TPTP Problem File: SLH0586^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Separation_Logic_Unbounded/0003_FixedPoint/prob_00520_016246__6859938_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 780 ( 333 unt; 125 typ; 0 def)
% Number of atoms : 1898 ( 436 equ; 0 cnn)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 8733 ( 231 ~; 2 |; 90 &;7866 @)
% ( 0 <=>; 544 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 11 avg)
% Number of types : 18 ( 17 usr)
% Number of type conns : 4202 (4202 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 108 usr; 8 con; 0-13 aty)
% Number of variables : 3474 ( 62 ^;3393 !; 19 ?;3474 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 16:05:27.274
%------------------------------------------------------------------------------
% Could-be-implicit typings (17)
thf(ty_n_t__Product____Type__Oprod_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J_J,type,
produc5105196854009589546_a_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J_J,type,
set_Pr1275464188344874039_a_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J,type,
produc5278197477302038359_a_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J,type,
produc5213381314664832452_a_c_d: $tType ).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
option6413918287372586467_a_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
set_as909545710669178647_b_d_c: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
assertion_a_b_d_c: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__a_Mtf__d_Mtf__c_J,type,
assertion_a_a_d_c: $tType ).
thf(ty_n_t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
product_prod_a_c_d: $tType ).
thf(ty_n_t__Option__Ooption_Itf__a_J,type,
option_a: $tType ).
thf(ty_n_t__Set__Oset_Itf__c_J,type,
set_c: $tType ).
thf(ty_n_t__Set__Oset_Itf__b_J,type,
set_b: $tType ).
thf(ty_n_t__Set__Oset_Itf__a_J,type,
set_a: $tType ).
thf(ty_n_tf__d,type,
d: $tType ).
thf(ty_n_tf__c,type,
c: $tType ).
thf(ty_n_tf__b,type,
b: $tType ).
thf(ty_n_tf__a,type,
a: $tType ).
% Explicit typings (108)
thf(sy_c_BNF__Def_OGrp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
bNF_Gr8554578625086265742_b_d_c: set_as909545710669178647_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_BNF__Def_OGrp_001tf__b_001tf__b,type,
bNF_Grp_b_b: set_b > ( b > b ) > b > b > $o ).
thf(sy_c_BNF__Def_Oeq__onp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
bNF_eq6553376382750210344_b_d_c: ( assertion_a_b_d_c > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_BNF__Def_Oeq__onp_001tf__b,type,
bNF_eq_onp_b: ( b > $o ) > b > b > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_I_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5462665785578358557_b_d_c: ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > $o ) > ( ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
bNF_re1770667264140748071_b_d_c: ( ( ( c > d ) > a > $o ) > ( ( c > d ) > a > $o ) > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5536568207858047837_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J,type,
bNF_re3555337462168811729_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J,type,
bNF_re5146714292400357853_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J,type,
bNF_re6312048780865235365_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J,type,
bNF_re3015297470480446045_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J,type,
bNF_re6606623624522348157_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
bNF_re8402442907184412917_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re969776683416675581_b_d_c: ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_J,type,
bNF_re6697097071762359901_d_c_o: ( ( b > b > $o ) > ( b > b > $o ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > $o ) > ( ( b > b > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( b > b > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_Eo_J_001_062_Itf__b_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J,type,
bNF_re3168247226632236905_d_c_o: ( ( b > $o ) > ( b > $o ) > $o ) > ( ( assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > $o ) > $o ) > ( ( b > $o ) > assertion_a_b_d_c > $o ) > ( ( b > $o ) > assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
bNF_re4457485704112703733_b_d_c: ( ( b > b ) > ( b > b ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( b > b ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( b > b ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J,type,
bNF_re6171781090946898727_b_d_c: ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J,type,
bNF_re4264221303238623901_b_d_c: ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J,type,
bNF_re515523818749706873_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J,type,
bNF_re7564741212224818219_d_c_o: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > $o ) > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
bNF_re8872988018146346089_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001_Eo_001_Eo,type,
bNF_re7425909319474424221_c_o_o: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( $o > $o > $o ) > ( assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
bNF_re5048873211533932509_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
bNF_re377125674677652585_b_d_c: ( b > b > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_Itf__b_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
bNF_re4413358128099268379_o_b_o: ( b > b > $o ) > ( ( b > $o ) > ( b > $o ) > $o ) > ( b > b > $o ) > ( b > b > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_Eo_001_Eo,type,
bNF_rel_fun_b_b_o_o: ( b > b > $o ) > ( $o > $o > $o ) > ( b > $o ) > ( b > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001tf__b_001tf__b,type,
bNF_rel_fun_b_b_b_b: ( b > b > $o ) > ( b > b > $o ) > ( b > b ) > ( b > b ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__c_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
bNF_re133962660596780713_b_d_c: ( c > c > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_Combinability_Ologic_Ocombinable_001tf__a_001tf__b_001tf__c_001tf__d,type,
combinable_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( b > b > b ) > ( a > $o ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).
thf(sy_c_Combinability_Ologic_Ounambiguous_001tf__a_001tf__b_001tf__c_001tf__d,type,
unambiguous_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > c > $o ).
thf(sy_c_FixedPoint_Ologic_Oapplies__eq_001tf__a_001tf__b_001tf__d_001tf__c,type,
applies_eq_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).
thf(sy_c_FixedPoint_Ologic_Oapplies__eq__rel_001tf__a_001tf__b_001tf__d_001tf__c,type,
applie8886407701077375079_b_d_c: produc5105196854009589546_a_c_d > produc5105196854009589546_a_c_d > $o ).
thf(sy_c_FixedPoint_Ologic_Oempty__interp_001_062_Itf__c_Mtf__d_J_001tf__a,type,
empty_interp_c_d_a: ( c > d ) > set_a ).
thf(sy_c_FixedPoint_Ologic_Oindep__interp_001tf__a_001tf__b_001tf__d_001tf__c,type,
indep_interp_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > $o ).
thf(sy_c_FixedPoint_Ologic_Omonotonic_001tf__c_001tf__d_001tf__a,type,
monotonic_c_d_a: ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > $o ).
thf(sy_c_FixedPoint_Ologic_Onon__increasing_001tf__c_001tf__d_001tf__a,type,
non_increasing_c_d_a: ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > $o ).
thf(sy_c_FixedPoint_Ologic_Osmaller__interp_001tf__c_001tf__d_001tf__a,type,
smaller_interp_c_d_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).
thf(sy_c_Fun_Ocomp_001tf__b_001_Eo_001tf__b,type,
comp_b_o_b: ( b > $o ) > ( b > b ) > b > $o ).
thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001tf__b,type,
comp_b_b_b: ( b > b ) > ( b > b ) > b > b ).
thf(sy_c_Fun_Ofun__upd_001tf__c_001tf__d,type,
fun_upd_c_d: ( c > d ) > c > d > c > d ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__b_J,type,
sup_sup_set_b: set_b > set_b > set_b ).
thf(sy_c_Option_Ooption_ONone_001tf__a,type,
none_a: option_a ).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
some_P1084500821511757806_a_c_d: product_prod_a_c_d > option6413918287372586467_a_c_d ).
thf(sy_c_Option_Ooption_OSome_001tf__a,type,
some_a: a > option_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
bot_bot_set_a: set_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
bot_bot_set_b: set_b ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_M_Eo_J,type,
top_top_c_d_a_o_o: ( ( c > d ) > a > $o ) > $o ).
thf(sy_c_Product__Type_OPair_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_Itf__c_Mtf__d_J,type,
produc7376592049607813182_a_c_d: ( ( c > d ) > set_a ) > ( c > d ) > produc5213381314664832452_a_c_d ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
produc8093790510458973071_a_c_d: product_prod_a_c_d > option6413918287372586467_a_c_d > produc5278197477302038359_a_c_d ).
thf(sy_c_Product__Type_OPair_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J,type,
produc8894421531525210148_a_c_d: assertion_a_b_d_c > produc5213381314664832452_a_c_d > produc5105196854009589546_a_c_d ).
thf(sy_c_Product__Type_OPair_001tf__a_001_062_Itf__c_Mtf__d_J,type,
product_Pair_a_c_d: a > ( c > d ) > product_prod_a_c_d ).
thf(sy_c_Set_OCollect_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
collec7183461376620183714_b_d_c: ( assertion_a_b_d_c > $o ) > set_as909545710669178647_b_d_c ).
thf(sy_c_Set_OCollect_001tf__a,type,
collect_a: ( a > $o ) > set_a ).
thf(sy_c_Set_OCollect_001tf__b,type,
collect_b: ( b > $o ) > set_b ).
thf(sy_c_Set_Oimage_001tf__b_001tf__b,type,
image_b_b: ( b > b ) > set_b > set_b ).
thf(sy_c_Set_Oinsert_001tf__b,type,
insert_b: b > set_b > set_b ).
thf(sy_c_UnboundedLogic_Oassertion_OAnd_001tf__a_001tf__b_001tf__d_001tf__c,type,
and_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OBounded_001tf__a_001tf__b_001tf__d_001tf__c,type,
bounded_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OExists_001tf__c_001tf__a_001tf__b_001tf__d,type,
exists_c_a_b_d: c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OForall_001tf__c_001tf__a_001tf__b_001tf__d,type,
forall_c_a_b_d: c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OImp_001tf__a_001tf__b_001tf__d_001tf__c,type,
imp_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OMult_001tf__b_001tf__a_001tf__d_001tf__c,type,
mult_b_a_d_c: b > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OOr_001tf__a_001tf__b_001tf__d_001tf__c,type,
or_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OPred_001tf__a_001tf__b_001tf__d_001tf__c,type,
pred_a_b_d_c: assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OSem_001tf__c_001tf__d_001tf__a_001tf__b,type,
sem_c_d_a_b: ( ( c > d ) > a > $o ) > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OStar_001tf__a_001tf__b_001tf__d_001tf__c,type,
star_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OWand_001tf__a_001tf__b_001tf__d_001tf__c,type,
wand_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OWildcard_001tf__a_001tf__b_001tf__d_001tf__c,type,
wildcard_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_Ocase__assertion_001tf__c_001tf__d_001tf__a_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001tf__b,type,
case_a2736964712663357406_d_c_b: ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_Omap__assertion_001tf__b_001tf__b_001tf__a_001tf__d_001tf__c,type,
map_as2132001898603344138_a_d_c: ( b > b ) > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_Opred__assertion_001tf__b_001tf__a_001tf__d_001tf__c,type,
pred_a5408123710409757427_a_d_c: ( b > $o ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__a_001tf__b_001tf__a_001tf__d_001tf__c,type,
rel_as1194089545255703174_a_d_c: ( a > b > $o ) > assertion_a_a_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001tf__a_001tf__a_001tf__d_001tf__c,type,
rel_as373026983500813000_a_d_c: ( b > a > $o ) > assertion_a_b_d_c > assertion_a_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001tf__b_001tf__a_001tf__d_001tf__c,type,
rel_as1860989020795611527_a_d_c: ( b > b > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_001tf__a_001tf__d_001tf__c,type,
set_as1636463702398212043_a_d_c: assertion_a_a_d_c > set_a ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_001tf__b_001tf__d_001tf__c,type,
set_as7232682317586342732_b_d_c: assertion_a_b_d_c > set_b ).
thf(sy_c_UnboundedLogic_Ologic_001tf__a_001tf__b,type,
logic_a_b: ( a > a > option_a ) > ( b > a > a ) > ( b > b > b ) > ( b > b > b ) > ( b > b ) > b > ( a > $o ) > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oentails_001tf__a_001tf__b_001tf__d_001tf__c,type,
entails_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oequal__outside_001tf__c_001tf__d,type,
equal_outside_c_d: ( c > d ) > ( c > d ) > set_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oequivalent_001tf__a_001tf__b_001tf__d_001tf__c,type,
equivalent_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oframe__property_001tf__a_001tf__c_001tf__d,type,
frame_property_a_c_d: ( a > a > option_a ) > ( a > $o ) > set_Pr1275464188344874039_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Ointuitionistic_001tf__a_001tf__b_001tf__c_001tf__d,type,
intuit7508411120625971703_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > ( c > d ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Omodified_001tf__a_001tf__c_001tf__d,type,
modified_a_c_d: set_Pr1275464188344874039_a_c_d > set_c ).
thf(sy_c_UnboundedLogic_Ologic_Onot__in__fv_001tf__a_001tf__b_001tf__d_001tf__c,type,
not_in_fv_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > set_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Opure_001tf__a_001tf__b_001tf__d_001tf__c,type,
pure_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Osafe_001tf__a_001tf__c_001tf__d,type,
safe_a_c_d: set_Pr1275464188344874039_a_c_d > product_prod_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Osafety__monotonicity_001tf__a_001tf__c_001tf__d,type,
safety844553430189520448_a_c_d: ( a > a > option_a ) > ( a > $o ) > set_Pr1275464188344874039_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Osat_001tf__a_001tf__b_001tf__c_001tf__d,type,
sat_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > a > ( c > d ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Ovalid__command_001tf__a_001tf__c_001tf__d,type,
valid_command_a_c_d: ( a > $o ) > set_Pr1275464188344874039_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Ovalid__hoare__triple_001tf__a_001tf__b_001tf__d_001tf__c,type,
valid_6037315502795721655_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > set_Pr1275464188344874039_a_c_d > assertion_a_b_d_c > ( ( c > d ) > set_a ) > $o ).
thf(sy_c_UnboundedLogic_Opre__logic_Ocompatible_001tf__a,type,
pre_compatible_a: ( a > a > option_a ) > a > a > $o ).
thf(sy_c_UnboundedLogic_Opre__logic_Olarger_001tf__a,type,
pre_larger_a: ( a > a > option_a ) > a > a > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J_J,type,
accp_P5381461700908302305_a_c_d: ( produc5105196854009589546_a_c_d > produc5105196854009589546_a_c_d > $o ) > produc5105196854009589546_a_c_d > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J,type,
member1180172933830803072_a_c_d: produc5278197477302038359_a_c_d > set_Pr1275464188344874039_a_c_d > $o ).
thf(sy_c_member_001tf__a,type,
member_a: a > set_a > $o ).
thf(sy_c_member_001tf__b,type,
member_b: b > set_b > $o ).
thf(sy_v_A,type,
a2: assertion_a_b_d_c ).
thf(sy_v_mult,type,
mult: b > a > a ).
thf(sy_v_one,type,
one: b ).
thf(sy_v_plus,type,
plus: a > a > option_a ).
thf(sy_v_sadd,type,
sadd: b > b > b ).
thf(sy_v_sinv,type,
sinv: b > b ).
thf(sy_v_smult,type,
smult: b > b > b ).
thf(sy_v_v,type,
v: c ).
thf(sy_v_valid,type,
valid: a > $o ).
% Relevant facts (654)
thf(fact_0_commutative,axiom,
! [A: a,B: a] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ) ).
% commutative
thf(fact_1_can__divide,axiom,
! [P: b,A: a,B: a] :
( ( ( mult @ P @ A )
= ( mult @ P @ B ) )
=> ( A = B ) ) ).
% can_divide
thf(fact_2_assms,axiom,
non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ a2 ) ).
% assms
thf(fact_3_unique__inv,axiom,
! [A: a,P: b,B: a] :
( ( A
= ( mult @ P @ B ) )
= ( B
= ( mult @ ( sinv @ P ) @ A ) ) ) ).
% unique_inv
thf(fact_4_indep__implies__non__increasing,axiom,
! [A2: assertion_a_b_d_c] :
( ( indep_interp_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) ) ) ).
% indep_implies_non_increasing
thf(fact_5_logic_Oapplies__eq_Ocong,axiom,
applies_eq_a_b_d_c = applies_eq_a_b_d_c ).
% logic.applies_eq.cong
thf(fact_6_non__increasing__instantiate,axiom,
! [A2: assertion_a_b_d_c,X: a,Delta: ( c > d ) > set_a,S: c > d,Delta2: ( c > d ) > set_a] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( member_a @ X @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ S ) )
=> ( ( smaller_interp_c_d_a @ Delta2 @ Delta )
=> ( member_a @ X @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ S ) ) ) ) ) ).
% non_increasing_instantiate
thf(fact_7_non__increasing__bounded,axiom,
! [A2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ).
% non_increasing_bounded
thf(fact_8_non__increasing__or,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% non_increasing_or
thf(fact_9_non__increasing__and,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% non_increasing_and
thf(fact_10_non__increasing__mult,axiom,
! [A2: assertion_a_b_d_c,Pi: b] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ).
% non_increasing_mult
thf(fact_11_non__inc__star,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% non_inc_star
thf(fact_12_non__increasing__sem,axiom,
! [B2: ( c > d ) > a > $o] : ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( sem_c_d_a_b @ B2 ) ) ) ).
% non_increasing_sem
thf(fact_13_non__increasing__wild,axiom,
! [A2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% non_increasing_wild
thf(fact_14_mono__exists,axiom,
! [A2: assertion_a_b_d_c,V: c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ V @ A2 ) ) ) ) ).
% mono_exists
thf(fact_15_valid__mono,axiom,
! [A: a,B: a] :
( ( ( valid @ A )
& ( pre_larger_a @ plus @ A @ B ) )
=> ( valid @ B ) ) ).
% valid_mono
thf(fact_16_larger__same,axiom,
! [A: a,B: a,P: b] :
( ( pre_larger_a @ plus @ A @ B )
= ( pre_larger_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).
% larger_same
thf(fact_17_compatible__iff,axiom,
! [A: a,B: a,P: b] :
( ( pre_compatible_a @ plus @ A @ B )
= ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).
% compatible_iff
thf(fact_18_smaller__interp__trans,axiom,
! [A: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ A @ B )
=> ( ( smaller_interp_c_d_a @ B @ C )
=> ( smaller_interp_c_d_a @ A @ C ) ) ) ).
% smaller_interp_trans
thf(fact_19_smaller__interp__refl,axiom,
! [Delta2: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ Delta2 @ Delta2 ) ).
