TPTP Problem File: SLH0387^1.p
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%------------------------------------------------------------------------------
% 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_00396_011941__6846206_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1388 ( 521 unt; 406 typ; 0 def)
% Number of atoms : 2748 ( 930 equ; 0 cnn)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 11955 ( 351 ~; 13 |; 171 &;10566 @)
% ( 0 <=>; 854 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 41 ( 40 usr)
% Number of type conns : 7123 (7123 >; 0 *; 0 +; 0 <<)
% Number of symbols : 369 ( 366 usr; 29 con; 0-14 aty)
% Number of variables : 4596 ( 158 ^;4360 !; 78 ?;4596 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 16:05:23.562
%------------------------------------------------------------------------------
% Could-be-implicit typings (40)
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% Explicit typings (366)
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__d_Mtf__c_J_J_J_J_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re2658820731495178543_b_d_c: ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( ( c > d ) > a > $o ) > 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 > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > 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 > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > 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 > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_re7112637536428693683_b_d_c: ( ( ( c > d ) > a > $o ) > ( ( c > d ) > a > $o ) > $o ) > ( ( 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 > assertion_a_b_d_c ) > ( ( ( c > d ) > a > $o ) > 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_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_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_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_M_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_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_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_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_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J_J_J_J_J,type,
bNF_re1913961672366121877_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 > assertion_a_b_d_c ) > ( 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 > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_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_M_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J_J_J_J,type,
bNF_re251176583891200149_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 > 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 > 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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > assertion_a_b_d_c ) > ( 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 > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_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_M_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J_J_J,type,
bNF_re8060521475475539349_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( 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 > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > 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 > 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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_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_M_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_J_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J_J,type,
bNF_re3682814332405119637_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( 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 > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 ) > ( 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 > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_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_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J,type,
bNF_re4121371422775248789_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 ) > ( 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 > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_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_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_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_J,type,
bNF_re8482286197440273641_b_d_c: ( ( assertion_a_b_d_c > assertion_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 ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_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_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_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_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_J_J,type,
bNF_re4842871906108351673_b_d_c: ( ( assertion_a_b_d_c > assertion_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 ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_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_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,type,
bNF_re9183090372639188701_b_d_c: ( ( assertion_a_b_d_c > assertion_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 ) > $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_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_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_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_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_J_J,type,
bNF_re3297605885130694505_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 ) > 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 > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_M_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_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_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_re8313538116629745697_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_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,type,
bNF_re2031598785229489641_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 ) > $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 ) > $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__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_J,type,
bNF_re4933961146405920325tion_a: ( ( a > option_a ) > ( a > option_a ) > $o ) > ( ( a > option_a > a > option_a ) > ( a > option_a > a > option_a ) > $o ) > ( ( a > option_a ) > a > option_a > a > option_a ) > ( ( a > option_a ) > a > option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__c_Mtf__d_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_J_001_062_Itf__c_M_062_Itf__d_M_062_Itf__c_Mtf__d_J_J_J,type,
bNF_re3817954351838466806_d_c_d: ( ( a > option_a ) > ( c > d ) > $o ) > ( ( a > option_a > a > option_a ) > ( c > d > c > d ) > $o ) > ( ( a > option_a ) > a > option_a > a > option_a ) > ( ( c > d ) > c > d > c > d ) > $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_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_Itf__b_M_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_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_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_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_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_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_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_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_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_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_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_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_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_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_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_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_M_062_I_062_Itf__c_M_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_J_M_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_J_J_J_J_J_J,type,
bNF_re8066222765365709061_b_d_c: ( ( b > 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 ) > $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 > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_Itf__c_M_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_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_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_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_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_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_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_J_J_J,type,
bNF_re672856011677040387_b_d_c: ( ( 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 ) > $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 > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 > assertion_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 > assertion_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_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_Itf__c_M_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_J_001_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J_001_062_I_062_Itf__c_M_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_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_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_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_J_J_J_J,type,
bNF_re4985889110256990915_b_d_c: ( ( 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 ) > $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 > assertion_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 > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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 ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_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_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_001_062_Itf__c_Mtf__d_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__c_M_062_Itf__d_M_062_Itf__c_Mtf__d_J_J_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_J,type,
bNF_re5308688359564752758tion_a: ( ( c > d ) > ( a > option_a ) > $o ) > ( ( c > d > c > d ) > ( a > option_a > a > option_a ) > $o ) > ( ( c > d ) > c > d > c > d ) > ( ( a > option_a ) > a > option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__d_J_001_062_Itf__c_Mtf__d_J_001_062_Itf__c_M_062_Itf__d_M_062_Itf__c_Mtf__d_J_J_J_001_062_Itf__c_M_062_Itf__d_M_062_Itf__c_Mtf__d_J_J_J,type,
bNF_re4162436072719156391_d_c_d: ( ( c > d ) > ( c > d ) > $o ) > ( ( c > d > c > d ) > ( c > d > c > d ) > $o ) > ( ( c > d ) > c > d > c > d ) > ( ( c > d ) > c > d > c > d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re8162217253061806133tion_a: ( option_a > option_a > $o ) > ( ( a > option_a ) > ( a > option_a ) > $o ) > ( option_a > a > option_a ) > ( option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001tf__d_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__c_Mtf__d_J,type,
bNF_re6291851909076488365_a_c_d: ( option_a > d > $o ) > ( ( a > option_a ) > ( c > d ) > $o ) > ( option_a > a > option_a ) > ( d > c > d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_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_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
bNF_re7631950180739184205_a_c_d: ( product_prod_a_c_d > product_prod_a_c_d > $o ) > ( option6413918287372586467_a_c_d > option6413918287372586467_a_c_d > $o ) > ( product_prod_a_c_d > option6413918287372586467_a_c_d ) > ( product_prod_a_c_d > option6413918287372586467_a_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001tf__a_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_001t__Option__Ooption_Itf__a_J,type,
bNF_re3106999726094018323tion_a: ( product_prod_a_c_d > a > $o ) > ( option6413918287372586467_a_c_d > option_a > $o ) > ( product_prod_a_c_d > option6413918287372586467_a_c_d ) > ( a > option_a ) > $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_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_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_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_J,type,
bNF_re5290459592999203293_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 ) > $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_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_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,type,
bNF_re39574443744948061_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 ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c > assertion_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__a_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
bNF_re9155705077389660979_a_c_d: ( a > product_prod_a_c_d > $o ) > ( option_a > option6413918287372586467_a_c_d > $o ) > ( a > option_a ) > ( product_prod_a_c_d > option6413918287372586467_a_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J,type,
bNF_re845666378725559389tion_a: ( a > a > $o ) > ( ( option_a > a > option_a ) > ( option_a > a > option_a ) > $o ) > ( a > option_a > a > option_a ) > ( a > option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bNF_re1187871780581372509tion_a: ( a > a > $o ) > ( option_a > option_a > $o ) > ( a > option_a ) > ( a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__c_001_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_001_062_Itf__d_M_062_Itf__c_Mtf__d_J_J,type,
bNF_re7925548642511003351_d_c_d: ( a > c > $o ) > ( ( option_a > a > option_a ) > ( d > c > d ) > $o ) > ( a > option_a > a > option_a ) > ( c > d > c > d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__c_001t__Option__Ooption_Itf__a_J_001tf__d,type,
bNF_re3628769949165654428on_a_d: ( a > c > $o ) > ( option_a > d > $o ) > ( a > option_a ) > ( c > d ) > $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_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,type,
bNF_re7963540674472851293_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 > 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 ) > ( b > 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__a_001_062_Itf__d_M_062_Itf__c_Mtf__d_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J,type,
bNF_re2730572489753928035tion_a: ( c > a > $o ) > ( ( d > c > d ) > ( option_a > a > option_a ) > $o ) > ( c > d > c > d ) > ( a > option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__a_001tf__d_001t__Option__Ooption_Itf__a_J,type,
bNF_re2367443474453270238tion_a: ( c > a > $o ) > ( d > option_a > $o ) > ( c > d ) > ( a > option_a ) > $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_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,type,
bNF_re6592304143361956253_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 > 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 ) > ( 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__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_BNF__Def_Orel__fun_001tf__c_001tf__c_001_062_Itf__d_M_062_Itf__c_Mtf__d_J_J_001_062_Itf__d_M_062_Itf__c_Mtf__d_J_J,type,
bNF_re6283605750710864861_d_c_d: ( c > c > $o ) > ( ( d > c > d ) > ( d > c > d ) > $o ) > ( c > d > c > d ) > ( c > d > c > d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__c_001tf__d_001tf__d,type,
bNF_rel_fun_c_c_d_d: ( c > c > $o ) > ( d > d > $o ) > ( c > d ) > ( c > d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001t__Option__Ooption_Itf__a_J_001_062_Itf__c_Mtf__d_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re4105512943801057267tion_a: ( d > option_a > $o ) > ( ( c > d ) > ( a > option_a ) > $o ) > ( d > c > d ) > ( option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001_062_Itf__c_Mtf__d_J_001_062_Itf__c_Mtf__d_J,type,
bNF_re2118925435710938475_d_c_d: ( d > d > $o ) > ( ( c > d ) > ( c > d ) > $o ) > ( d > c > d ) > ( d > c > d ) > $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__a_001t__Option__Ooption_Itf__a_J,type,
unambi704529886615442436tion_a: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > ( ( a > option_a ) > set_a ) > assert1556940916145061938on_a_a > a > $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_Finite__Set_Ofinite_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
finite8114217219359860531tion_a: set_option_option_a > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
finite3027439597799462906_a_c_d: set_op3383557829362473625_a_c_d > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__a_J,type,
finite1674126218327898605tion_a: set_option_a > $o ).
