) @ sz) @ Theta)))))))).
% 2.94/1.56 thf(fact_198_ids_Osterm__determines__frechet, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,A1:$tType,B1:$tType,B22:$tType,A22:$tType,C:$tType]: ((((finite_finite @ C) & ((finite_finite @ A22) & ((finite_finite @ B22) & ((finite_finite @ B1) & ((finite_finite @ A1) & ((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz))))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,I3:((((denota1663640101rp_ext @ A1) @ B1) @ C) @ product_unit),J:((((denota1663640101rp_ext @ A22) @ B22) @ C) @ product_unit),Theta_12:((trm @ A1) @ C),Theta_22:((trm @ A22) @ C),Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C))]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((denota2077489681interp @ A1) @ B1) @ C) @ I3) => (((((denota2077489681interp @ A22) @ B22) @ C) @ J) => ((((dfree @ A1) @ C) @ Theta_12) => ((((dfree @ A22) @ C) @ Theta_22) => (((((((denota126604975rm_sem @ A1) @ B1) @ C) @ I3) @ Theta_12) = (((((denota126604975rm_sem @ A22) @ B22) @ C) @ J) @ Theta_22)) => ((((((((denotational_frechet @ A1) @ B1) @ C) @ I3) @ Theta_12) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) = (((((((denotational_frechet @ A22) @ B22) @ C) @ J) @ Theta_22) @ (((product_fst @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu)) @ (((product_snd @ ((finite_Cartesian_vec @ real) @ C)) @ ((finite_Cartesian_vec @ real) @ C)) @ Nu))))))))))))))).
% 2.94/1.56 thf(fact_199_ids_Osterm__continuous, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & ((finite_finite @ B) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Theta:((trm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((denota2077489681interp @ A) @ B) @ C) @ I3) => ((((dfree @ A) @ C) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ C)) @ real) @ (top_top @ (set @ ((finite_Cartesian_vec @ real) @ C)))) @ (((((denota126604975rm_sem @ A) @ B) @ C) @ I3) @ Theta))))))))))).
% 2.94/1.56 thf(fact_200_top__empty__eq2, axiom, (! [B:$tType,A:$tType]: (((top_top @ (A > (B > $o))) = (^ [X2:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) @ (top_top @ (set @ ((product_prod @ A) @ B)))))))))).
% 2.94/1.56 thf(fact_201_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.94/1.56 thf(fact_202_Vagree__univ, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A3:((finite_Cartesian_vec @ real) @ A),B3:((finite_Cartesian_vec @ real) @ A),C3:((finite_Cartesian_vec @ real) @ A),D4:((finite_Cartesian_vec @ real) @ A)]: ((((((denotational_Vagree @ A) @ ((((product_Pair @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ A3) @ B3)) @ ((((product_Pair @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)) @ C3) @ D4)) @ (top_top @ (set @ ((sum_sum @ A) @ A)))) => ((A3 = C3) & (B3 = D4))))))))).
% 2.94/1.56 thf(fact_203_agree__UNIV__eq, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [Nu:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A)),Omega:((product_prod @ ((finite_Cartesian_vec @ real) @ A)) @ ((finite_Cartesian_vec @ real) @ A))]: ((((((denotational_Vagree @ A) @ Nu) @ Omega) @ (top_top @ (set @ ((sum_sum @ A) @ A)))) => (Nu = Omega)))))))).
% 2.94/1.56 thf(fact_204_ids_Oraw__term__inject, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((frechet_strm @ A) @ C),Y:((frechet_strm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((frechet_raw_term @ A) @ C) @ X) = (((frechet_raw_term @ A) @ C) @ Y)) = (X = Y))))))))).
% 2.94/1.56 thf(fact_205_ids_Oraw__interp__inject, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:(((frechet_good_interp @ A) @ B) @ C),Y:(((frechet_good_interp @ A) @ B) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((((freche229654227interp @ A) @ B) @ C) @ X) = ((((freche229654227interp @ A) @ B) @ C) @ Y)) = (X = Y))))))))).
% 2.94/1.56 thf(fact_206_ids_Ofrechet__continuous, axiom, (! [Sc:$tType,Sz:$tType,Sf:$tType]: ((((finite_finite @ Sf) & ((finite_finite @ Sz) & ((linorder @ Sz) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,I3:((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit),Theta:((trm @ Sf) @ Sz)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((denota2077489681interp @ Sf) @ Sc) @ Sz) @ I3) => ((((dfree @ Sf) @ Sz) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ Sz)) @ ((bounde2145540817linfun @ ((finite_Cartesian_vec @ real) @ Sz)) @ real)) @ (top_top @ (set @ ((finite_Cartesian_vec @ real) @ Sz)))) @ (((((frechet_blin_frechet @ Sf) @ Sc) @ Sz) @ ((((freche227871258interp @ Sf) @ Sc) @ Sz) @ I3)) @ (((frechet_simple_term @ Sf) @ Sz) @ Theta)))))))))))).
% 2.94/1.56 thf(fact_207_ids_Oraw__interp__inverse, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:(((frechet_good_interp @ A) @ B) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((freche227871258interp @ A) @ B) @ C) @ ((((freche229654227interp @ A) @ B) @ C) @ X)) = X)))))))).
% 2.94/1.56 thf(fact_208_ids_Oraw__term__inverse, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((frechet_strm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((frechet_simple_term @ A) @ C) @ (((frechet_raw_term @ A) @ C) @ X)) = X)))))))).
% 2.94/1.56 thf(fact_209_ids_Oraw__term, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((frechet_strm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((member @ ((trm @ A) @ C)) @ (((frechet_raw_term @ A) @ C) @ X)) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C)))))))))).
% 2.94/1.56 thf(fact_210_ids_Oraw__term__cases, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Y:((trm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (~ ((! [X3:((frechet_strm @ A) @ C)]: ((Y != (((frechet_raw_term @ A) @ C) @ X3)))))))))))))).
% 2.94/1.56 thf(fact_211_ids_Oraw__term__induct, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Y:((trm @ A) @ C),P:(((trm @ A) @ C) > $o)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((! [X3:((frechet_strm @ A) @ C)]: ((P @ (((frechet_raw_term @ A) @ C) @ X3)))) => (P @ Y)))))))))).
% 2.94/1.56 thf(fact_212_ids_Osimple__term__cases, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((frechet_strm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (~ ((! [Y3:((trm @ A) @ C)]: (((X = (((frechet_simple_term @ A) @ C) @ Y3)) => (~ ((((member @ ((trm @ A) @ C)) @ Y3) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))))))))))))))))).
% 2.94/1.56 thf(fact_213_ids_Osimple__term__induct, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,P:(((frechet_strm @ A) @ C) > $o),X:((frechet_strm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((! [Y3:((trm @ A) @ C)]: (((((member @ ((trm @ A) @ C)) @ Y3) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (P @ (((frechet_simple_term @ A) @ C) @ Y3))))) => (P @ X))))))))).
% 2.94/1.56 thf(fact_214_ids_Osimple__term__inject, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((trm @ A) @ C),Y:((trm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((trm @ A) @ C)) @ X) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => (((((frechet_simple_term @ A) @ C) @ X) = (((frechet_simple_term @ A) @ C) @ Y)) = (X = Y))))))))))).
% 2.94/1.56 thf(fact_215_ids_Oraw__interp__induct, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),P:(((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit) > $o)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((! [X3:(((frechet_good_interp @ A) @ B) @ C)]: ((P @ ((((freche229654227interp @ A) @ B) @ C) @ X3)))) => (P @ Y)))))))))).
% 2.94/1.56 thf(fact_216_ids_Oraw__interp__cases, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (~ ((! [X3:(((frechet_good_interp @ A) @ B) @ C)]: ((Y != ((((freche229654227interp @ A) @ B) @ C) @ X3)))))))))))))).
% 2.94/1.56 thf(fact_217_ids_Oraw__interp, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:(((frechet_good_interp @ A) @ B) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ ((((freche229654227interp @ A) @ B) @ C) @ X)) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C)))))))))).
% 2.94/1.56 thf(fact_218_ids_Ogood__interp__cases, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:(((frechet_good_interp @ A) @ B) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (~ ((! [Y3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((X = ((((freche227871258interp @ A) @ B) @ C) @ Y3)) => (~ ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y3) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))))))))))))))))).
% 2.94/1.56 thf(fact_219_ids_Ogood__interp__induct, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,P:((((frechet_good_interp @ A) @ B) @ C) > $o),X:(((frechet_good_interp @ A) @ B) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((! [Y3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y3) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (P @ ((((freche227871258interp @ A) @ B) @ C) @ Y3))))) => (P @ X))))))))).
% 2.94/1.56 thf(fact_220_ids_Ogood__interp__inject, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,X:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ X) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => ((((((freche227871258interp @ A) @ B) @ C) @ X) = ((((freche227871258interp @ A) @ B) @ C) @ Y)) = (X = Y))))))))))).
% 2.94/1.56 thf(fact_221_ids_Ocr__strm__def, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,B:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((frechet_cr_strm @ A) @ B) = (^ [X2:((trm @ A) @ B),Y2:((frechet_strm @ A) @ B)]: ((X2 = (((frechet_raw_term @ A) @ B) @ Y2)))))))))))).
% 2.94/1.56 thf(fact_222_ids_Ocr__good__interp__def, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((freche457001096interp @ A) @ B) @ C) = (^ [X2:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Y2:(((frechet_good_interp @ A) @ B) @ C)]: ((X2 = ((((freche229654227interp @ A) @ B) @ C) @ Y2)))))))))))).
% 2.94/1.56 thf(fact_223_ids_Osimple__term__inverse, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Y:((trm @ A) @ C)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((trm @ A) @ C)) @ Y) @ ((collect @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) => ((((frechet_raw_term @ A) @ C) @ (((frechet_simple_term @ A) @ C) @ Y)) = Y))))))))).
% 2.94/1.56 thf(fact_224_ids_Ogood__interp__inverse, axiom, (! [Sz:$tType,Sf:$tType,Sc:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sc) & ((finite_finite @ Sf) & ((finite_finite @ Sz) & (linorder @ Sz))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Y:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((member @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ Y) @ ((collect @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) => (((((freche229654227interp @ A) @ B) @ C) @ ((((freche227871258interp @ A) @ B) @ C) @ Y)) = Y))))))))).
% 2.94/1.56 thf(fact_225_ids_Osterm__continuous_H, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,B:$tType,C:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ C) & ((finite_finite @ B) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,I3:((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit),Theta:((trm @ A) @ C),S5:(set @ ((finite_Cartesian_vec @ real) @ C))]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((denota2077489681interp @ A) @ B) @ C) @ I3) => ((((dfree @ A) @ C) @ Theta) => ((((topolo2071040574ous_on @ ((finite_Cartesian_vec @ real) @ C)) @ real) @ S5) @ (((((denota126604975rm_sem @ A) @ B) @ C) @ I3) @ Theta))))))))))).
% 2.94/1.56 thf(fact_226_ids_Otype__definition__strm, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((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)))))))))).
% 2.94/1.56 thf(fact_227_ids_Otype__definition__good__interp, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((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)))))))))).
% 2.94/1.56 thf(fact_228_frechet__blin, axiom, (! [I3:((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit),Theta:((trm @ sf) @ sz)]: ((((((denota2077489681interp @ sf) @ sc) @ sz) @ I3) => ((((dfree @ sf) @ sz) @ Theta) => ((^ [V2:((finite_Cartesian_vec @ real) @ sz)]: ((((bounde688532126linfun @ ((finite_Cartesian_vec @ real) @ sz)) @ real) @ ((((((denotational_frechet @ sf) @ sc) @ sz) @ I3) @ Theta) @ V2)))) = (((((frechet_blin_frechet @ sf) @ sc) @ sz) @ ((((freche227871258interp @ sf) @ sc) @ sz) @ I3)) @ (((frechet_simple_term @ sf) @ sz) @ Theta)))))))).
% 2.94/1.56 thf(fact_229_continuous__on__snd, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((topolo503727757_space @ A) & ((topolo503727757_space @ B) & (topolo503727757_space @ C))) => (! [S6:(set @ A),F:(A > ((product_prod @ B) @ C))]: ((((((topolo2071040574ous_on @ A) @ ((product_prod @ B) @ C)) @ S6) @ F) => ((((topolo2071040574ous_on @ A) @ C) @ S6) @ (^ [X2:A]: ((((product_snd @ B) @ C) @ (F @ X2)))))))))))).
% 2.94/1.56 thf(fact_230_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 2.94/1.56 thf(fact_231_top2I, axiom, (! [A:$tType,B:$tType,X:A,Y:B]: ((((top_top @ (A > (B > $o))) @ X) @ Y)))).
% 2.94/1.56 thf(fact_232_continuous__on__const, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S6:(set @ A),C3:B]: (((((topolo2071040574ous_on @ A) @ B) @ S6) @ (^ [X2:A]: (C3))))))))).
% 2.94/1.56 thf(fact_233_continuous__on__id, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => (! [S6:(set @ A)]: (((((topolo2071040574ous_on @ A) @ A) @ S6) @ (^ [X2:A]: (X2))))))))).
% 2.94/1.56 thf(fact_234_continuous__on__subset, axiom, (! [B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ B)) => (! [S6:(set @ A),F:(A > B),T4:(set @ A)]: ((((((topolo2071040574ous_on @ A) @ B) @ S6) @ F) => ((((ord_less_eq @ (set @ A)) @ T4) @ S6) => ((((topolo2071040574ous_on @ A) @ B) @ T4) @ F))))))))).
% 2.94/1.56 thf(fact_235_continuous__on__Pair, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((topolo503727757_space @ A) & ((topolo503727757_space @ B) & (topolo503727757_space @ C))) => (! [S6:(set @ A),F:(A > B),G:(A > C)]: ((((((topolo2071040574ous_on @ A) @ B) @ S6) @ F) => (((((topolo2071040574ous_on @ A) @ C) @ S6) @ G) => ((((topolo2071040574ous_on @ A) @ ((product_prod @ B) @ C)) @ S6) @ (^ [X2:A]: (((((product_Pair @ B) @ C) @ (F @ X2)) @ (G @ X2))))))))))))).
% 2.94/1.56 thf(fact_236_ids_Ofrechet__blin, axiom, (! [Sc:$tType,Sz:$tType,Sf:$tType]: ((((finite_finite @ Sf) & ((finite_finite @ Sz) & ((linorder @ Sz) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,I3:((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit),Theta:((trm @ Sf) @ Sz)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((denota2077489681interp @ Sf) @ Sc) @ Sz) @ I3) => ((((dfree @ Sf) @ Sz) @ Theta) => ((^ [V2:((finite_Cartesian_vec @ real) @ Sz)]: ((((bounde688532126linfun @ ((finite_Cartesian_vec @ real) @ Sz)) @ real) @ ((((((denotational_frechet @ Sf) @ Sc) @ Sz) @ I3) @ Theta) @ V2)))) = (((((frechet_blin_frechet @ Sf) @ Sc) @ Sz) @ ((((freche227871258interp @ Sf) @ Sc) @ Sz) @ I3)) @ (((frechet_simple_term @ Sf) @ Sz) @ Theta)))))))))))).
% 2.94/1.56 thf(fact_237_continuous__on__fst, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((topolo503727757_space @ A) & ((topolo503727757_space @ B) & (topolo503727757_space @ C))) => (! [S6:(set @ A),F:(A > ((product_prod @ B) @ C))]: ((((((topolo2071040574ous_on @ A) @ ((product_prod @ B) @ C)) @ S6) @ F) => ((((topolo2071040574ous_on @ A) @ B) @ S6) @ (^ [X2:A]: ((((product_fst @ B) @ C) @ (F @ X2)))))))))))).
% 2.94/1.56 thf(fact_238_continuous__on__product__then__coordinatewise__UNIV, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ C)) => (! [F:(A > (B > C)),I:B]: ((((((topolo2071040574ous_on @ A) @ (B > C)) @ (top_top @ (set @ A))) @ F) => ((((topolo2071040574ous_on @ A) @ C) @ (top_top @ (set @ A))) @ (^ [X2:A]: (((F @ X2) @ I))))))))))).
% 2.94/1.56 thf(fact_239_blin__frechet_Oabs__eq, axiom, (! [Xb:((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit),Xa:((trm @ sf) @ sz),X:((finite_Cartesian_vec @ real) @ sz)]: ((((((bNF_eq_onp @ ((((denota1663640101rp_ext @ sf) @ sc) @ sz) @ product_unit)) @ (((denota2077489681interp @ sf) @ sc) @ sz)) @ Xb) @ Xb) => (((((bNF_eq_onp @ ((trm @ sf) @ sz)) @ ((dfree @ sf) @ sz)) @ Xa) @ Xa) => (((((((frechet_blin_frechet @ sf) @ sc) @ sz) @ ((((freche227871258interp @ sf) @ sc) @ sz) @ Xb)) @ (((frechet_simple_term @ sf) @ sz) @ Xa)) @ X) = (((bounde688532126linfun @ ((finite_Cartesian_vec @ real) @ sz)) @ real) @ ((((((denotational_frechet @ sf) @ sc) @ sz) @ Xb) @ Xa) @ X)))))))).
% 2.94/1.56 thf(fact_240_ids_Oblin__frechet_Oabs__eq, axiom, (! [Sf:$tType,Sc:$tType,Sz:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sc) & (finite_finite @ Sf)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc,Xb:((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit),Xa:((trm @ Sf) @ Sz),X:((finite_Cartesian_vec @ real) @ Sz)]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => (((((bNF_eq_onp @ ((((denota1663640101rp_ext @ Sf) @ Sc) @ Sz) @ product_unit)) @ (((denota2077489681interp @ Sf) @ Sc) @ Sz)) @ Xb) @ Xb) => (((((bNF_eq_onp @ ((trm @ Sf) @ Sz)) @ ((dfree @ Sf) @ Sz)) @ Xa) @ Xa) => (((((((frechet_blin_frechet @ Sf) @ Sc) @ Sz) @ ((((freche227871258interp @ Sf) @ Sc) @ Sz) @ Xb)) @ (((frechet_simple_term @ Sf) @ Sz) @ Xa)) @ X) = (((bounde688532126linfun @ ((finite_Cartesian_vec @ real) @ Sz)) @ real) @ ((((((denotational_frechet @ Sf) @ Sc) @ Sz) @ Xb) @ Xa) @ X)))))))))))).
% 2.94/1.56 thf(fact_241_continuous__on__coordinatewise__then__product, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ C)) => (! [S5:(set @ A),F:(A > (B > C))]: (((! [I4:B]: (((((topolo2071040574ous_on @ A) @ C) @ S5) @ (^ [X2:A]: (((F @ X2) @ I4)))))) => ((((topolo2071040574ous_on @ A) @ (B > C)) @ S5) @ F)))))))).
% 2.94/1.56 thf(fact_242_continuous__on__product__then__coordinatewise, axiom, (! [B:$tType,C:$tType,A:$tType]: ((((topolo503727757_space @ A) & (topolo503727757_space @ C)) => (! [S5:(set @ A),F:(A > (B > C)),I:B]: ((((((topolo2071040574ous_on @ A) @ (B > C)) @ S5) @ F) => ((((topolo2071040574ous_on @ A) @ C) @ S5) @ (^ [X2:A]: (((F @ X2) @ I))))))))))).
% 2.94/1.56 thf(fact_243_Quotient__good__interp, axiom, (! [C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & (finite_finite @ C))) => ((((((quotient @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((frechet_good_interp @ A) @ B) @ C)) @ ((bNF_eq_onp @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) @ (((freche227871258interp @ A) @ B) @ C)) @ (((freche229654227interp @ A) @ B) @ C)) @ (((freche457001096interp @ A) @ B) @ C)))))).
% 2.94/1.56 thf(fact_244_Quotient__strm, axiom, (! [C:$tType,A:$tType]: (((((((quotient @ ((trm @ A) @ C)) @ ((frechet_strm @ A) @ C)) @ ((bNF_eq_onp @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) @ ((frechet_simple_term @ A) @ C)) @ ((frechet_raw_term @ A) @ C)) @ ((frechet_cr_strm @ A) @ C))))).
% 2.94/1.56 thf(fact_245_ids_OQuotient__strm, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,A:$tType]: ((((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc)))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((((quotient @ ((trm @ A) @ C)) @ ((frechet_strm @ A) @ C)) @ ((bNF_eq_onp @ ((trm @ A) @ C)) @ ((dfree @ A) @ C))) @ ((frechet_simple_term @ A) @ C)) @ ((frechet_raw_term @ A) @ C)) @ ((frechet_cr_strm @ A) @ C))))))))).
% 2.94/1.56 thf(fact_246_ids_OQuotient__good__interp, axiom, (! [Sc:$tType,Sf:$tType,Sz:$tType,C:$tType,B:$tType,A:$tType]: ((((finite_finite @ A) & ((finite_finite @ B) & ((finite_finite @ C) & ((finite_finite @ Sz) & ((linorder @ Sz) & ((finite_finite @ Sf) & (finite_finite @ Sc))))))) => (! [Vid1:Sz,Vid2:Sz,Vid3:Sz,Fid1:Sf,Fid2:Sf,Fid3:Sf,Pid1:Sc,Pid2:Sc,Pid3:Sc,Pid4:Sc]: (((((((((((((((ids @ Sz) @ Sf) @ Sc) @ Vid1) @ Vid2) @ Vid3) @ Fid1) @ Fid2) @ Fid3) @ Pid1) @ Pid2) @ Pid3) @ Pid4) => ((((((quotient @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((frechet_good_interp @ A) @ B) @ C)) @ ((bNF_eq_onp @ ((((denota1663640101rp_ext @ A) @ B) @ C) @ product_unit)) @ (((denota2077489681interp @ A) @ B) @ C))) @ (((freche227871258interp @ A) @ B) @ C)) @ (((freche229654227interp @ A) @ B) @ C)) @ (((freche457001096interp @ A) @ B) @ C))))))))).
% 2.94/1.56 thf(fact_247_typedef__to__Quotient, axiom, (! [A:$tType,B:$tType,Rep:(A > B),Abs:(B > A),S5:(set @ B),T7:(B > (A > $o))]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ S5) => ((T7 = (^ [X2:B,Y2:A]: ((X2 = (Rep @ Y2))))) => ((((((quotient @ B) @ A) @ ((bNF_eq_onp @ B) @ (^ [X2:B]: ((((member @ B) @ X2) @ S5))))) @ Abs) @ Rep) @ T7)))))).
% 2.94/1.56 thf(fact_248_open__typedef__to__Quotient, axiom, (! [A:$tType,B:$tType,Rep:(A > B),Abs:(B > A),P:(B > $o),T7:(B > (A > $o))]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ ((collect @ B) @ P)) => ((T7 = (^ [X2:B,Y2:A]: ((X2 = (Rep @ Y2))))) => ((((((quotient @ B) @ A) @ ((bNF_eq_onp @ B) @ P)) @ Abs) @ Rep) @ T7)))))).
% 2.94/1.56 thf(fact_249_QuotientI, axiom, (! [A:$tType,B:$tType,Abs:(B > A),Rep:(A > B),R3:(B > (B > $o)),T7:(B > (A > $o))]: (((! [A5:A]: (((Abs @ (Rep @ A5)) = A5))) => ((! [A5:A]: (((R3 @ (Rep @ A5)) @ (Rep @ A5)))) => ((! [R2:B,S4:B]: ((((R3 @ R2) @ S4) = (((R3 @ R2) @ R2) & (((R3 @ S4) @ S4) & ((Abs @ R2) = (Abs @ S4))))))) => ((T7 = (^ [X2:B,Y2:A]: ((((R3 @ X2) @ X2) & ((Abs @ X2) = Y2))))) => ((((((quotient @ B) @ A) @ R3) @ Abs) @ Rep) @ T7)))))))).
% 2.94/1.56 thf(fact_250_Quotient__def, axiom, (! [B:$tType,A:$tType]: ((((quotient @ A) @ B) = (^ [R5:(A > (A > $o)),Abs2:(A > B),Rep2:(B > A),T8:(A > (B > $o))]: (((! [A7:B]: (((Abs2 @ (Rep2 @ A7)) = A7))) & ((! [A7:B]: (((R5 @ (Rep2 @ A7)) @ (Rep2 @ A7)))) & ((! [R6:A,S2:A]: ((((R5 @ R6) @ S2) = (((R5 @ R6) @ R6) & (((R5 @ S2) @ S2) & ((Abs2 @ R6) = (Abs2 @ S2))))))) & (T8 = (^ [X2:A,Y2:B]: ((((R5 @ X2) @ X2) & ((Abs2 @ X2) = Y2)))))))))))))).
% 2.94/1.56 thf(fact_251_Quotient__cr__rel, axiom, (! [B:$tType,A:$tType,R3:(A > (A > $o)),Abs:(A > B),Rep:(B > A),T7:(A > (B > $o))]: ((((((((quotient @ A) @ B) @ R3) @ Abs) @ Rep) @ T7) => (T7 = (^ [X2:A,Y2:B]: ((((R3 @ X2) @ X2) & ((Abs @ X2) = Y2))))))))).
% 2.94/1.56 thf(fact_252_eq__onp__le__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((ord_less_eq @ (A > (A > $o))) @ ((bNF_eq_onp @ A) @ P)) @ (^ [Y4:A,Z:A]: ((Y4 = Z))))))).