% smaller_interp_refl
thf(fact_20_smaller__interpI,axiom,
! [Delta2: ( c > d ) > set_a,Delta: ( c > d ) > set_a] :
( ! [S2: c > d,X2: a] :
( ( member_a @ X2 @ ( Delta2 @ S2 ) )
=> ( member_a @ X2 @ ( Delta @ S2 ) ) )
=> ( smaller_interp_c_d_a @ Delta2 @ Delta ) ) ).
% smaller_interpI
thf(fact_21_monotonicI,axiom,
! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta3 ) @ ( F @ Delta4 ) ) )
=> ( monotonic_c_d_a @ F ) ) ).
% monotonicI
thf(fact_22_monotonic__def,axiom,
( monotonic_c_d_a
= ( ^ [F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F2 @ Delta5 ) @ ( F2 @ Delta6 ) ) ) ) ) ).
% monotonic_def
thf(fact_23_non__increasing__def,axiom,
( non_increasing_c_d_a
= ( ^ [F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F2 @ Delta6 ) @ ( F2 @ Delta5 ) ) ) ) ) ).
% non_increasing_def
thf(fact_24_non__increasingI,axiom,
! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta4 ) @ ( F @ Delta3 ) ) )
=> ( non_increasing_c_d_a @ F ) ) ).
% non_increasingI
thf(fact_25_larger__implies__compatible,axiom,
! [X: a,Y: a] :
( ( pre_larger_a @ plus @ X @ Y )
=> ( pre_compatible_a @ plus @ X @ Y ) ) ).
% larger_implies_compatible
thf(fact_26_compatible__smaller,axiom,
! [A: a,B: a,X: a] :
( ( pre_larger_a @ plus @ A @ B )
=> ( ( pre_compatible_a @ plus @ X @ A )
=> ( pre_compatible_a @ plus @ X @ B ) ) ) ).
% compatible_smaller
thf(fact_27_compatible__multiples,axiom,
! [P: b,A: a,Q: b,B: a] :
( ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) )
=> ( pre_compatible_a @ plus @ A @ B ) ) ).
% compatible_multiples
thf(fact_28_compatible__imp,axiom,
! [A: a,B: a,P: b] :
( ( pre_compatible_a @ plus @ A @ B )
=> ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).
% compatible_imp
thf(fact_29_smaller__empty,axiom,
! [X: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ empty_interp_c_d_a @ X ) ).
% smaller_empty
thf(fact_30_local_Omono__mult,axiom,
! [A2: assertion_a_b_d_c,Pi: b] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ).
% local.mono_mult
thf(fact_31_mono__wild,axiom,
! [A2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% mono_wild
thf(fact_32_mono__instantiate,axiom,
! [A2: assertion_a_b_d_c,X: a,Delta2: ( c > d ) > set_a,S: c > d,Delta: ( c > d ) > set_a] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( member_a @ X @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ S ) )
=> ( ( smaller_interp_c_d_a @ Delta2 @ Delta )
=> ( member_a @ X @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ S ) ) ) ) ) ).
% mono_instantiate
thf(fact_33_mono__star,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% mono_star
thf(fact_34_mono__and,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% mono_and
thf(fact_35_mono__or,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% mono_or
thf(fact_36_mono__bounded,axiom,
! [A2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ).
% mono_bounded
thf(fact_37_mono__sem,axiom,
! [B2: ( c > d ) > a > $o] : ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( sem_c_d_a_b @ B2 ) ) ) ).
% mono_sem
thf(fact_38_logic_Oindep__interp_Ocong,axiom,
indep_interp_a_b_d_c = indep_interp_a_b_d_c ).
% logic.indep_interp.cong
thf(fact_39_unambiguous__star,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c,B2: assertion_a_b_d_c] :
( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta2 @ A2 @ X )
=> ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta2 @ ( star_a_b_d_c @ A2 @ B2 ) @ X ) ) ).
% unambiguous_star
thf(fact_40_hoare__triple__input,axiom,
! [P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta2 )
= ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ P2 ) @ C @ Q2 @ Delta2 ) ) ).
% hoare_triple_input
thf(fact_41_mono__interp,axiom,
monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ pred_a_b_d_c ) ).
% mono_interp
thf(fact_42_mem__Collect__eq,axiom,
! [A: b,P2: b > $o] :
( ( member_b @ A @ ( collect_b @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_43_mem__Collect__eq,axiom,
! [A: a,P2: a > $o] :
( ( member_a @ A @ ( collect_a @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_44_Collect__mem__eq,axiom,
! [A2: set_b] :
( ( collect_b
@ ^ [X3: b] : ( member_b @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_45_Collect__mem__eq,axiom,
! [A2: set_a] :
( ( collect_a
@ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_46_Collect__cong,axiom,
! [P2: a > $o,Q2: a > $o] :
( ! [X2: a] :
( ( P2 @ X2 )
= ( Q2 @ X2 ) )
=> ( ( collect_a @ P2 )
= ( collect_a @ Q2 ) ) ) ).
% Collect_cong
thf(fact_47_WildOr,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( or_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( or_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B2 ) ) ) ).
% WildOr
thf(fact_48_WildExists,axiom,
! [X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( exists_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( exists_c_a_b_d @ X @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% WildExists
thf(fact_49_DotOr,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% DotOr
thf(fact_50_DotExists,axiom,
! [P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( exists_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% DotExists
thf(fact_51_DotAnd,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ).
% DotAnd
thf(fact_52_DotStar,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% DotStar
thf(fact_53_WildDot,axiom,
! [P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ).
% WildDot
thf(fact_54_DotWild,axiom,
! [P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ).
% DotWild
thf(fact_55_WildWild,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ).
% WildWild
thf(fact_56_hoare__triple__output,axiom,
! [C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( valid_command_a_c_d @ valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta2 )
= ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ ( bounded_a_b_d_c @ Q2 ) @ Delta2 ) ) ) ).
% hoare_triple_output
thf(fact_57_WildPure,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta2 @ A2 ) ) ).
% WildPure
thf(fact_58_DotPure,axiom,
! [A2: assertion_a_b_d_c,P: b,Delta2: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta2 @ A2 ) ) ).
% DotPure
thf(fact_59_DotFull,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ one @ A2 ) @ Delta2 @ A2 ) ).
% DotFull
thf(fact_60_mono__imp,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% mono_imp
thf(fact_61_mono__wand,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% mono_wand
thf(fact_62_non__increasing__imp,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% non_increasing_imp
thf(fact_63_non__increasing__wand,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% non_increasing_wand
thf(fact_64_DotImp,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% DotImp
thf(fact_65_DotWand,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% DotWand
thf(fact_66_DotDot,axiom,
! [P: b,Q: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ ( smult @ P @ Q ) @ A2 ) ) ).
% DotDot
thf(fact_67_DotForall,axiom,
! [P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( forall_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% DotForall
thf(fact_68_smult__comm,axiom,
! [P: b,Q: b] :
( ( smult @ P @ Q )
= ( smult @ Q @ P ) ) ).
% smult_comm
thf(fact_69_smult__asso,axiom,
! [P: b,Q: b,R: b] :
( ( smult @ ( smult @ P @ Q ) @ R )
= ( smult @ P @ ( smult @ Q @ R ) ) ) ).
% smult_asso
thf(fact_70_can__factorize,axiom,
! [Q: b,P: b] :
? [R2: b] :
( Q
= ( smult @ R2 @ P ) ) ).
% can_factorize
thf(fact_71_double__mult,axiom,
! [P: b,Q: b,A: a] :
( ( mult @ P @ ( mult @ Q @ A ) )
= ( mult @ ( smult @ P @ Q ) @ A ) ) ).
% double_mult
thf(fact_72_one__neutral,axiom,
! [A: a] :
( ( mult @ one @ A )
= A ) ).
% one_neutral
thf(fact_73_sone__neutral,axiom,
! [P: b] :
( ( smult @ one @ P )
= P ) ).
% sone_neutral
thf(fact_74_sinv__inverse,axiom,
! [P: b] :
( ( smult @ P @ ( sinv @ P ) )
= one ) ).
% sinv_inverse
thf(fact_75_mono__forall,axiom,
! [A2: assertion_a_b_d_c,V: c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( forall_c_a_b_d @ V @ A2 ) ) ) ) ).
% mono_forall
thf(fact_76_assertion_Oexhaust,axiom,
! [Y: assertion_a_b_d_c] :
( ! [X1: ( c > d ) > a > $o] :
( Y
!= ( sem_c_d_a_b @ X1 ) )
=> ( ! [X21: b,X22: assertion_a_b_d_c] :
( Y
!= ( mult_b_a_d_c @ X21 @ X22 ) )
=> ( ! [X31: assertion_a_b_d_c,X32: assertion_a_b_d_c] :
( Y
!= ( star_a_b_d_c @ X31 @ X32 ) )
=> ( ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c] :
( Y
!= ( wand_a_b_d_c @ X41 @ X42 ) )
=> ( ! [X51: assertion_a_b_d_c,X52: assertion_a_b_d_c] :
( Y
!= ( or_a_b_d_c @ X51 @ X52 ) )
=> ( ! [X61: assertion_a_b_d_c,X62: assertion_a_b_d_c] :
( Y
!= ( and_a_b_d_c @ X61 @ X62 ) )
=> ( ! [X71: assertion_a_b_d_c,X72: assertion_a_b_d_c] :
( Y
!= ( imp_a_b_d_c @ X71 @ X72 ) )
=> ( ! [X81: c,X82: assertion_a_b_d_c] :
( Y
!= ( exists_c_a_b_d @ X81 @ X82 ) )
=> ( ! [X91: c,X92: assertion_a_b_d_c] :
( Y
!= ( forall_c_a_b_d @ X91 @ X92 ) )
=> ( ( Y != pred_a_b_d_c )
=> ( ! [X11: assertion_a_b_d_c] :
( Y
!= ( bounded_a_b_d_c @ X11 ) )
=> ~ ! [X12: assertion_a_b_d_c] :
( Y
!= ( wildcard_a_b_d_c @ X12 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% assertion.exhaust
thf(fact_77_mult__one__same2,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ ( mult_b_a_d_c @ one @ A2 ) ) ).
% mult_one_same2
thf(fact_78_mult__one__same1,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ one @ A2 ) @ Delta2 @ A2 ) ).
% mult_one_same1
thf(fact_79_dot__mult2,axiom,
! [P: b,Q: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ ( smult @ P @ Q ) @ A2 ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) ) ).
% dot_mult2
thf(fact_80_dot__mult1,axiom,
! [P: b,Q: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ ( smult @ P @ Q ) @ A2 ) ) ).
% dot_mult1
thf(fact_81_pure__mult2,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,P: b] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% pure_mult2
thf(fact_82_pure__mult1,axiom,
! [A2: assertion_a_b_d_c,P: b,Delta2: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta2 @ A2 ) ) ).
% pure_mult1
thf(fact_83_WildForall,axiom,
! [X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( forall_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( forall_c_a_b_d @ X @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% WildForall
thf(fact_84_WildAnd,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( and_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( and_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B2 ) ) ) ).
% WildAnd
thf(fact_85_assertion_Oinject_I2_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,Y21: b,Y22: assertion_a_b_d_c] :
( ( ( mult_b_a_d_c @ X212 @ X222 )
= ( mult_b_a_d_c @ Y21 @ Y22 ) )
= ( ( X212 = Y21 )
& ( X222 = Y22 ) ) ) ).
% assertion.inject(2)
thf(fact_86_assertion_Oinject_I11_J,axiom,
! [X122: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
( ( ( wildcard_a_b_d_c @ X122 )
= ( wildcard_a_b_d_c @ Y12 ) )
= ( X122 = Y12 ) ) ).
% assertion.inject(11)
thf(fact_87_assertion_Oinject_I3_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c] :
( ( ( star_a_b_d_c @ X312 @ X322 )
= ( star_a_b_d_c @ Y31 @ Y32 ) )
= ( ( X312 = Y31 )
& ( X322 = Y32 ) ) ) ).
% assertion.inject(3)
thf(fact_88_assertion_Oinject_I6_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
( ( ( and_a_b_d_c @ X612 @ X622 )
= ( and_a_b_d_c @ Y61 @ Y62 ) )
= ( ( X612 = Y61 )
& ( X622 = Y62 ) ) ) ).
% assertion.inject(6)
thf(fact_89_assertion_Oinject_I9_J,axiom,
! [X912: c,X922: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
( ( ( forall_c_a_b_d @ X912 @ X922 )
= ( forall_c_a_b_d @ Y91 @ Y92 ) )
= ( ( X912 = Y91 )
& ( X922 = Y92 ) ) ) ).
% assertion.inject(9)
thf(fact_90_assertion_Oinject_I5_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
( ( ( or_a_b_d_c @ X512 @ X522 )
= ( or_a_b_d_c @ Y51 @ Y52 ) )
= ( ( X512 = Y51 )
& ( X522 = Y52 ) ) ) ).
% assertion.inject(5)
thf(fact_91_assertion_Oinject_I4_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
( ( ( wand_a_b_d_c @ X412 @ X422 )
= ( wand_a_b_d_c @ Y41 @ Y42 ) )
= ( ( X412 = Y41 )
& ( X422 = Y42 ) ) ) ).
% assertion.inject(4)
thf(fact_92_assertion_Oinject_I7_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
( ( ( imp_a_b_d_c @ X712 @ X722 )
= ( imp_a_b_d_c @ Y71 @ Y72 ) )
= ( ( X712 = Y71 )
& ( X722 = Y72 ) ) ) ).
% assertion.inject(7)
thf(fact_93_assertion_Oinject_I8_J,axiom,
! [X812: c,X822: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
( ( ( exists_c_a_b_d @ X812 @ X822 )
= ( exists_c_a_b_d @ Y81 @ Y82 ) )
= ( ( X812 = Y81 )
& ( X822 = Y82 ) ) ) ).
% assertion.inject(8)
thf(fact_94_assertion_Oinject_I10_J,axiom,
! [X112: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
( ( ( bounded_a_b_d_c @ X112 )
= ( bounded_a_b_d_c @ Y11 ) )
= ( X112 = Y11 ) ) ).
% assertion.inject(10)
thf(fact_95_assertion_Oinject_I1_J,axiom,
! [X13: ( c > d ) > a > $o,Y1: ( c > d ) > a > $o] :
( ( ( sem_c_d_a_b @ X13 )
= ( sem_c_d_a_b @ Y1 ) )
= ( X13 = Y1 ) ) ).
% assertion.inject(1)
thf(fact_96_DotPos,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c,Pi: b] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 )
= ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A2 ) @ Delta2 @ ( mult_b_a_d_c @ Pi @ B2 ) ) ) ).
% DotPos
thf(fact_97_WildPos,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta2 @ ( wildcard_a_b_d_c @ B2 ) ) ) ).
% WildPos
thf(fact_98_equivalent__def,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( equivalent_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 )
= ( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 )
& ( entails_a_b_d_c @ plus @ mult @ valid @ B2 @ Delta2 @ A2 ) ) ) ).
% equivalent_def
thf(fact_99_dot__star1,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% dot_star1
thf(fact_100_dot__star2,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ).
% dot_star2
thf(fact_101_dot__and1,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% dot_and1
thf(fact_102_dot__and2,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ).
% dot_and2
thf(fact_103_dot__forall1,axiom,
! [P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( forall_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% dot_forall1
thf(fact_104_dot__forall2,axiom,
! [X: c,P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( forall_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X @ A2 ) ) ) ).
% dot_forall2
thf(fact_105_dot__exists1,axiom,
! [P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( exists_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% dot_exists1
thf(fact_106_dot__exists2,axiom,
! [X: c,P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X @ A2 ) ) ) ).
% dot_exists2
thf(fact_107_dot__or1,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% dot_or1
thf(fact_108_dot__or2,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B2 ) ) ) ).
% dot_or2
thf(fact_109_dot__imp1,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ).
% dot_imp1
thf(fact_110_dot__imp2,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% dot_imp2
thf(fact_111_dot__wand1,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ).
% dot_wand1
thf(fact_112_dot__wand2,axiom,
! [P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ).
% dot_wand2
thf(fact_113_WildStar1,axiom,
! [A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( star_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( star_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B2 ) ) ) ).
% WildStar1
thf(fact_114_logic_Oentails_Ocong,axiom,
entails_a_b_d_c = entails_a_b_d_c ).
% logic.entails.cong
thf(fact_115_logic_Oequivalent_Ocong,axiom,
equivalent_a_b_d_c = equivalent_a_b_d_c ).
% logic.equivalent.cong
thf(fact_116_pre__logic_Ocompatible_Ocong,axiom,
pre_compatible_a = pre_compatible_a ).
% pre_logic.compatible.cong
thf(fact_117_pre__logic_Olarger_Ocong,axiom,
pre_larger_a = pre_larger_a ).
% pre_logic.larger.cong
thf(fact_118_assertion_Odistinct_I41_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(41)
thf(fact_119_assertion_Odistinct_I23_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.distinct(23)
thf(fact_120_assertion_Odistinct_I29_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(29)
thf(fact_121_assertion_Odistinct_I35_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(35)
thf(fact_122_assertion_Odistinct_I27_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.distinct(27)
thf(fact_123_assertion_Odistinct_I25_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.distinct(25)
thf(fact_124_assertion_Odistinct_I31_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(31)
thf(fact_125_assertion_Odistinct_I33_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(33)
thf(fact_126_assertion_Odistinct_I39_J,axiom,
! [X212: b,X222: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(39)
thf(fact_127_assertion_Odistinct_I1_J,axiom,
! [X13: ( c > d ) > a > $o,X212: b,X222: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.distinct(1)
thf(fact_128_assertion_Odistinct_I59_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(59)
thf(fact_129_assertion_Odistinct_I37_J,axiom,
! [X212: b,X222: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X222 )
!= pred_a_b_d_c ) ).