thf(sy_c_Finite__Set_Ofinite_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,
finite5665696198532655488_a_c_d: set_Pr1275464188344874039_a_c_d > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
finite6487500827408305578_a_c_d: set_Pr334309860168054345_a_c_d > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
finite_finite_a: set_a > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__b,type,
finite_finite_b: set_b > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__c,type,
finite_finite_c: set_c > $o ).
thf(sy_c_Finite__Set_Ofold_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,
finite125887116680883648_a_c_d: ( product_prod_a_c_d > option6413918287372586467_a_c_d > option6413918287372586467_a_c_d ) > option6413918287372586467_a_c_d > set_Pr334309860168054345_a_c_d > option6413918287372586467_a_c_d ).
thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_Itf__b_J_001t__Option__Ooption_It__Set__Oset_Itf__b_J_J,type,
finite4684332809091328718_set_b: ( set_b > option_set_b > option_set_b ) > option_set_b > set_set_b > option_set_b ).
thf(sy_c_Finite__Set_Ofold_001tf__a_001t__Option__Ooption_Itf__a_J,type,
finite6501707464432451470tion_a: ( a > option_a > option_a ) > option_a > set_a > option_a ).
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_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_001t__Option__Ooption_Itf__a_J_001tf__a,type,
comp_o5927112796044265472on_a_a: ( option6413918287372586467_a_c_d > option_a ) > ( a > option6413918287372586467_a_c_d ) > a > option_a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
comp_o6230065071311576686_a_c_d: ( option6413918287372586467_a_c_d > product_prod_a_c_d ) > ( product_prod_a_c_d > option6413918287372586467_a_c_d ) > product_prod_a_c_d > product_prod_a_c_d ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_001tf__a,type,
comp_o5508582540435784312_c_d_a: ( option_a > option6413918287372586467_a_c_d ) > ( a > option_a ) > a > option6413918287372586467_a_c_d ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a,type,
comp_o6087033147929006299on_a_a: ( option_a > option_a ) > ( a > option_a ) > a > option_a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__a,type,
comp_option_a_a_a: ( option_a > a ) > ( a > option_a ) > a > a ).
thf(sy_c_Fun_Ocomp_001tf__a_001t__Option__Ooption_Itf__a_J_001tf__a,type,
comp_a_option_a_a: ( a > option_a ) > ( a > a ) > a > option_a ).
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_Ocomp_001tf__d_001tf__d_001tf__c,type,
comp_d_d_c: ( d > d ) > ( c > d ) > c > d ).
thf(sy_c_Fun_Ofun__upd_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001t__Option__Ooption_I_062_Itf__c_Mtf__d_J_J,type,
fun_up2820008246124789800on_c_d: ( ( ( c > d ) > set_a ) > option_c_d ) > ( ( c > d ) > set_a ) > option_c_d > ( ( c > d ) > set_a ) > option_c_d ).
thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
fun_up5969202740897331946_a_c_d: ( option_a > option6413918287372586467_a_c_d ) > option_a > option6413918287372586467_a_c_d > option_a > option6413918287372586467_a_c_d ).
thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
fun_up1079276522633388797tion_a: ( option_a > option_a ) > option_a > option_a > option_a > option_a ).
thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_Itf__a_J_001tf__a,type,
fun_upd_option_a_a: ( option_a > a ) > option_a > a > option_a > a ).
thf(sy_c_Fun_Ofun__upd_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_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
fun_up4007221454163596925_a_c_d: ( produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d ) > produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d > produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d ).
thf(sy_c_Fun_Ofun__upd_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_001t__Option__Ooption_Itf__a_J,type,
fun_up7463025390225626410tion_a: ( produc5278197477302038359_a_c_d > option_a ) > produc5278197477302038359_a_c_d > option_a > produc5278197477302038359_a_c_d > option_a ).
thf(sy_c_Fun_Ofun__upd_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_001tf__a,type,
fun_up2227350886784581604_c_d_a: ( produc5278197477302038359_a_c_d > a ) > produc5278197477302038359_a_c_d > a > produc5278197477302038359_a_c_d > a ).
thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001t__Option__Ooption_It__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J,type,
fun_up3914643275129436357_a_c_d: ( product_prod_a_c_d > option6212624336325788467_a_c_d ) > product_prod_a_c_d > option6212624336325788467_a_c_d > product_prod_a_c_d > option6212624336325788467_a_c_d ).
thf(sy_c_Fun_Ofun__upd_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,type,
fun_up8437948482231556639_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_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_Fun_Ofun__upd_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__Option__Ooption_It__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,
fun_up8563802042059451790_a_c_d: ( assertion_a_b_d_c > option3890169911263941780_a_c_d ) > assertion_a_b_d_c > option3890169911263941780_a_c_d > assertion_a_b_d_c > option3890169911263941780_a_c_d ).
thf(sy_c_Fun_Ofun__upd_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,
fun_up5644072878873480765_b_d_c: ( assertion_a_b_d_c > assertion_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_Fun_Ofun__upd_001tf__a_001t__Option__Ooption_I_062_Itf__c_Mtf__d_J_J,type,
fun_upd_a_option_c_d: ( a > option_c_d ) > a > option_c_d > a > option_c_d ).
thf(sy_c_Fun_Ofun__upd_001tf__a_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
fun_up6642239869823773348_a_c_d: ( a > option6413918287372586467_a_c_d ) > a > option6413918287372586467_a_c_d > a > option6413918287372586467_a_c_d ).
thf(sy_c_Fun_Ofun__upd_001tf__a_001t__Option__Ooption_Itf__a_J,type,
fun_upd_a_option_a: ( a > option_a ) > a > option_a > a > option_a ).
thf(sy_c_Fun_Ofun__upd_001tf__a_001tf__a,type,
fun_upd_a_a: ( a > a ) > a > a > a > a ).
thf(sy_c_Fun_Ofun__upd_001tf__b_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
fun_up6513502963972302373_a_c_d: ( b > option6413918287372586467_a_c_d ) > b > option6413918287372586467_a_c_d > b > option6413918287372586467_a_c_d ).
thf(sy_c_Fun_Ofun__upd_001tf__b_001t__Option__Ooption_Itf__a_J,type,
fun_upd_b_option_a: ( b > option_a ) > b > option_a > b > option_a ).
thf(sy_c_Fun_Ofun__upd_001tf__b_001tf__a,type,
fun_upd_b_a: ( b > a ) > b > a > b > a ).
thf(sy_c_Fun_Ofun__upd_001tf__c_001tf__d,type,
fun_upd_c_d: ( c > d ) > c > d > c > d ).
thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
id_Pro4866527663230331490_a_c_d: product_prod_a_c_d > product_prod_a_c_d ).
thf(sy_c_Fun_Oid_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
id_assertion_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_Fun_Oid_001tf__a,type,
id_a: a > a ).
thf(sy_c_Fun_Oid_001tf__b,type,
id_b: b > b ).
thf(sy_c_Fun_Oinj__on_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,
inj_on7837763817969280361_a_c_d: ( product_prod_a_c_d > option6413918287372586467_a_c_d ) > set_Pr334309860168054345_a_c_d > $o ).
thf(sy_c_Fun_Oinj__on_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,
inj_on3926713243670117681_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c ) > set_as909545710669178647_b_d_c > $o ).
thf(sy_c_Fun_Oinj__on_001tf__a_001t__Option__Ooption_Itf__a_J,type,
inj_on_a_option_a: ( a > option_a ) > set_a > $o ).
thf(sy_c_Fun_Oinj__on_001tf__b_001tf__b,type,
inj_on_b_b: ( b > b ) > set_b > $o ).
thf(sy_c_Fun_Oinj__on_001tf__c_001tf__d,type,
inj_on_c_d: ( c > d ) > set_c > $o ).
thf(sy_c_Fun_Ooverride__on_001tf__a_001t__Option__Ooption_Itf__a_J,type,
overri633547075744967556tion_a: ( a > option_a ) > ( a > option_a ) > set_a > a > option_a ).
thf(sy_c_Fun_Ooverride__on_001tf__c_001tf__d,type,
override_on_c_d: ( c > d ) > ( c > d ) > set_c > c > d ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
minus_1574173051537231627tion_a: set_option_a > set_option_a > set_option_a ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__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,
minus_4271488753454470558_a_c_d: set_Pr1275464188344874039_a_c_d > set_Pr1275464188344874039_a_c_d > set_Pr1275464188344874039_a_c_d ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__b_J,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__c_J,type,
minus_minus_set_c: set_c > set_c > set_c ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
uminus6205308855922866075tion_a: set_option_a > set_option_a ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_Itf__a_J,type,
uminus_uminus_set_a: set_a > set_a ).
thf(sy_c_If_001t__Option__Ooption_Itf__a_J,type,
if_option_a: $o > option_a > option_a > option_a ).
thf(sy_c_If_001tf__d,type,
if_d: $o > d > d > d ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
sup_sup_set_a: set_a > set_a > set_a ).