% 2.94/1.56 thf(fact_253_Quotient__rep__abs__eq, axiom, (! [B:$tType,A:$tType,R3:(A > (A > $o)),Abs:(A > B),Rep:(B > A),T7:(A > (B > $o)),T4:A]: ((((((((quotient @ A) @ B) @ R3) @ Abs) @ Rep) @ T7) => (((R3 @ T4) @ T4) => ((((ord_less_eq @ (A > (A > $o))) @ R3) @ (^ [Y4:A,Z:A]: ((Y4 = Z)))) => ((Rep @ (Abs @ T4)) = T4))))))).
% 2.94/1.56 thf(fact_254_UNIV__typedef__to__Quotient, axiom, (! [A:$tType,B:$tType,Rep:(A > B),Abs:(B > A),T7:(B > (A > $o))]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((T7 = (^ [X2:B,Y2:A]: ((X2 = (Rep @ Y2))))) => ((((((quotient @ B) @ A) @ (^ [Y4:B,Z:B]: ((Y4 = Z)))) @ Abs) @ Rep) @ T7)))))).
% 2.94/1.56 thf(fact_255_Quotient__eq__onp__typedef, axiom, (! [B:$tType,A:$tType,P:(A > $o),Abs:(A > B),Rep:(B > A),Cr:(A > (B > $o))]: ((((((((quotient @ A) @ B) @ ((bNF_eq_onp @ A) @ P)) @ Abs) @ Rep) @ Cr) => (((((type_definition @ B) @ A) @ Rep) @ Abs) @ ((collect @ A) @ P)))))).
% 2.94/1.56 thf(subcl_Finite__Set_Ofinite___HOL_Otype, axiom, (! [A:$tType]: (((finite_finite @ A) => (type @ A))))).
% 2.94/1.56 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.94/1.56 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 2.94/1.56 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: (((linorder @ A) => (order @ A))))).
% 2.94/1.56 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: (((linorder @ A) => (preorder @ A))))).
% 2.94/1.56 thf(tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector, axiom, (! [A8:$tType,A9:$tType]: ((((real_V55928688vector @ A8) & (real_V55928688vector @ A9)) => (real_V55928688vector @ ((bounde2145540817linfun @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1, axiom, (! [A8:$tType,A9:$tType]: ((((real_V55928688vector @ A8) & (finite_finite @ A9)) => (real_V55928688vector @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_2, axiom, (! [A8:$tType,A9:$tType]: ((((real_V55928688vector @ A8) & (real_V55928688vector @ A9)) => (real_V55928688vector @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_3, axiom, (real_V55928688vector @ real)).
% 2.94/1.56 thf(tcon_fun___Topological__Spaces_Otopological__space, axiom, (! [A8:$tType,A9:$tType]: (((topolo503727757_space @ A9) => (topolo503727757_space @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: (((order_top @ A9) => (order_top @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: (((top @ A9) => (top @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Oorder__top_4, axiom, (! [A8:$tType]: ((order_top @ (set @ A8))))).
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 2.94/1.56 thf(tcon_Set_Oset___Finite__Set_Ofinite_6, axiom, (! [A8:$tType]: (((finite_finite @ A8) => (finite_finite @ (set @ A8)))))).
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Oorder_7, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Otop_8, axiom, (! [A8:$tType]: ((top @ (set @ A8))))).
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Oord_9, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 2.94/1.56 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_10, axiom, (topolo503727757_space @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Oorder__top_11, axiom, (order_top @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_12, axiom, (preorder @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Finite__Set_Ofinite_13, axiom, (finite_finite @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_14, axiom, (order @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Otop_15, axiom, (top @ $o)).
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Oord_16, axiom, (ord @ $o)).
% 2.94/1.56 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_17, axiom, (topolo503727757_space @ real)).
% 2.94/1.56 thf(tcon_Real_Oreal___Orderings_Opreorder_18, axiom, (preorder @ real)).
% 2.94/1.56 thf(tcon_Real_Oreal___Orderings_Olinorder_19, axiom, (linorder @ real)).
% 2.94/1.56 thf(tcon_Real_Oreal___Orderings_Oorder_20, axiom, (order @ real)).
% 2.94/1.56 thf(tcon_Real_Oreal___Orderings_Oord_21, axiom, (ord @ real)).
% 2.94/1.56 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_22, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ ((sum_sum @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_23, axiom, (! [A8:$tType,A9:$tType]: ((((topolo503727757_space @ A8) & (topolo503727757_space @ A9)) => (topolo503727757_space @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oorder__top_24, axiom, (! [A8:$tType,A9:$tType]: ((((order_top @ A8) & (order_top @ A9)) => (order_top @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_25, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A8) & (preorder @ A9)) => (preorder @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_26, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oorder_27, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A8) & (order @ A9)) => (order @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Orderings_Otop_28, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A8) & (top @ A9)) => (top @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oord_29, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A8) & (ord @ A9)) => (ord @ ((product_prod @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_30, axiom, (order_top @ product_unit)).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31, axiom, (preorder @ product_unit)).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32, axiom, (linorder @ product_unit)).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Finite__Set_Ofinite_33, axiom, (finite_finite @ product_unit)).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oorder_34, axiom, (order @ product_unit)).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Orderings_Otop_35, axiom, (top @ product_unit)).
% 2.94/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oord_36, axiom, (ord @ product_unit)).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_37, axiom, (! [A8:$tType,A9:$tType]: ((((topolo503727757_space @ A8) & (finite_finite @ A9)) => (topolo503727757_space @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_38, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A8) & (finite_finite @ A9)) => (preorder @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_39, axiom, (! [A8:$tType,A9:$tType]: ((((linorder @ A8) & (cARD_1 @ A9)) => (linorder @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_40, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_41, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A8) & (finite_finite @ A9)) => (order @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_42, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A8) & (finite_finite @ A9)) => (ord @ ((finite_Cartesian_vec @ A8) @ A9)))))).
% 2.94/1.56 thf(tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_43, axiom, (! [A8:$tType,A9:$tType]: ((((real_V55928688vector @ A8) & (real_V55928688vector @ A9)) => (topolo503727757_space @ ((bounde2145540817linfun @ A8) @ A9)))))).
% 2.94/1.56 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.94/1.56 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.94/1.56 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.94/1.56 thf(tfree_0, hypothesis, (finite_finite @ c)).
% 2.94/1.56 thf(tfree_1, hypothesis, (finite_finite @ a)).
% 2.94/1.56 thf(tfree_2, hypothesis, (finite_finite @ sz)).
% 2.94/1.56 thf(tfree_3, hypothesis, (linorder @ sz)).
% 2.94/1.56 thf(tfree_4, hypothesis, (finite_finite @ sf)).
% 2.94/1.56 thf(tfree_5, hypothesis, (finite_finite @ sc)).
% 2.94/1.56 thf(tfree_6, hypothesis, (finite_finite @ b)).
% 2.94/1.56 thf(conj_0, conjecture, ((((denotational_Vagree @ c) @ nu) @ nu2) @ (((static_FVDiff @ a) @ c) @ t2))).
% 2.94/1.56 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EGxl0yY1Vf/DTF2DTF18030.p
% 2.94/1.56 ------------------------
% 3.10/1.60 ---- Cleaned THF ---
% 3.10/1.60 thf(ty_t_Denotational__Semantics_Ointerp_Ointerp__ext,type,
% 3.10/1.60 denota1663640101rp_ext: $tType > $tType > $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Frechet__Correctness_Oids_Ogood__interp,type,
% 3.10/1.60 frechet_good_interp: $tType > $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Bounded__Linear__Function_Oblinfun,type,
% 3.10/1.60 bounde2145540817linfun: $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Frechet__Correctness_Oids_Ostrm,type,
% 3.10/1.60 frechet_strm: $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 3.10/1.60 finite_Cartesian_vec: $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Product__Type_Ounit,type,
% 3.10/1.60 product_unit: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Product__Type_Oprod,type,
% 3.10/1.60 product_prod: $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Syntax_Oformula,type,
% 3.10/1.60 formula: $tType > $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Sum__Type_Osum,type,
% 3.10/1.60 sum_sum: $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Syntax_Otrm,type,
% 3.10/1.60 trm: $tType > $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Real_Oreal,type,
% 3.10/1.60 real: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_List_Olist,type,
% 3.10/1.60 list: $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_t_Set_Oset,type,
% 3.10/1.60 set: $tType > $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_tf_sz,type,
% 3.10/1.60 sz: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_tf_sf,type,
% 3.10/1.60 sf: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_tf_sc,type,
% 3.10/1.60 sc: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_tf_c,type,
% 3.10/1.60 c: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_tf_b,type,
% 3.10/1.60 b: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_tf_a,type,
% 3.10/1.60 a: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 3.10/1.60 real_V55928688vector:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Cardinality_OCARD__1,type,
% 3.10/1.60 cARD_1:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_HOL_Otype,type,
% 3.10/1.60 type:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Orderings_Oord,type,
% 3.10/1.60 ord:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Orderings_Otop,type,
% 3.10/1.60 top:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Orderings_Oorder,type,
% 3.10/1.60 order:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Finite__Set_Ofinite,type,
% 3.10/1.60 finite_finite:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Orderings_Olinorder,type,
% 3.10/1.60 linorder:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Orderings_Opreorder,type,
% 3.10/1.60 preorder:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Orderings_Oorder__top,type,
% 3.10/1.60 order_top:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 3.10/1.60 topolo503727757_space:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Euclidean__Algorithm_Oeuclidean__ring__gcd,type,
% 3.10/1.60 euclid1678468529ng_gcd:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_cl_Euclidean__Algorithm_Onormalization__euclidean__semiring,type,
% 3.10/1.60 euclid1155270486miring:
% 3.10/1.60 !>[A: $tType] : $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_BNF__Def_Oeq__onp,type,
% 3.10/1.60 bNF_eq_onp:
% 3.10/1.60 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2,type,
% 3.10/1.60 bNF_Greatest_image2:
% 3.10/1.60 !>[C: $tType,A: $tType,B: $tType] : ( ( set @ C ) > ( C > A ) > ( C > B ) > ( set @ ( product_prod @ A @ B ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Bounded__Linear__Function_Oblinfun_OBlinfun,type,
% 3.10/1.60 bounde688532126linfun:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( ( A > B ) > ( bounde2145540817linfun @ A @ B ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Denotational__Semantics_OIagree,type,
% 3.10/1.60 denotational_Iagree:
% 3.10/1.60 !>[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 ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Denotational__Semantics_OVagree,type,
% 3.10/1.60 denotational_Vagree:
% 3.10/1.60 !>[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 ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Denotational__Semantics_Odirectional__derivative,type,
% 3.10/1.60 denota2078997598vative:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) ) > real ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Denotational__Semantics_Ofrechet,type,
% 3.10/1.60 denotational_frechet:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( finite_Cartesian_vec @ real @ C ) > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Denotational__Semantics_Ois__interp,type,
% 3.10/1.60 denota2077489681interp:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Denotational__Semantics_Osterm__sem,type,
% 3.10/1.60 denota126604975rm_sem:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( trm @ A @ C ) > ( finite_Cartesian_vec @ real @ C ) > real ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Oblin__frechet,type,
% 3.10/1.60 frechet_blin_frechet:
% 3.10/1.60 !>[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 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Ocr__good__interp,type,
% 3.10/1.60 freche457001096interp:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm,type,
% 3.10/1.60 frechet_cr_strm:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( ( trm @ A @ B ) > ( frechet_strm @ A @ B ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Ogood__interp,type,
% 3.10/1.60 freche227871258interp:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > ( frechet_good_interp @ A @ B @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Ogood__interp_Oraw__interp,type,
% 3.10/1.60 freche229654227interp:
% 3.10/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( frechet_good_interp @ A @ B @ C ) > ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Oraw__term,type,
% 3.10/1.60 frechet_raw_term:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( frechet_strm @ A @ C ) > ( trm @ A @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Frechet__Correctness_Oids_Ostrm_Osimple__term,type,
% 3.10/1.60 frechet_simple_term:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( frechet_strm @ A @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Ids_Oids,type,
% 3.10/1.60 ids:
% 3.10/1.60 !>[Sz: $tType,Sf: $tType,Sc: $tType] : ( Sz > Sz > Sz > Sf > Sf > Sf > Sc > Sc > Sc > Sc > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_If,type,
% 3.10/1.60 if:
% 3.10/1.60 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Lifting_OQuotient,type,
% 3.10/1.60 quotient:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > ( B > A ) > ( A > B > $o ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.10/1.60 ord_less_eq:
% 3.10/1.60 !>[A: $tType] : ( A > A > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Orderings_Otop__class_Otop,type,
% 3.10/1.60 top_top:
% 3.10/1.60 !>[A: $tType] : A ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Product__Type_OPair,type,
% 3.10/1.60 product_Pair:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.10/1.60 product_rec_prod:
% 3.10/1.60 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 3.10/1.60 product_fst:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 3.10/1.60 product_snd:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Set_OCollect,type,
% 3.10/1.60 collect:
% 3.10/1.60 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Static__Semantics_OFVDiff,type,
% 3.10/1.60 static_FVDiff:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ ( sum_sum @ C @ C ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Static__Semantics_OFVT,type,
% 3.10/1.60 static_FVT:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ ( sum_sum @ C @ C ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Static__Semantics_OSIGT,type,
% 3.10/1.60 static_SIGT:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( set @ A ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Sum__Type_OInl,type,
% 3.10/1.60 sum_Inl:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 3.10/1.60 sum_rec_sum:
% 3.10/1.60 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_OPredicational,type,
% 3.10/1.60 predicational:
% 3.10/1.60 !>[B: $tType,A: $tType,C: $tType] : ( B > ( formula @ A @ B @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Odfree,type,
% 3.10/1.60 dfree:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Oids_OP,type,
% 3.10/1.60 p:
% 3.10/1.60 !>[Sc: $tType,Sf: $tType,Sz: $tType] : ( Sc > ( formula @ Sf @ Sc @ Sz ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Oids_Oempty,type,
% 3.10/1.60 empty:
% 3.10/1.60 !>[B: $tType,A: $tType] : ( B > ( trm @ A @ B ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Oids_Of0,type,
% 3.10/1.60 f0:
% 3.10/1.60 !>[Sf: $tType,Sz: $tType] : ( Sf > ( trm @ Sf @ Sz ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Otrm_OFunction,type,
% 3.10/1.60 function:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( A > ( C > ( trm @ A @ C ) ) > ( trm @ A @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Otrm_OPlus,type,
% 3.10/1.60 plus:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( trm @ A @ C ) > ( trm @ A @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Syntax_Otrm_OTimes,type,
% 3.10/1.60 times:
% 3.10/1.60 !>[A: $tType,C: $tType] : ( ( trm @ A @ C ) > ( trm @ A @ C ) > ( trm @ A @ C ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Topological__Spaces_Ocontinuous__on,type,
% 3.10/1.60 topolo2071040574ous_on:
% 3.10/1.60 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Typedef_Otype__definition,type,
% 3.10/1.60 type_definition:
% 3.10/1.60 !>[B: $tType,A: $tType] : ( ( B > A ) > ( A > B ) > ( set @ A ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_member,type,
% 3.10/1.60 member:
% 3.10/1.60 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_v_I,type,
% 3.10/1.60 i: denota1663640101rp_ext @ a @ b @ c @ product_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_v_J,type,
% 3.10/1.60 j: denota1663640101rp_ext @ a @ b @ c @ product_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_v__092_060nu_062,type,
% 3.10/1.60 nu: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_v__092_060nu_062_H,type,
% 3.10/1.60 nu2: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ).
% 3.10/1.60
% 3.10/1.60 thf(sy_v_t1____,type,
% 3.10/1.60 t1: trm @ a @ c ).
% 3.10/1.60
% 3.10/1.60 thf(sy_v_t2____,type,
% 3.10/1.60 t2: trm @ a @ c ).
% 3.10/1.60
% 3.10/1.60 thf(fact_0_agree__plus2,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 3.10/1.60 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( plus @ B @ A @ T1 @ T2 ) ) )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T2 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_1_agree,axiom,
% 3.10/1.60 denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_2_agree1,axiom,
% 3.10/1.60 denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t1 ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_3_dfree2,axiom,
% 3.10/1.60 dfree @ a @ c @ t2 ).
% 3.10/1.60
% 3.10/1.60 thf(fact_4_agree__plus1,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 3.10/1.60 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( plus @ B @ A @ T1 @ T2 ) ) )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T1 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_5_agree__comm,axiom,
% 3.10/1.60 ! [A: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [A2: 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 )] :
% 3.10/1.60 ( ( denotational_Vagree @ A @ A2 @ B2 @ V )
% 3.10/1.60 => ( denotational_Vagree @ A @ B2 @ A2 @ V ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_6_agree__refl,axiom,
% 3.10/1.60 ! [A: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [Nu: product_prod @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ),A2: set @ ( sum_sum @ A @ A )] : ( denotational_Vagree @ A @ Nu @ Nu @ A2 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_7_dfree1,axiom,
% 3.10/1.60 dfree @ a @ c @ t1 ).
% 3.10/1.60
% 3.10/1.60 thf(fact_8_raw__interp__inject,axiom,
% 3.10/1.60 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.60 ( ( ( finite_finite @ A )
% 3.10/1.60 & ( finite_finite @ B )
% 3.10/1.60 & ( finite_finite @ C ) )
% 3.10/1.60 => ! [X: frechet_good_interp @ A @ B @ C,Y: frechet_good_interp @ A @ B @ C] :
% 3.10/1.60 ( ( ( freche229654227interp @ A @ B @ C @ X )
% 3.10/1.60 = ( freche229654227interp @ A @ B @ C @ Y ) )
% 3.10/1.60 = ( X = Y ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_9_raw__term__inject,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C,Y: frechet_strm @ A @ C] :
% 3.10/1.60 ( ( ( frechet_raw_term @ A @ C @ X )
% 3.10/1.60 = ( frechet_raw_term @ A @ C @ Y ) )
% 3.10/1.60 = ( X = Y ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_10_agree__times1,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 3.10/1.60 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( times @ B @ A @ T1 @ T2 ) ) )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T1 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_11_agree__times2,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [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 ),T1: trm @ B @ A,T2: trm @ B @ A] :
% 3.10/1.60 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( times @ B @ A @ T1 @ T2 ) ) )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ T2 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_12_agree__func,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [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 ),Var: B,Args: A > ( trm @ B @ A ),I: A] :
% 3.10/1.60 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( function @ B @ A @ Var @ Args ) ) )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVDiff @ B @ A @ ( Args @ I ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_13_P__def,axiom,
% 3.10/1.60 ( ( p @ sc @ sf @ sz )
% 3.10/1.60 = ( predicational @ sc @ sf @ sz ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_14_IH2,axiom,
% 3.10/1.60 ( ( denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t2 ) )
% 3.10/1.60 => ( ( denotational_Iagree @ a @ b @ c @ i @ j
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t2 ) ) ) ) )
% 3.10/1.60 => ( ( denotational_frechet @ a @ b @ c @ i @ t2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) )
% 3.10/1.60 = ( denotational_frechet @ a @ b @ c @ j @ t2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_15_seq__sem_Ocases,axiom,
% 3.10/1.60 ! [X: product_prod @ ( denota1663640101rp_ext @ sf @ sc @ sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ sf @ sc @ sz ) ) @ ( list @ ( formula @ sf @ sc @ sz ) ) )] :
% 3.10/1.60 ~ ! [I2: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,S: product_prod @ ( list @ ( formula @ sf @ sc @ sz ) ) @ ( list @ ( formula @ sf @ sc @ sz ) )] :
% 3.10/1.60 ( X
% 3.10/1.60 != ( product_Pair @ ( denota1663640101rp_ext @ sf @ sc @ sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ sf @ sc @ sz ) ) @ ( list @ ( formula @ sf @ sc @ sz ) ) ) @ I2 @ S ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_16_raw__term,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C] : ( member @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C @ X ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_17_raw__term__cases,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 3.10/1.60 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.60 => ~ ! [X3: frechet_strm @ A @ C] :
% 3.10/1.60 ( Y
% 3.10/1.60 != ( frechet_raw_term @ A @ C @ X3 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_18_raw__term__induct,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,Y: trm @ A @ C,P: ( trm @ A @ C ) > $o] :
% 3.10/1.60 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.60 => ( ! [X3: frechet_strm @ A @ C] : ( P @ ( frechet_raw_term @ A @ C @ X3 ) )
% 3.10/1.60 => ( P @ Y ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_19_coincidence__frechet,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,C: $tType] :
% 3.10/1.60 ( ( ( finite_finite @ C )
% 3.10/1.60 & ( finite_finite @ A )
% 3.10/1.60 & ( finite_finite @ B ) )
% 3.10/1.60 => ! [Theta: trm @ A @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),I3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.60 ( ( dfree @ A @ C @ Theta )
% 3.10/1.60 => ( ( denotational_Vagree @ C @ Nu @ Nu2 @ ( static_FVDiff @ A @ C @ Theta ) )
% 3.10/1.60 => ( ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 3.10/1.60 = ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_20_IA,axiom,
% 3.10/1.60 ( denotational_Iagree @ a @ b @ c @ i @ j
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_21_IA1,axiom,
% 3.10/1.60 ( denotational_Iagree @ a @ b @ c @ i @ j
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t1 ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_22_IA2,axiom,
% 3.10/1.60 ( denotational_Iagree @ a @ b @ c @ i @ j
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t2 ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_23_IH1,axiom,
% 3.10/1.60 ( ( denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t1 ) )
% 3.10/1.60 => ( ( denotational_Iagree @ a @ b @ c @ i @ j
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ ( sum_sum @ b @ c ) )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ ( sum_sum @ b @ c )] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ ( sum_sum @ b @ c ) @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t1 ) ) ) ) )
% 3.10/1.60 => ( ( denotational_frechet @ a @ b @ c @ i @ t1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu ) )
% 3.10/1.60 = ( denotational_frechet @ a @ b @ c @ j @ t1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) @ nu2 ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_24_Iagree__comm,axiom,
% 3.10/1.60 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.60 ( ( ( finite_finite @ A )
% 3.10/1.60 & ( finite_finite @ B )
% 3.10/1.60 & ( finite_finite @ C ) )
% 3.10/1.60 => ! [A2: denota1663640101rp_ext @ A @ B @ C @ product_unit,B2: denota1663640101rp_ext @ A @ B @ C @ product_unit,V: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] :
% 3.10/1.60 ( ( denotational_Iagree @ A @ B @ C @ A2 @ B2 @ V )
% 3.10/1.60 => ( denotational_Iagree @ A @ B @ C @ B2 @ A2 @ V ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_25_Iagree__refl,axiom,
% 3.10/1.60 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.60 ( ( ( finite_finite @ A )
% 3.10/1.60 & ( finite_finite @ B )
% 3.10/1.60 & ( finite_finite @ C ) )
% 3.10/1.60 => ! [I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,A2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) )] : ( denotational_Iagree @ A @ B @ C @ I3 @ I3 @ A2 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_26_FunctionFrechet_Ocases,axiom,
% 3.10/1.60 ! [B: $tType,C: $tType,A: $tType] :
% 3.10/1.60 ( ( ( finite_finite @ A )
% 3.10/1.60 & ( finite_finite @ C )
% 3.10/1.60 & ( finite_finite @ B ) )
% 3.10/1.60 => ! [X: product_prod @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ A] :
% 3.10/1.60 ~ ! [I2: denota1663640101rp_ext @ A @ B @ C @ product_unit,I4: A] :
% 3.10/1.60 ( X
% 3.10/1.60 != ( product_Pair @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ A @ I2 @ I4 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_27_subs_I2_J,axiom,
% 3.10/1.60 ! [E: $tType] :
% 3.10/1.60 ( ord_less_eq @ ( set @ ( sum_sum @ a @ E ) )
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ E )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ E] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ E @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t2 ) ) ) )
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ E )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ E] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ E @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_28_subs_I1_J,axiom,
% 3.10/1.60 ! [D: $tType] :
% 3.10/1.60 ( ord_less_eq @ ( set @ ( sum_sum @ a @ D ) )
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ D )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ D] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ D @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ t1 ) ) ) )
% 3.10/1.60 @ ( collect @ ( sum_sum @ a @ D )
% 3.10/1.60 @ ^ [Uu: sum_sum @ a @ D] :
% 3.10/1.60 ? [X2: a] :
% 3.10/1.60 ( ( Uu
% 3.10/1.60 = ( sum_Inl @ a @ D @ X2 ) )
% 3.10/1.60 & ( member @ a @ X2 @ ( static_SIGT @ a @ c @ ( plus @ a @ c @ t1 @ t2 ) ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_29_simple__term__inverse,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,Y: trm @ A @ C] :
% 3.10/1.60 ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.60 => ( ( frechet_raw_term @ A @ C @ ( frechet_simple_term @ A @ C @ Y ) )
% 3.10/1.60 = Y ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_30_prod_Ocollapse,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 3.10/1.60 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 3.10/1.60 = Prod ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_31_cr__good__interp__def,axiom,
% 3.10/1.60 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.60 ( ( ( finite_finite @ A )