% assertion.distinct(37)
thf(fact_130_assertion_Odistinct_I101_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(101)
thf(fact_131_assertion_Odistinct_I125_J,axiom,
! [X912: c,X922: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( forall_c_a_b_d @ X912 @ X922 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(125)
thf(fact_132_assertion_Odistinct_I89_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(89)
thf(fact_133_assertion_Odistinct_I75_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(75)
thf(fact_134_assertion_Odistinct_I111_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( imp_a_b_d_c @ X712 @ X722 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(111)
thf(fact_135_assertion_Odistinct_I119_J,axiom,
! [X812: c,X822: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( exists_c_a_b_d @ X812 @ X822 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(119)
thf(fact_136_assertion_Odistinct_I47_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(47)
thf(fact_137_assertion_Odistinct_I53_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(53)
thf(fact_138_assertion_Odistinct_I131_J,axiom,
! [X112: assertion_a_b_d_c,X122: assertion_a_b_d_c] :
( ( bounded_a_b_d_c @ X112 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(131)
thf(fact_139_assertion_Odistinct_I45_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.distinct(45)
thf(fact_140_assertion_Odistinct_I43_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.distinct(43)
thf(fact_141_assertion_Odistinct_I49_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(49)
thf(fact_142_assertion_Odistinct_I51_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(51)
thf(fact_143_assertion_Odistinct_I95_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(95)
thf(fact_144_assertion_Odistinct_I21_J,axiom,
! [X13: ( c > d ) > a > $o,X122: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(21)
thf(fact_145_assertion_Odistinct_I77_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(77)
thf(fact_146_assertion_Odistinct_I63_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(63)
thf(fact_147_assertion_Odistinct_I91_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(91)
thf(fact_148_assertion_Odistinct_I83_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(83)
thf(fact_149_assertion_Odistinct_I69_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(69)
thf(fact_150_assertion_Odistinct_I105_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( imp_a_b_d_c @ X712 @ X722 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(105)
thf(fact_151_assertion_Odistinct_I93_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(93)
thf(fact_152_assertion_Odistinct_I61_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.distinct(61)
thf(fact_153_assertion_Odistinct_I79_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(79)
thf(fact_154_assertion_Odistinct_I65_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(65)
thf(fact_155_assertion_Odistinct_I113_J,axiom,
! [X812: c,X822: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( exists_c_a_b_d @ X812 @ X822 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(113)
thf(fact_156_assertion_Odistinct_I81_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(81)
thf(fact_157_assertion_Odistinct_I103_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( imp_a_b_d_c @ X712 @ X722 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(103)
thf(fact_158_assertion_Odistinct_I67_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(67)
thf(fact_159_assertion_Odistinct_I57_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(57)
thf(fact_160_assertion_Odistinct_I129_J,axiom,
! [X122: assertion_a_b_d_c] :
( pred_a_b_d_c
!= ( wildcard_a_b_d_c @ X122 ) ) ).
% assertion.distinct(129)
thf(fact_161_assertion_Odistinct_I3_J,axiom,
! [X13: ( c > d ) > a > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.distinct(3)
thf(fact_162_assertion_Odistinct_I99_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(99)
thf(fact_163_assertion_Odistinct_I123_J,axiom,
! [X912: c,X922: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( forall_c_a_b_d @ X912 @ X922 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(123)
thf(fact_164_assertion_Odistinct_I87_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(87)
thf(fact_165_assertion_Odistinct_I73_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(73)
thf(fact_166_assertion_Odistinct_I109_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( imp_a_b_d_c @ X712 @ X722 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(109)
thf(fact_167_assertion_Odistinct_I117_J,axiom,
! [X812: c,X822: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( exists_c_a_b_d @ X812 @ X822 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(117)
thf(fact_168_assertion_Odistinct_I9_J,axiom,
! [X13: ( c > d ) > a > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(9)
thf(fact_169_assertion_Odistinct_I15_J,axiom,
! [X13: ( c > d ) > a > $o,X912: c,X922: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(15)
thf(fact_170_assertion_Odistinct_I7_J,axiom,
! [X13: ( c > d ) > a > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.distinct(7)
thf(fact_171_assertion_Odistinct_I5_J,axiom,
! [X13: ( c > d ) > a > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.distinct(5)
thf(fact_172_assertion_Odistinct_I11_J,axiom,
! [X13: ( c > d ) > a > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(11)
thf(fact_173_assertion_Odistinct_I13_J,axiom,
! [X13: ( c > d ) > a > $o,X812: c,X822: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(13)
thf(fact_174_assertion_Odistinct_I55_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= pred_a_b_d_c ) ).
% assertion.distinct(55)
thf(fact_175_assertion_Odistinct_I97_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= pred_a_b_d_c ) ).
% assertion.distinct(97)
thf(fact_176_assertion_Odistinct_I121_J,axiom,
! [X912: c,X922: assertion_a_b_d_c] :
( ( forall_c_a_b_d @ X912 @ X922 )
!= pred_a_b_d_c ) ).
% assertion.distinct(121)
thf(fact_177_assertion_Odistinct_I85_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= pred_a_b_d_c ) ).
% assertion.distinct(85)
thf(fact_178_assertion_Odistinct_I71_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= pred_a_b_d_c ) ).
% assertion.distinct(71)
thf(fact_179_assertion_Odistinct_I107_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( imp_a_b_d_c @ X712 @ X722 )
!= pred_a_b_d_c ) ).
% assertion.distinct(107)
thf(fact_180_assertion_Odistinct_I115_J,axiom,
! [X812: c,X822: assertion_a_b_d_c] :
( ( exists_c_a_b_d @ X812 @ X822 )
!= pred_a_b_d_c ) ).
% assertion.distinct(115)
thf(fact_181_assertion_Odistinct_I19_J,axiom,
! [X13: ( c > d ) > a > $o,X112: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X13 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(19)
thf(fact_182_assertion_Odistinct_I127_J,axiom,
! [X112: assertion_a_b_d_c] :
( pred_a_b_d_c
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(127)
thf(fact_183_assertion_Odistinct_I17_J,axiom,
! [X13: ( c > d ) > a > $o] :
( ( sem_c_d_a_b @ X13 )
!= pred_a_b_d_c ) ).
% assertion.distinct(17)
thf(fact_184_smaller__interp__applies__cons,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,Delta: ( c > d ) > set_a,A: a,S: c > d] :
( ( smaller_interp_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 ) @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta ) )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S @ Delta @ A2 ) ) ) ).
% smaller_interp_applies_cons
thf(fact_185_sat_Osimps_I10_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ pred_a_b_d_c )
= ( member_a @ Sigma @ ( Delta2 @ S ) ) ) ).
% sat.simps(10)
thf(fact_186_indep__interp__def,axiom,
! [A2: assertion_a_b_d_c] :
( ( indep_interp_a_b_d_c @ plus @ mult @ valid @ A2 )
= ( ! [X3: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ X3 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ X3 @ S3 @ Delta6 @ A2 ) ) ) ) ).
% indep_interp_def
thf(fact_187_sat_Osimps_I4_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,B: ( c > d ) > a > $o] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( sem_c_d_a_b @ B ) )
= ( B @ S @ Sigma ) ) ).
% sat.simps(4)
thf(fact_188_sat_Osimps_I11_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( bounded_a_b_d_c @ A2 ) )
= ( ( valid @ Sigma )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ A2 ) ) ) ).
% sat.simps(11)
thf(fact_189_pure__def,axiom,
! [A2: assertion_a_b_d_c] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
= ( ! [Sigma2: a,Sigma3: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S3 @ Delta6 @ A2 ) ) ) ) ).
% pure_def
thf(fact_190_sat_Osimps_I6_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( or_a_b_d_c @ A2 @ B2 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ A2 )
| ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ B2 ) ) ) ).
% sat.simps(6)
thf(fact_191_sat_Osimps_I5_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( imp_a_b_d_c @ A2 @ B2 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ B2 ) ) ) ).
% sat.simps(5)
thf(fact_192_sat__imp,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ B2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ).
% sat_imp
thf(fact_193_sat_Osimps_I7_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( and_a_b_d_c @ A2 @ B2 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ B2 ) ) ) ).
% sat.simps(7)
thf(fact_194_sat__mult,axiom,
! [Sigma: a,P: b,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [A3: a] :
( ( Sigma
= ( mult @ P @ A3 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S @ Delta2 @ A2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% sat_mult
thf(fact_195_sat_Osimps_I1_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,P: b,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( mult_b_a_d_c @ P @ A2 ) )
= ( ? [A4: a] :
( ( Sigma
= ( mult @ P @ A4 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ).
% sat.simps(1)
thf(fact_196_entails__def,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 )
= ( ! [Sigma2: a,S3: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta2 @ B2 ) ) ) ) ).
% entails_def
thf(fact_197_entailsI,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ! [Sigma4: a,S2: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ B2 ) )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 ) ) ).
% entailsI
thf(fact_198_sat_Osimps_I12_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) )
= ( ? [A4: a,P3: b] :
( ( Sigma
= ( mult @ P3 @ A4 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ).
% sat.simps(12)
thf(fact_199_equivalentI,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ! [Sigma4: a,S2: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ B2 ) )
=> ( ! [Sigma4: a,S2: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ B2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ A2 ) )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ B2 ) ) ) ).
% equivalentI
thf(fact_200_intuitionistic__def,axiom,
! [S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S @ Delta2 @ A2 )
= ( ! [A4: a,B3: a] :
( ( ( pre_larger_a @ plus @ A4 @ B3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B3 @ S @ Delta2 @ A2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ).
% intuitionistic_def
thf(fact_201_intuitionisticI,axiom,
! [S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [A3: a,B4: a] :
( ( ( pre_larger_a @ plus @ A3 @ B4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B4 @ S @ Delta2 @ A2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S @ Delta2 @ A2 ) )
=> ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S @ Delta2 @ A2 ) ) ).
% intuitionisticI
thf(fact_202_not__in__fv__def,axiom,
! [A2: assertion_a_b_d_c,S4: set_c] :
( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A2 @ S4 )
= ( ! [Sigma2: a,S3: c > d,Delta5: ( c > d ) > set_a,S5: c > d] :
( ( equal_outside_c_d @ S3 @ S5 @ S4 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S5 @ Delta5 @ A2 ) ) ) ) ) ).
% not_in_fv_def
thf(fact_203_logic_Osat_Ocong,axiom,
sat_a_b_c_d = sat_a_b_c_d ).
% logic.sat.cong
thf(fact_204_unambiguous__def,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c] :
( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta2 @ A2 @ X )
= ( ! [Sigma_1: a,Sigma_2: a,V1: d,V2: d,S3: c > d] :
( ( ( pre_compatible_a @ plus @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_1 @ ( fun_upd_c_d @ S3 @ X @ V1 ) @ Delta2 @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_2 @ ( fun_upd_c_d @ S3 @ X @ V2 ) @ Delta2 @ A2 ) )
=> ( V1 = V2 ) ) ) ) ).
% unambiguous_def
thf(fact_205_unambiguousI,axiom,
! [X: c,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [Sigma_12: a,Sigma_22: a,V12: d,V22: d,S2: c > d] :
( ( ( pre_compatible_a @ plus @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_12 @ ( fun_upd_c_d @ S2 @ X @ V12 ) @ Delta2 @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_22 @ ( fun_upd_c_d @ S2 @ X @ V22 ) @ Delta2 @ A2 ) )
=> ( V12 = V22 ) )
=> ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta2 @ A2 @ X ) ) ).
% unambiguousI
thf(fact_206_sat_Osimps_I8_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( exists_c_a_b_d @ X @ A2 ) )
= ( ? [V3: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ ( fun_upd_c_d @ S @ X @ V3 ) @ Delta2 @ A2 ) ) ) ).
% sat.simps(8)
thf(fact_207_sat__forall,axiom,
! [Sigma: a,S: c > d,X: c,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [V4: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ ( fun_upd_c_d @ S @ X @ V4 ) @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( forall_c_a_b_d @ X @ A2 ) ) ) ).
% sat_forall
thf(fact_208_sat_Osimps_I9_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( forall_c_a_b_d @ X @ A2 ) )
= ( ! [V3: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ ( fun_upd_c_d @ S @ X @ V3 ) @ Delta2 @ A2 ) ) ) ).
% sat.simps(9)
thf(fact_209_sat__wand,axiom,
! [S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,Sigma: a,B2: assertion_a_b_d_c] :
( ! [A3: a,Sigma5: a] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S @ Delta2 @ A2 )
& ( ( some_a @ Sigma5 )
= ( plus @ Sigma @ A3 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S @ Delta2 @ B2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ).
% sat_wand
thf(fact_210_sat_Osimps_I3_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( wand_a_b_d_c @ A2 @ B2 ) )
= ( ! [A4: a,Sigma3: a] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta2 @ A2 )
& ( ( some_a @ Sigma3 )
= ( plus @ Sigma @ A4 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S @ Delta2 @ B2 ) ) ) ) ).
% sat.simps(3)
thf(fact_211_sat_Osimps_I2_J,axiom,
! [Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta2 @ ( star_a_b_d_c @ A2 @ B2 ) )
= ( ? [A4: a,B3: a] :
( ( ( some_a @ Sigma )
= ( plus @ A4 @ B3 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta2 @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B3 @ S @ Delta2 @ B2 ) ) ) ) ).
% sat.simps(2)
thf(fact_212_asso1,axiom,
! [A: a,B: a,Ab: a,C: a,Bc: a] :
( ( ( ( plus @ A @ B )
= ( some_a @ Ab ) )
& ( ( plus @ B @ C )
= ( some_a @ Bc ) ) )
=> ( ( plus @ Ab @ C )
= ( plus @ A @ Bc ) ) ) ).
% asso1
thf(fact_213_move__sum,axiom,
! [A: a,A1: a,A22: a,B: a,B1: a,B22: a,X: a,X13: a,X23: a] :
( ( ( some_a @ A )
= ( plus @ A1 @ A22 ) )
=> ( ( ( some_a @ B )
= ( plus @ B1 @ B22 ) )
=> ( ( ( some_a @ X )
= ( plus @ A @ B ) )
=> ( ( ( some_a @ X13 )
= ( plus @ A1 @ B1 ) )
=> ( ( ( some_a @ X23 )
= ( plus @ A22 @ B22 ) )
=> ( ( some_a @ X )
= ( plus @ X13 @ X23 ) ) ) ) ) ) ) ).
% move_sum
thf(fact_214_asso2,axiom,
! [A: a,B: a,Ab: a,C: a] :
( ( ( ( plus @ A @ B )
= ( some_a @ Ab ) )
& ~ ( pre_compatible_a @ plus @ B @ C ) )
=> ~ ( pre_compatible_a @ plus @ Ab @ C ) ) ).
% asso2
thf(fact_215_asso3,axiom,
! [A: a,B: a,C: a,Bc: a] :
( ~ ( pre_compatible_a @ plus @ A @ B )
=> ( ( ( plus @ B @ C )
= ( some_a @ Bc ) )
=> ~ ( pre_compatible_a @ plus @ A @ Bc ) ) ) ).
% asso3
thf(fact_216_larger__def,axiom,
! [A: a,B: a] :
( ( pre_larger_a @ plus @ A @ B )
= ( ? [C2: a] :
( ( some_a @ A )
= ( plus @ B @ C2 ) ) ) ) ).
% larger_def
thf(fact_217_larger__first__sum,axiom,
! [Y: a,A: a,B: a,X: a] :
( ( ( some_a @ Y )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ X @ Y )
=> ? [A5: a] :
( ( ( some_a @ X )
= ( plus @ A5 @ B ) )
& ( pre_larger_a @ plus @ A5 @ A ) ) ) ) ).
% larger_first_sum
thf(fact_218_sum__both__larger,axiom,
! [X4: a,A6: a,B5: a,X: a,A: a,B: a] :
( ( ( some_a @ X4 )
= ( plus @ A6 @ B5 ) )
=> ( ( ( some_a @ X )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ A6 @ A )
=> ( ( pre_larger_a @ plus @ B5 @ B )
=> ( pre_larger_a @ plus @ X4 @ X ) ) ) ) ) ).
% sum_both_larger
thf(fact_219_plus__mult,axiom,
! [A: a,B: a,C: a,P: b] :
( ( ( some_a @ A )
= ( plus @ B @ C ) )
=> ( ( some_a @ ( mult @ P @ A ) )
= ( plus @ ( mult @ P @ B ) @ ( mult @ P @ C ) ) ) ) ).
% plus_mult
thf(fact_220_pre__logic_Olarger__def,axiom,
( pre_larger_a
= ( ^ [Plus: a > a > option_a,A4: a,B3: a] :
? [C2: a] :
( ( some_a @ A4 )
= ( Plus @ B3 @ C2 ) ) ) ) ).
% pre_logic.larger_def
thf(fact_221_frame__rule,axiom,
! [C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,R3: assertion_a_b_d_c] :
( ( valid_command_a_c_d @ valid @ C )
=> ( ( safety844553430189520448_a_c_d @ plus @ valid @ C )
=> ( ( frame_property_a_c_d @ plus @ valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta2 )
=> ( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ R3 @ ( modified_a_c_d @ C ) )
=> ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ P2 @ R3 ) @ C @ ( star_a_b_d_c @ Q2 @ R3 ) @ Delta2 ) ) ) ) ) ) ).
% frame_rule
thf(fact_222_logic__axioms,axiom,
logic_a_b @ plus @ mult @ smult @ sadd @ sinv @ one @ valid ).
% logic_axioms
thf(fact_223_compatible__def,axiom,
! [A: a,B: a] :
( ( pre_compatible_a @ plus @ A @ B )
= ( ( plus @ A @ B )
!= none_a ) ) ).
% compatible_def
thf(fact_224_distrib__mult,axiom,
! [P: b,Q: b,X: a] :
( ( some_a @ ( mult @ ( sadd @ P @ Q ) @ X ) )
= ( plus @ ( mult @ P @ X ) @ ( mult @ Q @ X ) ) ) ).
% distrib_mult
thf(fact_225_empty__interp__def,axiom,
( empty_interp_c_d_a
= ( ^ [S3: c > d] : bot_bot_set_a ) ) ).
% empty_interp_def
thf(fact_226_sadd__comm,axiom,
! [P: b,Q: b] :
( ( sadd @ P @ Q )
= ( sadd @ Q @ P ) ) ).
% sadd_comm
thf(fact_227_smaller__interp__def,axiom,
( smaller_interp_c_d_a
= ( ^ [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
! [S3: c > d] : ( ord_less_eq_set_a @ ( Delta5 @ S3 ) @ ( Delta6 @ S3 ) ) ) ) ).