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_Lattices__Big_Osemilattice__set_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
lattic4068221337090480901_a_c_d: ( product_prod_a_c_d > product_prod_a_c_d > product_prod_a_c_d ) > $o ).
thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
lattic5961991414251573132_set_a: ( a > a > a ) > $o ).
thf(sy_c_Lattices__Big_Osemilattice__set_OF_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
lattic8819272484393134521_a_c_d: ( product_prod_a_c_d > product_prod_a_c_d > product_prod_a_c_d ) > set_Pr334309860168054345_a_c_d > product_prod_a_c_d ).
thf(sy_c_Lattices__Big_Osemilattice__set_OF_001tf__a,type,
lattic5116578512385870296ce_F_a: ( a > a > a ) > set_a > a ).
thf(sy_c_Lattices__Big_Osemilattice__sup__class_OSup__fin_001t__Set__Oset_Itf__b_J,type,
lattic2918178361130032022_set_b: set_set_b > set_b ).
thf(sy_c_Map_Odom_001t__Option__Ooption_Itf__a_J_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
dom_op6156779764657312645_a_c_d: ( option_a > option6413918287372586467_a_c_d ) > set_option_a ).
thf(sy_c_Map_Odom_001t__Option__Ooption_Itf__a_J_001tf__a,type,
dom_option_a_a: ( option_a > option_a ) > set_option_a ).
thf(sy_c_Map_Odom_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_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
dom_Pr2275460399045561368_a_c_d: ( produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d ) > set_Pr1275464188344874039_a_c_d ).
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dom_Pr210953022859676729_c_d_a: ( produc5278197477302038359_a_c_d > option_a ) > set_Pr1275464188344874039_a_c_d ).
thf(sy_c_Map_Odom_001tf__a_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
dom_a_3529858286862933695_a_c_d: ( a > option6413918287372586467_a_c_d ) > set_a ).
thf(sy_c_Map_Odom_001tf__a_001tf__a,type,
dom_a_a: ( a > option_a ) > set_a ).
thf(sy_c_Map_Odom_001tf__b_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
dom_b_1825636403396063168_a_c_d: ( b > option6413918287372586467_a_c_d ) > set_b ).
thf(sy_c_Map_Odom_001tf__b_001tf__a,type,
dom_b_a: ( b > option_a ) > set_b ).
thf(sy_c_Map_Ograph_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_Itf__c_Mtf__d_J,type,
graph_c_d_set_a_c_d: ( ( ( c > d ) > set_a ) > option_c_d ) > set_Pr336584576397674490_a_c_d ).
thf(sy_c_Map_Ograph_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,
graph_7244981646656495094_a_c_d: ( product_prod_a_c_d > option6212624336325788467_a_c_d ) > set_Pr1275464188344874039_a_c_d ).
thf(sy_c_Map_Ograph_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,
graph_7603009230766167293_a_c_d: ( assertion_a_b_d_c > option3890169911263941780_a_c_d ) > set_Pr1216123688828223200_a_c_d ).
thf(sy_c_Map_Ograph_001tf__a_001_062_Itf__c_Mtf__d_J,type,
graph_a_c_d: ( a > option_c_d ) > set_Pr334309860168054345_a_c_d ).
thf(sy_c_Map_Ograph_001tf__a_001tf__a,type,
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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_001t__Option__Ooption_Itf__a_J_001tf__d_001tf__c,type,
set_as971186299496371729_a_d_c: assert3107445333071088380_a_d_c > set_option_a ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_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_001tf__d_001tf__c,type,
set_as6006471827460666276_d_d_c: assert7138933933671473679_d_d_c > set_Pr1275464188344874039_a_c_d ).
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__a_001t__Option__Ooption_Itf__a_J,type,
sat_a_b_a_option_a: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > a > ( a > option_a ) > ( ( a > option_a ) > set_a ) > assert1556940916145061938on_a_a > $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_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
pre_la7759296445815288060_a_c_d: ( product_prod_a_c_d > product_prod_a_c_d > option6413918287372586467_a_c_d ) > product_prod_a_c_d > product_prod_a_c_d > $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__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
member5113800082084363315tion_a: option_option_a > set_option_option_a > $o ).
thf(sy_c_member_001t__Option__Ooption_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,
member7124857669314633414_a_c_d: option6736415434736681245_a_c_d > set_op7411283011066580861_a_c_d > $o ).
thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
member5926479794665358074_a_c_d: option6413918287372586467_a_c_d > set_op3383557829362473625_a_c_d > $o ).
thf(sy_c_member_001t__Option__Ooption_Itf__a_J,type,
member_option_a: option_a > set_option_a > $o ).
thf(sy_c_member_001t__Option__Ooption_Itf__b_J,type,
member_option_b: option_b > set_option_b > $o ).
thf(sy_c_member_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,
member1642667639779969243_a_c_d: produc5213381314664832452_a_c_d > set_Pr336584576397674490_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_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,
member537768723423446209_a_c_d: produc5105196854009589546_a_c_d > set_Pr1216123688828223200_a_c_d > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
member8846983874477766826_a_c_d: product_prod_a_c_d > set_Pr334309860168054345_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_c_member_001tf__c,type,
member_c: c > set_c > $o ).
thf(sy_c_member_001tf__d,type,
member_d: d > set_d > $o ).
thf(sy_v_A,type,
a2: assertion_a_b_d_c ).
thf(sy_v_B,type,
b2: assertion_a_b_d_c ).
thf(sy_v__092_060Delta_062_H____,type,
delta: ( c > d ) > set_a ).
thf(sy_v__092_060Delta_062____,type,
delta2: ( c > d ) > set_a ).
thf(sy_v_a____,type,
a3: a ).
thf(sy_v_b____,type,
b3: a ).
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_s____,type,
s: c > d ).
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_valid,type,
valid: a > $o ).
thf(sy_v_x____,type,
x: a ).
% Relevant facts (976)
thf(fact_0_equal__outside__def,axiom,
( equal_outside_c_d
= ( ^ [S: c > d,S2: c > d,S3: set_c] :
! [X: c] :
( ~ ( member_c @ X @ S3 )
=> ( ( S @ X )
= ( S2 @ X ) ) ) ) ) ).
% equal_outside_def
thf(fact_1_commutative,axiom,
! [A: a,B: a] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ) ).
% commutative
thf(fact_2_can__divide,axiom,
! [P: b,A: a,B: a] :
( ( ( mult @ P @ A )
= ( mult @ P @ B ) )
=> ( A = B ) ) ).
% can_divide
thf(fact_3_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_4_move__sum,axiom,
! [A: a,A1: a,A2: a,B: a,B1: a,B2: a,X2: a,X1: a,X22: a] :
( ( ( some_a @ A )
= ( plus @ A1 @ A2 ) )
=> ( ( ( some_a @ B )
= ( plus @ B1 @ B2 ) )
=> ( ( ( some_a @ X2 )
= ( plus @ A @ B ) )
=> ( ( ( some_a @ X1 )
= ( plus @ A1 @ B1 ) )
=> ( ( ( some_a @ X22 )
= ( plus @ A2 @ B2 ) )
=> ( ( some_a @ X2 )
= ( plus @ X1 @ X22 ) ) ) ) ) ) ) ).
% move_sum
thf(fact_5_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_6_asm2,axiom,
( ( sat_a_b_c_d @ plus @ mult @ valid @ a3 @ s @ delta2 @ a2 )
& ( ( some_a @ b3 )
= ( plus @ x @ a3 ) ) ) ).
% asm2
thf(fact_7_unique__inv,axiom,
! [A: a,P: b,B: a] :
( ( A
= ( mult @ P @ B ) )
= ( B
= ( mult @ ( sinv @ P ) @ A ) ) ) ).
% unique_inv
thf(fact_8_asm0,axiom,
smaller_interp_c_d_a @ delta2 @ delta ).
% asm0
thf(fact_9_indep__interp__def,axiom,
! [A3: assertion_a_b_d_c] :
( ( indep_interp_a_b_d_c @ plus @ mult @ valid @ A3 )
= ( ! [X: a,S: c > d,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S @ Delta @ A3 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S @ Delta2 @ A3 ) ) ) ) ).
% indep_interp_def
thf(fact_10_pure__def,axiom,
! [A3: assertion_a_b_d_c] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
= ( ! [Sigma: a,Sigma2: a,S: c > d,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta @ A3 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S @ Delta2 @ A3 ) ) ) ) ).
% pure_def
thf(fact_11_sat_Osimps_I10_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ pred_a_b_d_c )
= ( member_a @ Sigma3 @ ( Delta3 @ S4 ) ) ) ).
% sat.simps(10)
thf(fact_12_not__in__fv__def,axiom,
! [A3: assertion_a_b_d_c,S5: set_c] :
( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A3 @ S5 )
= ( ! [Sigma: a,S: c > d,Delta: ( c > d ) > set_a,S2: c > d] :
( ( equal_outside_c_d @ S @ S2 @ S5 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta @ A3 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ A3 ) ) ) ) ) ).