% 3.10/1.60 & ( finite_finite @ B )
% 3.10/1.60 & ( finite_finite @ C ) )
% 3.10/1.60 => ( ( freche457001096interp @ A @ B @ C )
% 3.10/1.60 = ( ^ [X2: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y2: frechet_good_interp @ A @ B @ C] :
% 3.10/1.60 ( X2
% 3.10/1.60 = ( freche229654227interp @ A @ B @ C @ Y2 ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_32_cr__strm__def,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType] :
% 3.10/1.60 ( ( frechet_cr_strm @ A @ B )
% 3.10/1.60 = ( ^ [X2: trm @ A @ B,Y2: frechet_strm @ A @ B] :
% 3.10/1.60 ( X2
% 3.10/1.60 = ( frechet_raw_term @ A @ B @ Y2 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_33_dfree__Times__simps,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,A3: trm @ A @ B,B3: trm @ A @ B] :
% 3.10/1.60 ( ( dfree @ A @ B @ ( times @ A @ B @ A3 @ B3 ) )
% 3.10/1.60 = ( ( dfree @ A @ B @ A3 )
% 3.10/1.60 & ( dfree @ A @ B @ B3 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_34_dfree__Plus__simps,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,A3: trm @ A @ B,B3: trm @ A @ B] :
% 3.10/1.60 ( ( dfree @ A @ B @ ( plus @ A @ B @ A3 @ B3 ) )
% 3.10/1.60 = ( ( dfree @ A @ B @ A3 )
% 3.10/1.60 & ( dfree @ A @ B @ B3 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_35_dfree__Fun__simps,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,I: A,Args: B > ( trm @ A @ B )] :
% 3.10/1.60 ( ( dfree @ A @ B @ ( function @ A @ B @ I @ Args ) )
% 3.10/1.60 = ( ! [X2: B] : ( dfree @ A @ B @ ( Args @ X2 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_36_simple__term__cases,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C] :
% 3.10/1.60 ~ ! [Y3: trm @ A @ C] :
% 3.10/1.60 ( ( X
% 3.10/1.60 = ( frechet_simple_term @ A @ C @ Y3 ) )
% 3.10/1.60 => ~ ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_37_raw__term__inverse,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X: frechet_strm @ A @ C] :
% 3.10/1.60 ( ( frechet_simple_term @ A @ C @ ( frechet_raw_term @ A @ C @ X ) )
% 3.10/1.60 = X ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_38_simple__term__inject,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X: trm @ A @ C,Y: trm @ A @ C] :
% 3.10/1.60 ( ( member @ ( trm @ A @ C ) @ X @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.60 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.60 => ( ( ( frechet_simple_term @ A @ C @ X )
% 3.10/1.60 = ( frechet_simple_term @ A @ C @ Y ) )
% 3.10/1.60 = ( X = Y ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_39_simple__term__induct,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,P: ( frechet_strm @ A @ C ) > $o,X: frechet_strm @ A @ C] :
% 3.10/1.60 ( ! [Y3: trm @ A @ C] :
% 3.10/1.60 ( ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.60 => ( P @ ( frechet_simple_term @ A @ C @ Y3 ) ) )
% 3.10/1.60 => ( P @ X ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_40_old_Oprod_Oinject,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,A3: A,B3: B,A4: A,B4: B] :
% 3.10/1.60 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 3.10/1.60 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 3.10/1.60 = ( ( A3 = A4 )
% 3.10/1.60 & ( B3 = B4 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_41_prod_Oinject,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 3.10/1.60 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 3.10/1.60 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 3.10/1.60 = ( ( X1 = Y1 )
% 3.10/1.60 & ( X22 = Y22 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_42_trm_Oinject_I3_J,axiom,
% 3.10/1.60 ! [A: $tType,C: $tType,X31: A,X32: C > ( trm @ A @ C ),Y31: A,Y32: C > ( trm @ A @ C )] :
% 3.10/1.60 ( ( ( function @ A @ C @ X31 @ X32 )
% 3.10/1.60 = ( function @ A @ C @ Y31 @ Y32 ) )
% 3.10/1.60 = ( ( X31 = Y31 )
% 3.10/1.60 & ( X32 = Y32 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_43_trm_Oinject_I4_J,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X41: trm @ A @ C,X42: trm @ A @ C,Y41: trm @ A @ C,Y42: trm @ A @ C] :
% 3.10/1.60 ( ( ( plus @ A @ C @ X41 @ X42 )
% 3.10/1.60 = ( plus @ A @ C @ Y41 @ Y42 ) )
% 3.10/1.60 = ( ( X41 = Y41 )
% 3.10/1.60 & ( X42 = Y42 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_44_trm_Oinject_I5_J,axiom,
% 3.10/1.60 ! [C: $tType,A: $tType,X51: trm @ A @ C,X52: trm @ A @ C,Y51: trm @ A @ C,Y52: trm @ A @ C] :
% 3.10/1.60 ( ( ( times @ A @ C @ X51 @ X52 )
% 3.10/1.60 = ( times @ A @ C @ Y51 @ Y52 ) )
% 3.10/1.60 = ( ( X51 = Y51 )
% 3.10/1.60 & ( X52 = Y52 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_45_mem__Collect__eq,axiom,
% 3.10/1.60 ! [A: $tType,A3: A,P: A > $o] :
% 3.10/1.60 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 3.10/1.60 = ( P @ A3 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_46_Collect__mem__eq,axiom,
% 3.10/1.60 ! [A: $tType,A2: set @ A] :
% 3.10/1.60 ( ( collect @ A
% 3.10/1.60 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 3.10/1.60 = A2 ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_47_Collect__cong,axiom,
% 3.10/1.60 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.10/1.60 ( ! [X3: A] :
% 3.10/1.60 ( ( P @ X3 )
% 3.10/1.60 = ( Q @ X3 ) )
% 3.10/1.60 => ( ( collect @ A @ P )
% 3.10/1.60 = ( collect @ A @ Q ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_48_ext,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.10/1.60 ( ! [X3: A] :
% 3.10/1.60 ( ( F @ X3 )
% 3.10/1.60 = ( G @ X3 ) )
% 3.10/1.60 => ( F = G ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_49_agree__sub,axiom,
% 3.10/1.60 ! [A: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [A2: 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 )] :
% 3.10/1.60 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ A2 @ B2 )
% 3.10/1.60 => ( ( denotational_Vagree @ A @ Nu @ Omega @ B2 )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Omega @ A2 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_50_agree__supset,axiom,
% 3.10/1.60 ! [A: $tType] :
% 3.10/1.60 ( ( finite_finite @ A )
% 3.10/1.60 => ! [B2: set @ ( sum_sum @ A @ A ),A2: 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 )] :
% 3.10/1.60 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ B2 @ A2 )
% 3.10/1.60 => ( ( denotational_Vagree @ A @ Nu @ Nu2 @ A2 )
% 3.10/1.60 => ( denotational_Vagree @ A @ Nu @ Nu2 @ B2 ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_51_old_Oprod_Oinducts,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.10/1.60 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 3.10/1.60 => ( P @ Prod ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 3.10/1.60 ~ ! [A5: A,B5: B] :
% 3.10/1.60 ( Y
% 3.10/1.60 != ( product_Pair @ A @ B @ A5 @ B5 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_53_Pair__inject,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,A3: A,B3: B,A4: A,B4: B] :
% 3.10/1.60 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 3.10/1.60 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 3.10/1.60 => ~ ( ( A3 = A4 )
% 3.10/1.60 => ( B3 != B4 ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_54_prod__cases,axiom,
% 3.10/1.60 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 3.10/1.60 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 3.10/1.60 => ( P @ P2 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_55_surj__pair,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 3.10/1.60 ? [X3: A,Y3: B] :
% 3.10/1.60 ( P2
% 3.10/1.60 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_56_prod__induct7,axiom,
% 3.10/1.60 ! [G2: $tType,F2: $tType,E2: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 3.10/1.60 ( ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) @ D3 @ ( product_Pair @ E2 @ ( product_prod @ F2 @ G2 ) @ E3 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 3.10/1.60 => ( P @ X ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_57_prod__induct6,axiom,
% 3.10/1.60 ! [F2: $tType,E2: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) )] :
% 3.10/1.60 ( ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ F2 ) @ D3 @ ( product_Pair @ E2 @ F2 @ E3 @ F3 ) ) ) ) ) )
% 3.10/1.60 => ( P @ X ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_58_prod__induct5,axiom,
% 3.10/1.60 ! [E2: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) )] :
% 3.10/1.60 ( ! [A5: A,B5: B,C2: C,D3: D2,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E2 ) @ C2 @ ( product_Pair @ D2 @ E2 @ D3 @ E3 ) ) ) ) )
% 3.10/1.60 => ( P @ X ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_59_prod__induct4,axiom,
% 3.10/1.60 ! [D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 3.10/1.60 ( ! [A5: A,B5: B,C2: C,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) )
% 3.10/1.60 => ( P @ X ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_60_prod__induct3,axiom,
% 3.10/1.60 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.10/1.60 ( ! [A5: A,B5: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 3.10/1.60 => ( P @ X ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_61_prod__cases7,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E2: $tType,F2: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 3.10/1.60 ~ ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2,G3: G2] :
% 3.10/1.60 ( Y
% 3.10/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ ( product_prod @ F2 @ G2 ) ) @ D3 @ ( product_Pair @ E2 @ ( product_prod @ F2 @ G2 ) @ E3 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_62_prod__cases6,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E2: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) )] :
% 3.10/1.60 ~ ! [A5: A,B5: B,C2: C,D3: D2,E3: E2,F3: F2] :
% 3.10/1.60 ( Y
% 3.10/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E2 @ F2 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E2 @ F2 ) @ D3 @ ( product_Pair @ E2 @ F2 @ E3 @ F3 ) ) ) ) ) ) ).
% 3.10/1.60
% 3.10/1.60 thf(fact_63_prod__cases5,axiom,
% 3.10/1.60 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) )] :
% 3.10/1.60 ~ ! [A5: A,B5: B,C2: C,D3: D2,E3: E2] :
% 3.10/1.60 ( Y
% 3.10/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D2 @ E2 ) @ C2 @ ( product_Pair @ D2 @ E2 @ D3 @ E3 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_64_prod__cases4,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,C: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 3.10/1.61 ~ ! [A5: A,B5: B,C2: C,D3: D2] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B5 @ ( product_Pair @ C @ D2 @ C2 @ D3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_65_prod__cases3,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.10/1.61 ~ ! [A5: A,B5: B,C2: C] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_66_fst__conv,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,X1: A,X22: B] :
% 3.10/1.61 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X22 ) )
% 3.10/1.61 = X1 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_67_fst__eqD,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,X: A,Y: B,A3: A] :
% 3.10/1.61 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y ) )
% 3.10/1.61 = A3 )
% 3.10/1.61 => ( X = A3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_68_snd__conv,axiom,
% 3.10/1.61 ! [Aa: $tType,A: $tType,X1: Aa,X22: A] :
% 3.10/1.61 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X1 @ X22 ) )
% 3.10/1.61 = X22 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_69_snd__eqD,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,X: B,Y: A,A3: A] :
% 3.10/1.61 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 3.10/1.61 = A3 )
% 3.10/1.61 => ( Y = A3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_70_prod__eq__iff,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ^ [Y4: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y4 = Z ) )
% 3.10/1.61 = ( ^ [S2: product_prod @ A @ B,T3: product_prod @ A @ B] :
% 3.10/1.61 ( ( ( product_fst @ A @ B @ S2 )
% 3.10/1.61 = ( product_fst @ A @ B @ T3 ) )
% 3.10/1.61 & ( ( product_snd @ A @ B @ S2 )
% 3.10/1.61 = ( product_snd @ A @ B @ T3 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_71_prod_Oexpand,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 3.10/1.61 ( ( ( ( product_fst @ A @ B @ Prod )
% 3.10/1.61 = ( product_fst @ A @ B @ Prod2 ) )
% 3.10/1.61 & ( ( product_snd @ A @ B @ Prod )
% 3.10/1.61 = ( product_snd @ A @ B @ Prod2 ) ) )
% 3.10/1.61 => ( Prod = Prod2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_72_prod__eqI,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,P2: product_prod @ A @ B,Q2: product_prod @ A @ B] :
% 3.10/1.61 ( ( ( product_fst @ A @ B @ P2 )
% 3.10/1.61 = ( product_fst @ A @ B @ Q2 ) )
% 3.10/1.61 => ( ( ( product_snd @ A @ B @ P2 )
% 3.10/1.61 = ( product_snd @ A @ B @ Q2 ) )
% 3.10/1.61 => ( P2 = Q2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_73_dfree__Fun,axiom,
% 3.10/1.61 ! [A: $tType,C: $tType,Args: C > ( trm @ A @ C ),I: A] :
% 3.10/1.61 ( ! [I4: C] : ( dfree @ A @ C @ ( Args @ I4 ) )
% 3.10/1.61 => ( dfree @ A @ C @ ( function @ A @ C @ I @ Args ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_74_dfree_Odfree__Plus,axiom,
% 3.10/1.61 ! [C: $tType,A: $tType,Theta_1: trm @ A @ C,Theta_2: trm @ A @ C] :
% 3.10/1.61 ( ( dfree @ A @ C @ Theta_1 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta_2 )
% 3.10/1.61 => ( dfree @ A @ C @ ( plus @ A @ C @ Theta_1 @ Theta_2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_75_dfree__Times,axiom,
% 3.10/1.61 ! [C: $tType,A: $tType,Theta_1: trm @ A @ C,Theta_2: trm @ A @ C] :
% 3.10/1.61 ( ( dfree @ A @ C @ Theta_1 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta_2 )
% 3.10/1.61 => ( dfree @ A @ C @ ( times @ A @ C @ Theta_1 @ Theta_2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_76_trm_Odistinct_I23_J,axiom,
% 3.10/1.61 ! [C: $tType,A: $tType,X31: A,X32: C > ( trm @ A @ C ),X41: trm @ A @ C,X42: trm @ A @ C] :
% 3.10/1.61 ( ( function @ A @ C @ X31 @ X32 )
% 3.10/1.61 != ( plus @ A @ C @ X41 @ X42 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_77_trm_Odistinct_I25_J,axiom,
% 3.10/1.61 ! [C: $tType,A: $tType,X31: A,X32: C > ( trm @ A @ C ),X51: trm @ A @ C,X52: trm @ A @ C] :
% 3.10/1.61 ( ( function @ A @ C @ X31 @ X32 )
% 3.10/1.61 != ( times @ A @ C @ X51 @ X52 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_78_trm_Odistinct_I31_J,axiom,
% 3.10/1.61 ! [C: $tType,A: $tType,X41: trm @ A @ C,X42: trm @ A @ C,X51: trm @ A @ C,X52: trm @ A @ C] :
% 3.10/1.61 ( ( plus @ A @ C @ X41 @ X42 )
% 3.10/1.61 != ( times @ A @ C @ X51 @ X52 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_79_surjective__pairing,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,T4: product_prod @ A @ B] :
% 3.10/1.61 ( T4
% 3.10/1.61 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T4 ) @ ( product_snd @ A @ B @ T4 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_80_prod_Oexhaust__sel,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 3.10/1.61 ( Prod
% 3.10/1.61 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_81_Pair__le,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType] :
% 3.10/1.61 ( ( ( ord @ B )
% 3.10/1.61 & ( ord @ A ) )
% 3.10/1.61 => ! [A3: A,B3: B,C3: A,D4: B] :
% 3.10/1.61 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A3 @ B3 ) @ ( product_Pair @ A @ B @ C3 @ D4 ) )
% 3.10/1.61 = ( ( ord_less_eq @ A @ A3 @ C3 )
% 3.10/1.61 & ( ord_less_eq @ B @ B3 @ D4 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_82_directional__derivative__def,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ( ( denota2078997598vative @ A @ B @ C )
% 3.10/1.61 = ( ^ [I5: denota1663640101rp_ext @ A @ B @ C @ product_unit,T3: trm @ A @ C,V2: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C )] : ( denotational_frechet @ A @ B @ C @ I5 @ T3 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ V2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ V2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_83_raw__interp__inverse,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ( freche227871258interp @ A @ B @ C @ ( freche229654227interp @ A @ B @ C @ X ) )
% 3.10/1.61 = X ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_84_old_Oprod_Orec,axiom,
% 3.10/1.61 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A3: A,B3: B] :
% 3.10/1.61 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 3.10/1.61 = ( F1 @ A3 @ B3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_85_type__definition__strm,axiom,
% 3.10/1.61 ! [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 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_86_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,P: A > B > $o,X: A,Y: B,A3: product_prod @ A @ B] :
% 3.10/1.61 ( ( P @ X @ Y )
% 3.10/1.61 => ( ( A3
% 3.10/1.61 = ( product_Pair @ A @ B @ X @ Y ) )
% 3.10/1.61 => ( P @ ( product_fst @ A @ B @ A3 ) @ ( product_snd @ A @ B @ A3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_87_conjI__realizer,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,P: A > $o,P2: A,Q: B > $o,Q2: B] :
% 3.10/1.61 ( ( P @ P2 )
% 3.10/1.61 => ( ( Q @ Q2 )
% 3.10/1.61 => ( ( P @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) )
% 3.10/1.61 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_88_exI__realizer,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,P: A > B > $o,Y: A,X: B] :
% 3.10/1.61 ( ( P @ Y @ X )
% 3.10/1.61 => ( P @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_89_less__eq__prod__def,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( ord @ A )
% 3.10/1.61 & ( ord @ B ) )
% 3.10/1.61 => ( ( ord_less_eq @ ( product_prod @ A @ B ) )
% 3.10/1.61 = ( ^ [X2: product_prod @ A @ B,Y2: product_prod @ A @ B] :
% 3.10/1.61 ( ( ord_less_eq @ A @ ( product_fst @ A @ B @ X2 ) @ ( product_fst @ A @ B @ Y2 ) )
% 3.10/1.61 & ( ord_less_eq @ B @ ( product_snd @ A @ B @ X2 ) @ ( product_snd @ A @ B @ Y2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_90_Iagree__sub,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [A2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),B2: set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ),I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,J: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ ( sum_sum @ A @ ( sum_sum @ B @ C ) ) ) @ A2 @ B2 )
% 3.10/1.61 => ( ( denotational_Iagree @ A @ B @ C @ I3 @ J @ B2 )
% 3.10/1.61 => ( denotational_Iagree @ A @ B @ C @ I3 @ J @ A2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_91_subset__Collect__iff,axiom,
% 3.10/1.61 ! [A: $tType,B2: set @ A,A2: set @ A,P: A > $o] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 3.10/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2
% 3.10/1.61 @ ( collect @ A
% 3.10/1.61 @ ^ [X2: A] :
% 3.10/1.61 ( ( member @ A @ X2 @ A2 )
% 3.10/1.61 & ( P @ X2 ) ) ) )
% 3.10/1.61 = ( ! [X2: A] :
% 3.10/1.61 ( ( member @ A @ X2 @ B2 )
% 3.10/1.61 => ( P @ X2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_92_subset__CollectI,axiom,
% 3.10/1.61 ! [A: $tType,B2: set @ A,A2: set @ A,Q: A > $o,P: A > $o] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 3.10/1.61 => ( ! [X3: A] :
% 3.10/1.61 ( ( member @ A @ X3 @ B2 )
% 3.10/1.61 => ( ( Q @ X3 )
% 3.10/1.61 => ( P @ X3 ) ) )
% 3.10/1.61 => ( ord_less_eq @ ( set @ A )
% 3.10/1.61 @ ( collect @ A
% 3.10/1.61 @ ^ [X2: A] :
% 3.10/1.61 ( ( member @ A @ X2 @ B2 )
% 3.10/1.61 & ( Q @ X2 ) ) )
% 3.10/1.61 @ ( collect @ A
% 3.10/1.61 @ ^ [X2: A] :
% 3.10/1.61 ( ( member @ A @ X2 @ A2 )
% 3.10/1.61 & ( P @ X2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_93_Pair__mono,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType] :
% 3.10/1.61 ( ( ( ord @ B )
% 3.10/1.61 & ( ord @ A ) )
% 3.10/1.61 => ! [X: A,X4: A,Y: B,Y5: B] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X @ X4 )
% 3.10/1.61 => ( ( ord_less_eq @ B @ Y @ Y5 )
% 3.10/1.61 => ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( product_Pair @ A @ B @ X4 @ Y5 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_94_fst__mono,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( ord @ A )
% 3.10/1.61 & ( ord @ B ) )
% 3.10/1.61 => ! [X: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 3.10/1.61 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X @ Y )
% 3.10/1.61 => ( ord_less_eq @ A @ ( product_fst @ A @ B @ X ) @ ( product_fst @ A @ B @ Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_95_snd__mono,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( ord @ A )
% 3.10/1.61 & ( ord @ B ) )
% 3.10/1.61 => ! [X: product_prod @ A @ B,Y: product_prod @ A @ B] :
% 3.10/1.61 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X @ Y )
% 3.10/1.61 => ( ord_less_eq @ B @ ( product_snd @ A @ B @ X ) @ ( product_snd @ A @ B @ Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_96_exE__realizer_H,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,P: A > B > $o,P2: product_prod @ B @ A] :
% 3.10/1.61 ( ( P @ ( product_snd @ B @ A @ P2 ) @ ( product_fst @ B @ A @ P2 ) )
% 3.10/1.61 => ~ ! [X3: B,Y3: A] :
% 3.10/1.61 ~ ( P @ Y3 @ X3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_97_euclid__ext__aux_Ocases,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( euclid1678468529ng_gcd @ A )
% 3.10/1.61 => ! [X: product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) ) )] :
% 3.10/1.61 ~ ! [S3: A,S4: A,T5: A,T6: A,R: A,R2: A] :
% 3.10/1.61 ( X
% 3.10/1.61 != ( product_Pair @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) ) ) @ S3 @ ( product_Pair @ A @ ( product_prod @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) ) @ S4 @ ( product_Pair @ A @ ( product_prod @ A @ ( product_prod @ A @ A ) ) @ T5 @ ( product_Pair @ A @ ( product_prod @ A @ A ) @ T6 @ ( product_Pair @ A @ A @ R @ R2 ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_98_sum_Oinject_I1_J,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 3.10/1.61 ( ( ( sum_Inl @ A @ B @ X1 )
% 3.10/1.61 = ( sum_Inl @ A @ B @ Y1 ) )
% 3.10/1.61 = ( X1 = Y1 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_99_old_Osum_Oinject_I1_J,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,A3: A,A4: A] :
% 3.10/1.61 ( ( ( sum_Inl @ A @ B @ A3 )
% 3.10/1.61 = ( sum_Inl @ A @ B @ A4 ) )
% 3.10/1.61 = ( A3 = A4 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_100_good__interp__inverse,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ( freche229654227interp @ A @ B @ C @ ( freche227871258interp @ A @ B @ C @ Y ) )
% 3.10/1.61 = Y ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_101_f0__def,axiom,
% 3.10/1.61 ( ( f0 @ sf @ sz )
% 3.10/1.61 = ( ^ [F4: sf] : ( function @ sf @ sz @ F4 @ ( empty @ sz @ sf ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_102_subsetI,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.10/1.61 ( ! [X3: A] :
% 3.10/1.61 ( ( member @ A @ X3 @ A2 )
% 3.10/1.61 => ( member @ A @ X3 @ B2 ) )
% 3.10/1.61 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_103_raw__interp__induct,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit,P: ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o] :
% 3.10/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ! [X3: frechet_good_interp @ A @ B @ C] : ( P @ ( freche229654227interp @ A @ B @ C @ X3 ) )
% 3.10/1.61 => ( P @ Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_104_raw__interp__cases,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ~ ! [X3: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( freche229654227interp @ A @ B @ C @ X3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_105_raw__interp,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [X: frechet_good_interp @ A @ B @ C] : ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C @ X ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_106_good__interp__cases,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ~ ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( X
% 3.10/1.61 = ( freche227871258interp @ A @ B @ C @ Y3 ) )
% 3.10/1.61 => ~ ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_107_good__interp__induct,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [P: ( frechet_good_interp @ A @ B @ C ) > $o,X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( P @ ( freche227871258interp @ A @ B @ C @ Y3 ) ) )
% 3.10/1.61 => ( P @ X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_108_good__interp__inject,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ! [X: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ X @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ( ( freche227871258interp @ A @ B @ C @ X )
% 3.10/1.61 = ( freche227871258interp @ A @ B @ C @ Y ) )
% 3.10/1.61 = ( X = Y ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_109_subset__antisym,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 3.10/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 3.10/1.61 => ( A2 = B2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_110_gcd_Ocases,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( euclid1155270486miring @ A )
% 3.10/1.61 => ! [X: product_prod @ A @ A] :
% 3.10/1.61 ~ ! [A5: A,B5: A] :
% 3.10/1.61 ( X
% 3.10/1.61 != ( product_Pair @ A @ A @ A5 @ B5 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_111_Collect__mono__iff,axiom,
% 3.10/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.10/1.61 = ( ! [X2: A] :
% 3.10/1.61 ( ( P @ X2 )
% 3.10/1.61 => ( Q @ X2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_112_set__eq__subset,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 3.10/1.61 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 3.10/1.61 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_113_subset__trans,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 3.10/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C4 )
% 3.10/1.61 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_114_Collect__mono,axiom,
% 3.10/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.10/1.61 ( ! [X3: A] :
% 3.10/1.61 ( ( P @ X3 )
% 3.10/1.61 => ( Q @ X3 ) )
% 3.10/1.61 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_115_subset__refl,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_116_subset__iff,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 3.10/1.61 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.10/1.61 ! [T3: A] :
% 3.10/1.61 ( ( member @ A @ T3 @ A6 )
% 3.10/1.61 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_117_equalityD2,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.10/1.61 ( ( A2 = B2 )
% 3.10/1.61 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_118_equalityD1,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.10/1.61 ( ( A2 = B2 )
% 3.10/1.61 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_119_subset__eq,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 3.10/1.61 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.10/1.61 ! [X2: A] :
% 3.10/1.61 ( ( member @ A @ X2 @ A6 )
% 3.10/1.61 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_120_equalityE,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.10/1.61 ( ( A2 = B2 )
% 3.10/1.61 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 3.10/1.61 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_121_subsetD,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A,C3: A] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 3.10/1.61 => ( ( member @ A @ C3 @ A2 )
% 3.10/1.61 => ( member @ A @ C3 @ B2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_122_in__mono,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 3.10/1.61 => ( ( member @ A @ X @ A2 )
% 3.10/1.61 => ( member @ A @ X @ B2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_123_Inl__inject,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,X: A,Y: A] :
% 3.10/1.61 ( ( ( sum_Inl @ A @ B @ X )
% 3.10/1.61 = ( sum_Inl @ A @ B @ Y ) )
% 3.10/1.61 => ( X = Y ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_124_Collect__subset,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A,P: A > $o] :
% 3.10/1.61 ( ord_less_eq @ ( set @ A )
% 3.10/1.61 @ ( collect @ A
% 3.10/1.61 @ ^ [X2: A] :
% 3.10/1.61 ( ( member @ A @ X2 @ A2 )
% 3.10/1.61 & ( P @ X2 ) ) )
% 3.10/1.61 @ A2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_125_less__eq__set__def,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 3.10/1.61 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.10/1.61 ( ord_less_eq @ ( A > $o )
% 3.10/1.61 @ ^ [X2: A] : ( member @ A @ X2 @ A6 )
% 3.10/1.61 @ ^ [X2: A] : ( member @ A @ X2 @ B6 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_126_sterm__determines__frechet,axiom,
% 3.10/1.61 ! [A1: $tType,B1: $tType,B22: $tType,A22: $tType,C: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ A22 )
% 3.10/1.61 & ( finite_finite @ B22 )
% 3.10/1.61 & ( finite_finite @ B1 )
% 3.10/1.61 & ( finite_finite @ A1 ) )
% 3.10/1.61 => ! [I3: denota1663640101rp_ext @ A1 @ B1 @ C @ product_unit,J: denota1663640101rp_ext @ A22 @ B22 @ C @ product_unit,Theta_12: trm @ A1 @ C,Theta_22: trm @ A22 @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C )] :
% 3.10/1.61 ( ( denota2077489681interp @ A1 @ B1 @ C @ I3 )