% smaller_interp_def
thf(fact_228_smult__distrib,axiom,
! [P: b,Q: b,R: b] :
( ( smult @ P @ ( sadd @ Q @ R ) )
= ( sadd @ ( smult @ P @ Q ) @ ( smult @ P @ R ) ) ) ).
% smult_distrib
thf(fact_229_logic_Osmult__distrib,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ ( Sadd @ Q @ R ) )
= ( Sadd @ ( Smult @ P @ Q ) @ ( Smult @ P @ R ) ) ) ) ).
% logic.smult_distrib
thf(fact_230_logic_Osone__neutral,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ One @ P )
= P ) ) ).
% logic.sone_neutral
thf(fact_231_logic_Osinv__inverse,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ ( Sinv @ P ) )
= One ) ) ).
% logic.sinv_inverse
thf(fact_232_logic_Oone__neutral,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Mult @ One @ A )
= A ) ) ).
% logic.one_neutral
thf(fact_233_logic_Odouble__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Mult @ P @ ( Mult @ Q @ A ) )
= ( Mult @ ( Smult @ P @ Q ) @ A ) ) ) ).
% logic.double_mult
thf(fact_234_logic_Ocommutative,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Plus2 @ A @ B )
= ( Plus2 @ B @ A ) ) ) ).
% logic.commutative
thf(fact_235_logic_Ounique__inv,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,P: b,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( A
= ( Mult @ P @ B ) )
= ( B
= ( Mult @ ( Sinv @ P ) @ A ) ) ) ) ).
% logic.unique_inv
thf(fact_236_logic_Osmult__comm,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ Q )
= ( Smult @ Q @ P ) ) ) ).
% logic.smult_comm
thf(fact_237_logic_Osmult__asso,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ ( Smult @ P @ Q ) @ R )
= ( Smult @ P @ ( Smult @ Q @ R ) ) ) ) ).
% logic.smult_asso
thf(fact_238_logic_Ocan__divide,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( Mult @ P @ A )
= ( Mult @ P @ B ) )
=> ( A = B ) ) ) ).
% logic.can_divide
thf(fact_239_logic_Osadd__comm,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Sadd @ P @ Q )
= ( Sadd @ Q @ P ) ) ) ).
% logic.sadd_comm
thf(fact_240_logic_Osmaller__interp__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( smaller_interp_c_d_a @ Delta2 @ Delta )
= ( ! [S3: c > d] : ( ord_less_eq_set_a @ ( Delta2 @ S3 ) @ ( Delta @ S3 ) ) ) ) ) ).
% logic.smaller_interp_def
thf(fact_241_logic_Oempty__interp__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( empty_interp_c_d_a @ S )
= bot_bot_set_a ) ) ).
% logic.empty_interp_def
thf(fact_242_logic_Odistrib__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,X: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( some_a @ ( Mult @ ( Sadd @ P @ Q ) @ X ) )
= ( Plus2 @ ( Mult @ P @ X ) @ ( Mult @ Q @ X ) ) ) ) ).
% logic.distrib_mult
thf(fact_243_logic_Oplus__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,C: a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ A )
= ( Plus2 @ B @ C ) )
=> ( ( some_a @ ( Mult @ P @ A ) )
= ( Plus2 @ ( Mult @ P @ B ) @ ( Mult @ P @ C ) ) ) ) ) ).
% logic.plus_mult
thf(fact_244_logic_Omove__sum,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,A1: a,A22: a,B: a,B1: a,B22: a,X: a,X13: a,X23: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ A )
= ( Plus2 @ A1 @ A22 ) )
=> ( ( ( some_a @ B )
= ( Plus2 @ B1 @ B22 ) )
=> ( ( ( some_a @ X )
= ( Plus2 @ A @ B ) )
=> ( ( ( some_a @ X13 )
= ( Plus2 @ A1 @ B1 ) )
=> ( ( ( some_a @ X23 )
= ( Plus2 @ A22 @ B22 ) )
=> ( ( some_a @ X )
= ( Plus2 @ X13 @ X23 ) ) ) ) ) ) ) ) ).
% logic.move_sum
thf(fact_245_logic_Oasso1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,Ab: a,C: a,Bc: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( ( Plus2 @ A @ B )
= ( some_a @ Ab ) )
& ( ( Plus2 @ B @ C )
= ( some_a @ Bc ) ) )
=> ( ( Plus2 @ Ab @ C )
= ( Plus2 @ A @ Bc ) ) ) ) ).
% logic.asso1
thf(fact_246_logic_Osmaller__interpI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [S2: c > d,X2: a] :
( ( member_a @ X2 @ ( Delta2 @ S2 ) )
=> ( member_a @ X2 @ ( Delta @ S2 ) ) )
=> ( smaller_interp_c_d_a @ Delta2 @ Delta ) ) ) ).
% logic.smaller_interpI
thf(fact_247_logic_Osmaller__interp__refl,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( smaller_interp_c_d_a @ Delta2 @ Delta2 ) ) ).
% logic.smaller_interp_refl
thf(fact_248_logic_Osmaller__interp__trans,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( smaller_interp_c_d_a @ A @ B )
=> ( ( smaller_interp_c_d_a @ B @ C )
=> ( smaller_interp_c_d_a @ A @ C ) ) ) ) ).
% logic.smaller_interp_trans
thf(fact_249_logic_Ocompatible__iff,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus2 @ A @ B )
= ( pre_compatible_a @ Plus2 @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).
% logic.compatible_iff
thf(fact_250_logic_Ocompatible__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus2 @ A @ B )
=> ( pre_compatible_a @ Plus2 @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).
% logic.compatible_imp
thf(fact_251_logic_Ocompatible__multiples,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,Q: b,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) )
=> ( pre_compatible_a @ Plus2 @ A @ B ) ) ) ).
% logic.compatible_multiples
thf(fact_252_logic_Ovalid__mono,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( Valid @ A )
& ( pre_larger_a @ Plus2 @ A @ B ) )
=> ( Valid @ B ) ) ) ).
% logic.valid_mono
thf(fact_253_logic_Olarger__same,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus2 @ A @ B )
= ( pre_larger_a @ Plus2 @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).
% logic.larger_same
thf(fact_254_pre__logic_Ocompatible__def,axiom,
( pre_compatible_a
= ( ^ [Plus: a > a > option_a,A4: a,B3: a] :
( ( Plus @ A4 @ B3 )
!= none_a ) ) ) ).
% pre_logic.compatible_def
thf(fact_255_logic_Osat_Osimps_I1_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,P: b,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( mult_b_a_d_c @ P @ A2 ) )
= ( ? [A4: a] :
( ( Sigma
= ( Mult @ P @ A4 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ) ).
% logic.sat.simps(1)
thf(fact_256_logic_Osat__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,P: b,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A3: a] :
( ( Sigma
= ( Mult @ P @ A3 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S @ Delta2 @ A2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.sat_mult
thf(fact_257_logic_Osat_Osimps_I12_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) )
= ( ? [A4: a,P3: b] :
( ( Sigma
= ( Mult @ P3 @ A4 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ) ).
% logic.sat.simps(12)
thf(fact_258_logic_Osat_Osimps_I7_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( and_a_b_d_c @ A2 @ B2 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ B2 ) ) ) ) ).
% logic.sat.simps(7)
thf(fact_259_logic_Osat_Osimps_I5_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( imp_a_b_d_c @ A2 @ B2 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ B2 ) ) ) ) ).
% logic.sat.simps(5)
thf(fact_260_logic_Osat__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ B2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.sat_imp
thf(fact_261_logic_Osat_Osimps_I6_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( or_a_b_d_c @ A2 @ B2 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ A2 )
| ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ B2 ) ) ) ) ).
% logic.sat.simps(6)
thf(fact_262_logic_Oentails__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 )
= ( ! [Sigma2: a,S3: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S3 @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S3 @ Delta2 @ B2 ) ) ) ) ) ).
% logic.entails_def
thf(fact_263_logic_OentailsI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S2: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ B2 ) )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 ) ) ) ).
% logic.entailsI
thf(fact_264_logic_Osat_Osimps_I11_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( bounded_a_b_d_c @ A2 ) )
= ( ( Valid @ Sigma )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ A2 ) ) ) ) ).
% logic.sat.simps(11)
thf(fact_265_logic_Osat_Osimps_I4_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,B: ( c > d ) > a > $o] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( sem_c_d_a_b @ B ) )
= ( B @ S @ Sigma ) ) ) ).
% logic.sat.simps(4)
thf(fact_266_logic_Osat_Osimps_I10_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ pred_a_b_d_c )
= ( member_a @ Sigma @ ( Delta2 @ S ) ) ) ) ).
% logic.sat.simps(10)
thf(fact_267_logic_Oasso2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,Ab: a,C: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( ( Plus2 @ A @ B )
= ( some_a @ Ab ) )
& ~ ( pre_compatible_a @ Plus2 @ B @ C ) )
=> ~ ( pre_compatible_a @ Plus2 @ Ab @ C ) ) ) ).
% logic.asso2
thf(fact_268_logic_Oasso3,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,C: a,Bc: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ~ ( pre_compatible_a @ Plus2 @ A @ B )
=> ( ( ( Plus2 @ B @ C )
= ( some_a @ Bc ) )
=> ~ ( pre_compatible_a @ Plus2 @ A @ Bc ) ) ) ) ).
% logic.asso3
thf(fact_269_logic_Osum__both__larger,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X4: a,A6: a,B5: a,X: a,A: a,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ X4 )
= ( Plus2 @ A6 @ B5 ) )
=> ( ( ( some_a @ X )
= ( Plus2 @ A @ B ) )
=> ( ( pre_larger_a @ Plus2 @ A6 @ A )
=> ( ( pre_larger_a @ Plus2 @ B5 @ B )
=> ( pre_larger_a @ Plus2 @ X4 @ X ) ) ) ) ) ) ).
% logic.sum_both_larger
thf(fact_270_logic_Olarger__first__sum,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Y: a,A: a,B: a,X: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ Y )
= ( Plus2 @ A @ B ) )
=> ( ( pre_larger_a @ Plus2 @ X @ Y )
=> ? [A5: a] :
( ( ( some_a @ X )
= ( Plus2 @ A5 @ B ) )
& ( pre_larger_a @ Plus2 @ A5 @ A ) ) ) ) ) ).
% logic.larger_first_sum
thf(fact_271_logic_OequivalentI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S2: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ B2 ) )
=> ( ! [Sigma4: a,S2: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ B2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ A2 ) )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 ) ) ) ) ).
% logic.equivalentI
thf(fact_272_logic_Oequivalent__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 )
= ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 )
& ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 @ Delta2 @ A2 ) ) ) ) ).
% logic.equivalent_def
thf(fact_273_logic_OmonotonicI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta3 ) @ ( F @ Delta4 ) ) )
=> ( monotonic_c_d_a @ F ) ) ) ).
% logic.monotonicI
thf(fact_274_logic_Omonotonic__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ F )
= ( ! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F @ Delta5 ) @ ( F @ Delta6 ) ) ) ) ) ) ).
% logic.monotonic_def
thf(fact_275_logic_Onon__increasing__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ F )
= ( ! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F @ Delta6 ) @ ( F @ Delta5 ) ) ) ) ) ) ).
% logic.non_increasing_def
thf(fact_276_logic_Onon__increasingI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta4 ) @ ( F @ Delta3 ) ) )
=> ( non_increasing_c_d_a @ F ) ) ) ).
% logic.non_increasingI
thf(fact_277_logic_Opure__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
= ( ! [Sigma2: a,Sigma3: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S3 @ Delta6 @ A2 ) ) ) ) ) ).
% logic.pure_def
thf(fact_278_logic_Ocompatible__smaller,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,X: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus2 @ A @ B )
=> ( ( pre_compatible_a @ Plus2 @ X @ A )
=> ( pre_compatible_a @ Plus2 @ X @ B ) ) ) ) ).
% logic.compatible_smaller
thf(fact_279_logic_Olarger__implies__compatible,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: a,Y: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus2 @ X @ Y )
=> ( pre_compatible_a @ Plus2 @ X @ Y ) ) ) ).
% logic.larger_implies_compatible
thf(fact_280_logic_Ohoare__triple__input,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta2 )
= ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ P2 ) @ C @ Q2 @ Delta2 ) ) ) ).
% logic.hoare_triple_input
thf(fact_281_logic_Oframe__rule,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,R3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_c_d @ Valid @ C )
=> ( ( safety844553430189520448_a_c_d @ Plus2 @ Valid @ C )
=> ( ( frame_property_a_c_d @ Plus2 @ Valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta2 )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ R3 @ ( modified_a_c_d @ C ) )
=> ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ P2 @ R3 ) @ C @ ( star_a_b_d_c @ Q2 @ R3 ) @ Delta2 ) ) ) ) ) ) ) ).
% logic.frame_rule
thf(fact_282_logic_Oindep__interp__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( indep_interp_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
= ( ! [X3: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X3 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X3 @ S3 @ Delta6 @ A2 ) ) ) ) ) ).
% logic.indep_interp_def
thf(fact_283_logic_Osat_Osimps_I2_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( star_a_b_d_c @ A2 @ B2 ) )
= ( ? [A4: a,B3: a] :
( ( ( some_a @ Sigma )
= ( Plus2 @ A4 @ B3 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta2 @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B3 @ S @ Delta2 @ B2 ) ) ) ) ) ).
% logic.sat.simps(2)
thf(fact_284_logic_Osat_Osimps_I3_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( wand_a_b_d_c @ A2 @ B2 ) )
= ( ! [A4: a,Sigma3: a] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta2 @ A2 )
& ( ( some_a @ Sigma3 )
= ( Plus2 @ Sigma @ A4 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S @ Delta2 @ B2 ) ) ) ) ) ).
% logic.sat.simps(3)
thf(fact_285_logic_Osat__wand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,Sigma: a,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A3: a,Sigma5: a] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S @ Delta2 @ A2 )
& ( ( some_a @ Sigma5 )
= ( Plus2 @ Sigma @ A3 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma5 @ S @ Delta2 @ B2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.sat_wand
thf(fact_286_logic_Omono__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ) ).
% logic.mono_mult
thf(fact_287_logic_Onon__increasing__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ) ).
% logic.non_increasing_mult
thf(fact_288_logic_Osat_Osimps_I9_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( forall_c_a_b_d @ X @ A2 ) )
= ( ! [V3: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ ( fun_upd_c_d @ S @ X @ V3 ) @ Delta2 @ A2 ) ) ) ) ).
% logic.sat.simps(9)
thf(fact_289_logic_Osat__forall,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,X: c,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [V4: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ ( fun_upd_c_d @ S @ X @ V4 ) @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( forall_c_a_b_d @ X @ A2 ) ) ) ) ).
% logic.sat_forall
thf(fact_290_logic_Osat_Osimps_I8_J,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma: a,S: c > d,Delta2: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta2 @ ( exists_c_a_b_d @ X @ A2 ) )
= ( ? [V3: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ ( fun_upd_c_d @ S @ X @ V3 ) @ Delta2 @ A2 ) ) ) ) ).
% logic.sat.simps(8)
thf(fact_291_logic_Omono__wild,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.mono_wild
thf(fact_292_logic_Onon__increasing__wild,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.non_increasing_wild
thf(fact_293_logic_Omono__star,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.mono_star
thf(fact_294_logic_Osmaller__interp__applies__cons,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,Delta: ( c > d ) > set_a,A: a,S: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( smaller_interp_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 ) @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta ) )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S @ Delta2 @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S @ Delta @ A2 ) ) ) ) ).
% logic.smaller_interp_applies_cons
thf(fact_295_logic_Omono__and,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.mono_and
thf(fact_296_logic_Omono__forall,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,V: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( forall_c_a_b_d @ V @ A2 ) ) ) ) ) ).
% logic.mono_forall
thf(fact_297_logic_Omono__or,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.mono_or
thf(fact_298_logic_Omono__exists,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,V: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( exists_c_a_b_d @ V @ A2 ) ) ) ) ) ).
% logic.mono_exists
thf(fact_299_logic_Onon__inc__star,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.non_inc_star
thf(fact_300_logic_Onon__increasing__and,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.non_increasing_and
thf(fact_301_logic_Osmaller__empty,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( smaller_interp_c_d_a @ empty_interp_c_d_a @ X ) ) ).
% logic.smaller_empty
thf(fact_302_logic_Onon__increasing__or,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.non_increasing_or
thf(fact_303_logic_Omono__bounded,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.mono_bounded
thf(fact_304_logic_Omono__sem,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,B2: ( c > d ) > a > $o] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( sem_c_d_a_b @ B2 ) ) ) ) ).
% logic.mono_sem
thf(fact_305_logic_Onon__increasing__bounded,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.non_increasing_bounded
thf(fact_306_logic_Onon__increasing__sem,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,B2: ( c > d ) > a > $o] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( sem_c_d_a_b @ B2 ) ) ) ) ).
% logic.non_increasing_sem
thf(fact_307_logic_Omono__interp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ pred_a_b_d_c ) ) ) ).
% logic.mono_interp
thf(fact_308_logic_Omono__instantiate,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,X: a,Delta2: ( c > d ) > set_a,S: c > d,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( member_a @ X @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ S ) )
=> ( ( smaller_interp_c_d_a @ Delta2 @ Delta )
=> ( member_a @ X @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ S ) ) ) ) ) ) ).
% logic.mono_instantiate
thf(fact_309_logic_Onon__increasing__instantiate,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,X: a,Delta: ( c > d ) > set_a,S: c > d,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( member_a @ X @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ S ) )
=> ( ( smaller_interp_c_d_a @ Delta2 @ Delta )
=> ( member_a @ X @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ S ) ) ) ) ) ) ).