% not_in_fv_def
thf(fact_13_equivalentI,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ! [Sigma4: a,S6: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ B3 ) )
=> ( ! [Sigma4: a,S6: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ B3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ A3 ) )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 ) ) ) ).
% equivalentI
thf(fact_14_sat_Osimps_I11_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( bounded_a_b_d_c @ A3 ) )
= ( ( valid @ Sigma3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ A3 ) ) ) ).
% sat.simps(11)
thf(fact_15_sat_Osimps_I6_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( or_a_b_d_c @ A3 @ B3 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ A3 )
| ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ B3 ) ) ) ).
% sat.simps(6)
thf(fact_16_sat_Osimps_I5_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( imp_a_b_d_c @ A3 @ B3 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ B3 ) ) ) ).
% sat.simps(5)
thf(fact_17_sat__imp,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ B3 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ).
% sat_imp
thf(fact_18_sat_Osimps_I7_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( and_a_b_d_c @ A3 @ B3 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ A3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ B3 ) ) ) ).
% sat.simps(7)
thf(fact_19_sat_Osimps_I1_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,P: b,A3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( mult_b_a_d_c @ P @ A3 ) )
= ( ? [A4: a] :
( ( Sigma3
= ( mult @ P @ A4 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ).
% sat.simps(1)
thf(fact_20_sat__mult,axiom,
! [Sigma3: a,P: b,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ! [A5: a] :
( ( Sigma3
= ( mult @ P @ A5 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A5 @ S4 @ Delta3 @ A3 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ).
% sat_mult
thf(fact_21_sat_Osimps_I4_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,B: ( c > d ) > a > $o] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( sem_c_d_a_b @ B ) )
= ( B @ S4 @ Sigma3 ) ) ).
% sat.simps(4)
thf(fact_22_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_23_smaller__interp__refl,axiom,
! [Delta3: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ Delta3 @ Delta3 ) ).
% smaller_interp_refl
thf(fact_24_smaller__interpI,axiom,
! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ! [S6: c > d,X3: a] :
( ( member_a @ X3 @ ( Delta3 @ S6 ) )
=> ( member_a @ X3 @ ( Delta4 @ S6 ) ) )
=> ( smaller_interp_c_d_a @ Delta3 @ Delta4 ) ) ).
% smaller_interpI
thf(fact_25_smaller__empty,axiom,
! [X2: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ empty_interp_c_d_a @ X2 ) ).
% smaller_empty
thf(fact_26_DotAnd,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ).
% DotAnd
thf(fact_27_DotOr,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% DotOr
thf(fact_28_DotImp,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% DotImp
thf(fact_29_DotPure,axiom,
! [A3: assertion_a_b_d_c,P: b,Delta3: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ A3 ) @ Delta3 @ A3 ) ) ).
% DotPure
thf(fact_30_logic_Oindep__interp_Ocong,axiom,
indep_interp_a_b_d_c = indep_interp_a_b_d_c ).
% logic.indep_interp.cong
thf(fact_31_DotFull,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ one @ A3 ) @ Delta3 @ A3 ) ).
% DotFull
thf(fact_32_hoare__triple__input,axiom,
! [P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q @ Delta3 )
= ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ P2 ) @ C @ Q @ Delta3 ) ) ).
% hoare_triple_input
thf(fact_33_DotWand,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% DotWand
thf(fact_34_DotExists,axiom,
! [P: b,X2: c,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A3 ) ) @ Delta3 @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ).
% DotExists
thf(fact_35_sat__wand,axiom,
! [S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,Sigma3: a,B3: assertion_a_b_d_c] :
( ! [A5: a,Sigma5: a] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A5 @ S4 @ Delta3 @ A3 )
& ( ( some_a @ Sigma5 )
= ( plus @ Sigma3 @ A5 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S4 @ Delta3 @ B3 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ).
% sat_wand
thf(fact_36_sat_Osimps_I3_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( wand_a_b_d_c @ A3 @ B3 ) )
= ( ! [A4: a,Sigma2: a] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S4 @ Delta3 @ A3 )
& ( ( some_a @ Sigma2 )
= ( plus @ Sigma3 @ A4 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S4 @ Delta3 @ B3 ) ) ) ) ).
% sat.simps(3)
thf(fact_37_DotDot,axiom,
! [P: b,Q2: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q2 @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( smult @ P @ Q2 ) @ A3 ) ) ).
% DotDot
thf(fact_38_DotForall,axiom,
! [P: b,X2: c,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A3 ) ) @ Delta3 @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ).
% DotForall
thf(fact_39_DotStar,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% DotStar
thf(fact_40_sat_Osimps_I2_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( star_a_b_d_c @ A3 @ B3 ) )
= ( ? [A4: a,B4: a] :
( ( ( some_a @ Sigma3 )
= ( plus @ A4 @ B4 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S4 @ Delta3 @ A3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B4 @ S4 @ Delta3 @ B3 ) ) ) ) ).
% sat.simps(2)
thf(fact_41_WildPure,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A3 ) @ Delta3 @ A3 ) ) ).
% WildPure
thf(fact_42_can__factorize,axiom,
! [Q2: b,P: b] :
? [R: b] :
( Q2
= ( smult @ R @ P ) ) ).
% can_factorize
thf(fact_43_mem__Collect__eq,axiom,
! [A: produc5278197477302038359_a_c_d,P2: produc5278197477302038359_a_c_d > $o] :
( ( member1180172933830803072_a_c_d @ A @ ( collec245936426562692802_a_c_d @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_44_mem__Collect__eq,axiom,
! [A: b,P2: b > $o] :
( ( member_b @ A @ ( collect_b @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_45_mem__Collect__eq,axiom,
! [A: option_a,P2: option_a > $o] :
( ( member_option_a @ A @ ( collect_option_a @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_46_mem__Collect__eq,axiom,
! [A: a,P2: a > $o] :
( ( member_a @ A @ ( collect_a @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_47_Collect__mem__eq,axiom,
! [A3: set_Pr1275464188344874039_a_c_d] :
( ( collec245936426562692802_a_c_d
@ ^ [X: produc5278197477302038359_a_c_d] : ( member1180172933830803072_a_c_d @ X @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_48_Collect__mem__eq,axiom,
! [A3: set_b] :
( ( collect_b
@ ^ [X: b] : ( member_b @ X @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_49_Collect__mem__eq,axiom,
! [A3: set_option_a] :
( ( collect_option_a
@ ^ [X: option_a] : ( member_option_a @ X @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_50_Collect__mem__eq,axiom,
! [A3: set_a] :
( ( collect_a
@ ^ [X: a] : ( member_a @ X @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_51_Collect__cong,axiom,
! [P2: a > $o,Q: a > $o] :
( ! [X3: a] :
( ( P2 @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_a @ P2 )
= ( collect_a @ Q ) ) ) ).
% Collect_cong
thf(fact_52_Collect__cong,axiom,
! [P2: option_a > $o,Q: option_a > $o] :
( ! [X3: option_a] :
( ( P2 @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_option_a @ P2 )
= ( collect_option_a @ Q ) ) ) ).
% Collect_cong
thf(fact_53_smult__asso,axiom,
! [P: b,Q2: b,R2: b] :
( ( smult @ ( smult @ P @ Q2 ) @ R2 )
= ( smult @ P @ ( smult @ Q2 @ R2 ) ) ) ).
% smult_asso
thf(fact_54_smult__comm,axiom,
! [P: b,Q2: b] :
( ( smult @ P @ Q2 )
= ( smult @ Q2 @ P ) ) ).
% smult_comm
thf(fact_55_double__mult,axiom,
! [P: b,Q2: b,A: a] :
( ( mult @ P @ ( mult @ Q2 @ A ) )
= ( mult @ ( smult @ P @ Q2 ) @ A ) ) ).
% double_mult
thf(fact_56_one__neutral,axiom,
! [A: a] :
( ( mult @ one @ A )
= A ) ).
% one_neutral
thf(fact_57_sone__neutral,axiom,
! [P: b] :
( ( smult @ one @ P )
= P ) ).
% sone_neutral
thf(fact_58_sinv__inverse,axiom,
! [P: b] :
( ( smult @ P @ ( sinv @ P ) )
= one ) ).
% sinv_inverse
thf(fact_59_sat_Osimps_I12_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) )
= ( ? [A4: a,P3: b] :
( ( Sigma3
= ( mult @ P3 @ A4 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ).
% sat.simps(12)
thf(fact_60_WildWild,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) ) @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ).
% WildWild
thf(fact_61_DotWild,axiom,
! [P: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wildcard_a_b_d_c @ A3 ) ) @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ).
% DotWild
thf(fact_62_WildDot,axiom,
! [P: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) ) @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ).
% WildDot
thf(fact_63_WildExists,axiom,
! [X2: c,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( exists_c_a_b_d @ X2 @ A3 ) ) @ Delta3 @ ( exists_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A3 ) ) ) ).
% WildExists
thf(fact_64_WildOr,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( or_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( or_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) @ ( wildcard_a_b_d_c @ B3 ) ) ) ).