% 3.10/1.61 => ( ( denota2077489681interp @ A22 @ B22 @ C @ J )
% 3.10/1.61 => ( ( dfree @ A1 @ C @ Theta_12 )
% 3.10/1.61 => ( ( dfree @ A22 @ C @ Theta_22 )
% 3.10/1.61 => ( ( ( denota126604975rm_sem @ A1 @ B1 @ C @ I3 @ Theta_12 )
% 3.10/1.61 = ( denota126604975rm_sem @ A22 @ B22 @ C @ J @ Theta_22 ) )
% 3.10/1.61 => ( ( denotational_frechet @ A1 @ B1 @ C @ I3 @ Theta_12 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 3.10/1.61 = ( denotational_frechet @ A22 @ B22 @ C @ J @ Theta_22 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_127_type__definition__good__interp,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ( 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 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_128_order__refl,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( preorder @ A )
% 3.10/1.61 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_129_old_Osum_Osimps_I7_J,axiom,
% 3.10/1.61 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A3: A] :
% 3.10/1.61 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A3 ) )
% 3.10/1.61 = ( F1 @ A3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_130_image2__def,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,C: $tType] :
% 3.10/1.61 ( ( bNF_Greatest_image2 @ C @ A @ B )
% 3.10/1.61 = ( ^ [A6: set @ C,F4: C > A,G4: C > B] :
% 3.10/1.61 ( collect @ ( product_prod @ A @ B )
% 3.10/1.61 @ ^ [Uu: product_prod @ A @ B] :
% 3.10/1.61 ? [A7: C] :
% 3.10/1.61 ( ( Uu
% 3.10/1.61 = ( product_Pair @ A @ B @ ( F4 @ A7 ) @ ( G4 @ A7 ) ) )
% 3.10/1.61 & ( member @ C @ A7 @ A6 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_131_predicate1I,axiom,
% 3.10/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.10/1.61 ( ! [X3: A] :
% 3.10/1.61 ( ( P @ X3 )
% 3.10/1.61 => ( Q @ X3 ) )
% 3.10/1.61 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_132_rev__predicate1D,axiom,
% 3.10/1.61 ! [A: $tType,P: A > $o,X: A,Q: A > $o] :
% 3.10/1.61 ( ( P @ X )
% 3.10/1.61 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 3.10/1.61 => ( Q @ X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_133_predicate1D,axiom,
% 3.10/1.61 ! [A: $tType,P: A > $o,Q: A > $o,X: A] :
% 3.10/1.61 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 3.10/1.61 => ( ( P @ X )
% 3.10/1.61 => ( Q @ X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_134_le__funD,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ord @ B )
% 3.10/1.61 => ! [F: A > B,G: A > B,X: A] :
% 3.10/1.61 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.10/1.61 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_135_le__funE,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ord @ B )
% 3.10/1.61 => ! [F: A > B,G: A > B,X: A] :
% 3.10/1.61 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.10/1.61 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_136_le__funI,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ord @ B )
% 3.10/1.61 => ! [F: A > B,G: A > B] :
% 3.10/1.61 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 3.10/1.61 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_137_le__fun__def,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ord @ B )
% 3.10/1.61 => ( ( ord_less_eq @ ( A > B ) )
% 3.10/1.61 = ( ^ [F4: A > B,G4: A > B] :
% 3.10/1.61 ! [X2: A] : ( ord_less_eq @ B @ ( F4 @ X2 ) @ ( G4 @ X2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_138_order__subst1,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType] :
% 3.10/1.61 ( ( ( order @ B )
% 3.10/1.61 & ( order @ A ) )
% 3.10/1.61 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 3.10/1.61 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 3.10/1.61 => ( ! [X3: B,Y3: B] :
% 3.10/1.61 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 3.10/1.61 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 3.10/1.61 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_139_order__subst2,axiom,
% 3.10/1.61 ! [A: $tType,C: $tType] :
% 3.10/1.61 ( ( ( order @ C )
% 3.10/1.61 & ( order @ A ) )
% 3.10/1.61 => ! [A3: A,B3: A,F: A > C,C3: C] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.10/1.61 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 3.10/1.61 => ( ! [X3: A,Y3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 3.10/1.61 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 3.10/1.61 => ( ord_less_eq @ C @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_140_ord__eq__le__subst,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType] :
% 3.10/1.61 ( ( ( ord @ B )
% 3.10/1.61 & ( ord @ A ) )
% 3.10/1.61 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 3.10/1.61 ( ( A3
% 3.10/1.61 = ( F @ B3 ) )
% 3.10/1.61 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 3.10/1.61 => ( ! [X3: B,Y3: B] :
% 3.10/1.61 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 3.10/1.61 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 3.10/1.61 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_141_ord__le__eq__subst,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType] :
% 3.10/1.61 ( ( ( ord @ B )
% 3.10/1.61 & ( ord @ A ) )
% 3.10/1.61 => ! [A3: A,B3: A,F: A > B,C3: B] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.10/1.61 => ( ( ( F @ B3 )
% 3.10/1.61 = C3 )
% 3.10/1.61 => ( ! [X3: A,Y3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 3.10/1.61 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 3.10/1.61 => ( ord_less_eq @ B @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_142_eq__iff,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.10/1.61 = ( ^ [X2: A,Y2: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.10/1.61 & ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_143_antisym,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [X: A,Y: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X @ Y )
% 3.10/1.61 => ( ( ord_less_eq @ A @ Y @ X )
% 3.10/1.61 => ( X = Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_144_linear,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ! [X: A,Y: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X @ Y )
% 3.10/1.61 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_145_eq__refl,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( preorder @ A )
% 3.10/1.61 => ! [X: A,Y: A] :
% 3.10/1.61 ( ( X = Y )
% 3.10/1.61 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_146_le__cases,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ! [X: A,Y: A] :
% 3.10/1.61 ( ~ ( ord_less_eq @ A @ X @ Y )
% 3.10/1.61 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_147_order_Otrans,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [A3: A,B3: A,C3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.10/1.61 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 3.10/1.61 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_148_le__cases3,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ! [X: A,Y: A,Z2: A] :
% 3.10/1.61 ( ( ( ord_less_eq @ A @ X @ Y )
% 3.10/1.61 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 3.10/1.61 => ( ( ( ord_less_eq @ A @ Y @ X )
% 3.10/1.61 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 3.10/1.61 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 3.10/1.61 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 3.10/1.61 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 3.10/1.61 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 3.10/1.61 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 3.10/1.61 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 3.10/1.61 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 3.10/1.61 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_149_antisym__conv,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [Y: A,X: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ Y @ X )
% 3.10/1.61 => ( ( ord_less_eq @ A @ X @ Y )
% 3.10/1.61 = ( X = Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_150_order__class_Oorder_Oeq__iff,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.10/1.61 = ( ^ [A7: A,B7: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A7 @ B7 )
% 3.10/1.61 & ( ord_less_eq @ A @ B7 @ A7 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_151_ord__eq__le__trans,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( ord @ A )
% 3.10/1.61 => ! [A3: A,B3: A,C3: A] :
% 3.10/1.61 ( ( A3 = B3 )
% 3.10/1.61 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 3.10/1.61 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_152_ord__le__eq__trans,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( ord @ A )
% 3.10/1.61 => ! [A3: A,B3: A,C3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.10/1.61 => ( ( B3 = C3 )
% 3.10/1.61 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_153_order__class_Oorder_Oantisym,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [A3: A,B3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.10/1.61 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 3.10/1.61 => ( A3 = B3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_154_order__trans,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( preorder @ A )
% 3.10/1.61 => ! [X: A,Y: A,Z2: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ X @ Y )
% 3.10/1.61 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 3.10/1.61 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_155_dual__order_Orefl,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_156_linorder__wlog,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ! [P: A > A > $o,A3: A,B3: A] :
% 3.10/1.61 ( ! [A5: A,B5: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ A5 @ B5 )
% 3.10/1.61 => ( P @ A5 @ B5 ) )
% 3.10/1.61 => ( ! [A5: A,B5: A] :
% 3.10/1.61 ( ( P @ B5 @ A5 )
% 3.10/1.61 => ( P @ A5 @ B5 ) )
% 3.10/1.61 => ( P @ A3 @ B3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_157_dual__order_Otrans,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [B3: A,A3: A,C3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ B3 @ A3 )
% 3.10/1.61 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 3.10/1.61 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_158_dual__order_Oeq__iff,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.10/1.61 = ( ^ [A7: A,B7: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ B7 @ A7 )
% 3.10/1.61 & ( ord_less_eq @ A @ A7 @ B7 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_159_dual__order_Oantisym,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order @ A )
% 3.10/1.61 => ! [B3: A,A3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ B3 @ A3 )
% 3.10/1.61 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.10/1.61 => ( A3 = B3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_160_image2__eqI,axiom,
% 3.10/1.61 ! [A: $tType,C: $tType,B: $tType,B3: A,F: B > A,X: B,C3: C,G: B > C,A2: set @ B] :
% 3.10/1.61 ( ( B3
% 3.10/1.61 = ( F @ X ) )
% 3.10/1.61 => ( ( C3
% 3.10/1.61 = ( G @ X ) )
% 3.10/1.61 => ( ( member @ B @ X @ A2 )
% 3.10/1.61 => ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ B3 @ C3 ) @ ( bNF_Greatest_image2 @ B @ A @ C @ A2 @ F @ G ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_161_coincidence__sterm_H,axiom,
% 3.10/1.61 ! [A: $tType,C: $tType,B: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ A ) )
% 3.10/1.61 => ! [Theta: trm @ A @ B,Nu: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),I3: denota1663640101rp_ext @ A @ C @ B @ product_unit,J: denota1663640101rp_ext @ A @ C @ B @ product_unit] :
% 3.10/1.61 ( ( dfree @ A @ B @ Theta )
% 3.10/1.61 => ( ( denotational_Vagree @ B @ Nu @ Nu2 @ ( static_FVT @ A @ B @ Theta ) )
% 3.10/1.61 => ( ( denotational_Iagree @ A @ C @ B @ I3 @ J
% 3.10/1.61 @ ( collect @ ( sum_sum @ A @ ( sum_sum @ C @ B ) )
% 3.10/1.61 @ ^ [Uu: sum_sum @ A @ ( sum_sum @ C @ B )] :
% 3.10/1.61 ? [X2: A] :
% 3.10/1.61 ( ( Uu
% 3.10/1.61 = ( sum_Inl @ A @ ( sum_sum @ C @ B ) @ X2 ) )
% 3.10/1.61 & ( member @ A @ X2 @ ( static_SIGT @ A @ B @ Theta ) ) ) ) )
% 3.10/1.61 => ( ( denota126604975rm_sem @ A @ C @ B @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu ) )
% 3.10/1.61 = ( denota126604975rm_sem @ A @ C @ B @ J @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu2 ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_162_coincidence__sterm,axiom,
% 3.10/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ B ) )
% 3.10/1.61 => ! [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,I3: denota1663640101rp_ext @ B @ C @ A @ product_unit] :
% 3.10/1.61 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ Theta ) )
% 3.10/1.61 => ( ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu ) )
% 3.10/1.61 = ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_163_pred__subset__eq,axiom,
% 3.10/1.61 ! [A: $tType,R3: set @ A,S5: set @ A] :
% 3.10/1.61 ( ( ord_less_eq @ ( A > $o )
% 3.10/1.61 @ ^ [X2: A] : ( member @ A @ X2 @ R3 )
% 3.10/1.61 @ ^ [X2: A] : ( member @ A @ X2 @ S5 ) )
% 3.10/1.61 = ( ord_less_eq @ ( set @ A ) @ R3 @ S5 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_164_sterm__continuous_H,axiom,
% 3.10/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ B ) )
% 3.10/1.61 => ! [I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C,S5: set @ ( finite_Cartesian_vec @ real @ C )] :
% 3.10/1.61 ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta )
% 3.10/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ S5 @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_165_agree__func__fvt,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( finite_finite @ A )
% 3.10/1.61 => ! [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 ),F: B,Args: A > ( trm @ B @ A ),I: A] :
% 3.10/1.61 ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ ( function @ B @ A @ F @ Args ) ) )
% 3.10/1.61 => ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ ( Args @ I ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_166_subrelI,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S6: set @ ( product_prod @ A @ B )] :
% 3.10/1.61 ( ! [X3: A,Y3: B] :
% 3.10/1.61 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R4 )
% 3.10/1.61 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S6 ) )
% 3.10/1.61 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R4 @ S6 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_167_FVDiff__sub,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,F: trm @ B @ A] : ( ord_less_eq @ ( set @ ( sum_sum @ A @ A ) ) @ ( static_FVT @ B @ A @ F ) @ ( static_FVDiff @ B @ A @ F ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_168_pred__equals__eq2,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S5: set @ ( product_prod @ A @ B )] :
% 3.10/1.61 ( ( ( ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ R3 ) )
% 3.10/1.61 = ( ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ S5 ) ) )
% 3.10/1.61 = ( R3 = S5 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_169_pred__subset__eq2,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S5: set @ ( product_prod @ A @ B )] :
% 3.10/1.61 ( ( ord_less_eq @ ( A > B > $o )
% 3.10/1.61 @ ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ R3 )
% 3.10/1.61 @ ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ S5 ) )
% 3.10/1.61 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S5 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_170_sterm__continuous,axiom,
% 3.10/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ B ) )
% 3.10/1.61 => ! [I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C] :
% 3.10/1.61 ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta )
% 3.10/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ C ) ) ) @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_171_ids_Ocoincidence__sterm_H,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,A: $tType,C: $tType,B: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Theta: trm @ A @ B,Nu: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ),I3: denota1663640101rp_ext @ A @ C @ B @ product_unit,J: denota1663640101rp_ext @ A @ C @ B @ product_unit] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( dfree @ A @ B @ Theta )
% 3.10/1.61 => ( ( denotational_Vagree @ B @ Nu @ Nu2 @ ( static_FVT @ A @ B @ Theta ) )
% 3.10/1.61 => ( ( denotational_Iagree @ A @ C @ B @ I3 @ J
% 3.10/1.61 @ ( collect @ ( sum_sum @ A @ ( sum_sum @ C @ B ) )
% 3.10/1.61 @ ^ [Uu: sum_sum @ A @ ( sum_sum @ C @ B )] :
% 3.10/1.61 ? [X2: A] :
% 3.10/1.61 ( ( Uu
% 3.10/1.61 = ( sum_Inl @ A @ ( sum_sum @ C @ B ) @ X2 ) )
% 3.10/1.61 & ( member @ A @ X2 @ ( static_SIGT @ A @ B @ Theta ) ) ) ) )
% 3.10/1.61 => ( ( denota126604975rm_sem @ A @ C @ B @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu ) )
% 3.10/1.61 = ( denota126604975rm_sem @ A @ C @ B @ J @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ B ) @ ( finite_Cartesian_vec @ real @ B ) @ Nu2 ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_172_continuous__on__cases__le,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ B ) )
% 3.10/1.61 => ! [S6: set @ A,H: A > real,A3: real,F: A > B,G: A > B] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ B
% 3.10/1.61 @ ( collect @ A
% 3.10/1.61 @ ^ [T3: A] :
% 3.10/1.61 ( ( member @ A @ T3 @ S6 )
% 3.10/1.61 & ( ord_less_eq @ real @ ( H @ T3 ) @ A3 ) ) )
% 3.10/1.61 @ F )
% 3.10/1.61 => ( ( topolo2071040574ous_on @ A @ B
% 3.10/1.61 @ ( collect @ A
% 3.10/1.61 @ ^ [T3: A] :
% 3.10/1.61 ( ( member @ A @ T3 @ S6 )
% 3.10/1.61 & ( ord_less_eq @ real @ A3 @ ( H @ T3 ) ) ) )
% 3.10/1.61 @ G )
% 3.10/1.61 => ( ( topolo2071040574ous_on @ A @ real @ S6 @ H )
% 3.10/1.61 => ( ! [T6: A] :
% 3.10/1.61 ( ( member @ A @ T6 @ S6 )
% 3.10/1.61 => ( ( ( H @ T6 )
% 3.10/1.61 = A3 )
% 3.10/1.61 => ( ( F @ T6 )
% 3.10/1.61 = ( G @ T6 ) ) ) )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ B @ S6
% 3.10/1.61 @ ^ [T3: A] : ( if @ B @ ( ord_less_eq @ real @ ( H @ T3 ) @ A3 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_173_top__apply,axiom,
% 3.10/1.61 ! [C: $tType,D2: $tType] :
% 3.10/1.61 ( ( top @ C )
% 3.10/1.61 => ( ( top_top @ ( D2 > C ) )
% 3.10/1.61 = ( ^ [X2: D2] : ( top_top @ C ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_174_UNIV__I,axiom,
% 3.10/1.61 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_175_predicate2I,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 3.10/1.61 ( ! [X3: A,Y3: B] :
% 3.10/1.61 ( ( P @ X3 @ Y3 )
% 3.10/1.61 => ( Q @ X3 @ Y3 ) )
% 3.10/1.61 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_176_fst__top,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( top @ A )
% 3.10/1.61 & ( top @ B ) )
% 3.10/1.61 => ( ( product_fst @ A @ B @ ( top_top @ ( product_prod @ A @ B ) ) )
% 3.10/1.61 = ( top_top @ A ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_177_snd__top,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( top @ A )
% 3.10/1.61 & ( top @ B ) )
% 3.10/1.61 => ( ( product_snd @ B @ A @ ( top_top @ ( product_prod @ B @ A ) ) )
% 3.10/1.61 = ( top_top @ A ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_178_continuous__on__cases__1,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( topolo503727757_space @ A )
% 3.10/1.61 => ! [S6: set @ real,A3: real,F: real > A,G: real > A] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ real @ A
% 3.10/1.61 @ ( collect @ real
% 3.10/1.61 @ ^ [T3: real] :
% 3.10/1.61 ( ( member @ real @ T3 @ S6 )
% 3.10/1.61 & ( ord_less_eq @ real @ T3 @ A3 ) ) )
% 3.10/1.61 @ F )
% 3.10/1.61 => ( ( topolo2071040574ous_on @ real @ A
% 3.10/1.61 @ ( collect @ real
% 3.10/1.61 @ ^ [T3: real] :
% 3.10/1.61 ( ( member @ real @ T3 @ S6 )
% 3.10/1.61 & ( ord_less_eq @ real @ A3 @ T3 ) ) )
% 3.10/1.61 @ G )
% 3.10/1.61 => ( ( ( member @ real @ A3 @ S6 )
% 3.10/1.61 => ( ( F @ A3 )
% 3.10/1.61 = ( G @ A3 ) ) )
% 3.10/1.61 => ( topolo2071040574ous_on @ real @ A @ S6
% 3.10/1.61 @ ^ [T3: real] : ( if @ A @ ( ord_less_eq @ real @ T3 @ A3 ) @ ( F @ T3 ) @ ( G @ T3 ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_179_top_Oextremum__uniqueI,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order_top @ A )
% 3.10/1.61 => ! [A3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 3.10/1.61 => ( A3
% 3.10/1.61 = ( top_top @ A ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_180_top_Oextremum__unique,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order_top @ A )
% 3.10/1.61 => ! [A3: A] :
% 3.10/1.61 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 3.10/1.61 = ( A3
% 3.10/1.61 = ( top_top @ A ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_181_top__greatest,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( order_top @ A )
% 3.10/1.61 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ ( top_top @ A ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_182_rev__predicate2D,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 3.10/1.61 ( ( P @ X @ Y )
% 3.10/1.61 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 3.10/1.61 => ( Q @ X @ Y ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_183_predicate2D,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 3.10/1.61 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 3.10/1.61 => ( ( P @ X @ Y )
% 3.10/1.61 => ( Q @ X @ Y ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_184_subset__UNIV,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_185_ids_Oseq__sem_Ocases,axiom,
% 3.10/1.61 ! [Sz: $tType,Sc: $tType,Sf: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: product_prod @ ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) )] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ~ ! [I2: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,S: product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) )] :
% 3.10/1.61 ( X
% 3.10/1.61 != ( product_Pair @ ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) @ ( product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) ) @ I2 @ S ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_186_UNIV__def,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( top_top @ ( set @ A ) )
% 3.10/1.61 = ( collect @ A
% 3.10/1.61 @ ^ [X2: A] : $true ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_187_UNIV__witness,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_188_UNIV__eq__I,axiom,
% 3.10/1.61 ! [A: $tType,A2: set @ A] :
% 3.10/1.61 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 3.10/1.61 => ( ( top_top @ ( set @ A ) )
% 3.10/1.61 = A2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_189_ids_Osingleton_Oinduct,axiom,
% 3.10/1.61 ! [Sf: $tType,Sc: $tType,A: $tType,Sz: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( trm @ A @ Sz ) > Sz > $o,A0: trm @ A @ Sz,A12: Sz] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ! [T6: trm @ A @ Sz,X_1: Sz] : ( P @ T6 @ X_1 )
% 3.10/1.61 => ( P @ A0 @ A12 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_190_ids_Oseq__sem_Oinduct,axiom,
% 3.10/1.61 ! [Sz: $tType,Sc: $tType,Sf: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) > ( product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) ) > $o,A0: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,A12: product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) )] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ! [I2: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,X_1: product_prod @ ( list @ ( formula @ Sf @ Sc @ Sz ) ) @ ( list @ ( formula @ Sf @ Sc @ Sz ) )] : ( P @ I2 @ X_1 )
% 3.10/1.61 => ( P @ A0 @ A12 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_191_ids_Osingleton_Ocases,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,A: $tType,Sz: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: product_prod @ ( trm @ A @ Sz ) @ Sz] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ~ ! [T6: trm @ A @ Sz,I4: Sz] :
% 3.10/1.61 ( X
% 3.10/1.61 != ( product_Pair @ ( trm @ A @ Sz ) @ Sz @ T6 @ I4 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_192_top__prod__def,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType] :
% 3.10/1.61 ( ( ( top @ B )
% 3.10/1.61 & ( top @ A ) )
% 3.10/1.61 => ( ( top_top @ ( product_prod @ A @ B ) )
% 3.10/1.61 = ( product_Pair @ A @ B @ ( top_top @ A ) @ ( top_top @ B ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_193_ids_OP__def,axiom,
% 3.10/1.61 ! [Sf: $tType,Sz: $tType,Sc: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P2: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( p @ Sc @ Sf @ Sz @ P2 )
% 3.10/1.61 = ( predicational @ Sc @ Sf @ Sz @ P2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_194_ids_Ocoincidence__sterm,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,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,I3: denota1663640101rp_ext @ B @ C @ A @ product_unit] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( denotational_Vagree @ A @ Nu @ Nu2 @ ( static_FVT @ B @ A @ Theta ) )
% 3.10/1.61 => ( ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu ) )
% 3.10/1.61 = ( denota126604975rm_sem @ B @ C @ A @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ Nu2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_195_ids_Of0__def,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,F: Sf] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( f0 @ Sf @ Sz @ F )
% 3.10/1.61 = ( function @ Sf @ Sz @ F @ ( empty @ Sz @ Sf ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_196_ids_Ocoincidence__frechet,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,A: $tType,C: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Theta: trm @ A @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),Nu2: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ),I3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta )
% 3.10/1.61 => ( ( denotational_Vagree @ C @ Nu @ Nu2 @ ( static_FVDiff @ A @ C @ Theta ) )
% 3.10/1.61 => ( ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 3.10/1.61 = ( denotational_frechet @ A @ B @ C @ I3 @ Theta @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu2 ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_197_frechet__continuous,axiom,
% 3.10/1.61 ! [I3: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Theta: trm @ sf @ sz] :
% 3.10/1.61 ( ( denota2077489681interp @ sf @ sc @ sz @ I3 )
% 3.10/1.61 => ( ( dfree @ sf @ sz @ Theta )
% 3.10/1.61 => ( 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 @ I3 ) @ ( frechet_simple_term @ sf @ sz @ Theta ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_198_ids_Osterm__determines__frechet,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,A1: $tType,B1: $tType,B22: $tType,A22: $tType,C: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ A22 )
% 3.10/1.61 & ( finite_finite @ B22 )
% 3.10/1.61 & ( finite_finite @ B1 )
% 3.10/1.61 & ( finite_finite @ A1 )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ A1 @ B1 @ C @ product_unit,J: denota1663640101rp_ext @ A22 @ B22 @ C @ product_unit,Theta_12: trm @ A1 @ C,Theta_22: trm @ A22 @ C,Nu: product_prod @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C )] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( denota2077489681interp @ A1 @ B1 @ C @ I3 )
% 3.10/1.61 => ( ( denota2077489681interp @ A22 @ B22 @ C @ J )
% 3.10/1.61 => ( ( dfree @ A1 @ C @ Theta_12 )
% 3.10/1.61 => ( ( dfree @ A22 @ C @ Theta_22 )
% 3.10/1.61 => ( ( ( denota126604975rm_sem @ A1 @ B1 @ C @ I3 @ Theta_12 )
% 3.10/1.61 = ( denota126604975rm_sem @ A22 @ B22 @ C @ J @ Theta_22 ) )
% 3.10/1.61 => ( ( denotational_frechet @ A1 @ B1 @ C @ I3 @ Theta_12 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) )
% 3.10/1.61 = ( denotational_frechet @ A22 @ B22 @ C @ J @ Theta_22 @ ( product_fst @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) @ ( product_snd @ ( finite_Cartesian_vec @ real @ C ) @ ( finite_Cartesian_vec @ real @ C ) @ Nu ) ) ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_199_ids_Osterm__continuous,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta )
% 3.10/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ C ) ) ) @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_200_top__empty__eq2,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( top_top @ ( A > B > $o ) )
% 3.10/1.61 = ( ^ [X2: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y2 ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_201_top__set__def,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( top_top @ ( set @ A ) )
% 3.10/1.61 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_202_Vagree__univ,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( finite_finite @ A )
% 3.10/1.61 => ! [A3: finite_Cartesian_vec @ real @ A,B3: finite_Cartesian_vec @ real @ A,C3: finite_Cartesian_vec @ real @ A,D4: finite_Cartesian_vec @ real @ A] :
% 3.10/1.61 ( ( denotational_Vagree @ A @ ( product_Pair @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ A3 @ B3 ) @ ( product_Pair @ ( finite_Cartesian_vec @ real @ A ) @ ( finite_Cartesian_vec @ real @ A ) @ C3 @ D4 ) @ ( top_top @ ( set @ ( sum_sum @ A @ A ) ) ) )
% 3.10/1.61 => ( ( A3 = C3 )
% 3.10/1.61 & ( B3 = D4 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_203_agree__UNIV__eq,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( finite_finite @ A )