% logic.non_increasing_instantiate
thf(fact_310_logic__def,axiom,
( logic_a_b
= ( ^ [Plus: a > a > option_a,Mult2: b > a > a,Smult2: b > b > b,Sadd2: b > b > b,Sinv2: b > b,One2: b,Valid2: a > $o] :
( ! [A4: a,B3: a] :
( ( Plus @ A4 @ B3 )
= ( Plus @ B3 @ A4 ) )
& ! [A4: a,B3: a,Ab2: a,C2: a,Bc2: a] :
( ( ( ( Plus @ A4 @ B3 )
= ( some_a @ Ab2 ) )
& ( ( Plus @ B3 @ C2 )
= ( some_a @ Bc2 ) ) )
=> ( ( Plus @ Ab2 @ C2 )
= ( Plus @ A4 @ Bc2 ) ) )
& ! [A4: a,B3: a,Ab2: a,C2: a] :
( ( ( ( Plus @ A4 @ B3 )
= ( some_a @ Ab2 ) )
& ~ ( pre_compatible_a @ Plus @ B3 @ C2 ) )
=> ~ ( pre_compatible_a @ Plus @ Ab2 @ C2 ) )
& ! [P3: b] :
( ( Smult2 @ P3 @ ( Sinv2 @ P3 ) )
= One2 )
& ! [P3: b] :
( ( Smult2 @ One2 @ P3 )
= P3 )
& ! [P3: b,Q3: b] :
( ( Sadd2 @ P3 @ Q3 )
= ( Sadd2 @ Q3 @ P3 ) )
& ! [P3: b,Q3: b] :
( ( Smult2 @ P3 @ Q3 )
= ( Smult2 @ Q3 @ P3 ) )
& ! [P3: b,Q3: b,R4: b] :
( ( Smult2 @ P3 @ ( Sadd2 @ Q3 @ R4 ) )
= ( Sadd2 @ ( Smult2 @ P3 @ Q3 ) @ ( Smult2 @ P3 @ R4 ) ) )
& ! [P3: b,Q3: b,R4: b] :
( ( Smult2 @ ( Smult2 @ P3 @ Q3 ) @ R4 )
= ( Smult2 @ P3 @ ( Smult2 @ Q3 @ R4 ) ) )
& ! [P3: b,Q3: b,A4: a] :
( ( Mult2 @ P3 @ ( Mult2 @ Q3 @ A4 ) )
= ( Mult2 @ ( Smult2 @ P3 @ Q3 ) @ A4 ) )
& ! [A4: a,B3: a,C2: a,P3: b] :
( ( ( some_a @ A4 )
= ( Plus @ B3 @ C2 ) )
=> ( ( some_a @ ( Mult2 @ P3 @ A4 ) )
= ( Plus @ ( Mult2 @ P3 @ B3 ) @ ( Mult2 @ P3 @ C2 ) ) ) )
& ! [P3: b,Q3: b,X3: a] :
( ( some_a @ ( Mult2 @ ( Sadd2 @ P3 @ Q3 ) @ X3 ) )
= ( Plus @ ( Mult2 @ P3 @ X3 ) @ ( Mult2 @ Q3 @ X3 ) ) )
& ! [A4: a] :
( ( Mult2 @ One2 @ A4 )
= A4 )
& ! [A4: a,B3: a] :
( ( ( Valid2 @ A4 )
& ( pre_larger_a @ Plus @ A4 @ B3 ) )
=> ( Valid2 @ B3 ) ) ) ) ) ).
% logic_def
thf(fact_311_logic_Oindep__implies__non__increasing,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( indep_interp_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) ) ) ) ).
% logic.indep_implies_non_increasing
thf(fact_312_logic_OintuitionisticI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A3: a,B4: a] :
( ( ( pre_larger_a @ Plus2 @ A3 @ B4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B4 @ S @ Delta2 @ A2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S @ Delta2 @ A2 ) )
=> ( intuit7508411120625971703_b_c_d @ Plus2 @ Mult @ Valid @ S @ Delta2 @ A2 ) ) ) ).
% logic.intuitionisticI
thf(fact_313_logic_Ointuitionistic__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: c > d,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( intuit7508411120625971703_b_c_d @ Plus2 @ Mult @ Valid @ S @ Delta2 @ A2 )
= ( ! [A4: a,B3: a] :
( ( ( pre_larger_a @ Plus2 @ A4 @ B3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B3 @ S @ Delta2 @ A2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ) ).
% logic.intuitionistic_def
thf(fact_314_logic_Ohoare__triple__output,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_c_d @ Valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta2 )
= ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ ( bounded_a_b_d_c @ Q2 ) @ Delta2 ) ) ) ) ).
% logic.hoare_triple_output
thf(fact_315_logic_Onot__in__fv__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,S4: set_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ S4 )
= ( ! [Sigma2: a,S3: c > d,Delta5: ( c > d ) > set_a,S5: c > d] :
( ( equal_outside_c_d @ S3 @ S5 @ S4 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S5 @ Delta5 @ A2 ) ) ) ) ) ) ).
% logic.not_in_fv_def
thf(fact_316_logic_Onon__increasing__wand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.non_increasing_wand
thf(fact_317_logic_Onon__increasing__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.non_increasing_imp
thf(fact_318_logic_Omono__wand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.mono_wand
thf(fact_319_logic_Omono__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ) ) ).
% logic.mono_imp
thf(fact_320_combinable__instantiate__one,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S: c > d,B: a,X: a,P: b,Q: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S @ Delta2 @ A2 )
=> ( ( ( some_a @ X )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
=> ( ( ( sadd @ P @ Q )
= one )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S @ Delta2 @ A2 ) ) ) ) ) ) ).
% combinable_instantiate_one
thf(fact_321_combinable__def,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
= ( ! [P3: b,Q3: b] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P3 @ A2 ) @ ( mult_b_a_d_c @ Q3 @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ ( sadd @ P3 @ Q3 ) @ A2 ) ) ) ) ).
% combinable_def
thf(fact_322_combinable__instantiate,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S: c > d,B: a,X: a,P: b,Q: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S @ Delta2 @ A2 )
=> ( ( ( some_a @ X )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S @ Delta2 @ ( mult_b_a_d_c @ ( sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ).
% combinable_instantiate
thf(fact_323_combinable__exists,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta2 @ A2 @ X )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( exists_c_a_b_d @ X @ A2 ) ) ) ) ).
% combinable_exists
thf(fact_324_combinable__imp,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% combinable_imp
thf(fact_325_combinableI__old,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [A3: a,B4: a,P4: b,Q4: b,X2: a,Sigma4: a,S2: c > d] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta2 @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B4 @ S2 @ Delta2 @ A2 )
& ( ( some_a @ Sigma4 )
= ( plus @ ( mult @ P4 @ A3 ) @ ( mult @ Q4 @ B4 ) ) )
& ( Sigma4
= ( mult @ ( sadd @ P4 @ Q4 ) @ X2 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S2 @ Delta2 @ A2 ) )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 ) ) ).
% combinableI_old
thf(fact_326_combinable__mult,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,Pi: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ).
% combinable_mult
thf(fact_327_combinable__wildcard,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% combinable_wildcard
thf(fact_328_combinable__star,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% combinable_star
thf(fact_329_combinable__and,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% combinable_and
thf(fact_330_combinable__forall,axiom,
! [Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( forall_c_a_b_d @ X @ A2 ) ) ) ).
% combinable_forall
thf(fact_331_combinable__wand,axiom,
! [Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c,A2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ).
% combinable_wand
thf(fact_332_combinable__pure,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta2 @ A2 ) ) ).
% combinable_pure
thf(fact_333_logic_OunambiguousI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: c,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma_12: a,Sigma_22: a,V12: d,V22: d,S2: c > d] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_12 @ ( fun_upd_c_d @ S2 @ X @ V12 ) @ Delta2 @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_22 @ ( fun_upd_c_d @ S2 @ X @ V22 ) @ Delta2 @ A2 ) )
=> ( V12 = V22 ) )
=> ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta2 @ A2 @ X ) ) ) ).
% logic.unambiguousI
thf(fact_334_logic_Ounambiguous__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta2 @ A2 @ X )
= ( ! [Sigma_1: a,Sigma_2: a,V1: d,V2: d,S3: c > d] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_1 @ ( fun_upd_c_d @ S3 @ X @ V1 ) @ Delta2 @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_2 @ ( fun_upd_c_d @ S3 @ X @ V2 ) @ Delta2 @ A2 ) )
=> ( V1 = V2 ) ) ) ) ) ).
% logic.unambiguous_def
thf(fact_335_logic_Ocombinable__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
= ( ! [P3: b,Q3: b] : ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P3 @ A2 ) @ ( mult_b_a_d_c @ Q3 @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ ( Sadd @ P3 @ Q3 ) @ A2 ) ) ) ) ) ).
% logic.combinable_def
thf(fact_336_logic_Ocombinable__instantiate,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S: c > d,B: a,X: a,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B @ S @ Delta2 @ A2 )
=> ( ( ( some_a @ X )
= ( Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S @ Delta2 @ ( mult_b_a_d_c @ ( Sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ) ).
% logic.combinable_instantiate
thf(fact_337_logic_Ocombinable__exists,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta2 @ A2 @ X )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( exists_c_a_b_d @ X @ A2 ) ) ) ) ) ).
% logic.combinable_exists
thf(fact_338_logic_OWildPure,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta2 @ A2 ) ) ) ).
% logic.WildPure
thf(fact_339_logic_Ounambiguous_Ocong,axiom,
unambiguous_a_b_c_d = unambiguous_a_b_c_d ).
% logic.unambiguous.cong
thf(fact_340_logic_Omult__one__same2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ ( mult_b_a_d_c @ One @ A2 ) ) ) ).
% logic.mult_one_same2
thf(fact_341_logic_Omult__one__same1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ One @ A2 ) @ Delta2 @ A2 ) ) ).
% logic.mult_one_same1
thf(fact_342_logic_Odot__mult2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ ( Smult @ P @ Q ) @ A2 ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) ) ) ).
% logic.dot_mult2
thf(fact_343_logic_Odot__mult1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ ( Smult @ P @ Q ) @ A2 ) ) ) ).
% logic.dot_mult1
thf(fact_344_logic_ODotPos,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 )
= ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A2 ) @ Delta2 @ ( mult_b_a_d_c @ Pi @ B2 ) ) ) ) ).
% logic.DotPos
thf(fact_345_logic_Ocombinable__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ).
% logic.combinable_mult
thf(fact_346_logic_OWildPos,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ B2 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta2 @ ( wildcard_a_b_d_c @ B2 ) ) ) ) ).
% logic.WildPos
thf(fact_347_logic_ODotFull,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ One @ A2 ) @ Delta2 @ A2 ) ) ).
% logic.DotFull
thf(fact_348_logic_ODotDot,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ ( Smult @ P @ Q ) @ A2 ) ) ) ).
% logic.DotDot
thf(fact_349_logic_Ocombinable__wildcard,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% logic.combinable_wildcard
thf(fact_350_logic_Ocombinable__star,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% logic.combinable_star
thf(fact_351_logic_Ocombinable__and,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% logic.combinable_and
thf(fact_352_logic_Ocombinable__forall,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( forall_c_a_b_d @ X @ A2 ) ) ) ) ).
% logic.combinable_forall
thf(fact_353_logic_Ocombinable__wand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.combinable_wand
thf(fact_354_logic_OWildWild,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% logic.WildWild
thf(fact_355_logic_Ocombinable__pure,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 ) ) ) ).
% logic.combinable_pure
thf(fact_356_logic_Ounambiguous__star,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,X: c,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta2 @ A2 @ X )
=> ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta2 @ ( star_a_b_d_c @ A2 @ B2 ) @ X ) ) ) ).
% logic.unambiguous_star
thf(fact_357_logic_OcombinableI__old,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A3: a,B4: a,P4: b,Q4: b,X2: a,Sigma4: a,S2: c > d] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta2 @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B4 @ S2 @ Delta2 @ A2 )
& ( ( some_a @ Sigma4 )
= ( Plus2 @ ( Mult @ P4 @ A3 ) @ ( Mult @ Q4 @ B4 ) ) )
& ( Sigma4
= ( Mult @ ( Sadd @ P4 @ Q4 ) @ X2 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S2 @ Delta2 @ A2 ) )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 ) ) ) ).
% logic.combinableI_old
thf(fact_358_logic_Ocombinable__instantiate__one,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S: c > d,B: a,X: a,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S @ Delta2 @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B @ S @ Delta2 @ A2 )
=> ( ( ( some_a @ X )
= ( Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
=> ( ( ( Sadd @ P @ Q )
= One )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S @ Delta2 @ A2 ) ) ) ) ) ) ) ).
% logic.combinable_instantiate_one
thf(fact_359_logic_Odot__star1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.dot_star1
thf(fact_360_logic_Odot__star2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.dot_star2
thf(fact_361_logic_Odot__and1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.dot_and1
thf(fact_362_logic_Odot__and2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.dot_and2
thf(fact_363_logic_Odot__forall2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: c,P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( forall_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X @ A2 ) ) ) ) ).
% logic.dot_forall2
thf(fact_364_logic_Odot__forall1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( forall_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.dot_forall1
thf(fact_365_logic_Odot__wand2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.dot_wand2
thf(fact_366_logic_Odot__wand1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.dot_wand1
thf(fact_367_logic_Odot__imp2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.dot_imp2
thf(fact_368_logic_Odot__imp1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.dot_imp1
thf(fact_369_logic_Odot__or1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.dot_or1
thf(fact_370_logic_Odot__or2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.dot_or2
thf(fact_371_logic_Odot__exists1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( exists_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.dot_exists1
thf(fact_372_logic_Odot__exists2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: c,P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( exists_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X @ A2 ) ) ) ) ).
% logic.dot_exists2
thf(fact_373_logic_ODotWild,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% logic.DotWild
thf(fact_374_logic_OWildDot,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% logic.WildDot
thf(fact_375_logic_OWildStar1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( star_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( star_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B2 ) ) ) ) ).
% logic.WildStar1
thf(fact_376_logic_OWildAnd,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( and_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( and_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B2 ) ) ) ) ).
% logic.WildAnd
thf(fact_377_logic_OWildForall,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( forall_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( forall_c_a_b_d @ X @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% logic.WildForall
thf(fact_378_logic_ODotStar,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.DotStar
thf(fact_379_logic_ODotAnd,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) @ Delta2 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B2 ) ) ) ) ).
% logic.DotAnd
thf(fact_380_logic_ODotForall,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( forall_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.DotForall
thf(fact_381_logic_ODotWand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.DotWand
thf(fact_382_logic_ODotImp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.DotImp
thf(fact_383_logic_ODotOr,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B2 ) ) ) ) ).
% logic.DotOr
thf(fact_384_logic_ODotExists,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( exists_c_a_b_d @ X @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.DotExists
thf(fact_385_logic_OWildOr,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( or_a_b_d_c @ A2 @ B2 ) ) @ Delta2 @ ( or_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B2 ) ) ) ) ).
% logic.WildOr
thf(fact_386_logic_OWildExists,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: c,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( exists_c_a_b_d @ X @ A2 ) ) @ Delta2 @ ( exists_c_a_b_d @ X @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% logic.WildExists
thf(fact_387_logic_Opure__mult2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.pure_mult2
thf(fact_388_logic_Opure__mult1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,P: b,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta2 @ A2 ) ) ) ).
% logic.pure_mult1
thf(fact_389_logic_ODotPure,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,P: b,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta2 @ A2 ) ) ) ).
% logic.DotPure
thf(fact_390_logic_Ocombinable__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ B2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta2 @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ) ).
% logic.combinable_imp
thf(fact_391_not__in__fv__mod,axiom,
! [A2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma: a,S: c > d,Sigma6: a,S6: c > d,X: a,Delta2: ( c > d ) > set_a] :
( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A2 @ ( modified_a_c_d @ C ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S6 ) ) ) @ C )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S @ Delta2 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S6 @ Delta2 @ A2 ) ) ) ) ).
% not_in_fv_mod
thf(fact_392_valid__hoare__triple__def,axiom,
! [P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta2 )
= ( ! [Sigma2: a,S3: c > d] :
( ( ( valid @ Sigma2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta2 @ P2 ) )
=> ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma2 @ S3 ) )
& ! [Sigma3: a,S5: c > d] :
( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma2 @ S3 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S5 ) ) ) @ C )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S5 @ Delta2 @ Q2 ) ) ) ) ) ) ).
% valid_hoare_triple_def
thf(fact_393_valid__hoare__tripleI,axiom,
! [Delta2: ( c > d ) > set_a,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c] :
( ! [Sigma4: a,S2: c > d] :
( ( ( valid @ Sigma4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ P2 ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma4 @ S2 ) ) )
=> ( ! [Sigma4: a,S2: c > d,Sigma5: a,S7: c > d] :
( ( ( valid @ Sigma4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S2 @ Delta2 @ P2 ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S2 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S7 ) ) ) @ C )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S7 @ Delta2 @ Q2 ) ) )
=> ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta2 ) ) ) ).
% valid_hoare_tripleI
thf(fact_394_logic_Ovalid__hoare__triple__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta2 )
= ( ! [Sigma2: a,S3: c > d] :
( ( ( Valid @ Sigma2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S3 @ Delta2 @ P2 ) )
=> ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma2 @ S3 ) )
& ! [Sigma3: a,S5: c > d] :
( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma2 @ S3 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S5 ) ) ) @ C )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S5 @ Delta2 @ Q2 ) ) ) ) ) ) ) ).
% logic.valid_hoare_triple_def
thf(fact_395_logic_Ovalid__hoare__tripleI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta2: ( c > d ) > set_a,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S2: c > d] :
( ( ( Valid @ Sigma4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ P2 ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma4 @ S2 ) ) )
=> ( ! [Sigma4: a,S2: c > d,Sigma5: a,S7: c > d] :
( ( ( Valid @ Sigma4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S2 @ Delta2 @ P2 ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S2 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S7 ) ) ) @ C )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma5 @ S7 @ Delta2 @ Q2 ) ) )
=> ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta2 ) ) ) ) ).
% logic.valid_hoare_tripleI
thf(fact_396_logic_Onot__in__fv__mod,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma: a,S: c > d,Sigma6: a,S6: c > d,X: a,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ ( modified_a_c_d @ C ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S6 ) ) ) @ C )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S @ Delta2 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S6 @ Delta2 @ A2 ) ) ) ) ) ).