% WildOr
thf(fact_65_hoare__triple__output,axiom,
! [C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( valid_command_a_c_d @ valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q @ Delta3 )
= ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ ( bounded_a_b_d_c @ Q ) @ Delta3 ) ) ) ).
% hoare_triple_output
thf(fact_66_unambiguous__star,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c,B3: assertion_a_b_d_c] :
( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta3 @ A3 @ X2 )
=> ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta3 @ ( star_a_b_d_c @ A3 @ B3 ) @ X2 ) ) ).
% unambiguous_star
thf(fact_67_assertion_Oexhaust,axiom,
! [Y: assertion_a_b_d_c] :
( ! [X12: ( c > d ) > a > $o] :
( Y
!= ( sem_c_d_a_b @ X12 ) )
=> ( ! [X21: b,X222: assertion_a_b_d_c] :
( Y
!= ( mult_b_a_d_c @ X21 @ X222 ) )
=> ( ! [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 ) )
=> ~ ! [X122: assertion_a_b_d_c] :
( Y
!= ( wildcard_a_b_d_c @ X122 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% assertion.exhaust
thf(fact_68_asm1,axiom,
member_a @ x @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ a2 @ b2 ) @ delta @ s ) ).
% asm1
thf(fact_69_sat_Osimps_I8_J,axiom,
! [Sigma3: a,S4: a > option_a,Delta3: ( a > option_a ) > set_a,X2: a,A3: assert1556940916145061938on_a_a] :
( ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( exists7165000112504185261tion_a @ X2 @ A3 ) )
= ( ? [V: option_a] : ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_a_option_a @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ).
% sat.simps(8)
thf(fact_70_sat_Osimps_I8_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,X2: c,A3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( exists_c_a_b_d @ X2 @ A3 ) )
= ( ? [V: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_c_d @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ).
% sat.simps(8)
thf(fact_71_sat_Osimps_I9_J,axiom,
! [Sigma3: a,S4: a > option_a,Delta3: ( a > option_a ) > set_a,X2: a,A3: assert1556940916145061938on_a_a] :
( ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( forall5484998627543102345tion_a @ X2 @ A3 ) )
= ( ! [V: option_a] : ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_a_option_a @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ).
% sat.simps(9)
thf(fact_72_sat_Osimps_I9_J,axiom,
! [Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,X2: c,A3: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( forall_c_a_b_d @ X2 @ A3 ) )
= ( ! [V: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_c_d @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ).
% sat.simps(9)
thf(fact_73_sat__forall,axiom,
! [Sigma3: a,S4: a > option_a,X2: a,Delta3: ( a > option_a ) > set_a,A3: assert1556940916145061938on_a_a] :
( ! [V2: option_a] : ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_a_option_a @ S4 @ X2 @ V2 ) @ Delta3 @ A3 )
=> ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( forall5484998627543102345tion_a @ X2 @ A3 ) ) ) ).
% sat_forall
thf(fact_74_sat__forall,axiom,
! [Sigma3: a,S4: c > d,X2: c,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ! [V2: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_c_d @ S4 @ X2 @ V2 ) @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S4 @ Delta3 @ ( forall_c_a_b_d @ X2 @ A3 ) ) ) ).
% sat_forall
thf(fact_75_mult__one__same1,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ one @ A3 ) @ Delta3 @ A3 ) ).
% mult_one_same1
thf(fact_76_mult__one__same2,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ ( mult_b_a_d_c @ one @ A3 ) ) ).
% mult_one_same2
thf(fact_77_dot__mult1,axiom,
! [P: b,Q2: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q2 @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( smult @ P @ Q2 ) @ A3 ) ) ).
% dot_mult1
thf(fact_78_dot__mult2,axiom,
! [P: b,Q2: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ ( smult @ P @ Q2 ) @ A3 ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q2 @ A3 ) ) ) ).
% dot_mult2
thf(fact_79_assertion_Oinject_I2_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,Y21: b,Y22: assertion_a_b_d_c] :
( ( ( mult_b_a_d_c @ X212 @ X223 )
= ( mult_b_a_d_c @ Y21 @ Y22 ) )
= ( ( X212 = Y21 )
& ( X223 = Y22 ) ) ) ).
% assertion.inject(2)
thf(fact_80_assertion_Oinject_I11_J,axiom,
! [X123: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
( ( ( wildcard_a_b_d_c @ X123 )
= ( wildcard_a_b_d_c @ Y12 ) )
= ( X123 = Y12 ) ) ).
% assertion.inject(11)
thf(fact_81_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_82_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_83_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_84_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_85_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_86_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_87_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_88_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_89_assertion_Oinject_I1_J,axiom,
! [X1: ( c > d ) > a > $o,Y1: ( c > d ) > a > $o] :
( ( ( sem_c_d_a_b @ X1 )
= ( sem_c_d_a_b @ Y1 ) )
= ( X1 = Y1 ) ) ).
% assertion.inject(1)
thf(fact_90_DotPos,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c,Pi: b] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 )
= ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A3 ) @ Delta3 @ ( mult_b_a_d_c @ Pi @ B3 ) ) ) ).
% DotPos
thf(fact_91_entails__def,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 )
= ( ! [Sigma: a,S: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta3 @ B3 ) ) ) ) ).
% entails_def
thf(fact_92_entailsI,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ! [Sigma4: a,S6: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ B3 ) )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 ) ) ).
% entailsI
thf(fact_93_WildPos,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A3 ) @ Delta3 @ ( wildcard_a_b_d_c @ B3 ) ) ) ).
% WildPos
thf(fact_94_equivalent__def,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( equivalent_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 )
= ( ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ B3 )
& ( entails_a_b_d_c @ plus @ mult @ valid @ B3 @ Delta3 @ A3 ) ) ) ).
% equivalent_def
thf(fact_95_smaller__interp__applies__cons,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a,A: a,S4: c > d] :
( ( smaller_interp_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 ) @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta4 ) )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S4 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S4 @ Delta4 @ A3 ) ) ) ).
% smaller_interp_applies_cons
thf(fact_96_dot__star2,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ).
% dot_star2
thf(fact_97_dot__star1,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% dot_star1
thf(fact_98_dot__forall2,axiom,
! [X2: c,P: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A3 ) ) ) ).
% dot_forall2
thf(fact_99_dot__forall1,axiom,
! [P: b,X2: c,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A3 ) ) @ Delta3 @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ).
% dot_forall1
thf(fact_100_dot__and2,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ).
% dot_and2
thf(fact_101_dot__and1,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% dot_and1
thf(fact_102_dot__wand2,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ).
% dot_wand2
thf(fact_103_dot__wand1,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% dot_wand1
thf(fact_104_dot__exists2,axiom,
! [X2: c,P: b,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A3 ) ) ) ).
% dot_exists2
thf(fact_105_dot__exists1,axiom,
! [P: b,X2: c,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A3 ) ) @ Delta3 @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ).
% dot_exists1
thf(fact_106_dot__or2,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A3 @ B3 ) ) ) ).
% dot_or2
thf(fact_107_dot__or1,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% dot_or1
thf(fact_108_dot__imp2,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ).
% dot_imp2
thf(fact_109_dot__imp1,axiom,
! [P: b,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ).
% dot_imp1
thf(fact_110_WildStar1,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( star_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( star_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) @ ( wildcard_a_b_d_c @ B3 ) ) ) ).
% WildStar1
thf(fact_111_WildForall,axiom,
! [X2: c,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( forall_c_a_b_d @ X2 @ A3 ) ) @ Delta3 @ ( forall_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A3 ) ) ) ).
% WildForall
thf(fact_112_WildAnd,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( and_a_b_d_c @ A3 @ B3 ) ) @ Delta3 @ ( and_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) @ ( wildcard_a_b_d_c @ B3 ) ) ) ).
% WildAnd
thf(fact_113_pure__mult2,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,P: b] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ).
% pure_mult2
thf(fact_114_pure__mult1,axiom,
! [A3: assertion_a_b_d_c,P: b,Delta3: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ A3 ) @ Delta3 @ A3 ) ) ).
% pure_mult1
thf(fact_115_assms_I2_J,axiom,
non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ b2 ) ).
% assms(2)
thf(fact_116_assms_I1_J,axiom,
monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ a2 ) ).
% assms(1)
thf(fact_117_logic_Oapplies__eq_Ocong,axiom,
applies_eq_a_b_d_c = applies_eq_a_b_d_c ).
% logic.applies_eq.cong
thf(fact_118_logic_Oentails_Ocong,axiom,
entails_a_b_d_c = entails_a_b_d_c ).
% logic.entails.cong
thf(fact_119_logic_Osat_Ocong,axiom,
sat_a_b_c_d = sat_a_b_c_d ).
% logic.sat.cong
thf(fact_120_logic_Oequivalent_Ocong,axiom,
equivalent_a_b_d_c = equivalent_a_b_d_c ).
% logic.equivalent.cong
thf(fact_121_logic_Ovalid__hoare__triple_Ocong,axiom,
valid_6037315502795721655_b_d_c = valid_6037315502795721655_b_d_c ).
% logic.valid_hoare_triple.cong
thf(fact_122_logic_Opure_Ocong,axiom,
pure_a_b_d_c = pure_a_b_d_c ).