% 3.10/1.61 => ! [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 )] :
% 3.10/1.61 ( ( denotational_Vagree @ A @ Nu @ Omega @ ( top_top @ ( set @ ( sum_sum @ A @ A ) ) ) )
% 3.10/1.61 => ( Nu = Omega ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_204_ids_Oraw__term__inject,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C,Y: frechet_strm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( ( frechet_raw_term @ A @ C @ X )
% 3.10/1.61 = ( frechet_raw_term @ A @ C @ Y ) )
% 3.10/1.61 = ( X = Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_205_ids_Oraw__interp__inject,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C,Y: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( ( freche229654227interp @ A @ B @ C @ X )
% 3.10/1.61 = ( freche229654227interp @ A @ B @ C @ Y ) )
% 3.10/1.61 = ( X = Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_206_ids_Ofrechet__continuous,axiom,
% 3.10/1.61 ! [Sc: $tType,Sz: $tType,Sf: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,Theta: trm @ Sf @ Sz] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( denota2077489681interp @ Sf @ Sc @ Sz @ I3 )
% 3.10/1.61 => ( ( dfree @ Sf @ Sz @ Theta )
% 3.10/1.61 => ( 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 @ I3 ) @ ( frechet_simple_term @ Sf @ Sz @ Theta ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_207_ids_Oraw__interp__inverse,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( freche227871258interp @ A @ B @ C @ ( freche229654227interp @ A @ B @ C @ X ) )
% 3.10/1.61 = X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_208_ids_Oraw__term__inverse,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( frechet_simple_term @ A @ C @ ( frechet_raw_term @ A @ C @ X ) )
% 3.10/1.61 = X ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_209_ids_Oraw__term,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( member @ ( trm @ A @ C ) @ ( frechet_raw_term @ A @ C @ X ) @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_210_ids_Oraw__term__cases,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: trm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.61 => ~ ! [X3: frechet_strm @ A @ C] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( frechet_raw_term @ A @ C @ X3 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_211_ids_Oraw__term__induct,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: trm @ A @ C,P: ( trm @ A @ C ) > $o] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.61 => ( ! [X3: frechet_strm @ A @ C] : ( P @ ( frechet_raw_term @ A @ C @ X3 ) )
% 3.10/1.61 => ( P @ Y ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_212_ids_Osimple__term__cases,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_strm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ~ ! [Y3: trm @ A @ C] :
% 3.10/1.61 ( ( X
% 3.10/1.61 = ( frechet_simple_term @ A @ C @ Y3 ) )
% 3.10/1.61 => ~ ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_213_ids_Osimple__term__induct,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( frechet_strm @ A @ C ) > $o,X: frechet_strm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ! [Y3: trm @ A @ C] :
% 3.10/1.61 ( ( member @ ( trm @ A @ C ) @ Y3 @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.61 => ( P @ ( frechet_simple_term @ A @ C @ Y3 ) ) )
% 3.10/1.61 => ( P @ X ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_214_ids_Osimple__term__inject,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: trm @ A @ C,Y: trm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( trm @ A @ C ) @ X @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.61 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.61 => ( ( ( frechet_simple_term @ A @ C @ X )
% 3.10/1.61 = ( frechet_simple_term @ A @ C @ Y ) )
% 3.10/1.61 = ( X = Y ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_215_ids_Oraw__interp__induct,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit,P: ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) > $o] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ! [X3: frechet_good_interp @ A @ B @ C] : ( P @ ( freche229654227interp @ A @ B @ C @ X3 ) )
% 3.10/1.61 => ( P @ Y ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_216_ids_Oraw__interp__cases,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ~ ! [X3: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( freche229654227interp @ A @ B @ C @ X3 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_217_ids_Oraw__interp,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( freche229654227interp @ A @ B @ C @ X ) @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_218_ids_Ogood__interp__cases,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ~ ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( X
% 3.10/1.61 = ( freche227871258interp @ A @ B @ C @ Y3 ) )
% 3.10/1.61 => ~ ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_219_ids_Ogood__interp__induct,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,P: ( frechet_good_interp @ A @ B @ C ) > $o,X: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ! [Y3: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y3 @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( P @ ( freche227871258interp @ A @ B @ C @ Y3 ) ) )
% 3.10/1.61 => ( P @ X ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_220_ids_Ogood__interp__inject,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,X: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ X @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ( ( freche227871258interp @ A @ B @ C @ X )
% 3.10/1.61 = ( freche227871258interp @ A @ B @ C @ Y ) )
% 3.10/1.61 = ( X = Y ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_221_ids_Ocr__strm__def,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( frechet_cr_strm @ A @ B )
% 3.10/1.61 = ( ^ [X2: trm @ A @ B,Y2: frechet_strm @ A @ B] :
% 3.10/1.61 ( X2
% 3.10/1.61 = ( frechet_raw_term @ A @ B @ Y2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_222_ids_Ocr__good__interp__def,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( freche457001096interp @ A @ B @ C )
% 3.10/1.61 = ( ^ [X2: denota1663640101rp_ext @ A @ B @ C @ product_unit,Y2: frechet_good_interp @ A @ B @ C] :
% 3.10/1.61 ( X2
% 3.10/1.61 = ( freche229654227interp @ A @ B @ C @ Y2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_223_ids_Osimple__term__inverse,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: trm @ A @ C] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( trm @ A @ C ) @ Y @ ( collect @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) )
% 3.10/1.61 => ( ( frechet_raw_term @ A @ C @ ( frechet_simple_term @ A @ C @ Y ) )
% 3.10/1.61 = Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_224_ids_Ogood__interp__inverse,axiom,
% 3.10/1.61 ! [Sz: $tType,Sf: $tType,Sc: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Y: denota1663640101rp_ext @ A @ B @ C @ product_unit] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( member @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ Y @ ( collect @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) )
% 3.10/1.61 => ( ( freche229654227interp @ A @ B @ C @ ( freche227871258interp @ A @ B @ C @ Y ) )
% 3.10/1.61 = Y ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_225_ids_Osterm__continuous_H,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ A @ B @ C @ product_unit,Theta: trm @ A @ C,S5: set @ ( finite_Cartesian_vec @ real @ C )] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( denota2077489681interp @ A @ B @ C @ I3 )
% 3.10/1.61 => ( ( dfree @ A @ C @ Theta )
% 3.10/1.61 => ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ C ) @ real @ S5 @ ( denota126604975rm_sem @ A @ B @ C @ I3 @ Theta ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_226_ids_Otype__definition__strm,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( 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 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_227_ids_Otype__definition__good__interp,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( 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 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_228_frechet__blin,axiom,
% 3.10/1.61 ! [I3: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Theta: trm @ sf @ sz] :
% 3.10/1.61 ( ( denota2077489681interp @ sf @ sc @ sz @ I3 )
% 3.10/1.61 => ( ( dfree @ sf @ sz @ Theta )
% 3.10/1.61 => ( ( ^ [V2: finite_Cartesian_vec @ real @ sz] : ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real @ ( denotational_frechet @ sf @ sc @ sz @ I3 @ Theta @ V2 ) ) )
% 3.10/1.61 = ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ I3 ) @ ( frechet_simple_term @ sf @ sz @ Theta ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_229_continuous__on__snd,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ B )
% 3.10/1.61 & ( topolo503727757_space @ C ) )
% 3.10/1.61 => ! [S6: set @ A,F: A > ( product_prod @ B @ C )] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S6 @ F )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ C @ S6
% 3.10/1.61 @ ^ [X2: A] : ( product_snd @ B @ C @ ( F @ X2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_230_top1I,axiom,
% 3.10/1.61 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_231_top2I,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,X: A,Y: B] : ( top_top @ ( A > B > $o ) @ X @ Y ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_232_continuous__on__const,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ B ) )
% 3.10/1.61 => ! [S6: set @ A,C3: B] :
% 3.10/1.61 ( topolo2071040574ous_on @ A @ B @ S6
% 3.10/1.61 @ ^ [X2: A] : C3 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_233_continuous__on__id,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( topolo503727757_space @ A )
% 3.10/1.61 => ! [S6: set @ A] :
% 3.10/1.61 ( topolo2071040574ous_on @ A @ A @ S6
% 3.10/1.61 @ ^ [X2: A] : X2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_234_continuous__on__subset,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ B ) )
% 3.10/1.61 => ! [S6: set @ A,F: A > B,T4: set @ A] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ B @ S6 @ F )
% 3.10/1.61 => ( ( ord_less_eq @ ( set @ A ) @ T4 @ S6 )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ B @ T4 @ F ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_235_continuous__on__Pair,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ B )
% 3.10/1.61 & ( topolo503727757_space @ C ) )
% 3.10/1.61 => ! [S6: set @ A,F: A > B,G: A > C] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ B @ S6 @ F )
% 3.10/1.61 => ( ( topolo2071040574ous_on @ A @ C @ S6 @ G )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S6
% 3.10/1.61 @ ^ [X2: A] : ( product_Pair @ B @ C @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_236_ids_Ofrechet__blin,axiom,
% 3.10/1.61 ! [Sc: $tType,Sz: $tType,Sf: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,I3: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,Theta: trm @ Sf @ Sz] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( denota2077489681interp @ Sf @ Sc @ Sz @ I3 )
% 3.10/1.61 => ( ( dfree @ Sf @ Sz @ Theta )
% 3.10/1.61 => ( ( ^ [V2: finite_Cartesian_vec @ real @ Sz] : ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ Sz ) @ real @ ( denotational_frechet @ Sf @ Sc @ Sz @ I3 @ Theta @ V2 ) ) )
% 3.10/1.61 = ( frechet_blin_frechet @ Sf @ Sc @ Sz @ ( freche227871258interp @ Sf @ Sc @ Sz @ I3 ) @ ( frechet_simple_term @ Sf @ Sz @ Theta ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_237_continuous__on__fst,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ B )
% 3.10/1.61 & ( topolo503727757_space @ C ) )
% 3.10/1.61 => ! [S6: set @ A,F: A > ( product_prod @ B @ C )] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ ( product_prod @ B @ C ) @ S6 @ F )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ B @ S6
% 3.10/1.61 @ ^ [X2: A] : ( product_fst @ B @ C @ ( F @ X2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_238_continuous__on__product__then__coordinatewise__UNIV,axiom,
% 3.10/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ C ) )
% 3.10/1.61 => ! [F: A > B > C,I: B] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ ( top_top @ ( set @ A ) ) @ F )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ C @ ( top_top @ ( set @ A ) )
% 3.10/1.61 @ ^ [X2: A] : ( F @ X2 @ I ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_239_blin__frechet_Oabs__eq,axiom,
% 3.10/1.61 ! [Xb: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,Xa: trm @ sf @ sz,X: finite_Cartesian_vec @ real @ sz] :
% 3.10/1.61 ( ( bNF_eq_onp @ ( denota1663640101rp_ext @ sf @ sc @ sz @ product_unit ) @ ( denota2077489681interp @ sf @ sc @ sz ) @ Xb @ Xb )
% 3.10/1.61 => ( ( bNF_eq_onp @ ( trm @ sf @ sz ) @ ( dfree @ sf @ sz ) @ Xa @ Xa )
% 3.10/1.61 => ( ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ Xb ) @ ( frechet_simple_term @ sf @ sz @ Xa ) @ X )
% 3.10/1.61 = ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real @ ( denotational_frechet @ sf @ sc @ sz @ Xb @ Xa @ X ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_240_ids_Oblin__frechet_Oabs__eq,axiom,
% 3.10/1.61 ! [Sf: $tType,Sc: $tType,Sz: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sc )
% 3.10/1.61 & ( finite_finite @ Sf ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc,Xb: denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit,Xa: trm @ Sf @ Sz,X: finite_Cartesian_vec @ real @ Sz] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( ( bNF_eq_onp @ ( denota1663640101rp_ext @ Sf @ Sc @ Sz @ product_unit ) @ ( denota2077489681interp @ Sf @ Sc @ Sz ) @ Xb @ Xb )
% 3.10/1.61 => ( ( bNF_eq_onp @ ( trm @ Sf @ Sz ) @ ( dfree @ Sf @ Sz ) @ Xa @ Xa )
% 3.10/1.61 => ( ( frechet_blin_frechet @ Sf @ Sc @ Sz @ ( freche227871258interp @ Sf @ Sc @ Sz @ Xb ) @ ( frechet_simple_term @ Sf @ Sz @ Xa ) @ X )
% 3.10/1.61 = ( bounde688532126linfun @ ( finite_Cartesian_vec @ real @ Sz ) @ real @ ( denotational_frechet @ Sf @ Sc @ Sz @ Xb @ Xa @ X ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_241_continuous__on__coordinatewise__then__product,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ C ) )
% 3.10/1.61 => ! [S5: set @ A,F: A > B > C] :
% 3.10/1.61 ( ! [I4: B] :
% 3.10/1.61 ( topolo2071040574ous_on @ A @ C @ S5
% 3.10/1.61 @ ^ [X2: A] : ( F @ X2 @ I4 ) )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ ( B > C ) @ S5 @ F ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_242_continuous__on__product__then__coordinatewise,axiom,
% 3.10/1.61 ! [B: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A )
% 3.10/1.61 & ( topolo503727757_space @ C ) )
% 3.10/1.61 => ! [S5: set @ A,F: A > B > C,I: B] :
% 3.10/1.61 ( ( topolo2071040574ous_on @ A @ ( B > C ) @ S5 @ F )
% 3.10/1.61 => ( topolo2071040574ous_on @ A @ C @ S5
% 3.10/1.61 @ ^ [X2: A] : ( F @ X2 @ I ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_243_Quotient__good__interp,axiom,
% 3.10/1.61 ! [C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C ) )
% 3.10/1.61 => ( quotient @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( bNF_eq_onp @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) @ ( freche227871258interp @ A @ B @ C ) @ ( freche229654227interp @ A @ B @ C ) @ ( freche457001096interp @ A @ B @ C ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_244_Quotient__strm,axiom,
% 3.10/1.61 ! [C: $tType,A: $tType] : ( quotient @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( bNF_eq_onp @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) @ ( frechet_simple_term @ A @ C ) @ ( frechet_raw_term @ A @ C ) @ ( frechet_cr_strm @ A @ C ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_245_ids_OQuotient__strm,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( quotient @ ( trm @ A @ C ) @ ( frechet_strm @ A @ C ) @ ( bNF_eq_onp @ ( trm @ A @ C ) @ ( dfree @ A @ C ) ) @ ( frechet_simple_term @ A @ C ) @ ( frechet_raw_term @ A @ C ) @ ( frechet_cr_strm @ A @ C ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_246_ids_OQuotient__good__interp,axiom,
% 3.10/1.61 ! [Sc: $tType,Sf: $tType,Sz: $tType,C: $tType,B: $tType,A: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A )
% 3.10/1.61 & ( finite_finite @ B )
% 3.10/1.61 & ( finite_finite @ C )
% 3.10/1.61 & ( finite_finite @ Sz )
% 3.10/1.61 & ( linorder @ Sz )
% 3.10/1.61 & ( finite_finite @ Sf )
% 3.10/1.61 & ( finite_finite @ Sc ) )
% 3.10/1.61 => ! [Vid1: Sz,Vid2: Sz,Vid3: Sz,Fid1: Sf,Fid2: Sf,Fid3: Sf,Pid1: Sc,Pid2: Sc,Pid3: Sc,Pid4: Sc] :
% 3.10/1.61 ( ( ids @ Sz @ Sf @ Sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.10/1.61 => ( quotient @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( frechet_good_interp @ A @ B @ C ) @ ( bNF_eq_onp @ ( denota1663640101rp_ext @ A @ B @ C @ product_unit ) @ ( denota2077489681interp @ A @ B @ C ) ) @ ( freche227871258interp @ A @ B @ C ) @ ( freche229654227interp @ A @ B @ C ) @ ( freche457001096interp @ A @ B @ C ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_247_typedef__to__Quotient,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,S5: set @ B,T7: B > A > $o] :
% 3.10/1.61 ( ( type_definition @ A @ B @ Rep @ Abs @ S5 )
% 3.10/1.61 => ( ( T7
% 3.10/1.61 = ( ^ [X2: B,Y2: A] :
% 3.10/1.61 ( X2
% 3.10/1.61 = ( Rep @ Y2 ) ) ) )
% 3.10/1.61 => ( quotient @ B @ A
% 3.10/1.61 @ ( bNF_eq_onp @ B
% 3.10/1.61 @ ^ [X2: B] : ( member @ B @ X2 @ S5 ) )
% 3.10/1.61 @ Abs
% 3.10/1.61 @ Rep
% 3.10/1.61 @ T7 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_248_open__typedef__to__Quotient,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,P: B > $o,T7: B > A > $o] :
% 3.10/1.61 ( ( type_definition @ A @ B @ Rep @ Abs @ ( collect @ B @ P ) )
% 3.10/1.61 => ( ( T7
% 3.10/1.61 = ( ^ [X2: B,Y2: A] :
% 3.10/1.61 ( X2
% 3.10/1.61 = ( Rep @ Y2 ) ) ) )
% 3.10/1.61 => ( quotient @ B @ A @ ( bNF_eq_onp @ B @ P ) @ Abs @ Rep @ T7 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_249_QuotientI,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,Abs: B > A,Rep: A > B,R3: B > B > $o,T7: B > A > $o] :
% 3.10/1.61 ( ! [A5: A] :
% 3.10/1.61 ( ( Abs @ ( Rep @ A5 ) )
% 3.10/1.61 = A5 )
% 3.10/1.61 => ( ! [A5: A] : ( R3 @ ( Rep @ A5 ) @ ( Rep @ A5 ) )
% 3.10/1.61 => ( ! [R2: B,S4: B] :
% 3.10/1.61 ( ( R3 @ R2 @ S4 )
% 3.10/1.61 = ( ( R3 @ R2 @ R2 )
% 3.10/1.61 & ( R3 @ S4 @ S4 )
% 3.10/1.61 & ( ( Abs @ R2 )
% 3.10/1.61 = ( Abs @ S4 ) ) ) )
% 3.10/1.61 => ( ( T7
% 3.10/1.61 = ( ^ [X2: B,Y2: A] :
% 3.10/1.61 ( ( R3 @ X2 @ X2 )
% 3.10/1.61 & ( ( Abs @ X2 )
% 3.10/1.61 = Y2 ) ) ) )
% 3.10/1.61 => ( quotient @ B @ A @ R3 @ Abs @ Rep @ T7 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_250_Quotient__def,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType] :
% 3.10/1.61 ( ( quotient @ A @ B )
% 3.10/1.61 = ( ^ [R5: A > A > $o,Abs2: A > B,Rep2: B > A,T8: A > B > $o] :
% 3.10/1.61 ( ! [A7: B] :
% 3.10/1.61 ( ( Abs2 @ ( Rep2 @ A7 ) )
% 3.10/1.61 = A7 )
% 3.10/1.61 & ! [A7: B] : ( R5 @ ( Rep2 @ A7 ) @ ( Rep2 @ A7 ) )
% 3.10/1.61 & ! [R6: A,S2: A] :
% 3.10/1.61 ( ( R5 @ R6 @ S2 )
% 3.10/1.61 = ( ( R5 @ R6 @ R6 )
% 3.10/1.61 & ( R5 @ S2 @ S2 )
% 3.10/1.61 & ( ( Abs2 @ R6 )
% 3.10/1.61 = ( Abs2 @ S2 ) ) ) )
% 3.10/1.61 & ( T8
% 3.10/1.61 = ( ^ [X2: A,Y2: B] :
% 3.10/1.61 ( ( R5 @ X2 @ X2 )
% 3.10/1.61 & ( ( Abs2 @ X2 )
% 3.10/1.61 = Y2 ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_251_Quotient__cr__rel,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,R3: A > A > $o,Abs: A > B,Rep: B > A,T7: A > B > $o] :
% 3.10/1.61 ( ( quotient @ A @ B @ R3 @ Abs @ Rep @ T7 )
% 3.10/1.61 => ( T7
% 3.10/1.61 = ( ^ [X2: A,Y2: B] :
% 3.10/1.61 ( ( R3 @ X2 @ X2 )
% 3.10/1.61 & ( ( Abs @ X2 )
% 3.10/1.61 = Y2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_252_eq__onp__le__eq,axiom,
% 3.10/1.61 ! [A: $tType,P: A > $o] :
% 3.10/1.61 ( ord_less_eq @ ( A > A > $o ) @ ( bNF_eq_onp @ A @ P )
% 3.10/1.61 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_253_Quotient__rep__abs__eq,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,R3: A > A > $o,Abs: A > B,Rep: B > A,T7: A > B > $o,T4: A] :
% 3.10/1.61 ( ( quotient @ A @ B @ R3 @ Abs @ Rep @ T7 )
% 3.10/1.61 => ( ( R3 @ T4 @ T4 )
% 3.10/1.61 => ( ( ord_less_eq @ ( A > A > $o ) @ R3
% 3.10/1.61 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.10/1.61 => ( ( Rep @ ( Abs @ T4 ) )
% 3.10/1.61 = T4 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_254_UNIV__typedef__to__Quotient,axiom,
% 3.10/1.61 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,T7: B > A > $o] :
% 3.10/1.61 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.10/1.61 => ( ( T7
% 3.10/1.61 = ( ^ [X2: B,Y2: A] :
% 3.10/1.61 ( X2
% 3.10/1.61 = ( Rep @ Y2 ) ) ) )
% 3.10/1.61 => ( quotient @ B @ A
% 3.10/1.61 @ ^ [Y4: B,Z: B] : ( Y4 = Z )
% 3.10/1.61 @ Abs
% 3.10/1.61 @ Rep
% 3.10/1.61 @ T7 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_255_Quotient__eq__onp__typedef,axiom,
% 3.10/1.61 ! [B: $tType,A: $tType,P: A > $o,Abs: A > B,Rep: B > A,Cr: A > B > $o] :
% 3.10/1.61 ( ( quotient @ A @ B @ ( bNF_eq_onp @ A @ P ) @ Abs @ Rep @ Cr )
% 3.10/1.61 => ( type_definition @ B @ A @ Rep @ Abs @ ( collect @ A @ P ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( finite_finite @ A )
% 3.10/1.61 => ( type @ A ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ( type @ A ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ( ord @ A ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ( order @ A ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 3.10/1.61 ! [A: $tType] :
% 3.10/1.61 ( ( linorder @ A )
% 3.10/1.61 => ( preorder @ A ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( real_V55928688vector @ A8 )
% 3.10/1.61 & ( real_V55928688vector @ A9 ) )
% 3.10/1.61 => ( real_V55928688vector @ ( bounde2145540817linfun @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( real_V55928688vector @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_2,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( real_V55928688vector @ A8 )
% 3.10/1.61 & ( real_V55928688vector @ A9 ) )
% 3.10/1.61 => ( real_V55928688vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_3,axiom,
% 3.10/1.61 real_V55928688vector @ real ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( topolo503727757_space @ A9 )
% 3.10/1.61 => ( topolo503727757_space @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( order_top @ A9 )
% 3.10/1.61 => ( order_top @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( preorder @ A9 )
% 3.10/1.61 => ( preorder @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( finite_finite @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( order @ A9 )
% 3.10/1.61 => ( order @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Orderings_Otop,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( top @ A9 )
% 3.10/1.61 => ( top @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_fun___Orderings_Oord,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ord @ A9 )
% 3.10/1.61 => ( ord @ ( A8 > A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Set_Oset___Orderings_Oorder__top_4,axiom,
% 3.10/1.61 ! [A8: $tType] : ( order_top @ ( set @ A8 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 3.10/1.61 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Set_Oset___Finite__Set_Ofinite_6,axiom,
% 3.10/1.61 ! [A8: $tType] :
% 3.10/1.61 ( ( finite_finite @ A8 )
% 3.10/1.61 => ( finite_finite @ ( set @ A8 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Set_Oset___Orderings_Oorder_7,axiom,
% 3.10/1.61 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Set_Oset___Orderings_Otop_8,axiom,
% 3.10/1.61 ! [A8: $tType] : ( top @ ( set @ A8 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 3.10/1.61 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_10,axiom,
% 3.10/1.61 topolo503727757_space @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Orderings_Oorder__top_11,axiom,
% 3.10/1.61 order_top @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 3.10/1.61 preorder @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.10/1.61 linorder @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Finite__Set_Ofinite_13,axiom,
% 3.10/1.61 finite_finite @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 3.10/1.61 order @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Orderings_Otop_15,axiom,
% 3.10/1.61 top @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 3.10/1.61 ord @ $o ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_17,axiom,
% 3.10/1.61 topolo503727757_space @ real ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Real_Oreal___Orderings_Opreorder_18,axiom,
% 3.10/1.61 preorder @ real ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Real_Oreal___Orderings_Olinorder_19,axiom,
% 3.10/1.61 linorder @ real ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Real_Oreal___Orderings_Oorder_20,axiom,
% 3.10/1.61 order @ real ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Real_Oreal___Orderings_Oord_21,axiom,
% 3.10/1.61 ord @ real ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_22,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( finite_finite @ ( sum_sum @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_23,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A8 )
% 3.10/1.61 & ( topolo503727757_space @ A9 ) )
% 3.10/1.61 => ( topolo503727757_space @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Orderings_Oorder__top_24,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( order_top @ A8 )
% 3.10/1.61 & ( order_top @ A9 ) )
% 3.10/1.61 => ( order_top @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_25,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( preorder @ A8 )
% 3.10/1.61 & ( preorder @ A9 ) )
% 3.10/1.61 => ( preorder @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_26,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( finite_finite @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Orderings_Oorder_27,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( order @ A8 )
% 3.10/1.61 & ( order @ A9 ) )
% 3.10/1.61 => ( order @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Orderings_Otop_28,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( top @ A8 )
% 3.10/1.61 & ( top @ A9 ) )
% 3.10/1.61 => ( top @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Oprod___Orderings_Oord_29,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( ord @ A8 )
% 3.10/1.61 & ( ord @ A9 ) )
% 3.10/1.61 => ( ord @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_30,axiom,
% 3.10/1.61 order_top @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31,axiom,
% 3.10/1.61 preorder @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32,axiom,
% 3.10/1.61 linorder @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Finite__Set_Ofinite_33,axiom,
% 3.10/1.61 finite_finite @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Orderings_Oorder_34,axiom,
% 3.10/1.61 order @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Orderings_Otop_35,axiom,
% 3.10/1.61 top @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Product__Type_Ounit___Orderings_Oord_36,axiom,
% 3.10/1.61 ord @ product_unit ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_37,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( topolo503727757_space @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( topolo503727757_space @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_38,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( order @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( preorder @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_39,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( linorder @ A8 )
% 3.10/1.61 & ( cARD_1 @ A9 ) )
% 3.10/1.61 => ( linorder @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_40,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( finite_finite @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( finite_finite @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_41,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( order @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( order @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_42,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( ord @ A8 )
% 3.10/1.61 & ( finite_finite @ A9 ) )
% 3.10/1.61 => ( ord @ ( finite_Cartesian_vec @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_43,axiom,
% 3.10/1.61 ! [A8: $tType,A9: $tType] :
% 3.10/1.61 ( ( ( real_V55928688vector @ A8 )
% 3.10/1.61 & ( real_V55928688vector @ A9 ) )
% 3.10/1.61 => ( topolo503727757_space @ ( bounde2145540817linfun @ A8 @ A9 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(help_If_3_1_T,axiom,
% 3.10/1.61 ! [P: $o] :
% 3.10/1.61 ( ( P = $true )
% 3.10/1.61 | ( P = $false ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(help_If_2_1_T,axiom,
% 3.10/1.61 ! [A: $tType,X: A,Y: A] :
% 3.10/1.61 ( ( if @ A @ $false @ X @ Y )
% 3.10/1.61 = Y ) ).