% logic.not_in_fv_mod
thf(fact_397_applies__eq_Oelims,axiom,
! [X: assertion_a_b_d_c,Xa: ( c > d ) > set_a,Xb: c > d,Y: set_a] :
( ( ( applies_eq_a_b_d_c @ plus @ mult @ valid @ X @ Xa @ Xb )
= Y )
=> ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ plus @ mult @ valid @ Uu @ Xb @ Xa @ X ) ) ) ) ).
% applies_eq.elims
thf(fact_398_applies__eq_Osimps,axiom,
! [A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,S: c > d] :
( ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ S )
= ( collect_a
@ ^ [Uu: a] :
? [A4: a] :
( ( Uu = A4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ).
% applies_eq.simps
thf(fact_399_assertion_Orel__distinct_I18_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(18)
thf(fact_400_assertion_Orel__distinct_I17_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(17)
thf(fact_401_assertion_Orel__distinct_I128_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(128)
thf(fact_402_assertion_Orel__intros_I2_J,axiom,
! [R3: b > b > $o,X212: b,Y21: b,X222: assertion_a_b_d_c,Y22: assertion_a_b_d_c] :
( ( R3 @ X212 @ Y21 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X222 @ Y22 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( mult_b_a_d_c @ Y21 @ Y22 ) ) ) ) ).
% assertion.rel_intros(2)
thf(fact_403_assertion_Orel__inject_I2_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y21: b,Y22: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( mult_b_a_d_c @ Y21 @ Y22 ) )
= ( ( R3 @ X212 @ Y21 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X222 @ Y22 ) ) ) ).
% assertion.rel_inject(2)
thf(fact_404_assertion_Orel__intros_I12_J,axiom,
! [R3: b > b > $o,X122: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X122 @ Y12 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ X122 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ) ).
% assertion.rel_intros(12)
thf(fact_405_assertion_Orel__inject_I12_J,axiom,
! [R3: b > b > $o,X122: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ X122 ) @ ( wildcard_a_b_d_c @ Y12 ) )
= ( rel_as1860989020795611527_a_d_c @ R3 @ X122 @ Y12 ) ) ).
% assertion.rel_inject(12)
thf(fact_406_assertion_Orel__intros_I3_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,Y31: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y32: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X312 @ Y31 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X322 @ Y32 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( star_a_b_d_c @ Y31 @ Y32 ) ) ) ) ).
% assertion.rel_intros(3)
thf(fact_407_assertion_Orel__inject_I3_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( star_a_b_d_c @ Y31 @ Y32 ) )
= ( ( rel_as1860989020795611527_a_d_c @ R3 @ X312 @ Y31 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X322 @ Y32 ) ) ) ).
% assertion.rel_inject(3)
thf(fact_408_assertion_Orel__intros_I6_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,Y61: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X612 @ Y61 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X622 @ Y62 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ) ) ).
% assertion.rel_intros(6)
thf(fact_409_assertion_Orel__inject_I6_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) )
= ( ( rel_as1860989020795611527_a_d_c @ R3 @ X612 @ Y61 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X622 @ Y62 ) ) ) ).
% assertion.rel_inject(6)
thf(fact_410_assertion_Orel__intros_I9_J,axiom,
! [X912: c,Y91: c,R3: b > b > $o,X922: assertion_a_b_d_c,Y92: assertion_a_b_d_c] :
( ( X912 = Y91 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X922 @ Y92 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ X912 @ X922 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ) ) ).
% assertion.rel_intros(9)
thf(fact_411_assertion_Orel__inject_I9_J,axiom,
! [R3: b > b > $o,X912: c,X922: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ X912 @ X922 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) )
= ( ( X912 = Y91 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X922 @ Y92 ) ) ) ).
% assertion.rel_inject(9)
thf(fact_412_assertion_Orel__intros_I5_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,Y51: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X512 @ Y51 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X522 @ Y52 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ) ) ).
% assertion.rel_intros(5)
thf(fact_413_assertion_Orel__inject_I5_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) )
= ( ( rel_as1860989020795611527_a_d_c @ R3 @ X512 @ Y51 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X522 @ Y52 ) ) ) ).
% assertion.rel_inject(5)
thf(fact_414_assertion_Orel__intros_I4_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,Y41: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X412 @ Y41 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X422 @ Y42 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) ) ) ) ).
% assertion.rel_intros(4)
thf(fact_415_assertion_Orel__intros_I7_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,Y71: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X712 @ Y71 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X722 @ Y72 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ) ) ).
% assertion.rel_intros(7)
thf(fact_416_assertion_Orel__inject_I4_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) )
= ( ( rel_as1860989020795611527_a_d_c @ R3 @ X412 @ Y41 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X422 @ Y42 ) ) ) ).
% assertion.rel_inject(4)
thf(fact_417_assertion_Orel__inject_I7_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) )
= ( ( rel_as1860989020795611527_a_d_c @ R3 @ X712 @ Y71 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X722 @ Y72 ) ) ) ).
% assertion.rel_inject(7)
thf(fact_418_assertion_Orel__inject_I8_J,axiom,
! [R3: b > b > $o,X812: c,X822: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ X812 @ X822 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) )
= ( ( X812 = Y81 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X822 @ Y82 ) ) ) ).
% assertion.rel_inject(8)
thf(fact_419_assertion_Orel__intros_I8_J,axiom,
! [X812: c,Y81: c,R3: b > b > $o,X822: assertion_a_b_d_c,Y82: assertion_a_b_d_c] :
( ( X812 = Y81 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X822 @ Y82 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ X812 @ X822 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ) ) ).
% assertion.rel_intros(8)
thf(fact_420_assertion_Orel__intros_I11_J,axiom,
! [R3: b > b > $o,X112: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X112 @ Y11 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ X112 ) @ ( bounded_a_b_d_c @ Y11 ) ) ) ).
% assertion.rel_intros(11)
thf(fact_421_assertion_Orel__inject_I11_J,axiom,
! [R3: b > b > $o,X112: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ X112 ) @ ( bounded_a_b_d_c @ Y11 ) )
= ( rel_as1860989020795611527_a_d_c @ R3 @ X112 @ Y11 ) ) ).
% assertion.rel_inject(11)
thf(fact_422_assertion_Orel__intros_I1_J,axiom,
! [X13: ( c > d ) > a > $o,Y1: ( c > d ) > a > $o,R3: b > b > $o] :
( ( X13 = Y1 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( sem_c_d_a_b @ Y1 ) ) ) ).
% assertion.rel_intros(1)
thf(fact_423_assertion_Orel__inject_I1_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y1: ( c > d ) > a > $o] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( sem_c_d_a_b @ Y1 ) )
= ( X13 = Y1 ) ) ).
% assertion.rel_inject(1)
thf(fact_424_assertion_Octr__transfer_I10_J,axiom,
! [R3: b > b > $o] : ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ pred_a_b_d_c ) ).
% assertion.ctr_transfer(10)
thf(fact_425_logic_Oapplies__eq_Oelims,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: assertion_a_b_d_c,Xa: ( c > d ) > set_a,Xb: c > d,Y: set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ X @ Xa @ Xb )
= Y )
=> ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Uu @ Xb @ Xa @ X ) ) ) ) ) ).
% logic.applies_eq.elims
thf(fact_426_logic_Oapplies__eq_Osimps,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta2: ( c > d ) > set_a,S: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ S )
= ( collect_a
@ ^ [Uu: a] :
? [A4: a] :
( ( Uu = A4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta2 @ A2 ) ) ) ) ) ).
% logic.applies_eq.simps
thf(fact_427_assertion_Orel__refl,axiom,
! [Ra: b > b > $o,X: assertion_a_b_d_c] :
( ! [X2: b] : ( Ra @ X2 @ X2 )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X @ X ) ) ).
% assertion.rel_refl
thf(fact_428_assertion_Orel__eq,axiom,
( ( rel_as1860989020795611527_a_d_c
@ ^ [Y2: b,Z: b] : ( Y2 = Z ) )
= ( ^ [Y2: assertion_a_b_d_c,Z: assertion_a_b_d_c] : ( Y2 = Z ) ) ) ).
% assertion.rel_eq
thf(fact_429_assertion_Orel__distinct_I42_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(42)
thf(fact_430_assertion_Orel__distinct_I41_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(41)
thf(fact_431_assertion_Orel__distinct_I24_J,axiom,
! [R3: b > b > $o,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ Y31 @ Y32 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(24)
thf(fact_432_assertion_Orel__distinct_I23_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( star_a_b_d_c @ Y31 @ Y32 ) ) ).
% assertion.rel_distinct(23)
thf(fact_433_assertion_Orel__distinct_I30_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(30)
thf(fact_434_assertion_Orel__distinct_I29_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(29)
thf(fact_435_assertion_Orel__distinct_I35_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(35)
thf(fact_436_assertion_Orel__distinct_I36_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(36)
thf(fact_437_assertion_Orel__distinct_I25_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(25)
thf(fact_438_assertion_Orel__distinct_I26_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ Y41 @ Y42 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(26)
thf(fact_439_assertion_Orel__distinct_I31_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(31)
thf(fact_440_assertion_Orel__distinct_I32_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(32)
thf(fact_441_assertion_Orel__distinct_I28_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ Y51 @ Y52 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(28)
thf(fact_442_assertion_Orel__distinct_I27_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(27)
thf(fact_443_assertion_Orel__distinct_I34_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(34)
thf(fact_444_assertion_Orel__distinct_I33_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(33)
thf(fact_445_assertion_Orel__distinct_I40_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(40)
thf(fact_446_assertion_Orel__distinct_I39_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(39)
thf(fact_447_assertion_Orel__distinct_I2_J,axiom,
! [R3: b > b > $o,Y21: b,Y22: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ Y21 @ Y22 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(2)
thf(fact_448_assertion_Orel__distinct_I1_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y21: b,Y22: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( mult_b_a_d_c @ Y21 @ Y22 ) ) ).
% assertion.rel_distinct(1)
thf(fact_449_assertion_Orel__distinct_I60_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(60)
thf(fact_450_assertion_Orel__distinct_I59_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(59)
thf(fact_451_assertion_Orel__distinct_I37_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X222 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(37)
thf(fact_452_assertion_Orel__distinct_I38_J,axiom,
! [R3: b > b > $o,X212: b,X222: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( mult_b_a_d_c @ X212 @ X222 ) ) ).
% assertion.rel_distinct(38)
thf(fact_453_assertion_Orel__distinct_I102_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.rel_distinct(102)
thf(fact_454_assertion_Orel__distinct_I101_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(101)
thf(fact_455_assertion_Orel__distinct_I125_J,axiom,
! [R3: b > b > $o,X912: c,X922: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ X912 @ X922 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(125)
thf(fact_456_assertion_Orel__distinct_I126_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.rel_distinct(126)
thf(fact_457_assertion_Orel__distinct_I75_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(75)
thf(fact_458_assertion_Orel__distinct_I76_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(76)
thf(fact_459_assertion_Orel__distinct_I111_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(111)
thf(fact_460_assertion_Orel__distinct_I112_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.rel_distinct(112)
thf(fact_461_assertion_Orel__distinct_I90_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(90)
thf(fact_462_assertion_Orel__distinct_I89_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(89)
thf(fact_463_assertion_Orel__distinct_I120_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.rel_distinct(120)
thf(fact_464_assertion_Orel__distinct_I119_J,axiom,
! [R3: b > b > $o,X812: c,X822: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ X812 @ X822 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(119)
thf(fact_465_assertion_Orel__distinct_I48_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(48)
thf(fact_466_assertion_Orel__distinct_I47_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(47)
thf(fact_467_assertion_Orel__distinct_I53_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(53)
thf(fact_468_assertion_Orel__distinct_I54_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(54)
thf(fact_469_assertion_Orel__distinct_I132_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.rel_distinct(132)
thf(fact_470_assertion_Orel__distinct_I131_J,axiom,
! [R3: b > b > $o,X112: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ X112 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(131)
thf(fact_471_assertion_Orel__distinct_I43_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(43)
thf(fact_472_assertion_Orel__distinct_I44_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ Y41 @ Y42 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(44)
thf(fact_473_assertion_Orel__distinct_I49_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(49)
thf(fact_474_assertion_Orel__distinct_I50_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(50)
thf(fact_475_assertion_Orel__distinct_I46_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ Y51 @ Y52 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(46)
thf(fact_476_assertion_Orel__distinct_I45_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(45)
thf(fact_477_assertion_Orel__distinct_I52_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(52)
thf(fact_478_assertion_Orel__distinct_I51_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(51)
thf(fact_479_assertion_Orel__distinct_I95_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(95)
thf(fact_480_assertion_Orel__distinct_I96_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.rel_distinct(96)
thf(fact_481_assertion_Orel__distinct_I22_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(22)
thf(fact_482_assertion_Orel__distinct_I21_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(21)
thf(fact_483_assertion_Orel__distinct_I63_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(63)
thf(fact_484_assertion_Orel__distinct_I64_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(64)
thf(fact_485_assertion_Orel__distinct_I91_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(91)
thf(fact_486_assertion_Orel__distinct_I92_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.rel_distinct(92)
thf(fact_487_assertion_Orel__distinct_I78_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(78)
thf(fact_488_assertion_Orel__distinct_I77_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(77)
thf(fact_489_assertion_Orel__distinct_I106_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.rel_distinct(106)
thf(fact_490_assertion_Orel__distinct_I105_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(105)
thf(fact_491_assertion_Orel__distinct_I70_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(70)
thf(fact_492_assertion_Orel__distinct_I69_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(69)
thf(fact_493_assertion_Orel__distinct_I83_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(83)
thf(fact_494_assertion_Orel__distinct_I84_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(84)
thf(fact_495_assertion_Orel__distinct_I94_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.rel_distinct(94)
thf(fact_496_assertion_Orel__distinct_I93_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(93)
thf(fact_497_assertion_Orel__distinct_I66_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(66)
thf(fact_498_assertion_Orel__distinct_I65_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(65)
thf(fact_499_assertion_Orel__distinct_I61_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(61)
thf(fact_500_assertion_Orel__distinct_I62_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ Y51 @ Y52 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(62)
thf(fact_501_assertion_Orel__distinct_I79_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(79)
thf(fact_502_assertion_Orel__distinct_I80_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(80)
thf(fact_503_assertion_Orel__distinct_I113_J,axiom,
! [R3: b > b > $o,X812: c,X822: assertion_a_b_d_c,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ X812 @ X822 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(113)
thf(fact_504_assertion_Orel__distinct_I114_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.rel_distinct(114)
thf(fact_505_assertion_Orel__distinct_I67_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(67)
thf(fact_506_assertion_Orel__distinct_I68_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(68)
thf(fact_507_assertion_Orel__distinct_I103_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(103)
thf(fact_508_assertion_Orel__distinct_I104_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.rel_distinct(104)
thf(fact_509_assertion_Orel__distinct_I82_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(82)
thf(fact_510_assertion_Orel__distinct_I81_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(81)
thf(fact_511_assertion_Orel__distinct_I58_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(58)
thf(fact_512_assertion_Orel__distinct_I57_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(57)
thf(fact_513_assertion_Orel__distinct_I129_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(129)
thf(fact_514_assertion_Orel__distinct_I130_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(130)
thf(fact_515_assertion_Orel__distinct_I4_J,axiom,
! [R3: b > b > $o,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ Y31 @ Y32 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(4)
thf(fact_516_assertion_Orel__distinct_I3_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( star_a_b_d_c @ Y31 @ Y32 ) ) ).
% assertion.rel_distinct(3)
thf(fact_517_assertion_Orel__distinct_I100_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.rel_distinct(100)
thf(fact_518_assertion_Orel__distinct_I99_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(99)
thf(fact_519_assertion_Orel__distinct_I123_J,axiom,
! [R3: b > b > $o,X912: c,X922: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ X912 @ X922 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(123)
thf(fact_520_assertion_Orel__distinct_I124_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.rel_distinct(124)
thf(fact_521_assertion_Orel__distinct_I73_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(73)
thf(fact_522_assertion_Orel__distinct_I74_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(74)
thf(fact_523_assertion_Orel__distinct_I109_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(109)
thf(fact_524_assertion_Orel__distinct_I110_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.rel_distinct(110)
thf(fact_525_assertion_Orel__distinct_I88_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(88)
thf(fact_526_assertion_Orel__distinct_I87_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(87)
thf(fact_527_assertion_Orel__distinct_I118_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.rel_distinct(118)
thf(fact_528_assertion_Orel__distinct_I117_J,axiom,
! [R3: b > b > $o,X812: c,X822: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ X812 @ X822 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(117)
thf(fact_529_assertion_Orel__distinct_I10_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(10)
thf(fact_530_assertion_Orel__distinct_I9_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(9)
thf(fact_531_assertion_Orel__distinct_I15_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(15)
thf(fact_532_assertion_Orel__distinct_I16_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(16)
thf(fact_533_assertion_Orel__distinct_I5_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(5)
thf(fact_534_assertion_Orel__distinct_I6_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ Y41 @ Y42 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(6)
thf(fact_535_assertion_Orel__distinct_I11_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(11)
thf(fact_536_assertion_Orel__distinct_I12_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(12)
thf(fact_537_assertion_Orel__distinct_I8_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ Y51 @ Y52 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(8)
thf(fact_538_assertion_Orel__distinct_I7_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(7)
thf(fact_539_assertion_Orel__distinct_I14_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(14)
thf(fact_540_assertion_Orel__distinct_I13_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(13)
thf(fact_541_assertion_Orel__distinct_I55_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ X312 @ X322 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(55)
thf(fact_542_assertion_Orel__distinct_I56_J,axiom,
! [R3: b > b > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.rel_distinct(56)
thf(fact_543_assertion_Orel__distinct_I97_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ X612 @ X622 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(97)
thf(fact_544_assertion_Orel__distinct_I98_J,axiom,
! [R3: b > b > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.rel_distinct(98)
thf(fact_545_assertion_Orel__distinct_I121_J,axiom,
! [R3: b > b > $o,X912: c,X922: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ X912 @ X922 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(121)
thf(fact_546_assertion_Orel__distinct_I122_J,axiom,
! [R3: b > b > $o,X912: c,X922: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.rel_distinct(122)
thf(fact_547_assertion_Orel__distinct_I71_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ X412 @ X422 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(71)
thf(fact_548_assertion_Orel__distinct_I72_J,axiom,
! [R3: b > b > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.rel_distinct(72)
thf(fact_549_assertion_Orel__distinct_I107_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ X712 @ X722 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(107)
thf(fact_550_assertion_Orel__distinct_I108_J,axiom,
! [R3: b > b > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.rel_distinct(108)
thf(fact_551_assertion_Orel__distinct_I85_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ X512 @ X522 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(85)
thf(fact_552_assertion_Orel__distinct_I86_J,axiom,
! [R3: b > b > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.rel_distinct(86)
thf(fact_553_assertion_Orel__distinct_I115_J,axiom,
! [R3: b > b > $o,X812: c,X822: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ X812 @ X822 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(115)
thf(fact_554_assertion_Orel__distinct_I116_J,axiom,
! [R3: b > b > $o,X812: c,X822: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.rel_distinct(116)
thf(fact_555_assertion_Orel__distinct_I20_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X13: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( sem_c_d_a_b @ X13 ) ) ).