% logic.pure.cong
thf(fact_123_logic_Onot__in__fv_Ocong,axiom,
not_in_fv_a_b_d_c = not_in_fv_a_b_d_c ).
% logic.not_in_fv.cong
thf(fact_124_assertion_Odistinct_I41_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(41)
thf(fact_125_assertion_Odistinct_I23_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.distinct(23)
thf(fact_126_assertion_Odistinct_I35_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(35)
thf(fact_127_assertion_Odistinct_I29_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(29)
thf(fact_128_assertion_Odistinct_I33_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(33)
thf(fact_129_assertion_Odistinct_I25_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.distinct(25)
thf(fact_130_assertion_Odistinct_I31_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(31)
thf(fact_131_assertion_Odistinct_I27_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.distinct(27)
thf(fact_132_assertion_Odistinct_I39_J,axiom,
! [X212: b,X223: assertion_a_b_d_c,X112: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(39)
thf(fact_133_assertion_Odistinct_I1_J,axiom,
! [X1: ( c > d ) > a > $o,X212: b,X223: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.distinct(1)
thf(fact_134_assertion_Odistinct_I59_J,axiom,
! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( star_a_b_d_c @ X312 @ X322 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(59)
thf(fact_135_assertion_Odistinct_I37_J,axiom,
! [X212: b,X223: assertion_a_b_d_c] :
( ( mult_b_a_d_c @ X212 @ X223 )
!= pred_a_b_d_c ) ).
% assertion.distinct(37)
thf(fact_136_assertion_Odistinct_I125_J,axiom,
! [X912: c,X922: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( forall_c_a_b_d @ X912 @ X922 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(125)
thf(fact_137_assertion_Odistinct_I101_J,axiom,
! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( and_a_b_d_c @ X612 @ X622 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(101)
thf(fact_138_assertion_Odistinct_I119_J,axiom,
! [X812: c,X822: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( exists_c_a_b_d @ X812 @ X822 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(119)
thf(fact_139_assertion_Odistinct_I75_J,axiom,
! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( wand_a_b_d_c @ X412 @ X422 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(75)
thf(fact_140_assertion_Odistinct_I111_J,axiom,
! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( imp_a_b_d_c @ X712 @ X722 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(111)
thf(fact_141_assertion_Odistinct_I89_J,axiom,
! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( or_a_b_d_c @ X512 @ X522 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(89)
thf(fact_142_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_143_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_144_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_145_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_146_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_147_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_148_assertion_Odistinct_I131_J,axiom,
! [X112: assertion_a_b_d_c,X123: assertion_a_b_d_c] :
( ( bounded_a_b_d_c @ X112 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(131)
thf(fact_149_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_150_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_151_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_152_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_153_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_154_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_155_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_156_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_157_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_158_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_159_assertion_Odistinct_I21_J,axiom,
! [X1: ( c > d ) > a > $o,X123: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(21)
thf(fact_160_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_161_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_162_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_163_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_164_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_165_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_166_assertion_Odistinct_I129_J,axiom,
! [X123: assertion_a_b_d_c] :
( pred_a_b_d_c
!= ( wildcard_a_b_d_c @ X123 ) ) ).
% assertion.distinct(129)
thf(fact_167_assertion_Odistinct_I3_J,axiom,
! [X1: ( c > d ) > a > $o,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( star_a_b_d_c @ X312 @ X322 ) ) ).
% assertion.distinct(3)
thf(fact_168_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_169_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_170_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_171_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_172_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_173_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_174_assertion_Odistinct_I15_J,axiom,
! [X1: ( c > d ) > a > $o,X912: c,X922: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( forall_c_a_b_d @ X912 @ X922 ) ) ).
% assertion.distinct(15)
thf(fact_175_assertion_Odistinct_I9_J,axiom,
! [X1: ( c > d ) > a > $o,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( and_a_b_d_c @ X612 @ X622 ) ) ).
% assertion.distinct(9)
thf(fact_176_assertion_Odistinct_I13_J,axiom,
! [X1: ( c > d ) > a > $o,X812: c,X822: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( exists_c_a_b_d @ X812 @ X822 ) ) ).
% assertion.distinct(13)
thf(fact_177_assertion_Odistinct_I5_J,axiom,
! [X1: ( c > d ) > a > $o,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( wand_a_b_d_c @ X412 @ X422 ) ) ).
% assertion.distinct(5)
thf(fact_178_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_179_assertion_Odistinct_I11_J,axiom,
! [X1: ( c > d ) > a > $o,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( imp_a_b_d_c @ X712 @ X722 ) ) ).
% assertion.distinct(11)
thf(fact_180_assertion_Odistinct_I7_J,axiom,
! [X1: ( c > d ) > a > $o,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( or_a_b_d_c @ X512 @ X522 ) ) ).
% assertion.distinct(7)
thf(fact_181_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_182_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_183_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_184_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_185_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_186_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_187_assertion_Odistinct_I19_J,axiom,
! [X1: ( c > d ) > a > $o,X112: assertion_a_b_d_c] :
( ( sem_c_d_a_b @ X1 )
!= ( bounded_a_b_d_c @ X112 ) ) ).
% assertion.distinct(19)
thf(fact_188_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_189_assertion_Odistinct_I17_J,axiom,
! [X1: ( c > d ) > a > $o] :
( ( sem_c_d_a_b @ X1 )
!= pred_a_b_d_c ) ).
% assertion.distinct(17)
thf(fact_190_indep__implies__non__increasing,axiom,
! [A3: assertion_a_b_d_c] :
( ( indep_interp_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) ) ) ).
% indep_implies_non_increasing
thf(fact_191_non__inc__star,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B3 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% non_inc_star
thf(fact_192_non__increasing__instantiate,axiom,
! [A3: assertion_a_b_d_c,X2: a,Delta4: ( c > d ) > set_a,S4: c > d,Delta3: ( c > d ) > set_a] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta4 @ S4 ) )
=> ( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ S4 ) ) ) ) ) ).
% non_increasing_instantiate
thf(fact_193_unambiguous__def,axiom,
! [Delta3: ( a > option_a ) > set_a,A3: assert1556940916145061938on_a_a,X2: a] :
( ( unambi704529886615442436tion_a @ plus @ mult @ valid @ Delta3 @ A3 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: option_a,V22: option_a,S: a > option_a] :
( ( ( pre_compatible_a @ plus @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma_1 @ ( fun_upd_a_option_a @ S @ X2 @ V1 ) @ Delta3 @ A3 )
& ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma_2 @ ( fun_upd_a_option_a @ S @ X2 @ V22 ) @ Delta3 @ A3 ) )
=> ( V1 = V22 ) ) ) ) ).
% unambiguous_def
thf(fact_194_unambiguous__def,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c] :
( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta3 @ A3 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: d,V22: d,S: c > d] :
( ( ( pre_compatible_a @ plus @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_1 @ ( fun_upd_c_d @ S @ X2 @ V1 ) @ Delta3 @ A3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_2 @ ( fun_upd_c_d @ S @ X2 @ V22 ) @ Delta3 @ A3 ) )
=> ( V1 = V22 ) ) ) ) ).
% unambiguous_def
thf(fact_195_unambiguousI,axiom,
! [X2: a,Delta3: ( a > option_a ) > set_a,A3: assert1556940916145061938on_a_a] :
( ! [Sigma_12: a,Sigma_22: a,V12: option_a,V23: option_a,S6: a > option_a] :
( ( ( pre_compatible_a @ plus @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma_12 @ ( fun_upd_a_option_a @ S6 @ X2 @ V12 ) @ Delta3 @ A3 )
& ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma_22 @ ( fun_upd_a_option_a @ S6 @ X2 @ V23 ) @ Delta3 @ A3 ) )
=> ( V12 = V23 ) )
=> ( unambi704529886615442436tion_a @ plus @ mult @ valid @ Delta3 @ A3 @ X2 ) ) ).
% unambiguousI
thf(fact_196_unambiguousI,axiom,
! [X2: c,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ! [Sigma_12: a,Sigma_22: a,V12: d,V23: d,S6: c > d] :
( ( ( pre_compatible_a @ plus @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_12 @ ( fun_upd_c_d @ S6 @ X2 @ V12 ) @ Delta3 @ A3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_22 @ ( fun_upd_c_d @ S6 @ X2 @ V23 ) @ Delta3 @ A3 ) )
=> ( V12 = V23 ) )
=> ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta3 @ A3 @ X2 ) ) ).
% unambiguousI
thf(fact_197_mono__sem,axiom,
! [B3: ( c > d ) > a > $o] : ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( sem_c_d_a_b @ B3 ) ) ) ).
% mono_sem
thf(fact_198_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_199_mono__bounded,axiom,
! [A3: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ A3 ) ) ) ) ).
% mono_bounded
thf(fact_200_mono__or,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% mono_or
thf(fact_201_mono__and,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% mono_and
thf(fact_202_monotonic__def,axiom,
( monotonic_c_d_a
= ( ^ [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
! [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( smaller_interp_c_d_a @ ( F @ Delta ) @ ( F @ Delta2 ) ) ) ) ) ).
% monotonic_def
thf(fact_203_monotonicI,axiom,
! [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_c_d_a @ F2 ) ) ).