% 3.10/1.61
% 3.10/1.61 thf(help_If_1_1_T,axiom,
% 3.10/1.61 ! [A: $tType,X: A,Y: A] :
% 3.10/1.61 ( ( if @ A @ $true @ X @ Y )
% 3.10/1.61 = X ) ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_0,hypothesis,
% 3.10/1.61 finite_finite @ c ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_1,hypothesis,
% 3.10/1.61 finite_finite @ a ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_2,hypothesis,
% 3.10/1.61 finite_finite @ sz ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_3,hypothesis,
% 3.10/1.61 linorder @ sz ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_4,hypothesis,
% 3.10/1.61 finite_finite @ sf ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_5,hypothesis,
% 3.10/1.61 finite_finite @ sc ).
% 3.10/1.61
% 3.10/1.61 thf(tfree_6,hypothesis,
% 3.10/1.61 finite_finite @ b ).
% 3.10/1.61
% 3.10/1.61 thf(conj_0,conjecture,
% 3.10/1.61 denotational_Vagree @ c @ nu @ nu2 @ ( static_FVDiff @ a @ c @ t2 ) ).
% 3.10/1.61 ------------------------
% 3.10/1.64 % (18131)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_18030 for (2999ds/4Mi)
% 3.10/1.64 % (18133)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/2Mi)
% 3.10/1.64 % (18133)Instruction limit reached!
% 3.10/1.64 % (18133)------------------------------
% 3.10/1.64 % (18133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (18133)Termination reason: Unknown
% 3.10/1.64 % (18133)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (18133)Memory used [KB]: 1535
% 3.10/1.64 % (18134)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_18030 for (2999ds/2Mi)
% 3.10/1.64 % (18133)Time elapsed: 0.002 s
% 3.10/1.64 % (18133)Instructions burned: 2 (million)
% 3.10/1.64 % (18133)------------------------------
% 3.10/1.64 % (18133)------------------------------
% 3.10/1.64 % (18136)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/18Mi)
% 3.10/1.64 % (18131)Instruction limit reached!
% 3.10/1.64 % (18131)------------------------------
% 3.10/1.64 % (18131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (18131)Termination reason: Unknown
% 3.10/1.64 % (18131)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (18131)Memory used [KB]: 1663
% 3.10/1.64 % (18131)Time elapsed: 0.003 s
% 3.10/1.64 % (18131)Instructions burned: 4 (million)
% 3.10/1.64 % (18131)------------------------------
% 3.10/1.64 % (18131)------------------------------
% 3.10/1.64 % (18134)Instruction limit reached!
% 3.10/1.64 % (18134)------------------------------
% 3.10/1.64 % (18134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (18134)Termination reason: Unknown
% 3.10/1.64 % (18134)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (18134)Memory used [KB]: 1535
% 3.10/1.64 % (18134)Time elapsed: 0.002 s
% 3.10/1.64 % (18134)Instructions burned: 3 (million)
% 3.10/1.64 % (18134)------------------------------
% 3.10/1.64 % (18134)------------------------------
% 3.10/1.64 % (18136)Instruction limit reached!
% 3.10/1.64 % (18136)------------------------------
% 3.10/1.64 % (18136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (18136)Termination reason: Unknown
% 3.10/1.64 % (18136)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (18136)Memory used [KB]: 1918
% 3.10/1.64 % (18136)Time elapsed: 0.007 s
% 3.10/1.64 % (18136)Instructions burned: 18 (million)
% 3.10/1.64 % (18136)------------------------------
% 3.10/1.64 % (18136)------------------------------
% 3.10/1.64 % (18130)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/183Mi)
% 3.10/1.64 % (18132)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_18030 for (2999ds/27Mi)
% 3.10/1.64 % (18135)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_18030 for (2999ds/275Mi)
% 3.10/1.65 % (18137)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/3Mi)
% 3.10/1.65 % (18138)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_18030 for (2999ds/37Mi)
% 3.10/1.65 % (18137)Instruction limit reached!
% 3.10/1.65 % (18137)------------------------------
% 3.10/1.65 % (18137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.65 % (18137)Termination reason: Unknown
% 3.10/1.65 % (18137)Termination phase: shuffling
% 3.10/1.65
% 3.10/1.65 % (18137)Memory used [KB]: 1535
% 3.10/1.65 % (18137)Time elapsed: 0.002 s
% 3.10/1.65 % (18137)Instructions burned: 3 (million)
% 3.10/1.65 % (18137)------------------------------
% 3.10/1.65 % (18137)------------------------------
% 3.10/1.65 % (18139)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_18030 for (2999ds/15Mi)
% 3.10/1.65 % (18140)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_18030 for (2999ds/3Mi)
% 3.10/1.65 % (18140)Instruction limit reached!
% 3.10/1.65 % (18140)------------------------------
% 3.10/1.65 % (18140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.65 % (18140)Termination reason: Unknown
% 3.10/1.65 % (18140)Termination phase: shuffling
% 3.10/1.65
% 3.10/1.65 % (18140)Memory used [KB]: 1535
% 3.10/1.65 % (18140)Time elapsed: 0.002 s
% 3.10/1.65 % (18140)Instructions burned: 3 (million)
% 3.10/1.65 % (18140)------------------------------
% 3.10/1.65 % (18140)------------------------------
% 3.10/1.65 % (18139)Instruction limit reached!
% 3.10/1.65 % (18139)------------------------------
% 3.10/1.65 % (18139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.65 % (18139)Termination reason: Unknown
% 3.10/1.65 % (18139)Termination phase: shuffling
% 3.10/1.65
% 3.10/1.65 % (18139)Memory used [KB]: 1918
% 3.10/1.65 % (18139)Time elapsed: 0.007 s
% 3.10/1.65 % (18139)Instructions burned: 17 (million)
% 3.10/1.65 % (18139)------------------------------
% 3.10/1.65 % (18139)------------------------------
% 3.10/1.66 % (18141)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_18030 for (2999ds/1041Mi)
% 3.10/1.66 % (18138)Instruction limit reached!
% 3.10/1.66 % (18138)------------------------------
% 3.10/1.66 % (18138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (18138)Termination reason: Unknown
% 3.10/1.66 % (18138)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (18138)Memory used [KB]: 2302
% 3.10/1.66 % (18138)Time elapsed: 0.012 s
% 3.10/1.66 % (18138)Instructions burned: 39 (million)
% 3.10/1.66 % (18138)------------------------------
% 3.10/1.66 % (18138)------------------------------
% 3.10/1.66 % (18132)Instruction limit reached!
% 3.10/1.66 % (18132)------------------------------
% 3.10/1.66 % (18132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (18132)Termination reason: Unknown
% 3.10/1.66 % (18132)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (18132)Memory used [KB]: 2046
% 3.10/1.66 % (18132)Time elapsed: 0.019 s
% 3.10/1.66 % (18132)Instructions burned: 27 (million)
% 3.10/1.66 % (18132)------------------------------
% 3.10/1.66 % (18132)------------------------------
% 3.10/1.66 % (18142)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/7Mi)
% 3.10/1.67 % (18142)Instruction limit reached!
% 3.10/1.67 % (18142)------------------------------
% 3.10/1.67 % (18142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (18142)Termination reason: Unknown
% 3.10/1.67 % (18142)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (18142)Memory used [KB]: 1791
% 3.10/1.67 % (18142)Time elapsed: 0.004 s
% 3.10/1.67 % (18142)Instructions burned: 9 (million)
% 3.10/1.67 % (18142)------------------------------
% 3.10/1.67 % (18142)------------------------------
% 3.10/1.67 % (18144)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_18030 for (2999ds/3Mi)
% 3.10/1.67 % (18143)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/16Mi)
% 3.10/1.67 % (18144)Instruction limit reached!
% 3.10/1.67 % (18144)------------------------------
% 3.10/1.67 % (18144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (18144)Termination reason: Unknown
% 3.10/1.67 % (18144)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (18144)Memory used [KB]: 1535
% 3.10/1.67 % (18144)Time elapsed: 0.002 s
% 3.10/1.67 % (18144)Instructions burned: 3 (million)
% 3.10/1.67 % (18144)------------------------------
% 3.10/1.67 % (18144)------------------------------
% 3.10/1.67 % (18143)Instruction limit reached!
% 3.10/1.67 % (18143)------------------------------
% 3.10/1.67 % (18143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (18143)Termination reason: Unknown
% 3.10/1.67 % (18143)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (18143)Memory used [KB]: 1918
% 3.10/1.67 % (18143)Time elapsed: 0.008 s
% 3.10/1.67 % (18143)Instructions burned: 17 (million)
% 3.10/1.67 % (18143)------------------------------
% 3.10/1.67 % (18143)------------------------------
% 3.10/1.67 % (18146)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/7Mi)
% 3.10/1.68 % (18147)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/3Mi)
% 3.10/1.68 % (18146)Instruction limit reached!
% 3.10/1.68 % (18146)------------------------------
% 3.10/1.68 % (18146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (18146)Termination reason: Unknown
% 3.10/1.68 % (18146)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (18146)Memory used [KB]: 1791
% 3.10/1.68 % (18146)Time elapsed: 0.004 s
% 3.10/1.68 % (18146)Instructions burned: 9 (million)
% 3.10/1.68 % (18146)------------------------------
% 3.10/1.68 % (18146)------------------------------
% 3.10/1.68 % (18145)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_18030 for (2999ds/3Mi)
% 3.10/1.68 % (18147)Instruction limit reached!
% 3.10/1.68 % (18147)------------------------------
% 3.10/1.68 % (18147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (18147)Termination reason: Unknown
% 3.10/1.68 % (18147)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (18147)Memory used [KB]: 1535
% 3.10/1.68 % (18147)Time elapsed: 0.002 s
% 3.10/1.68 % (18147)Instructions burned: 3 (million)
% 3.10/1.68 % (18147)------------------------------
% 3.10/1.68 % (18147)------------------------------
% 3.10/1.68 % (18145)Instruction limit reached!
% 3.10/1.68 % (18145)------------------------------
% 3.10/1.68 % (18145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (18145)Termination reason: Unknown
% 3.10/1.68 % (18145)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (18145)Memory used [KB]: 1535
% 3.10/1.68 % (18145)Time elapsed: 0.004 s
% 3.10/1.68 % (18145)Instructions burned: 3 (million)
% 3.10/1.68 % (18145)------------------------------
% 3.10/1.68 % (18145)------------------------------
% 3.10/1.68 % (18148)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/4Mi)
% 3.10/1.69 % (18148)Instruction limit reached!
% 3.10/1.69 % (18148)------------------------------
% 3.10/1.69 % (18148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (18148)Termination reason: Unknown
% 3.10/1.69 % (18148)Termination phase: shuffling
% 3.10/1.69
% 3.10/1.69 % (18148)Memory used [KB]: 1663
% 3.10/1.69 % (18148)Time elapsed: 0.004 s
% 3.10/1.69 % (18148)Instructions burned: 6 (million)
% 3.10/1.69 % (18148)------------------------------
% 3.10/1.69 % (18148)------------------------------
% 3.10/1.69 % (18149)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/18Mi)
% 3.10/1.69 % (18150)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/710Mi)
% 3.10/1.69 % (18149)Instruction limit reached!
% 3.10/1.69 % (18149)------------------------------
% 3.10/1.69 % (18149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (18149)Termination reason: Unknown
% 3.10/1.69 % (18149)Termination phase: shuffling
% 3.10/1.69
% 3.10/1.69 % (18149)Memory used [KB]: 1918
% 3.10/1.69 % (18149)Time elapsed: 0.007 s
% 3.10/1.69 % (18149)Instructions burned: 19 (million)
% 3.10/1.69 % (18149)------------------------------
% 3.10/1.69 % (18149)------------------------------
% 3.13/1.70 % (18152)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_18030 for (2999ds/902Mi)
% 3.13/1.70 % (18151)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/6Mi)
% 3.13/1.70 % (18151)Instruction limit reached!
% 3.13/1.70 % (18151)------------------------------
% 3.13/1.70 % (18151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (18151)Termination reason: Unknown
% 3.13/1.70 % (18151)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (18151)Memory used [KB]: 1663
% 3.13/1.70 % (18151)Time elapsed: 0.006 s
% 3.13/1.70 % (18151)Instructions burned: 6 (million)
% 3.13/1.70 % (18151)------------------------------
% 3.13/1.70 % (18151)------------------------------
% 3.13/1.70 % (18153)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_18030 for (2999ds/21Mi)
% 3.13/1.71 % (18153)Instruction limit reached!
% 3.13/1.71 % (18153)------------------------------
% 3.13/1.71 % (18153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.71 % (18153)Termination reason: Unknown
% 3.13/1.71 % (18153)Termination phase: shuffling
% 3.13/1.71
% 3.13/1.71 % (18153)Memory used [KB]: 1918
% 3.13/1.71 % (18153)Time elapsed: 0.008 s
% 3.13/1.71 % (18153)Instructions burned: 22 (million)
% 3.13/1.71 % (18153)------------------------------
% 3.13/1.71 % (18153)------------------------------
% 3.13/1.71 % (18130)Instruction limit reached!
% 3.13/1.71 % (18130)------------------------------
% 3.13/1.71 % (18130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.71 % (18130)Termination reason: Unknown
% 3.13/1.71 % (18130)Termination phase: Saturation
% 3.13/1.71
% 3.13/1.71 % (18130)Memory used [KB]: 7675
% 3.13/1.71 % (18130)Time elapsed: 0.073 s
% 3.13/1.71 % (18130)Instructions burned: 185 (million)
% 3.13/1.71 % (18130)------------------------------
% 3.13/1.71 % (18130)------------------------------
% 3.13/1.72 % (18154)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18030 for (2999ds/5Mi)
% 3.13/1.72 % (18155)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_18030 for (2998ds/6Mi)
% 3.13/1.72 % (18154)Instruction limit reached!
% 3.13/1.72 % (18154)------------------------------
% 3.13/1.72 % (18154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.72 % (18154)Termination reason: Unknown
% 3.13/1.72 % (18154)Termination phase: shuffling
% 3.13/1.72
% 3.13/1.72 % (18154)Memory used [KB]: 1663
% 3.13/1.72 % (18154)Time elapsed: 0.004 s
% 3.13/1.72 % (18154)Instructions burned: 5 (million)
% 3.13/1.72 % (18154)------------------------------
% 3.13/1.72 % (18154)------------------------------
% 3.13/1.72 % (18155)Instruction limit reached!
% 3.13/1.72 % (18155)------------------------------
% 3.13/1.72 % (18155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.72 % (18155)Termination reason: Unknown
% 3.13/1.72 % (18155)Termination phase: shuffling
% 3.13/1.72
% 3.13/1.72 % (18155)Memory used [KB]: 1663
% 3.13/1.72 % (18155)Time elapsed: 0.003 s
% 3.13/1.72 % (18155)Instructions burned: 7 (million)
% 3.13/1.72 % (18155)------------------------------
% 3.13/1.72 % (18155)------------------------------
% 3.13/1.72 % (18156)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18030 for (2998ds/377Mi)
% 3.13/1.73 % (18158)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_18030 for (2998ds/19Mi)
% 3.13/1.73 % (18157)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_18030 for (2998ds/779Mi)
% 3.13/1.74 % (18158)Instruction limit reached!
% 3.13/1.74 % (18158)------------------------------
% 3.13/1.74 % (18158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.74 % (18158)Termination reason: Unknown
% 3.13/1.74 % (18158)Termination phase: shuffling
% 3.13/1.74
% 3.13/1.74 % (18158)Memory used [KB]: 2046
% 3.13/1.74 % (18158)Time elapsed: 0.007 s
% 3.13/1.74 % (18158)Instructions burned: 20 (million)
% 3.13/1.74 % (18158)------------------------------
% 3.13/1.74 % (18158)------------------------------
% 3.13/1.75 % (18159)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18030 for (2998ds/879Mi)
% 3.13/1.76 % (18135)Instruction limit reached!
% 3.13/1.76 % (18135)------------------------------
% 3.13/1.76 % (18135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.76 % (18135)Termination reason: Unknown
% 3.13/1.76 % (18135)Termination phase: Saturation
% 3.13/1.76
% 3.13/1.76 % (18135)Memory used [KB]: 7931
% 3.13/1.76 % (18135)Time elapsed: 0.121 s
% 3.13/1.76 % (18135)Instructions burned: 277 (million)
% 3.13/1.76 % (18135)------------------------------
% 3.13/1.76 % (18135)------------------------------
% 3.13/1.77 % (18160)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18030 for (2998ds/17Mi)
% 3.13/1.78 % (18160)Instruction limit reached!
% 3.13/1.78 % (18160)------------------------------
% 3.13/1.78 % (18160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.78 % (18160)Termination reason: Unknown
% 3.13/1.78 % (18160)Termination phase: shuffling
% 3.13/1.78
% 3.13/1.78 % (18160)Memory used [KB]: 1918
% 3.13/1.78 % (18160)Time elapsed: 0.008 s
% 3.13/1.78 % (18160)Instructions burned: 19 (million)
% 3.13/1.78 % (18160)------------------------------
% 3.13/1.78 % (18160)------------------------------
% 3.13/1.79 % (18161)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18030 for (2998ds/3Mi)
% 3.13/1.79 % (18161)Instruction limit reached!
% 3.13/1.79 % (18161)------------------------------
% 3.13/1.79 % (18161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.79 % (18161)Termination reason: Unknown
% 3.13/1.79 % (18161)Termination phase: shuffling
% 3.13/1.79
% 3.13/1.79 % (18161)Memory used [KB]: 1535
% 3.13/1.79 % (18161)Time elapsed: 0.003 s
% 3.13/1.79 % (18161)Instructions burned: 3 (million)
% 3.13/1.79 % (18161)------------------------------
% 3.13/1.79 % (18161)------------------------------
% 3.13/1.80 % (18162)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18030 for (2998ds/30Mi)
% 3.13/1.81 % (18162)Instruction limit reached!
% 3.13/1.81 % (18162)------------------------------
% 3.13/1.81 % (18162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.81 % (18162)Termination reason: Unknown
% 3.13/1.81 % (18162)Termination phase: shuffling
% 3.13/1.81
% 3.13/1.81 % (18162)Memory used [KB]: 2174
% 3.13/1.81 % (18162)Time elapsed: 0.013 s
% 3.13/1.81 % (18162)Instructions burned: 30 (million)
% 3.13/1.81 % (18162)------------------------------
% 3.13/1.81 % (18162)------------------------------
% 3.13/1.82 % (18163)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18030 for (2997ds/127Mi)
% 3.13/1.85 % (18156)Instruction limit reached!
% 3.13/1.85 % (18156)------------------------------
% 3.13/1.85 % (18156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.85 % (18156)Termination reason: Unknown
% 3.13/1.85 % (18156)Termination phase: Saturation
% 3.13/1.85
% 3.13/1.85 % (18156)Memory used [KB]: 8955
% 3.13/1.85 % (18156)Time elapsed: 0.127 s
% 3.13/1.85 % (18156)Instructions burned: 378 (million)
% 3.13/1.85 % (18156)------------------------------
% 3.13/1.85 % (18156)------------------------------
% 3.13/1.86 % (18150)Refutation not found, non-redundant clauses discarded% (18150)------------------------------
% 3.13/1.86 % (18150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.86 % (18150)Termination reason: Refutation not found, non-redundant clauses discarded
% 3.13/1.86
% 3.13/1.86 % (18150)Memory used [KB]: 8571
% 3.13/1.86 % (18150)Time elapsed: 0.193 s
% 3.13/1.86 % (18150)Instructions burned: 556 (million)
% 3.13/1.86 % (18150)------------------------------
% 3.13/1.86 % (18150)------------------------------
% 3.13/1.86 % (18164)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18030 for (2997ds/100Mi)
% 3.13/1.87 % (18163)Instruction limit reached!