% assertion.rel_distinct(20)
thf(fact_556_assertion_Orel__distinct_I19_J,axiom,
! [R3: b > b > $o,X13: ( c > d ) > a > $o,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X13 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(19)
thf(fact_557_assertion_Orel__distinct_I127_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(127)
thf(fact_558_applies__eq_Opelims,axiom,
! [X: assertion_a_b_d_c,Xa: ( c > d ) > set_a,Xb: c > d,Y: set_a] :
( ( ( applies_eq_a_b_d_c @ plus @ mult @ valid @ X @ Xa @ Xb )
= Y )
=> ( ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) )
=> ~ ( ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ plus @ mult @ valid @ Uu @ Xb @ Xa @ X ) ) )
=> ~ ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) ) ) ) ) ).
% applies_eq.pelims
thf(fact_559_assertion_Osimps_I333_J,axiom,
( ( set_as7232682317586342732_b_d_c @ pred_a_b_d_c )
= bot_bot_set_b ) ).
% assertion.simps(333)
thf(fact_560_assertion_Osimps_I324_J,axiom,
! [X13: ( c > d ) > a > $o] :
( ( set_as7232682317586342732_b_d_c @ ( sem_c_d_a_b @ X13 ) )
= bot_bot_set_b ) ).
% assertion.simps(324)
thf(fact_561_assertion_Octr__transfer_I11_J,axiom,
! [R3: b > b > $o] : ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ bounded_a_b_d_c @ bounded_a_b_d_c ) ).
% assertion.ctr_transfer(11)
thf(fact_562_assertion_Octr__transfer_I12_J,axiom,
! [R3: b > b > $o] : ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ wildcard_a_b_d_c @ wildcard_a_b_d_c ) ).
% assertion.ctr_transfer(12)
thf(fact_563_applies__eq_Ocases,axiom,
! [X: produc5105196854009589546_a_c_d] :
~ ! [A7: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,S2: c > d] :
( X
!= ( produc8894421531525210148_a_c_d @ A7 @ ( produc7376592049607813182_a_c_d @ Delta3 @ S2 ) ) ) ).
% applies_eq.cases
thf(fact_564_logic_Oapplies__eq_Ocases,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: produc5105196854009589546_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ~ ! [A7: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,S2: c > d] :
( X
!= ( produc8894421531525210148_a_c_d @ A7 @ ( produc7376592049607813182_a_c_d @ Delta3 @ S2 ) ) ) ) ).
% logic.applies_eq.cases
thf(fact_565_assertion_Orel__refl__strong,axiom,
! [X: assertion_a_b_d_c,Ra: b > b > $o] :
( ! [Z2: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ X ) )
=> ( Ra @ Z2 @ Z2 ) )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X @ X ) ) ).
% assertion.rel_refl_strong
thf(fact_566_assertion_Orel__mono__strong,axiom,
! [R3: a > b > $o,X: assertion_a_a_d_c,Y: assertion_a_b_d_c,Ra: a > b > $o] :
( ( rel_as1194089545255703174_a_d_c @ R3 @ X @ Y )
=> ( ! [Z2: a,Yb: b] :
( ( member_a @ Z2 @ ( set_as1636463702398212043_a_d_c @ X ) )
=> ( ( member_b @ Yb @ ( set_as7232682317586342732_b_d_c @ Y ) )
=> ( ( R3 @ Z2 @ Yb )
=> ( Ra @ Z2 @ Yb ) ) ) )
=> ( rel_as1194089545255703174_a_d_c @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_567_assertion_Orel__mono__strong,axiom,
! [R3: b > a > $o,X: assertion_a_b_d_c,Y: assertion_a_a_d_c,Ra: b > a > $o] :
( ( rel_as373026983500813000_a_d_c @ R3 @ X @ Y )
=> ( ! [Z2: b,Yb: a] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ X ) )
=> ( ( member_a @ Yb @ ( set_as1636463702398212043_a_d_c @ Y ) )
=> ( ( R3 @ Z2 @ Yb )
=> ( Ra @ Z2 @ Yb ) ) ) )
=> ( rel_as373026983500813000_a_d_c @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_568_assertion_Orel__mono__strong,axiom,
! [R3: b > b > $o,X: assertion_a_b_d_c,Y: assertion_a_b_d_c,Ra: b > b > $o] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X @ Y )
=> ( ! [Z2: b,Yb: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ X ) )
=> ( ( member_b @ Yb @ ( set_as7232682317586342732_b_d_c @ Y ) )
=> ( ( R3 @ Z2 @ Yb )
=> ( Ra @ Z2 @ Yb ) ) ) )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_569_assertion_Orel__cong,axiom,
! [X: assertion_a_a_d_c,Ya: assertion_a_a_d_c,Y: assertion_a_b_d_c,Xa: assertion_a_b_d_c,R3: a > b > $o,Ra: a > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa )
=> ( ! [Z2: a,Yb: b] :
( ( member_a @ Z2 @ ( set_as1636463702398212043_a_d_c @ Ya ) )
=> ( ( member_b @ Yb @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( R3 @ Z2 @ Yb )
= ( Ra @ Z2 @ Yb ) ) ) )
=> ( ( rel_as1194089545255703174_a_d_c @ R3 @ X @ Y )
= ( rel_as1194089545255703174_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_570_assertion_Orel__cong,axiom,
! [X: assertion_a_b_d_c,Ya: assertion_a_b_d_c,Y: assertion_a_a_d_c,Xa: assertion_a_a_d_c,R3: b > a > $o,Ra: b > a > $o] :
( ( X = Ya )
=> ( ( Y = Xa )
=> ( ! [Z2: b,Yb: a] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( member_a @ Yb @ ( set_as1636463702398212043_a_d_c @ Xa ) )
=> ( ( R3 @ Z2 @ Yb )
= ( Ra @ Z2 @ Yb ) ) ) )
=> ( ( rel_as373026983500813000_a_d_c @ R3 @ X @ Y )
= ( rel_as373026983500813000_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_571_assertion_Orel__cong,axiom,
! [X: assertion_a_b_d_c,Ya: assertion_a_b_d_c,Y: assertion_a_b_d_c,Xa: assertion_a_b_d_c,R3: b > b > $o,Ra: b > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa )
=> ( ! [Z2: b,Yb: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( member_b @ Yb @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( R3 @ Z2 @ Yb )
= ( Ra @ Z2 @ Yb ) ) ) )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X @ Y )
= ( rel_as1860989020795611527_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_572_assertion_Osimps_I335_J,axiom,
! [X122: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( wildcard_a_b_d_c @ X122 ) )
= ( set_as7232682317586342732_b_d_c @ X122 ) ) ).
% assertion.simps(335)
thf(fact_573_assertion_Oset__intros_I16_J,axiom,
! [Yp: b,X122: assertion_a_b_d_c] :
( ( member_b @ Yp @ ( set_as7232682317586342732_b_d_c @ X122 ) )
=> ( member_b @ Yp @ ( set_as7232682317586342732_b_d_c @ ( wildcard_a_b_d_c @ X122 ) ) ) ) ).
% assertion.set_intros(16)
thf(fact_574_assertion_Oset__intros_I4_J,axiom,
! [Yd: b,X322: assertion_a_b_d_c,X312: assertion_a_b_d_c] :
( ( member_b @ Yd @ ( set_as7232682317586342732_b_d_c @ X322 ) )
=> ( member_b @ Yd @ ( set_as7232682317586342732_b_d_c @ ( star_a_b_d_c @ X312 @ X322 ) ) ) ) ).
% assertion.set_intros(4)
thf(fact_575_assertion_Oset__intros_I3_J,axiom,
! [Yc: b,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( member_b @ Yc @ ( set_as7232682317586342732_b_d_c @ X312 ) )
=> ( member_b @ Yc @ ( set_as7232682317586342732_b_d_c @ ( star_a_b_d_c @ X312 @ X322 ) ) ) ) ).
% assertion.set_intros(3)
thf(fact_576_assertion_Oset__intros_I10_J,axiom,
! [Yj: b,X622: assertion_a_b_d_c,X612: assertion_a_b_d_c] :
( ( member_b @ Yj @ ( set_as7232682317586342732_b_d_c @ X622 ) )
=> ( member_b @ Yj @ ( set_as7232682317586342732_b_d_c @ ( and_a_b_d_c @ X612 @ X622 ) ) ) ) ).
% assertion.set_intros(10)
thf(fact_577_assertion_Oset__intros_I9_J,axiom,
! [Yi: b,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( member_b @ Yi @ ( set_as7232682317586342732_b_d_c @ X612 ) )
=> ( member_b @ Yi @ ( set_as7232682317586342732_b_d_c @ ( and_a_b_d_c @ X612 @ X622 ) ) ) ) ).
% assertion.set_intros(9)
thf(fact_578_assertion_Osimps_I332_J,axiom,
! [X912: c,X922: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( forall_c_a_b_d @ X912 @ X922 ) )
= ( set_as7232682317586342732_b_d_c @ X922 ) ) ).
% assertion.simps(332)
thf(fact_579_assertion_Oset__intros_I14_J,axiom,
! [Yn: b,X922: assertion_a_b_d_c,X912: c] :
( ( member_b @ Yn @ ( set_as7232682317586342732_b_d_c @ X922 ) )
=> ( member_b @ Yn @ ( set_as7232682317586342732_b_d_c @ ( forall_c_a_b_d @ X912 @ X922 ) ) ) ) ).
% assertion.set_intros(14)
thf(fact_580_assertion_Oset__intros_I12_J,axiom,
! [Yl: b,X722: assertion_a_b_d_c,X712: assertion_a_b_d_c] :
( ( member_b @ Yl @ ( set_as7232682317586342732_b_d_c @ X722 ) )
=> ( member_b @ Yl @ ( set_as7232682317586342732_b_d_c @ ( imp_a_b_d_c @ X712 @ X722 ) ) ) ) ).
% assertion.set_intros(12)
thf(fact_581_assertion_Oset__intros_I11_J,axiom,
! [Yk: b,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( member_b @ Yk @ ( set_as7232682317586342732_b_d_c @ X712 ) )
=> ( member_b @ Yk @ ( set_as7232682317586342732_b_d_c @ ( imp_a_b_d_c @ X712 @ X722 ) ) ) ) ).
% assertion.set_intros(11)
thf(fact_582_assertion_Oset__intros_I6_J,axiom,
! [Yf: b,X422: assertion_a_b_d_c,X412: assertion_a_b_d_c] :
( ( member_b @ Yf @ ( set_as7232682317586342732_b_d_c @ X422 ) )
=> ( member_b @ Yf @ ( set_as7232682317586342732_b_d_c @ ( wand_a_b_d_c @ X412 @ X422 ) ) ) ) ).
% assertion.set_intros(6)
thf(fact_583_assertion_Oset__intros_I5_J,axiom,
! [Ye: b,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( member_b @ Ye @ ( set_as7232682317586342732_b_d_c @ X412 ) )
=> ( member_b @ Ye @ ( set_as7232682317586342732_b_d_c @ ( wand_a_b_d_c @ X412 @ X422 ) ) ) ) ).
% assertion.set_intros(5)
thf(fact_584_assertion_Oset__intros_I8_J,axiom,
! [Yh: b,X522: assertion_a_b_d_c,X512: assertion_a_b_d_c] :
( ( member_b @ Yh @ ( set_as7232682317586342732_b_d_c @ X522 ) )
=> ( member_b @ Yh @ ( set_as7232682317586342732_b_d_c @ ( or_a_b_d_c @ X512 @ X522 ) ) ) ) ).
% assertion.set_intros(8)
thf(fact_585_assertion_Oset__intros_I7_J,axiom,
! [Yg: b,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( member_b @ Yg @ ( set_as7232682317586342732_b_d_c @ X512 ) )
=> ( member_b @ Yg @ ( set_as7232682317586342732_b_d_c @ ( or_a_b_d_c @ X512 @ X522 ) ) ) ) ).
% assertion.set_intros(7)
thf(fact_586_assertion_Oset__intros_I13_J,axiom,
! [Ym: b,X822: assertion_a_b_d_c,X812: c] :
( ( member_b @ Ym @ ( set_as7232682317586342732_b_d_c @ X822 ) )
=> ( member_b @ Ym @ ( set_as7232682317586342732_b_d_c @ ( exists_c_a_b_d @ X812 @ X822 ) ) ) ) ).
% assertion.set_intros(13)
thf(fact_587_assertion_Osimps_I331_J,axiom,
! [X812: c,X822: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( exists_c_a_b_d @ X812 @ X822 ) )
= ( set_as7232682317586342732_b_d_c @ X822 ) ) ).
% assertion.simps(331)
thf(fact_588_assertion_Oset__intros_I2_J,axiom,
! [Yb2: b,X222: assertion_a_b_d_c,X212: b] :
( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ X222 ) )
=> ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ ( mult_b_a_d_c @ X212 @ X222 ) ) ) ) ).
% assertion.set_intros(2)
thf(fact_589_assertion_Oset__intros_I1_J,axiom,
! [X212: b,X222: assertion_a_b_d_c] : ( member_b @ X212 @ ( set_as7232682317586342732_b_d_c @ ( mult_b_a_d_c @ X212 @ X222 ) ) ) ).
% assertion.set_intros(1)
thf(fact_590_assertion_Oset__intros_I15_J,axiom,
! [Yo: b,X112: assertion_a_b_d_c] :
( ( member_b @ Yo @ ( set_as7232682317586342732_b_d_c @ X112 ) )
=> ( member_b @ Yo @ ( set_as7232682317586342732_b_d_c @ ( bounded_a_b_d_c @ X112 ) ) ) ) ).
% assertion.set_intros(15)
thf(fact_591_assertion_Osimps_I334_J,axiom,
! [X112: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( bounded_a_b_d_c @ X112 ) )
= ( set_as7232682317586342732_b_d_c @ X112 ) ) ).
% assertion.simps(334)
thf(fact_592_logic_Oapplies__eq_Opelims,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: assertion_a_b_d_c,Xa: ( c > d ) > set_a,Xb: c > d,Y: set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ X @ Xa @ Xb )
= Y )
=> ( ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) )
=> ~ ( ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Uu @ Xb @ Xa @ X ) ) )
=> ~ ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) ) ) ) ) ) ).
% logic.applies_eq.pelims
thf(fact_593_assertion_Omap__transfer,axiom,
! [Rb: b > b > $o,Sd: b > b > $o] : ( bNF_re4457485704112703733_b_d_c @ ( bNF_rel_fun_b_b_b_b @ Rb @ Sd ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ Rb ) @ ( rel_as1860989020795611527_a_d_c @ Sd ) ) @ map_as2132001898603344138_a_d_c @ map_as2132001898603344138_a_d_c ) ).
% assertion.map_transfer
thf(fact_594_assertion_Octr__transfer_I7_J,axiom,
! [R3: b > b > $o] : ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) ) @ imp_a_b_d_c @ imp_a_b_d_c ) ).
% assertion.ctr_transfer(7)
thf(fact_595_assertion_Orel__transfer,axiom,
! [Sa: b > b > $o,Sc: b > b > $o] :
( bNF_re6697097071762359901_d_c_o
@ ( bNF_re4413358128099268379_o_b_o @ Sa
@ ( bNF_rel_fun_b_b_o_o @ Sc
@ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
@ ( bNF_re7564741212224818219_d_c_o @ ( rel_as1860989020795611527_a_d_c @ Sa )
@ ( bNF_re7425909319474424221_c_o_o @ ( rel_as1860989020795611527_a_d_c @ Sc )
@ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
@ rel_as1860989020795611527_a_d_c
@ rel_as1860989020795611527_a_d_c ) ).
% assertion.rel_transfer
thf(fact_596_assertion_Omap__ident,axiom,
! [T: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c
@ ^ [X3: b] : X3
@ T )
= T ) ).
% assertion.map_ident
thf(fact_597_assertion_Omap__cong,axiom,
! [X: assertion_a_b_d_c,Ya: assertion_a_b_d_c,F: b > b,G: b > b] :
( ( X = Ya )
=> ( ! [Z2: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( F @ Z2 )
= ( G @ Z2 ) ) )
=> ( ( map_as2132001898603344138_a_d_c @ F @ X )
= ( map_as2132001898603344138_a_d_c @ G @ Ya ) ) ) ) ).
% assertion.map_cong
thf(fact_598_assertion_Omap__cong0,axiom,
! [X: assertion_a_b_d_c,F: b > b,G: b > b] :
( ! [Z2: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ X ) )
=> ( ( F @ Z2 )
= ( G @ Z2 ) ) )
=> ( ( map_as2132001898603344138_a_d_c @ F @ X )
= ( map_as2132001898603344138_a_d_c @ G @ X ) ) ) ).
% assertion.map_cong0
thf(fact_599_assertion_Oinj__map__strong,axiom,
! [X: assertion_a_b_d_c,Xa: assertion_a_b_d_c,F: b > b,Fa: b > b] :
( ! [Z2: b,Za: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ X ) )
=> ( ( member_b @ Za @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( ( F @ Z2 )
= ( Fa @ Za ) )
=> ( Z2 = Za ) ) ) )
=> ( ( ( map_as2132001898603344138_a_d_c @ F @ X )
= ( map_as2132001898603344138_a_d_c @ Fa @ Xa ) )
=> ( X = Xa ) ) ) ).