% monotonicI
thf(fact_204_non__increasing__def,axiom,
( non_increasing_c_d_a
= ( ^ [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
! [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( smaller_interp_c_d_a @ ( F @ Delta2 ) @ ( F @ Delta ) ) ) ) ) ).
% non_increasing_def
thf(fact_205_non__increasingI,axiom,
! [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_c_d_a @ F2 ) ) ).
% non_increasingI
thf(fact_206_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_207_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_208_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_209_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_210_compatible__multiples,axiom,
! [P: b,A: a,Q2: b,B: a] :
( ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ Q2 @ B ) )
=> ( pre_compatible_a @ plus @ A @ B ) ) ).
% compatible_multiples
thf(fact_211_local_Omono__mult,axiom,
! [A3: assertion_a_b_d_c,Pi: b] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A3 ) ) ) ) ).
% local.mono_mult
thf(fact_212_mono__wild,axiom,
! [A3: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A3 ) ) ) ) ).
% mono_wild
thf(fact_213_mono__instantiate,axiom,
! [A3: assertion_a_b_d_c,X2: a,Delta3: ( c > d ) > set_a,S4: c > d,Delta4: ( c > d ) > set_a] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ S4 ) )
=> ( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta4 @ S4 ) ) ) ) ) ).
% mono_instantiate
thf(fact_214_mono__star,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% mono_star
thf(fact_215_mono__forall,axiom,
! [A3: assertion_a_b_d_c,V3: c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( forall_c_a_b_d @ V3 @ A3 ) ) ) ) ).
% mono_forall
thf(fact_216_mono__exists,axiom,
! [A3: assertion_a_b_d_c,V3: c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ V3 @ A3 ) ) ) ) ).
% mono_exists
thf(fact_217_mono__wand,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% mono_wand
thf(fact_218_mono__imp,axiom,
! [A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% mono_imp
thf(fact_219_pre__logic_Ocompatible_Ocong,axiom,
pre_compatible_a = pre_compatible_a ).
% pre_logic.compatible.cong
thf(fact_220_frame__rule,axiom,
! [C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q: assertion_a_b_d_c,Delta3: ( 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 @ Q @ Delta3 )
=> ( ( 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 @ Q @ R3 ) @ Delta3 ) ) ) ) ) ) ).
% frame_rule
thf(fact_221_valid__mono,axiom,
! [A: a,B: a] :
( ( ( valid @ A )
& ( pre_larger_a @ plus @ A @ B ) )
=> ( valid @ B ) ) ).
% valid_mono
thf(fact_222_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_223_compatible__smaller,axiom,
! [A: a,B: a,X2: a] :
( ( pre_larger_a @ plus @ A @ B )
=> ( ( pre_compatible_a @ plus @ X2 @ A )
=> ( pre_compatible_a @ plus @ X2 @ B ) ) ) ).
% compatible_smaller
thf(fact_224_larger__implies__compatible,axiom,
! [X2: a,Y: a] :
( ( pre_larger_a @ plus @ X2 @ Y )
=> ( pre_compatible_a @ plus @ X2 @ Y ) ) ).
% larger_implies_compatible
thf(fact_225_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_226_larger__first__sum,axiom,
! [Y: a,A: a,B: a,X2: a] :
( ( ( some_a @ Y )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ X2 @ Y )
=> ? [A6: a] :
( ( ( some_a @ X2 )
= ( plus @ A6 @ B ) )
& ( pre_larger_a @ plus @ A6 @ A ) ) ) ) ).
% larger_first_sum
thf(fact_227_sum__both__larger,axiom,
! [X4: a,A7: a,B5: a,X2: a,A: a,B: a] :
( ( ( some_a @ X4 )
= ( plus @ A7 @ B5 ) )
=> ( ( ( some_a @ X2 )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ A7 @ A )
=> ( ( pre_larger_a @ plus @ B5 @ B )
=> ( pre_larger_a @ plus @ X4 @ X2 ) ) ) ) ) ).
% sum_both_larger
thf(fact_228_intuitionistic__def,axiom,
! [S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S4 @ Delta3 @ A3 )
= ( ! [A4: a,B4: a] :
( ( ( pre_larger_a @ plus @ A4 @ B4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B4 @ S4 @ Delta3 @ A3 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ).
% intuitionistic_def
thf(fact_229_intuitionisticI,axiom,
! [S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ! [A5: a,B6: a] :
( ( ( pre_larger_a @ plus @ A5 @ B6 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B6 @ S4 @ Delta3 @ A3 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A5 @ S4 @ Delta3 @ A3 ) )
=> ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S4 @ Delta3 @ A3 ) ) ).
% intuitionisticI
thf(fact_230_pre__logic_Olarger_Ocong,axiom,
pre_larger_a = pre_larger_a ).
% pre_logic.larger.cong
thf(fact_231_pre__logic_Olarger__def,axiom,
( pre_la7759296445815288060_a_c_d
= ( ^ [Plus: product_prod_a_c_d > product_prod_a_c_d > option6413918287372586467_a_c_d,A4: product_prod_a_c_d,B4: product_prod_a_c_d] :
? [C2: product_prod_a_c_d] :
( ( some_P1084500821511757806_a_c_d @ A4 )
= ( Plus @ B4 @ C2 ) ) ) ) ).
% pre_logic.larger_def
thf(fact_232_pre__logic_Olarger__def,axiom,
( pre_larger_a
= ( ^ [Plus: a > a > option_a,A4: a,B4: a] :
? [C2: a] :
( ( some_a @ A4 )
= ( Plus @ B4 @ C2 ) ) ) ) ).
% pre_logic.larger_def
thf(fact_233_fun__upd__upd,axiom,
! [F2: c > d,X2: c,Y: d,Z: d] :
( ( fun_upd_c_d @ ( fun_upd_c_d @ F2 @ X2 @ Y ) @ X2 @ Z )
= ( fun_upd_c_d @ F2 @ X2 @ Z ) ) ).
% fun_upd_upd
thf(fact_234_fun__upd__upd,axiom,
! [F2: a > option_a,X2: a,Y: option_a,Z: option_a] :
( ( fun_upd_a_option_a @ ( fun_upd_a_option_a @ F2 @ X2 @ Y ) @ X2 @ Z )
= ( fun_upd_a_option_a @ F2 @ X2 @ Z ) ) ).
% fun_upd_upd
thf(fact_235_fun__upd__triv,axiom,
! [F2: c > d,X2: c] :
( ( fun_upd_c_d @ F2 @ X2 @ ( F2 @ X2 ) )
= F2 ) ).
% fun_upd_triv
thf(fact_236_fun__upd__triv,axiom,
! [F2: a > option_a,X2: a] :
( ( fun_upd_a_option_a @ F2 @ X2 @ ( F2 @ X2 ) )
= F2 ) ).
% fun_upd_triv
thf(fact_237_fun__upd__apply,axiom,
( fun_upd_c_d
= ( ^ [F: c > d,X: c,Y2: d,Z2: c] : ( if_d @ ( Z2 = X ) @ Y2 @ ( F @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_238_fun__upd__apply,axiom,
( fun_upd_a_option_a
= ( ^ [F: a > option_a,X: a,Y2: option_a,Z2: a] : ( if_option_a @ ( Z2 = X ) @ Y2 @ ( F @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_239_logic__axioms,axiom,
logic_a_b @ plus @ mult @ smult @ sadd @ sinv @ one @ valid ).
% logic_axioms
thf(fact_240_option_Oinject,axiom,
! [X22: product_prod_a_c_d,Y23: product_prod_a_c_d] :
( ( ( some_P1084500821511757806_a_c_d @ X22 )
= ( some_P1084500821511757806_a_c_d @ Y23 ) )
= ( X22 = Y23 ) ) ).
% option.inject
thf(fact_241_option_Oinject,axiom,
! [X22: a,Y23: a] :
( ( ( some_a @ X22 )
= ( some_a @ Y23 ) )
= ( X22 = Y23 ) ) ).
% option.inject
thf(fact_242_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,Q: assertion_a_b_d_c,Delta3: ( 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 @ Q @ Delta3 )
=> ( ( 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 @ Q @ R3 ) @ Delta3 ) ) ) ) ) ) ) ).
% logic.frame_rule
thf(fact_243_compatible__def,axiom,
! [A: a,B: a] :
( ( pre_compatible_a @ plus @ A @ B )
= ( ( plus @ A @ B )
!= none_a ) ) ).
% compatible_def
thf(fact_244_sadd__comm,axiom,
! [P: b,Q2: b] :
( ( sadd @ P @ Q2 )
= ( sadd @ Q2 @ P ) ) ).
% sadd_comm
thf(fact_245_smult__distrib,axiom,
! [P: b,Q2: b,R2: b] :
( ( smult @ P @ ( sadd @ Q2 @ R2 ) )
= ( sadd @ ( smult @ P @ Q2 ) @ ( smult @ P @ R2 ) ) ) ).
% smult_distrib
thf(fact_246_distrib__mult,axiom,
! [P: b,Q2: b,X2: a] :
( ( some_a @ ( mult @ ( sadd @ P @ Q2 ) @ X2 ) )
= ( plus @ ( mult @ P @ X2 ) @ ( mult @ Q2 @ X2 ) ) ) ).