% 3.13/1.87 % (18163)------------------------------
% 3.13/1.87 % (18163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.87 % (18163)Termination reason: Unknown
% 3.13/1.87 % (18163)Termination phase: Property scanning
% 3.13/1.87
% 3.13/1.87 % (18163)Memory used [KB]: 3070
% 3.13/1.87 % (18163)Time elapsed: 0.044 s
% 3.13/1.87 % (18163)Instructions burned: 128 (million)
% 3.13/1.87 % (18163)------------------------------
% 3.13/1.87 % (18163)------------------------------
% 3.13/1.87 % (18165)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_18030 for (2997ds/3Mi)
% 3.13/1.87 % (18165)Instruction limit reached!
% 3.13/1.87 % (18165)------------------------------
% 3.13/1.87 % (18165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.87 % (18165)Termination reason: Unknown
% 3.13/1.87 % (18165)Termination phase: shuffling
% 3.13/1.87
% 3.13/1.87 % (18165)Memory used [KB]: 1535
% 3.13/1.87 % (18165)Time elapsed: 0.002 s
% 3.13/1.87 % (18165)Instructions burned: 3 (million)
% 3.13/1.87 % (18165)------------------------------
% 3.13/1.87 % (18165)------------------------------
% 3.13/1.88 % (18166)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_18030 for (2997ds/20Mi)
% 3.13/1.88 % (18167)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_18030 for (2997ds/86Mi)
% 3.13/1.88 % (18166)Instruction limit reached!
% 3.13/1.88 % (18166)------------------------------
% 3.13/1.88 % (18166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.88 % (18166)Termination reason: Unknown
% 3.13/1.88 % (18166)Termination phase: shuffling
% 3.13/1.88
% 3.13/1.88 % (18166)Memory used [KB]: 2046
% 3.13/1.88 % (18166)Time elapsed: 0.009 s
% 3.13/1.88 % (18166)Instructions burned: 20 (million)
% 3.13/1.88 % (18166)------------------------------
% 3.13/1.88 % (18166)------------------------------
% 3.13/1.89 % (18164)Instruction limit reached!
% 3.13/1.89 % (18164)------------------------------
% 3.13/1.89 % (18164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.89 % (18164)Termination reason: Unknown
% 3.13/1.89 % (18164)Termination phase: Property scanning
% 3.13/1.89
% 3.13/1.89 % (18164)Memory used [KB]: 2814
% 3.13/1.89 % (18164)Time elapsed: 0.031 s
% 3.13/1.89 % (18164)Instructions burned: 101 (million)
% 3.13/1.89 % (18164)------------------------------
% 3.13/1.89 % (18164)------------------------------
% 3.13/1.89 % (18168)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_18030 for (2997ds/107Mi)
% 3.13/1.90 % (18169)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_18030 for (2997ds/39Mi)
% 3.13/1.90 % (18167)Instruction limit reached!
% 3.13/1.90 % (18167)------------------------------
% 3.13/1.90 % (18167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.90 % (18167)Termination reason: Unknown
% 3.13/1.90 % (18167)Termination phase: Property scanning
% 3.13/1.90
% 3.13/1.90 % (18167)Memory used [KB]: 2942
% 3.13/1.90 % (18167)Time elapsed: 0.028 s
% 3.13/1.90 % (18167)Instructions burned: 87 (million)
% 3.13/1.90 % (18167)------------------------------
% 3.13/1.90 % (18167)------------------------------
% 3.13/1.91 % (18170)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_18030 for (2997ds/448Mi)
% 3.13/1.91 % (18169)Instruction limit reached!
% 3.13/1.91 % (18169)------------------------------
% 3.13/1.91 % (18169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.91 % (18169)Termination reason: Unknown
% 3.13/1.91 % (18169)Termination phase: shuffling
% 3.13/1.91
% 3.13/1.91 % (18169)Memory used [KB]: 2302
% 3.13/1.91 % (18169)Time elapsed: 0.013 s
% 3.13/1.91 % (18169)Instructions burned: 40 (million)
% 3.13/1.91 % (18169)------------------------------
% 3.13/1.91 % (18169)------------------------------
% 3.13/1.92 % (18159)Refutation not found, non-redundant clauses discarded% (18159)------------------------------
% 3.13/1.92 % (18159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.92 % (18159)Termination reason: Refutation not found, non-redundant clauses discarded
% 3.13/1.92
% 3.13/1.92 % (18159)Memory used [KB]: 8827
% 3.13/1.92 % (18159)Time elapsed: 0.178 s
% 3.13/1.92 % (18159)Instructions burned: 573 (million)
% 3.13/1.92 % (18159)------------------------------
% 3.13/1.92 % (18159)------------------------------
% 3.13/1.92 % (18171)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_18030 for (2996ds/46Mi)
% 3.13/1.93 % (18168)Instruction limit reached!
% 3.13/1.93 % (18168)------------------------------
% 3.13/1.93 % (18168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.93 % (18168)Termination reason: Unknown
% 3.13/1.93 % (18168)Termination phase: Property scanning
% 3.13/1.93
% 3.13/1.93 % (18168)Memory used [KB]: 2942
% 3.13/1.93 % (18168)Time elapsed: 0.038 s
% 3.13/1.93 % (18168)Instructions burned: 109 (million)
% 3.13/1.93 % (18168)------------------------------
% 3.13/1.93 % (18168)------------------------------
% 3.13/1.93 % (18172)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_18030 for (2996ds/98Mi)
% 3.13/1.94 % (18173)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_18030 for (2996ds/507Mi)
% 3.13/1.94 % (18171)Instruction limit reached!
% 3.13/1.94 % (18171)------------------------------
% 3.13/1.94 % (18171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.94 % (18171)Termination reason: Unknown
% 3.13/1.94 % (18171)Termination phase: Property scanning
% 3.13/1.94
% 3.13/1.94 % (18171)Memory used [KB]: 2430
% 3.13/1.94 % (18171)Time elapsed: 0.018 s
% 3.13/1.94 % (18171)Instructions burned: 49 (million)
% 3.13/1.94 % (18171)------------------------------
% 3.13/1.94 % (18171)------------------------------
% 3.13/1.95 % (18174)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_18030 for (2996ds/149Mi)
% 3.13/1.96 % (18172)Instruction limit reached!
% 3.13/1.96 % (18172)------------------------------
% 3.13/1.96 % (18172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.96 % (18172)Termination reason: Unknown
% 3.13/1.96 % (18172)Termination phase: Property scanning
% 3.13/1.96
% 3.13/1.96 % (18172)Memory used [KB]: 2814
% 3.13/1.96 % (18172)Time elapsed: 0.028 s
% 3.13/1.96 % (18172)Instructions burned: 101 (million)
% 3.13/1.96 % (18172)------------------------------
% 3.13/1.96 % (18172)------------------------------
% 3.13/1.96 % (18141)Instruction limit reached!
% 3.13/1.96 % (18141)------------------------------
% 3.13/1.96 % (18141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.96 % (18141)Termination reason: Unknown
% 3.13/1.96 % (18141)Termination phase: Saturation
% 3.13/1.96
% 3.13/1.96 % (18141)Memory used [KB]: 12409
% 3.13/1.96 % (18141)Time elapsed: 0.309 s
% 3.13/1.96 % (18141)Instructions burned: 1042 (million)
% 3.13/1.96 % (18141)------------------------------
% 3.13/1.96 % (18141)------------------------------
% 3.13/1.97 % (18152)Instruction limit reached!
% 3.13/1.97 % (18152)------------------------------
% 3.13/1.97 % (18152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.97 % (18152)Termination reason: Unknown
% 3.13/1.97 % (18152)Termination phase: Saturation
% 3.13/1.97
% 3.13/1.97 % (18152)Memory used [KB]: 9083
% 3.13/1.97 % (18152)Time elapsed: 0.273 s
% 3.13/1.97 % (18152)Instructions burned: 903 (million)
% 3.13/1.97 % (18152)------------------------------
% 3.13/1.97 % (18152)------------------------------
% 3.13/1.97 % (18157)Instruction limit reached!
% 3.13/1.97 % (18157)------------------------------
% 3.13/1.97 % (18157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.97 % (18157)Termination reason: Unknown
% 3.13/1.97 % (18157)Termination phase: Saturation
% 3.13/1.97
% 3.13/1.97 % (18157)Memory used [KB]: 11641
% 3.13/1.97 % (18157)Time elapsed: 0.239 s
% 3.13/1.97 % (18157)Instructions burned: 779 (million)
% 3.13/1.97 % (18157)------------------------------
% 3.13/1.97 % (18157)------------------------------
% 3.13/1.97 % (18175)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_18030 for (2996ds/39Mi)
% 3.13/1.97 % (18176)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_18030 for (2996ds/6Mi)
% 3.13/1.98 % (18176)Instruction limit reached!
% 3.13/1.98 % (18176)------------------------------
% 3.13/1.98 % (18176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (18176)Termination reason: Unknown
% 3.13/1.98 % (18176)Termination phase: shuffling
% 3.13/1.98
% 3.13/1.98 % (18176)Memory used [KB]: 1663
% 3.13/1.98 % (18176)Time elapsed: 0.003 s
% 3.13/1.98 % (18176)Instructions burned: 6 (million)
% 3.13/1.98 % (18176)------------------------------
% 3.13/1.98 % (18176)------------------------------
% 3.13/1.98 % (18177)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_18030 for (2996ds/1087Mi)
% 3.13/1.98 % (18178)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_18030 for (2996ds/47Mi)
% 3.13/1.98 % (18175)Instruction limit reached!
% 3.13/1.98 % (18175)------------------------------
% 3.13/1.98 % (18175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (18175)Termination reason: Unknown
% 3.13/1.98 % (18175)Termination phase: shuffling
% 3.13/1.98
% 3.13/1.98 % (18175)Memory used [KB]: 2302
% 3.13/1.98 % (18175)Time elapsed: 0.014 s
% 3.13/1.98 % (18175)Instructions burned: 40 (million)
% 3.13/1.98 % (18175)------------------------------
% 3.13/1.98 % (18175)------------------------------
% 3.13/1.99 % (18179)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_18030 for (2996ds/44Mi)
% 3.13/1.99 % (18180)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_18030 for (2996ds/432Mi)
% 3.13/2.00 % (18178)Instruction limit reached!
% 3.13/2.00 % (18178)------------------------------
% 3.13/2.00 % (18178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/2.00 % (18178)Termination reason: Unknown
% 3.13/2.00 % (18178)Termination phase: Property scanning
% 3.13/2.00
% 3.13/2.00 % (18178)Memory used [KB]: 2430
% 3.13/2.00 % (18178)Time elapsed: 0.018 s
% 3.13/2.00 % (18178)Instructions burned: 48 (million)
% 3.13/2.00 % (18178)------------------------------
% 3.13/2.00 % (18178)------------------------------
% 3.13/2.00 % (18179)Instruction limit reached!
% 3.13/2.00 % (18179)------------------------------
% 3.13/2.00 % (18179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/2.00 % (18179)Termination reason: Unknown
% 3.13/2.00 % (18179)Termination phase: shuffling
% 3.13/2.00
% 3.13/2.00 % (18179)Memory used [KB]: 2430
% 3.13/2.00 % (18179)Time elapsed: 0.014 s
% 3.13/2.00 % (18179)Instructions burned: 47 (million)
% 3.13/2.00 % (18179)------------------------------
% 3.13/2.00 % (18179)------------------------------
% 3.13/2.00 % (18174)Instruction limit reached!
% 3.13/2.00 % (18174)------------------------------
% 3.13/2.00 % (18174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/2.00 % (18174)Termination reason: Unknown
% 3.13/2.00 % (18174)Termination phase: Saturation
% 3.13/2.00
% 3.13/2.00 % (18174)Memory used [KB]: 7547
% 3.13/2.00 % (18174)Time elapsed: 0.048 s
% 3.13/2.00 % (18174)Instructions burned: 149 (million)
% 3.13/2.00 % (18174)------------------------------
% 3.13/2.00 % (18174)------------------------------
% 3.13/2.01 % (18181)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_18030 for (2996ds/62Mi)
% 3.13/2.01 % (18182)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_18030 for (2996ds/31Mi)
% 5.73/2.01 % (18183)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_18030 for (2996ds/96Mi)
% 5.73/2.02 % (18182)Instruction limit reached!
% 5.73/2.02 % (18182)------------------------------
% 5.73/2.02 % (18182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.02 % (18182)Termination reason: Unknown
% 5.73/2.02 % (18182)Termination phase: shuffling
% 5.73/2.02
% 5.73/2.02 % (18182)Memory used [KB]: 2174
% 5.73/2.02 % (18182)Time elapsed: 0.011 s
% 5.73/2.02 % (18182)Instructions burned: 31 (million)
% 5.73/2.02 % (18182)------------------------------
% 5.73/2.02 % (18182)------------------------------
% 5.73/2.03 % (18181)Instruction limit reached!
% 5.73/2.03 % (18181)------------------------------
% 5.73/2.03 % (18181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.03 % (18181)Termination reason: Unknown
% 5.73/2.03 % (18181)Termination phase: shuffling
% 5.73/2.03
% 5.73/2.03 % (18181)Memory used [KB]: 2814
% 5.73/2.03 % (18181)Time elapsed: 0.021 s
% 5.73/2.03 % (18181)Instructions burned: 63 (million)
% 5.73/2.03 % (18181)------------------------------
% 5.73/2.03 % (18181)------------------------------
% 5.73/2.03 % (18184)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_18030 for (2995ds/453Mi)
% 5.73/2.04 % (18170)Instruction limit reached!
% 5.73/2.04 % (18170)------------------------------
% 5.73/2.04 % (18170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.04 % (18170)Termination reason: Unknown
% 5.73/2.04 % (18170)Termination phase: Saturation
% 5.73/2.04
% 5.73/2.04 % (18170)Memory used [KB]: 9466
% 5.73/2.04 % (18170)Time elapsed: 0.124 s
% 5.73/2.04 % (18170)Instructions burned: 450 (million)
% 5.73/2.04 % (18170)------------------------------
% 5.73/2.04 % (18170)------------------------------
% 5.73/2.04 % (18185)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_18030 for (2995ds/71Mi)
% 5.73/2.04 % (18183)Instruction limit reached!
% 5.73/2.04 % (18183)------------------------------
% 5.73/2.04 % (18183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.04 % (18183)Termination reason: Unknown
% 5.73/2.04 % (18183)Termination phase: Property scanning
% 5.73/2.04
% 5.73/2.04 % (18183)Memory used [KB]: 3070
% 5.73/2.04 % (18183)Time elapsed: 0.033 s
% 5.73/2.04 % (18183)Instructions burned: 99 (million)
% 5.73/2.04 % (18183)------------------------------
% 5.73/2.04 % (18183)------------------------------
% 5.73/2.05 % (18186)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_18030 for (2995ds/83Mi)
% 5.73/2.05 % (18187)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_18030 for (2995ds/11Mi)
% 5.73/2.06 % (18187)Instruction limit reached!
% 5.73/2.06 % (18187)------------------------------
% 5.73/2.06 % (18187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.06 % (18187)Termination reason: Unknown
% 5.73/2.06 % (18187)Termination phase: shuffling
% 5.73/2.06
% 5.73/2.06 % (18187)Memory used [KB]: 1791
% 5.73/2.06 % (18187)Time elapsed: 0.005 s
% 5.73/2.06 % (18187)Instructions burned: 14 (million)
% 5.73/2.06 % (18187)------------------------------
% 5.73/2.06 % (18187)------------------------------
% 5.73/2.06 % (18185)Instruction limit reached!
% 5.73/2.06 % (18185)------------------------------
% 5.73/2.06 % (18185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.06 % (18185)Termination reason: Unknown
% 5.73/2.06 % (18185)Termination phase: Preprocessing 2
% 5.73/2.06
% 5.73/2.06 % (18185)Memory used [KB]: 2686
% 5.73/2.06 % (18185)Time elapsed: 0.026 s
% 5.73/2.06 % (18185)Instructions burned: 71 (million)
% 5.73/2.06 % (18185)------------------------------
% 5.73/2.06 % (18185)------------------------------
% 5.73/2.07 % (18188)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_18030 for (2995ds/41Mi)
% 5.73/2.07 % (18189)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18030 for (2995ds/6Mi)
% 5.73/2.07 % (18186)Instruction limit reached!
% 5.73/2.07 % (18186)------------------------------
% 5.73/2.07 % (18186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.07 % (18186)Termination reason: Unknown
% 5.73/2.07 % (18186)Termination phase: Preprocessing 3
% 5.73/2.07
% 5.73/2.07 % (18186)Memory used [KB]: 2558
% 5.73/2.07 % (18186)Time elapsed: 0.027 s
% 5.73/2.07 % (18186)Instructions burned: 84 (million)
% 5.73/2.07 % (18186)------------------------------
% 5.73/2.07 % (18186)------------------------------
% 5.73/2.07 % (18189)Instruction limit reached!
% 5.73/2.07 % (18189)------------------------------
% 5.73/2.07 % (18189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.07 % (18189)Termination reason: Unknown
% 5.73/2.07 % (18189)Termination phase: shuffling
% 5.73/2.07
% 5.73/2.07 % (18189)Memory used [KB]: 1663
% 5.73/2.07 % (18189)Time elapsed: 0.004 s
% 5.73/2.07 % (18189)Instructions burned: 8 (million)
% 5.73/2.07 % (18189)------------------------------
% 5.73/2.07 % (18189)------------------------------
% 5.73/2.08 % (18188)Instruction limit reached!
% 5.73/2.08 % (18188)------------------------------
% 5.73/2.08 % (18188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.08 % (18188)Termination reason: Unknown
% 5.73/2.08 % (18188)Termination phase: shuffling
% 5.73/2.08
% 5.73/2.08 % (18188)Memory used [KB]: 2430
% 5.73/2.08 % (18188)Time elapsed: 0.013 s
% 5.73/2.08 % (18188)Instructions burned: 43 (million)
% 5.73/2.08 % (18188)------------------------------
% 5.73/2.08 % (18188)------------------------------
% 5.73/2.08 % (18190)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_18030 for (2995ds/150Mi)
% 5.73/2.08 % (18191)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_18030 for (2995ds/343Mi)
% 5.73/2.09 % (18192)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_18030 for (2995ds/109Mi)
% 5.73/2.10 % (18173)Instruction limit reached!
% 5.73/2.10 % (18173)------------------------------
% 5.73/2.10 % (18173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.10 % (18173)Termination reason: Unknown
% 5.73/2.10 % (18173)Termination phase: Saturation
% 5.73/2.10
% 5.73/2.10 % (18173)Memory used [KB]: 9210
% 5.73/2.10 % (18173)Time elapsed: 0.166 s
% 5.73/2.10 % (18173)Instructions burned: 510 (million)
% 5.73/2.10 % (18173)------------------------------
% 5.73/2.10 % (18173)------------------------------
% 6.27/2.11 % (18193)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_18030 for (2995ds/253Mi)
% 6.27/2.12 % (18180)Instruction limit reached!
% 6.27/2.12 % (18180)------------------------------
% 6.27/2.12 % (18180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.12 % (18180)Termination reason: Unknown
% 6.27/2.12 % (18180)Termination phase: Saturation
% 6.27/2.12
% 6.27/2.12 % (18180)Memory used [KB]: 5500
% 6.27/2.12 % (18180)Time elapsed: 0.128 s
% 6.27/2.12 % (18180)Instructions burned: 432 (million)
% 6.27/2.12 % (18180)------------------------------
% 6.27/2.12 % (18180)------------------------------
% 6.27/2.12 % (18192)Instruction limit reached!
% 6.27/2.12 % (18192)------------------------------
% 6.27/2.12 % (18192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.12 % (18192)Termination reason: Unknown
% 6.27/2.12 % (18192)Termination phase: Property scanning
% 6.27/2.12
% 6.27/2.12 % (18192)Memory used [KB]: 3070
% 6.27/2.12 % (18192)Time elapsed: 0.035 s
% 6.27/2.12 % (18192)Instructions burned: 109 (million)
% 6.27/2.12 % (18192)------------------------------
% 6.27/2.12 % (18192)------------------------------
% 6.27/2.12 % (18190)Instruction limit reached!
% 6.27/2.12 % (18190)------------------------------
% 6.27/2.12 % (18190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.12 % (18190)Termination reason: Unknown
% 6.27/2.12 % (18190)Termination phase: Saturation
% 6.27/2.12
% 6.27/2.12 % (18190)Memory used [KB]: 7675
% 6.27/2.12 % (18190)Time elapsed: 0.045 s
% 6.27/2.12 % (18190)Instructions burned: 151 (million)
% 6.27/2.12 % (18190)------------------------------
% 6.27/2.12 % (18190)------------------------------
% 6.27/2.13 % (18194)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_18030 for (2995ds/140Mi)
% 6.27/2.13 % (18195)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_18030 for (2994ds/614Mi)
% 6.27/2.13 % (18196)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_18030 for (2994ds/202Mi)
% 6.27/2.15 % (18184)Instruction limit reached!
% 6.27/2.15 % (18184)------------------------------
% 6.27/2.15 % (18184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.15 % (18184)Termination reason: Unknown
% 6.27/2.15 % (18184)Termination phase: Saturation
% 6.27/2.15
% 6.27/2.15 % (18184)Memory used [KB]: 9083
% 6.27/2.15 % (18184)Time elapsed: 0.126 s
% 6.27/2.15 % (18184)Instructions burned: 453 (million)
% 6.27/2.15 % (18184)------------------------------
% 6.27/2.15 % (18184)------------------------------
% 6.27/2.16 % (18197)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_18030 for (2994ds/339Mi)
% 6.27/2.17 % (18194)Instruction limit reached!
% 6.27/2.17 % (18194)------------------------------
% 6.27/2.17 % (18194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.17 % (18194)Termination reason: Unknown
% 6.27/2.17 % (18194)Termination phase: Saturation
% 6.27/2.17
% 6.27/2.17 % (18194)Memory used [KB]: 7547
% 6.27/2.17 % (18194)Time elapsed: 0.067 s
% 6.27/2.17 % (18194)Instructions burned: 140 (million)
% 6.27/2.17 % (18194)------------------------------
% 6.27/2.17 % (18194)------------------------------
% 6.27/2.18 % (18198)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_18030 for (2994ds/283Mi)
% 6.27/2.19 % (18191)Instruction limit reached!
% 6.27/2.19 % (18191)------------------------------
% 6.27/2.19 % (18191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.19 % (18191)Termination reason: Unknown
% 6.27/2.19 % (18191)Termination phase: Saturation
% 6.27/2.19
% 6.27/2.19 % (18191)Memory used [KB]: 8443
% 6.27/2.19 % (18191)Time elapsed: 0.106 s
% 6.27/2.19 % (18191)Instructions burned: 344 (million)
% 6.27/2.19 % (18191)------------------------------
% 6.27/2.19 % (18191)------------------------------
% 6.27/2.19 % (18193)Instruction limit reached!
% 6.27/2.19 % (18193)------------------------------
% 6.27/2.19 % (18193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.19 % (18193)Termination reason: Unknown
% 6.27/2.19 % (18193)Termination phase: Saturation
% 6.27/2.19
% 6.27/2.19 % (18193)Memory used [KB]: 8699
% 6.27/2.19 % (18193)Time elapsed: 0.079 s
% 6.27/2.19 % (18193)Instructions burned: 253 (million)
% 6.27/2.19 % (18193)------------------------------
% 6.27/2.19 % (18193)------------------------------
% 6.27/2.20 % (18196)Instruction limit reached!
% 6.27/2.20 % (18196)------------------------------
% 6.27/2.20 % (18196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.20 % (18196)Termination reason: Unknown
% 6.27/2.20 % (18196)Termination phase: Saturation
% 6.27/2.20
% 6.27/2.20 % (18196)Memory used [KB]: 8187
% 6.27/2.20 % (18196)Time elapsed: 0.062 s
% 6.27/2.20 % (18196)Instructions burned: 203 (million)
% 6.27/2.20 % (18196)------------------------------
% 6.27/2.20 % (18196)------------------------------
% 6.92/2.20 % (18199)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_18030 for (2994ds/134Mi)
% 6.92/2.20 % (18200)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_18030 for (2994ds/298Mi)
% 6.92/2.21 % (18201)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_18030 for (2994ds/192Mi)
% 6.92/2.24 % (18199)Instruction limit reached!
% 6.92/2.24 % (18199)------------------------------
% 6.92/2.24 % (18199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.24 % (18199)Termination reason: Unknown
% 6.92/2.24 % (18199)Termination phase: Property scanning
% 6.92/2.24
% 6.92/2.24 % (18199)Memory used [KB]: 3070
% 6.92/2.24 % (18199)Time elapsed: 0.041 s
% 6.92/2.24 % (18199)Instructions burned: 135 (million)
% 6.92/2.24 % (18199)------------------------------
% 6.92/2.24 % (18199)------------------------------
% 6.92/2.25 % (18202)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_18030 for (2993ds/258Mi)
% 6.92/2.26 % (18198)Instruction limit reached!