% assertion.inj_map_strong
thf(fact_600_assertion_Omap__ident__strong,axiom,
! [T: assertion_a_b_d_c,F: b > b] :
( ! [Z2: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ T ) )
=> ( ( F @ Z2 )
= Z2 ) )
=> ( ( map_as2132001898603344138_a_d_c @ F @ T )
= T ) ) ).
% assertion.map_ident_strong
thf(fact_601_assertion_Osimps_I177_J,axiom,
! [F: b > b] :
( ( map_as2132001898603344138_a_d_c @ F @ pred_a_b_d_c )
= pred_a_b_d_c ) ).
% assertion.simps(177)
thf(fact_602_assertion_Orel__map_I2_J,axiom,
! [Sa: b > b > $o,X: assertion_a_b_d_c,G: b > b,Y: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ Sa @ X @ ( map_as2132001898603344138_a_d_c @ G @ Y ) )
= ( rel_as1860989020795611527_a_d_c
@ ^ [X3: b,Y3: b] : ( Sa @ X3 @ ( G @ Y3 ) )
@ X
@ Y ) ) ).
% assertion.rel_map(2)
thf(fact_603_assertion_Orel__map_I1_J,axiom,
! [Sb: b > b > $o,I: b > b,X: assertion_a_b_d_c,Y: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ Sb @ ( map_as2132001898603344138_a_d_c @ I @ X ) @ Y )
= ( rel_as1860989020795611527_a_d_c
@ ^ [X3: b] : ( Sb @ ( I @ X3 ) )
@ X
@ Y ) ) ).
% assertion.rel_map(1)
thf(fact_604_assertion_Osimps_I169_J,axiom,
! [F: b > b,X212: b,X222: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( mult_b_a_d_c @ X212 @ X222 ) )
= ( mult_b_a_d_c @ ( F @ X212 ) @ ( map_as2132001898603344138_a_d_c @ F @ X222 ) ) ) ).
% assertion.simps(169)
thf(fact_605_assertion_Osimps_I179_J,axiom,
! [F: b > b,X122: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( wildcard_a_b_d_c @ X122 ) )
= ( wildcard_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X122 ) ) ) ).
% assertion.simps(179)
thf(fact_606_assertion_Osimps_I170_J,axiom,
! [F: b > b,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( star_a_b_d_c @ X312 @ X322 ) )
= ( star_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X312 ) @ ( map_as2132001898603344138_a_d_c @ F @ X322 ) ) ) ).
% assertion.simps(170)
thf(fact_607_assertion_Osimps_I168_J,axiom,
! [F: b > b,X13: ( c > d ) > a > $o] :
( ( map_as2132001898603344138_a_d_c @ F @ ( sem_c_d_a_b @ X13 ) )
= ( sem_c_d_a_b @ X13 ) ) ).
% assertion.simps(168)
thf(fact_608_assertion_Osimps_I178_J,axiom,
! [F: b > b,X112: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( bounded_a_b_d_c @ X112 ) )
= ( bounded_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X112 ) ) ) ).
% assertion.simps(178)
thf(fact_609_assertion_Osimps_I175_J,axiom,
! [F: b > b,X812: c,X822: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( exists_c_a_b_d @ X812 @ X822 ) )
= ( exists_c_a_b_d @ X812 @ ( map_as2132001898603344138_a_d_c @ F @ X822 ) ) ) ).
% assertion.simps(175)
thf(fact_610_assertion_Osimps_I172_J,axiom,
! [F: b > b,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( or_a_b_d_c @ X512 @ X522 ) )
= ( or_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X512 ) @ ( map_as2132001898603344138_a_d_c @ F @ X522 ) ) ) ).
% assertion.simps(172)
thf(fact_611_assertion_Osimps_I171_J,axiom,
! [F: b > b,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( wand_a_b_d_c @ X412 @ X422 ) )
= ( wand_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X412 ) @ ( map_as2132001898603344138_a_d_c @ F @ X422 ) ) ) ).
% assertion.simps(171)
thf(fact_612_assertion_Osimps_I174_J,axiom,
! [F: b > b,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( imp_a_b_d_c @ X712 @ X722 ) )
= ( imp_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X712 ) @ ( map_as2132001898603344138_a_d_c @ F @ X722 ) ) ) ).
% assertion.simps(174)
thf(fact_613_assertion_Osimps_I176_J,axiom,
! [F: b > b,X912: c,X922: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( forall_c_a_b_d @ X912 @ X922 ) )
= ( forall_c_a_b_d @ X912 @ ( map_as2132001898603344138_a_d_c @ F @ X922 ) ) ) ).
% assertion.simps(176)
thf(fact_614_assertion_Osimps_I173_J,axiom,
! [F: b > b,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( and_a_b_d_c @ X612 @ X622 ) )
= ( and_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X612 ) @ ( map_as2132001898603344138_a_d_c @ F @ X622 ) ) ) ).
% assertion.simps(173)
thf(fact_615_assertion_Octr__transfer_I1_J,axiom,
! [R3: b > b > $o] :
( bNF_re1770667264140748071_b_d_c
@ ^ [Y2: ( c > d ) > a > $o,Z: ( c > d ) > a > $o] : ( Y2 = Z )
@ ( rel_as1860989020795611527_a_d_c @ R3 )
@ sem_c_d_a_b
@ sem_c_d_a_b ) ).
% assertion.ctr_transfer(1)
thf(fact_616_assertion_Octr__transfer_I2_J,axiom,
! [R3: b > b > $o] : ( bNF_re377125674677652585_b_d_c @ R3 @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) ) @ mult_b_a_d_c @ mult_b_a_d_c ) ).
% assertion.ctr_transfer(2)
thf(fact_617_assertion_Octr__transfer_I9_J,axiom,
! [R3: b > b > $o] :
( bNF_re133962660596780713_b_d_c
@ ^ [Y2: c,Z: c] : ( Y2 = Z )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) )
@ forall_c_a_b_d
@ forall_c_a_b_d ) ).
% assertion.ctr_transfer(9)
thf(fact_618_assertion_Octr__transfer_I8_J,axiom,
! [R3: b > b > $o] :
( bNF_re133962660596780713_b_d_c
@ ^ [Y2: c,Z: c] : ( Y2 = Z )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) )
@ exists_c_a_b_d
@ exists_c_a_b_d ) ).
% assertion.ctr_transfer(8)
thf(fact_619_assertion_Octr__transfer_I3_J,axiom,
! [R3: b > b > $o] : ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) ) @ star_a_b_d_c @ star_a_b_d_c ) ).
% assertion.ctr_transfer(3)
thf(fact_620_assertion_Octr__transfer_I6_J,axiom,
! [R3: b > b > $o] : ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) ) @ and_a_b_d_c @ and_a_b_d_c ) ).
% assertion.ctr_transfer(6)
thf(fact_621_assertion_Octr__transfer_I5_J,axiom,
! [R3: b > b > $o] : ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) ) @ or_a_b_d_c @ or_a_b_d_c ) ).
% assertion.ctr_transfer(5)
thf(fact_622_assertion_Octr__transfer_I4_J,axiom,
! [R3: b > b > $o] : ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( rel_as1860989020795611527_a_d_c @ R3 ) ) @ wand_a_b_d_c @ wand_a_b_d_c ) ).
% assertion.ctr_transfer(4)
thf(fact_623_assertion_Ocase__transfer,axiom,
! [S4: assertion_a_b_d_c > assertion_a_b_d_c > $o,R3: b > b > $o] :
( bNF_re5462665785578358557_b_d_c
@ ( bNF_re1770667264140748071_b_d_c
@ ^ [Y2: ( c > d ) > a > $o,Z: ( c > d ) > a > $o] : ( Y2 = Z )
@ S4 )
@ ( bNF_re969776683416675581_b_d_c @ ( bNF_re377125674677652585_b_d_c @ R3 @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re5536568207858047837_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re3555337462168811729_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re5146714292400357853_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re6312048780865235365_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re3015297470480446045_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re6171781090946898727_b_d_c
@ ( bNF_re133962660596780713_b_d_c
@ ^ [Y2: c,Z: c] : ( Y2 = Z )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re4264221303238623901_b_d_c
@ ( bNF_re133962660596780713_b_d_c
@ ^ [Y2: c,Z: c] : ( Y2 = Z )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re515523818749706873_b_d_c @ S4 @ ( bNF_re6606623624522348157_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) @ ( bNF_re8402442907184412917_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) ) ) ) ) ) ) ) ) ) ) )
@ case_a2736964712663357406_d_c_b
@ case_a2736964712663357406_d_c_b ) ).
% assertion.case_transfer
thf(fact_624_assertion_Osimps_I325_J,axiom,
! [X212: b,X222: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( mult_b_a_d_c @ X212 @ X222 ) )
= ( insert_b @ X212 @ ( set_as7232682317586342732_b_d_c @ X222 ) ) ) ).
% assertion.simps(325)
thf(fact_625_assertion_Omap__comp,axiom,
! [G: b > b,F: b > b,V: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ G @ ( map_as2132001898603344138_a_d_c @ F @ V ) )
= ( map_as2132001898603344138_a_d_c @ ( comp_b_b_b @ G @ F ) @ V ) ) ).
% assertion.map_comp
thf(fact_626_assertion_Opred__transfer,axiom,
! [R3: b > b > $o] :
( bNF_re3168247226632236905_d_c_o
@ ( bNF_rel_fun_b_b_o_o @ R3
@ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
@ ( bNF_re7425909319474424221_c_o_o @ ( rel_as1860989020795611527_a_d_c @ R3 )
@ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
@ pred_a5408123710409757427_a_d_c
@ pred_a5408123710409757427_a_d_c ) ).
% assertion.pred_transfer
thf(fact_627_assertion_Orel__Grp,axiom,
! [A2: set_b,F: b > b] :
( ( rel_as1860989020795611527_a_d_c @ ( bNF_Grp_b_b @ A2 @ F ) )
= ( bNF_Gr8554578625086265742_b_d_c
@ ( collec7183461376620183714_b_d_c
@ ^ [X3: assertion_a_b_d_c] : ( ord_less_eq_set_b @ ( set_as7232682317586342732_b_d_c @ X3 ) @ A2 ) )
@ ( map_as2132001898603344138_a_d_c @ F ) ) ) ).
% assertion.rel_Grp
thf(fact_628_assertion_Osimps_I328_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( or_a_b_d_c @ X512 @ X522 ) )
= ( sup_sup_set_b @ ( set_as7232682317586342732_b_d_c @ X512 ) @ ( set_as7232682317586342732_b_d_c @ X522 ) ) ) ).
% assertion.simps(328)
thf(fact_629_assertion_Opred__inject_I2_J,axiom,
! [P2: b > $o,A: b,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( mult_b_a_d_c @ A @ Aa ) )
= ( ( P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ) ).
% assertion.pred_inject(2)
thf(fact_630_assertion_Opred__inject_I12_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( wildcard_a_b_d_c @ A ) )
= ( pred_a5408123710409757427_a_d_c @ P2 @ A ) ) ).
% assertion.pred_inject(12)
thf(fact_631_assertion_Opred__inject_I3_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( star_a_b_d_c @ A @ Aa ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ) ).
% assertion.pred_inject(3)
thf(fact_632_assertion_Opred__inject_I6_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( and_a_b_d_c @ A @ Aa ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ) ).
% assertion.pred_inject(6)
thf(fact_633_assertion_Opred__inject_I9_J,axiom,
! [P2: b > $o,A: c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( forall_c_a_b_d @ A @ Aa ) )
= ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ).
% assertion.pred_inject(9)
thf(fact_634_assertion_Opred__inject_I5_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( or_a_b_d_c @ A @ Aa ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ) ).
% assertion.pred_inject(5)
thf(fact_635_assertion_Opred__inject_I4_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( wand_a_b_d_c @ A @ Aa ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ) ).
% assertion.pred_inject(4)
thf(fact_636_assertion_Opred__inject_I7_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( imp_a_b_d_c @ A @ Aa ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ) ).
% assertion.pred_inject(7)
thf(fact_637_assertion_Opred__inject_I8_J,axiom,
! [P2: b > $o,A: c,Aa: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( exists_c_a_b_d @ A @ Aa ) )
= ( pred_a5408123710409757427_a_d_c @ P2 @ Aa ) ) ).
% assertion.pred_inject(8)
thf(fact_638_assertion_Opred__inject_I11_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( bounded_a_b_d_c @ A ) )
= ( pred_a5408123710409757427_a_d_c @ P2 @ A ) ) ).
% assertion.pred_inject(11)
thf(fact_639_assertion_Omap__cong__pred,axiom,
! [X: assertion_a_b_d_c,Ya: assertion_a_b_d_c,F: b > b,G: b > b] :
( ( X = Ya )
=> ( ( pred_a5408123710409757427_a_d_c
@ ^ [Z3: b] :
( ( F @ Z3 )
= ( G @ Z3 ) )
@ Ya )
=> ( ( map_as2132001898603344138_a_d_c @ F @ X )
= ( map_as2132001898603344138_a_d_c @ G @ Ya ) ) ) ) ).
% assertion.map_cong_pred
thf(fact_640_assertion_Opred__map,axiom,
! [Q2: b > $o,F: b > b,X: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ Q2 @ ( map_as2132001898603344138_a_d_c @ F @ X ) )
= ( pred_a5408123710409757427_a_d_c @ ( comp_b_o_b @ Q2 @ F ) @ X ) ) ).
% assertion.pred_map
thf(fact_641_assertion_Opred__True,axiom,
( ( pred_a5408123710409757427_a_d_c
@ ^ [Uu: b] : $true )
= ( ^ [Uu: assertion_a_b_d_c] : $true ) ) ).
% assertion.pred_True
thf(fact_642_assertion_Opred__cong,axiom,
! [X: assertion_a_b_d_c,Ya: assertion_a_b_d_c,P2: b > $o,Pa: b > $o] :
( ( X = Ya )
=> ( ! [Z2: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( P2 @ Z2 )
= ( Pa @ Z2 ) ) )
=> ( ( pred_a5408123710409757427_a_d_c @ P2 @ X )
= ( pred_a5408123710409757427_a_d_c @ Pa @ Ya ) ) ) ) ).
% assertion.pred_cong
thf(fact_643_assertion_Opred__mono__strong,axiom,
! [P2: b > $o,X: assertion_a_b_d_c,Pa: b > $o] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ X )
=> ( ! [Z2: b] :
( ( member_b @ Z2 @ ( set_as7232682317586342732_b_d_c @ X ) )
=> ( ( P2 @ Z2 )
=> ( Pa @ Z2 ) ) )
=> ( pred_a5408123710409757427_a_d_c @ Pa @ X ) ) ) ).
% assertion.pred_mono_strong
thf(fact_644_assertion_Opred__inject_I10_J,axiom,
! [P2: b > $o] : ( pred_a5408123710409757427_a_d_c @ P2 @ pred_a_b_d_c ) ).
% assertion.pred_inject(10)
thf(fact_645_assertion_Osimps_I326_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( star_a_b_d_c @ X312 @ X322 ) )
= ( sup_sup_set_b @ ( set_as7232682317586342732_b_d_c @ X312 ) @ ( set_as7232682317586342732_b_d_c @ X322 ) ) ) ).
% assertion.simps(326)
thf(fact_646_assertion_Osimps_I329_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( and_a_b_d_c @ X612 @ X622 ) )
= ( sup_sup_set_b @ ( set_as7232682317586342732_b_d_c @ X612 ) @ ( set_as7232682317586342732_b_d_c @ X622 ) ) ) ).
% assertion.simps(329)
thf(fact_647_assertion_Osimps_I330_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( imp_a_b_d_c @ X712 @ X722 ) )
= ( sup_sup_set_b @ ( set_as7232682317586342732_b_d_c @ X712 ) @ ( set_as7232682317586342732_b_d_c @ X722 ) ) ) ).
% assertion.simps(330)
thf(fact_648_assertion_Osimps_I327_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( wand_a_b_d_c @ X412 @ X422 ) )
= ( sup_sup_set_b @ ( set_as7232682317586342732_b_d_c @ X412 ) @ ( set_as7232682317586342732_b_d_c @ X422 ) ) ) ).
% assertion.simps(327)
thf(fact_649_assertion_Opred__rel,axiom,
( pred_a5408123710409757427_a_d_c
= ( ^ [P5: b > $o,X3: assertion_a_b_d_c] : ( rel_as1860989020795611527_a_d_c @ ( bNF_eq_onp_b @ P5 ) @ X3 @ X3 ) ) ) ).
% assertion.pred_rel
thf(fact_650_assertion_Opred__inject_I1_J,axiom,
! [P2: b > $o,A: ( c > d ) > a > $o] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( sem_c_d_a_b @ A ) )
= ( top_top_c_d_a_o_o @ A ) ) ).
% assertion.pred_inject(1)
thf(fact_651_assertion_Oset__map,axiom,
! [F: b > b,V: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ V ) )
= ( image_b_b @ F @ ( set_as7232682317586342732_b_d_c @ V ) ) ) ).
% assertion.set_map
thf(fact_652_assertion_Orel__eq__onp,axiom,
! [P2: b > $o] :
( ( rel_as1860989020795611527_a_d_c @ ( bNF_eq_onp_b @ P2 ) )
= ( bNF_eq6553376382750210344_b_d_c @ ( pred_a5408123710409757427_a_d_c @ P2 ) ) ) ).
% assertion.rel_eq_onp
thf(fact_653_assertion_Opred__set,axiom,
( pred_a5408123710409757427_a_d_c
= ( ^ [P5: b > $o,X3: assertion_a_b_d_c] :
! [Y3: b] :
( ( member_b @ Y3 @ ( set_as7232682317586342732_b_d_c @ X3 ) )
=> ( P5 @ Y3 ) ) ) ) ).
% assertion.pred_set
% Conjectures (1)
thf(conj_0,conjecture,
non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ v @ a2 ) ) ).
%------------------------------------------------------------------------------