% 6.92/2.26 % (18198)------------------------------
% 6.92/2.26 % (18198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.26 % (18198)Termination reason: Unknown
% 6.92/2.26 % (18198)Termination phase: Saturation
% 6.92/2.26
% 6.92/2.26 % (18198)Memory used [KB]: 8955
% 6.92/2.26 % (18198)Time elapsed: 0.081 s
% 6.92/2.26 % (18198)Instructions burned: 283 (million)
% 6.92/2.26 % (18198)------------------------------
% 6.92/2.26 % (18198)------------------------------
% 6.92/2.26 % (18201)Instruction limit reached!
% 6.92/2.26 % (18201)------------------------------
% 6.92/2.26 % (18201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.26 % (18201)Termination reason: Unknown
% 6.92/2.26 % (18201)Termination phase: Saturation
% 6.92/2.26
% 6.92/2.26 % (18201)Memory used [KB]: 3837
% 6.92/2.26 % (18201)Time elapsed: 0.060 s
% 6.92/2.26 % (18201)Instructions burned: 194 (million)
% 6.92/2.26 % (18201)------------------------------
% 6.92/2.26 % (18201)------------------------------
% 6.92/2.27 % (18197)Instruction limit reached!
% 6.92/2.27 % (18197)------------------------------
% 6.92/2.27 % (18197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.27 % (18197)Termination reason: Unknown
% 6.92/2.27 % (18197)Termination phase: Saturation
% 6.92/2.27
% 6.92/2.27 % (18197)Memory used [KB]: 8315
% 6.92/2.27 % (18197)Time elapsed: 0.106 s
% 6.92/2.27 % (18197)Instructions burned: 339 (million)
% 6.92/2.27 % (18197)------------------------------
% 6.92/2.27 % (18197)------------------------------
% 6.92/2.27 % (18203)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_18030 for (2993ds/90Mi)
% 6.92/2.27 % (18204)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_18030 for (2993ds/231Mi)
% 6.92/2.28 % (18205)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_18030 for (2993ds/458Mi)
% 6.92/2.28 % (18200)Instruction limit reached!
% 6.92/2.28 % (18200)------------------------------
% 6.92/2.28 % (18200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.28 % (18200)Termination reason: Unknown
% 6.92/2.28 % (18200)Termination phase: Saturation
% 6.92/2.28
% 6.92/2.28 % (18200)Memory used [KB]: 8955
% 6.92/2.28 % (18200)Time elapsed: 0.083 s
% 6.92/2.28 % (18200)Instructions burned: 300 (million)
% 6.92/2.28 % (18200)------------------------------
% 6.92/2.28 % (18200)------------------------------
% 6.92/2.29 % (18206)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_18030 for (2993ds/31Mi)
% 7.44/2.30 % (18203)Instruction limit reached!
% 7.44/2.30 % (18203)------------------------------
% 7.44/2.30 % (18203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.44/2.30 % (18203)Termination reason: Unknown
% 7.44/2.30 % (18203)Termination phase: Property scanning
% 7.44/2.30
% 7.44/2.30 % (18203)Memory used [KB]: 2942
% 7.44/2.30 % (18203)Time elapsed: 0.029 s
% 7.44/2.30 % (18203)Instructions burned: 90 (million)
% 7.44/2.30 % (18203)------------------------------
% 7.44/2.30 % (18203)------------------------------
% 7.44/2.30 % (18206)Instruction limit reached!
% 7.44/2.30 % (18206)------------------------------
% 7.44/2.30 % (18206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.44/2.30 % (18206)Termination reason: Unknown
% 7.44/2.30 % (18206)Termination phase: shuffling
% 7.44/2.30
% 7.44/2.30 % (18206)Memory used [KB]: 2302
% 7.44/2.30 % (18206)Time elapsed: 0.012 s
% 7.44/2.30 % (18206)Instructions burned: 33 (million)
% 7.44/2.30 % (18206)------------------------------
% 7.44/2.30 % (18206)------------------------------
% 7.44/2.31 % (18207)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_18030 for (2993ds/297Mi)
% 7.44/2.31 % (18208)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_18030 for (2993ds/987Mi)
% 7.44/2.32 % (18195)Instruction limit reached!
% 7.44/2.32 % (18195)------------------------------
% 7.44/2.32 % (18195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.44/2.32 % (18195)Termination reason: Unknown
% 7.44/2.32 % (18195)Termination phase: Saturation
% 7.44/2.32
% 7.44/2.32 % (18195)Memory used [KB]: 9466
% 7.44/2.32 % (18195)Time elapsed: 0.186 s
% 7.44/2.32 % (18195)Instructions burned: 614 (million)
% 7.44/2.32 % (18195)------------------------------
% 7.44/2.32 % (18195)------------------------------
% 7.44/2.32 % (18202)Instruction limit reached!
% 7.44/2.32 % (18202)------------------------------
% 7.44/2.32 % (18202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.44/2.32 % (18202)Termination reason: Unknown
% 7.44/2.32 % (18202)Termination phase: Saturation
% 7.44/2.32
% 7.44/2.32 % (18202)Memory used [KB]: 8699
% 7.44/2.32 % (18202)Time elapsed: 0.078 s
% 7.44/2.32 % (18202)Instructions burned: 260 (million)
% 7.44/2.32 % (18202)------------------------------
% 7.44/2.32 % (18202)------------------------------
% 7.44/2.33 % (18209)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_18030 for (2992ds/182Mi)
% 7.44/2.33 % (18210)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_18030 for (2992ds/182Mi)
% 7.44/2.34 % (18204)Instruction limit reached!
% 7.44/2.34 % (18204)------------------------------
% 7.44/2.34 % (18204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.44/2.34 % (18204)Termination reason: Unknown
% 7.44/2.34 % (18204)Termination phase: Property scanning
% 7.44/2.34
% 7.44/2.34 % (18204)Memory used [KB]: 3965
% 7.44/2.34 % (18204)Time elapsed: 0.063 s
% 7.44/2.34 % (18204)Instructions burned: 233 (million)
% 7.44/2.34 % (18204)------------------------------
% 7.44/2.34 % (18204)------------------------------
% 7.44/2.34 % (18177)First to succeed.
% 7.44/2.34 % (18177)Refutation found. Thanks to Tanya!
% 7.44/2.34 % SZS status Theorem for DTF2THF_18030
% 7.44/2.34 % SZS output start Proof for DTF2THF_18030
% 7.44/2.34 thf(type_def_6, type, set: ($tType) > $tType).
% 7.44/2.34 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_8, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_9, type, product_unit: $tType).
% 7.44/2.34 thf(type_def_10, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_11, type, sum_sum: ($tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_12, type, real: $tType).
% 7.44/2.34 thf(type_def_13, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_14, type, trm: ($tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_15, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_16, type, frechet_strm: ($tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_17, type, formula: ($tType * $tType * $tType) > $tType).
% 7.44/2.34 thf(type_def_18, type, a: $tType).
% 7.44/2.34 thf(type_def_19, type, b: $tType).
% 7.44/2.34 thf(type_def_20, type, c: $tType).
% 7.44/2.34 thf(type_def_21, type, sc: $tType).
% 7.44/2.34 thf(type_def_22, type, sf: $tType).
% 7.44/2.34 thf(type_def_23, type, sz: $tType).
% 7.44/2.34 thf(type_def_24, type, list: ($tType) > $tType).
% 7.44/2.34 thf(func_def_0, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_1, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_2, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_3, type, frechet_strm: ($tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_4, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_5, type, product_unit: $tType).
% 7.44/2.34 thf(func_def_6, type, product_prod: ($tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_7, type, formula: ($tType * $tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_8, type, sum_sum: ($tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_9, type, trm: ($tType * $tType) > $tType).
% 7.44/2.34 thf(func_def_10, type, real: $tType).
% 7.44/2.34 thf(func_def_11, type, list: ($tType) > $tType).
% 7.44/2.34 thf(func_def_12, type, set: ($tType) > $tType).
% 7.44/2.34 thf(func_def_13, type, sz: $tType).
% 7.44/2.34 thf(func_def_14, type, sf: $tType).
% 7.44/2.34 thf(func_def_15, type, sc: $tType).
% 7.44/2.34 thf(func_def_16, type, c: $tType).
% 7.44/2.34 thf(func_def_17, type, b: $tType).
% 7.44/2.34 thf(func_def_18, type, a: $tType).
% 7.44/2.34 thf(func_def_19, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_20, type, cARD_1: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_21, type, type: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_22, type, ord: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_23, type, top: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_24, type, order: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_25, type, finite_finite: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_26, type, linorder: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_27, type, preorder: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_28, type, order_top: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_29, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_30, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_31, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 7.44/2.34 thf(func_def_32, type, bNF_eq_onp: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_33, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2)).
% 7.44/2.34 thf(func_def_34, type, bounde688532126linfun: !>[X0: $tType, X1: $tType]:((X0 > X1) > bounde2145540817linfun @ X0 @ X1)).
% 7.44/2.34 thf(func_def_35, 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)).
% 7.44/2.34 thf(func_def_36, 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)).
% 7.44/2.34 thf(func_def_37, type, denota2078997598vative: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > real)).
% 7.44/2.34 thf(func_def_38, type, denotational_frechet: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2 > real)).
% 7.44/2.34 thf(func_def_39, type, denota2077489681interp: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o)).
% 7.44/2.34 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)).
% 7.44/2.34 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)).
% 7.44/2.34 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)).
% 7.44/2.34 thf(func_def_43, type, frechet_cr_strm: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > frechet_strm @ X0 @ X1 > $o)).
% 7.44/2.34 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)).
% 7.44/2.34 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)).
% 7.44/2.34 thf(func_def_46, type, frechet_raw_term: !>[X0: $tType, X1: $tType]:(frechet_strm @ X0 @ X1 > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_47, type, frechet_simple_term: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > frechet_strm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_48, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o)).
% 7.44/2.34 thf(func_def_49, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 7.44/2.34 thf(func_def_50, type, quotient: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > (X1 > X0) > (X0 > X1 > $o) > $o)).
% 7.44/2.34 thf(func_def_51, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_52, type, top_top: !>[X0: $tType]:(X0)).
% 7.44/2.34 thf(func_def_53, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 7.44/2.34 thf(func_def_54, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 7.44/2.34 thf(func_def_55, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 7.44/2.34 thf(func_def_56, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 7.44/2.34 thf(func_def_57, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 7.44/2.34 thf(func_def_58, type, static_FVDiff: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > set @ sum_sum @ X1 @ X1)).
% 7.44/2.34 thf(func_def_59, type, static_FVT: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > set @ sum_sum @ X1 @ X1)).
% 7.44/2.34 thf(func_def_60, type, static_SIGT: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > set @ X0)).
% 7.44/2.34 thf(func_def_61, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 7.44/2.34 thf(func_def_62, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 7.44/2.34 thf(func_def_63, type, predicational: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > formula @ X1 @ X0 @ X2)).
% 7.44/2.34 thf(func_def_64, type, dfree: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > $o)).
% 7.44/2.34 thf(func_def_65, type, p: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > formula @ X1 @ X0 @ X2)).
% 7.44/2.34 thf(func_def_66, type, empty: !>[X0: $tType, X1: $tType]:(X0 > trm @ X1 @ X0)).
% 7.44/2.34 thf(func_def_67, type, f0: !>[X0: $tType, X1: $tType]:(X0 > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_68, type, function: !>[X0: $tType, X1: $tType]:(X0 > (X1 > trm @ X0 @ X1) > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_69, type, plus: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_70, type, times: !>[X0: $tType, X1: $tType]:(trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_71, type, topolo2071040574ous_on: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > X1) > $o)).
% 7.44/2.34 thf(func_def_72, type, type_definition: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > set @ X1 > $o)).
% 7.44/2.34 thf(func_def_73, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 7.44/2.34 thf(func_def_74, type, i: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 7.44/2.34 thf(func_def_75, type, j: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 7.44/2.34 thf(func_def_76, type, nu: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 7.44/2.34 thf(func_def_77, type, nu2: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 7.44/2.34 thf(func_def_78, type, t1: trm @ a @ c).
% 7.44/2.34 thf(func_def_79, type, t2: trm @ a @ c).
% 7.44/2.34 thf(func_def_95, type, sP0: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 7.44/2.34 thf(func_def_96, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_97, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_98, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_99, type, sP4: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_100, type, sP5: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 7.44/2.34 thf(func_def_101, type, sK6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_102, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 7.44/2.34 thf(func_def_103, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 7.44/2.34 thf(func_def_104, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 7.44/2.34 thf(func_def_105, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 7.44/2.34 thf(func_def_106, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 7.44/2.34 thf(func_def_107, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 7.44/2.34 thf(func_def_108, type, sK13: !>[X0: $tType, X1: $tType]:((frechet_strm @ X1 @ X0 > $o) > trm @ X1 @ X0)).
% 7.44/2.34 thf(func_def_109, type, sK14: !>[X0: $tType, X1: $tType]:(trm @ X1 @ X0 > frechet_strm @ X1 @ X0)).
% 7.44/2.34 thf(func_def_110, type, sK15: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_111, type, sK16: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 7.44/2.34 thf(func_def_112, type, sK17: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 7.44/2.34 thf(func_def_113, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 7.44/2.34 thf(func_def_114, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 7.44/2.34 thf(func_def_115, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 7.44/2.34 thf(func_def_116, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 7.44/2.34 thf(func_def_117, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 7.44/2.34 thf(func_def_118, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_119, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_120, type, sK25: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_121, type, sK26: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_122, type, sK27: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_123, type, sK28: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_124, type, sK29: !>[X0: $tType, X1: $tType]:(frechet_strm @ X1 @ X0 > trm @ X1 @ X0)).
% 7.44/2.34 thf(func_def_125, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 7.44/2.34 thf(func_def_126, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_127, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_128, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 7.44/2.34 thf(func_def_129, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 7.44/2.34 thf(func_def_130, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 7.44/2.34 thf(func_def_131, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 7.44/2.34 thf(func_def_132, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 7.44/2.34 thf(func_def_133, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 7.44/2.34 thf(func_def_134, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 7.44/2.34 thf(func_def_135, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 7.44/2.34 thf(func_def_136, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 7.44/2.34 thf(func_def_137, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_138, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_139, type, sK44: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_140, type, sK45: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_141, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > $o) > frechet_good_interp @ X2 @ X1 @ X0)).
% 7.44/2.34 thf(func_def_142, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X2 @ X1 @ X0 > $o) > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit)).
% 7.44/2.34 thf(func_def_143, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 7.44/2.34 thf(func_def_144, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 7.44/2.34 thf(func_def_145, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 7.44/2.34 thf(func_def_146, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 7.44/2.34 thf(func_def_147, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 7.44/2.34 thf(func_def_148, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 7.44/2.34 thf(func_def_149, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 7.44/2.34 thf(func_def_150, type, sK55: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 7.44/2.34 thf(func_def_151, type, sK56: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 7.44/2.34 thf(func_def_152, type, sK57: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 7.44/2.34 thf(func_def_153, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 7.44/2.34 thf(func_def_154, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 7.44/2.34 thf(func_def_155, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 7.44/2.34 thf(func_def_156, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 7.44/2.34 thf(func_def_157, type, sK62: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 7.44/2.34 thf(func_def_158, type, sK63: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 7.44/2.34 thf(func_def_159, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 7.44/2.34 thf(func_def_160, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 7.44/2.34 thf(func_def_161, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_162, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_163, type, sK68: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_164, type, sK69: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_165, type, sK70: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_166, type, sK71: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_167, type, sK72: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1 > $o) > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_168, type, sK73: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1 > $o) > X1)).
% 7.44/2.34 thf(func_def_169, type, sK74: !>[X0: $tType, X1: $tType]:(product_prod @ trm @ X0 @ X1 @ X1 > trm @ X0 @ X1)).
% 7.44/2.34 thf(func_def_170, type, sK75: !>[X0: $tType, X1: $tType]:(product_prod @ trm @ X0 @ X1 @ X1 > X1)).
% 7.44/2.34 thf(func_def_171, type, sK76: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_172, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(frechet_good_interp @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit)).
% 7.44/2.34 thf(func_def_173, type, sK78: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 7.44/2.34 thf(func_def_174, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit @ X2 > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit)).
% 7.44/2.34 thf(func_def_175, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit @ X2 > X2)).
% 7.44/2.34 thf(func_def_176, type, sK81: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0)).
% 7.44/2.34 thf(func_def_177, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 7.44/2.34 thf(func_def_178, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 7.44/2.34 thf(func_def_179, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 7.44/2.34 thf(func_def_180, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 7.44/2.34 thf(func_def_181, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_182, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 7.44/2.34 thf(func_def_183, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 7.44/2.34 thf(func_def_184, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 7.44/2.34 thf(func_def_185, type, sK90: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.44/2.34 thf(func_def_186, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType]:(denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > frechet_good_interp @ X2 @ X1 @ X0)).
% 7.44/2.34 thf(func_def_187, type, sK92: product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > denota1663640101rp_ext @ sf @ sc @ sz @ product_unit).
% 7.44/2.34 thf(func_def_188, type, sK93: product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz).
% 7.44/2.34 thf(func_def_191, type, ph95: !>[X0: $tType]:(X0)).
% 7.44/2.34 thf(func_def_192, type, sK96: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 7.44/2.34 thf(f3065,plain,(
% 7.44/2.34 $false),
% 7.44/2.34 inference(avatar_sat_refutation,[status(thm)],[f1438,f3064])).
% 7.44/2.34 thf(f3064,plain,(
% 7.44/2.34 spl94_6),
% 7.44/2.34 inference(avatar_contradiction_clause,[status(thm)],[f3063])).
% 7.44/2.34 thf(f3063,plain,(
% 7.44/2.34 $false | spl94_6),
% 7.44/2.34 inference(subsumption_resolution,[status(thm)],[f3062,f1254])).
% 7.44/2.34 thf(f1254,plain,(
% 7.44/2.34 (finite_finite @ c = $true)),
% 7.44/2.34 inference(cnf_transformation,[status(thm)],[f774])).
% 7.44/2.34 thf(f774,plain,(
% 7.44/2.34 (finite_finite @ c = $true)),
% 7.44/2.34 inference(fool_elimination,[status(thm)],[f773])).
% 7.44/2.34 thf(f773,plain,(
% 7.44/2.34 finite_finite @ c),
% 7.44/2.34 inference(rectify,[status(thm)],[f317])).
% 7.44/2.34 thf(f317,axiom,(
% 7.44/2.34 finite_finite @ c),
% 7.44/2.34 file('/export/starexec/sandbox2/tmp/tmp.EGxl0yY1Vf/DTF2THF_18030.p',tfree_0)).
% 7.44/2.34 thf(f3062,plain,(
% 7.44/2.34 (finite_finite @ c != $true) | spl94_6),
% 7.44/2.34 inference(subsumption_resolution,[status(thm)],[f3053,f1390])).
% 7.44/2.34 thf(f1390,plain,(
% 7.44/2.34 ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) != $true) | spl94_6),
% 7.44/2.34 inference(avatar_component_clause,[status(thm)],[f1389])).
% 7.44/2.34 thf(f1389,definition,(
% 7.44/2.34 spl94_6 <=> ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) = $true)),
% 7.44/2.34 introduced(definition,[new_symbols(naming,[spl94_6])],[avatar_definition])).
% 7.44/2.34 thf(f3053,plain,(
% 7.44/2.34 ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) = $true) | (finite_finite @ c != $true)),
% 7.44/2.34 inference(trivial_inequality_removal,[status(thm)],[f3050])).
% 7.44/2.34 thf(f3050,plain,(
% 7.44/2.34 ($true != $true) | ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) = $true) | (finite_finite @ c != $true)),
% 7.44/2.34 inference(superposition,[status(thm)],[f1331,f1286])).
% 7.44/2.34 thf(f1286,plain,(
% 7.44/2.34 ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ (plus @ a @ c @ t1 @ t2))) = $true)),
% 7.44/2.34 inference(cnf_transformation,[status(thm)],[f824])).
% 7.44/2.34 thf(f824,plain,(
% 7.44/2.34 ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ (plus @ a @ c @ t1 @ t2))) = $true)),
% 7.44/2.34 inference(fool_elimination,[status(thm)],[f823])).
% 7.44/2.34 thf(f823,plain,(
% 7.44/2.34 (denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ (plus @ a @ c @ t1 @ t2)))),
% 7.44/2.34 inference(rectify,[status(thm)],[f2])).
% 7.44/2.34 thf(f2,axiom,(
% 7.44/2.34 (denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ (plus @ a @ c @ t1 @ t2)))),
% 7.44/2.34 file('/export/starexec/sandbox2/tmp/tmp.EGxl0yY1Vf/DTF2THF_18030.p',fact_1_agree)).
% 7.44/2.34 thf(f1331,plain,(
% 7.44/2.34 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X4 : trm @ X1 @ X0,X5 : trm @ X1 @ X0] : (($true != (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ (plus @ X1 @ X0 @ X4 @ X5)))) | (finite_finite @ X0 != $true) | ($true = (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ X5)))) )),
% 7.44/2.34 inference(cnf_transformation,[status(thm)],[f943])).
% 7.44/2.34 thf(f943,plain,(
% 7.44/2.34 ! [X0 : $tType,X1 : $tType] : (! [X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X4 : trm @ X1 @ X0,X5 : trm @ X1 @ X0] : (($true != (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ (plus @ X1 @ X0 @ X4 @ X5)))) | ($true = (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ X5)))) | (finite_finite @ X0 != $true))),
% 7.44/2.34 inference(ennf_transformation,[status(thm)],[f544])).
% 7.44/2.34 thf(f544,plain,(
% 7.44/2.34 ! [X0 : $tType,X1 : $tType] : ((finite_finite @ X0 = $true) => ! [X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X4 : trm @ X1 @ X0,X5 : trm @ X1 @ X0] : (($true = (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ (plus @ X1 @ X0 @ X4 @ X5)))) => ($true = (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ X5)))))),
% 7.44/2.34 inference(fool_elimination,[status(thm)],[f543])).
% 7.44/2.34 thf(f543,plain,(
% 7.44/2.34 ! [X0 : $tType,X1 : $tType] : (finite_finite @ X0 => ! [X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X4 : trm @ X1 @ X0,X5 : trm @ X1 @ X0] : ((denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ (plus @ X1 @ X0 @ X4 @ X5))) => (denotational_Vagree @ X0 @ X2 @ X3 @ (static_FVDiff @ X1 @ X0 @ X5))))),
% 7.44/2.34 inference(rectify,[status(thm)],[f1])).
% 7.44/2.34 thf(f1,axiom,(
% 7.44/2.34 ! [X0 : $tType,X2 : $tType] : (finite_finite @ X0 => ! [X7 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X8 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X9 : trm @ X2 @ X0,X10 : trm @ X2 @ X0] : ((denotational_Vagree @ X0 @ X7 @ X8 @ (static_FVDiff @ X2 @ X0 @ (plus @ X2 @ X0 @ X9 @ X10))) => (denotational_Vagree @ X0 @ X7 @ X8 @ (static_FVDiff @ X2 @ X0 @ X10))))),
% 7.44/2.34 file('/export/starexec/sandbox2/tmp/tmp.EGxl0yY1Vf/DTF2THF_18030.p',fact_0_agree__plus2)).
% 7.44/2.34 thf(f1438,plain,(
% 7.44/2.34 ~spl94_6),
% 7.44/2.34 inference(avatar_split_clause,[status(thm)],[f1276,f1389])).
% 7.44/2.34 thf(f1276,plain,(
% 7.44/2.34 ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) != $true)),
% 7.44/2.34 inference(cnf_transformation,[status(thm)],[f915])).
% 7.44/2.34 thf(f915,plain,(
% 7.44/2.34 ((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) != $true)),
% 7.44/2.34 inference(flattening,[status(thm)],[f838])).
% 7.44/2.34 thf(f838,plain,(
% 7.44/2.34 ~((denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2)) = $true)),
% 7.44/2.34 inference(fool_elimination,[status(thm)],[f837])).
% 7.44/2.34 thf(f837,plain,(
% 7.44/2.34 ~(denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2))),
% 7.44/2.34 inference(rectify,[status(thm)],[f325])).
% 7.44/2.34 thf(f325,negated_conjecture,(
% 7.44/2.34 ~(denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2))),
% 7.44/2.34 inference(negated_conjecture,[status(cth)],[f324])).
% 7.44/2.34 thf(f324,conjecture,(
% 7.44/2.34 (denotational_Vagree @ c @ nu @ nu2 @ (static_FVDiff @ a @ c @ t2))),
% 7.44/2.34 file('/export/starexec/sandbox2/tmp/tmp.EGxl0yY1Vf/DTF2THF_18030.p',conj_0)).
% 7.44/2.34 % SZS output end Proof for DTF2THF_18030
% 7.44/2.34 % (18177)------------------------------
% 7.44/2.34 % (18177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.44/2.34 % (18177)Termination reason: Refutation
% 7.44/2.34
% 7.44/2.34 % (18177)Memory used [KB]: 9210
% 7.44/2.34 % (18177)Time elapsed: 0.378 s
% 7.44/2.34 % (18177)Instructions burned: 1086 (million)
% 7.44/2.34 % (18177)------------------------------
% 7.44/2.34 % (18177)------------------------------
% 7.44/2.34 % (18129)Success in time 0.732 s
%------------------------------------------------------------------------------