% distrib_mult
thf(fact_247_not__None__eq,axiom,
! [X2: option6413918287372586467_a_c_d] :
( ( X2 != none_P2239999354720063602_a_c_d )
= ( ? [Y2: product_prod_a_c_d] :
( X2
= ( some_P1084500821511757806_a_c_d @ Y2 ) ) ) ) ).
% not_None_eq
thf(fact_248_not__None__eq,axiom,
! [X2: option_a] :
( ( X2 != none_a )
= ( ? [Y2: a] :
( X2
= ( some_a @ Y2 ) ) ) ) ).
% not_None_eq
thf(fact_249_not__Some__eq,axiom,
! [X2: option6413918287372586467_a_c_d] :
( ( ! [Y2: product_prod_a_c_d] :
( X2
!= ( some_P1084500821511757806_a_c_d @ Y2 ) ) )
= ( X2 = none_P2239999354720063602_a_c_d ) ) ).
% not_Some_eq
thf(fact_250_not__Some__eq,axiom,
! [X2: option_a] :
( ( ! [Y2: a] :
( X2
!= ( some_a @ Y2 ) ) )
= ( X2 = none_a ) ) ).
% not_Some_eq
thf(fact_251_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,Q2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Sadd @ P @ Q2 )
= ( Sadd @ Q2 @ P ) ) ) ).
% logic.sadd_comm
thf(fact_252_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_253_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,Q2: b,R2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ ( Smult @ P @ Q2 ) @ R2 )
= ( Smult @ P @ ( Smult @ Q2 @ R2 ) ) ) ) ).
% logic.smult_asso
thf(fact_254_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,Q2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ Q2 )
= ( Smult @ Q2 @ P ) ) ) ).
% logic.smult_comm
thf(fact_255_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_256_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_257_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,Q2: b,A: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Mult @ P @ ( Mult @ Q2 @ A ) )
= ( Mult @ ( Smult @ P @ Q2 ) @ A ) ) ) ).
% logic.double_mult
thf(fact_258_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_259_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_260_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_261_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,Q2: b,R2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ ( Sadd @ Q2 @ R2 ) )
= ( Sadd @ ( Smult @ P @ Q2 ) @ ( Smult @ P @ R2 ) ) ) ) ).
% logic.smult_distrib
thf(fact_262_logic_Ointuitionistic_Ocong,axiom,
intuit7508411120625971703_b_c_d = intuit7508411120625971703_b_c_d ).
% logic.intuitionistic.cong
thf(fact_263_option_Odistinct_I1_J,axiom,
! [X22: product_prod_a_c_d] :
( none_P2239999354720063602_a_c_d
!= ( some_P1084500821511757806_a_c_d @ X22 ) ) ).
% option.distinct(1)
thf(fact_264_option_Odistinct_I1_J,axiom,
! [X22: a] :
( none_a
!= ( some_a @ X22 ) ) ).
% option.distinct(1)
thf(fact_265_option_OdiscI,axiom,
! [Option: option6413918287372586467_a_c_d,X22: product_prod_a_c_d] :
( ( Option
= ( some_P1084500821511757806_a_c_d @ X22 ) )
=> ( Option != none_P2239999354720063602_a_c_d ) ) ).
% option.discI
thf(fact_266_option_OdiscI,axiom,
! [Option: option_a,X22: a] :
( ( Option
= ( some_a @ X22 ) )
=> ( Option != none_a ) ) ).
% option.discI
thf(fact_267_option_Oexhaust,axiom,
! [Y: option6413918287372586467_a_c_d] :
( ( Y != none_P2239999354720063602_a_c_d )
=> ~ ! [X23: product_prod_a_c_d] :
( Y
!= ( some_P1084500821511757806_a_c_d @ X23 ) ) ) ).
% option.exhaust
thf(fact_268_option_Oexhaust,axiom,
! [Y: option_a] :
( ( Y != none_a )
=> ~ ! [X23: a] :
( Y
!= ( some_a @ X23 ) ) ) ).
% option.exhaust
thf(fact_269_split__option__ex,axiom,
( ( ^ [P4: option6413918287372586467_a_c_d > $o] :
? [X5: option6413918287372586467_a_c_d] : ( P4 @ X5 ) )
= ( ^ [P5: option6413918287372586467_a_c_d > $o] :
( ( P5 @ none_P2239999354720063602_a_c_d )
| ? [X: product_prod_a_c_d] : ( P5 @ ( some_P1084500821511757806_a_c_d @ X ) ) ) ) ) ).
% split_option_ex
thf(fact_270_split__option__ex,axiom,
( ( ^ [P4: option_a > $o] :
? [X5: option_a] : ( P4 @ X5 ) )
= ( ^ [P5: option_a > $o] :
( ( P5 @ none_a )
| ? [X: a] : ( P5 @ ( some_a @ X ) ) ) ) ) ).
% split_option_ex
thf(fact_271_split__option__all,axiom,
( ( ^ [P4: option6413918287372586467_a_c_d > $o] :
! [X5: option6413918287372586467_a_c_d] : ( P4 @ X5 ) )
= ( ^ [P5: option6413918287372586467_a_c_d > $o] :
( ( P5 @ none_P2239999354720063602_a_c_d )
& ! [X: product_prod_a_c_d] : ( P5 @ ( some_P1084500821511757806_a_c_d @ X ) ) ) ) ) ).
% split_option_all
thf(fact_272_split__option__all,axiom,
( ( ^ [P4: option_a > $o] :
! [X5: option_a] : ( P4 @ X5 ) )
= ( ^ [P5: option_a > $o] :
( ( P5 @ none_a )
& ! [X: a] : ( P5 @ ( some_a @ X ) ) ) ) ) ).
% split_option_all
thf(fact_273_combine__options__cases,axiom,
! [X2: option_a,P2: option_a > option6413918287372586467_a_c_d > $o,Y: option6413918287372586467_a_c_d] :
( ( ( X2 = none_a )
=> ( P2 @ X2 @ Y ) )
=> ( ( ( Y = none_P2239999354720063602_a_c_d )
=> ( P2 @ X2 @ Y ) )
=> ( ! [A5: a,B6: product_prod_a_c_d] :
( ( X2
= ( some_a @ A5 ) )
=> ( ( Y
= ( some_P1084500821511757806_a_c_d @ B6 ) )
=> ( P2 @ X2 @ Y ) ) )
=> ( P2 @ X2 @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_274_combine__options__cases,axiom,
! [X2: option6413918287372586467_a_c_d,P2: option6413918287372586467_a_c_d > option_a > $o,Y: option_a] :
( ( ( X2 = none_P2239999354720063602_a_c_d )
=> ( P2 @ X2 @ Y ) )
=> ( ( ( Y = none_a )
=> ( P2 @ X2 @ Y ) )
=> ( ! [A5: product_prod_a_c_d,B6: a] :
( ( X2
= ( some_P1084500821511757806_a_c_d @ A5 ) )
=> ( ( Y
= ( some_a @ B6 ) )
=> ( P2 @ X2 @ Y ) ) )
=> ( P2 @ X2 @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_275_combine__options__cases,axiom,
! [X2: option6413918287372586467_a_c_d,P2: option6413918287372586467_a_c_d > option6413918287372586467_a_c_d > $o,Y: option6413918287372586467_a_c_d] :
( ( ( X2 = none_P2239999354720063602_a_c_d )
=> ( P2 @ X2 @ Y ) )
=> ( ( ( Y = none_P2239999354720063602_a_c_d )
=> ( P2 @ X2 @ Y ) )
=> ( ! [A5: product_prod_a_c_d,B6: product_prod_a_c_d] :
( ( X2
= ( some_P1084500821511757806_a_c_d @ A5 ) )
=> ( ( Y
= ( some_P1084500821511757806_a_c_d @ B6 ) )
=> ( P2 @ X2 @ Y ) ) )
=> ( P2 @ X2 @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_276_combine__options__cases,axiom,
! [X2: option_a,P2: option_a > option_a > $o,Y: option_a] :
( ( ( X2 = none_a )
=> ( P2 @ X2 @ Y ) )
=> ( ( ( Y = none_a )
=> ( P2 @ X2 @ Y ) )
=> ( ! [A5: a,B6: a] :
( ( X2
= ( some_a @ A5 ) )
=> ( ( Y
= ( some_a @ B6 ) )
=> ( P2 @ X2 @ Y ) ) )
=> ( P2 @ X2 @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_277_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,Q2: b,X2: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( some_a @ ( Mult @ ( Sadd @ P @ Q2 ) @ X2 ) )
= ( Plus2 @ ( Mult @ P @ X2 ) @ ( Mult @ Q2 @ X2 ) ) ) ) ).
% logic.distrib_mult
thf(fact_278_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_279_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,A2: a,B: a,B1: a,B2: a,X2: a,X1: a,X22: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ A )
= ( Plus2 @ A1 @ A2 ) )
=> ( ( ( some_a @ B )
= ( Plus2 @ B1 @ B2 ) )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ A @ B ) )
=> ( ( ( some_a @ X1 )
= ( Plus2 @ A1 @ B1 ) )
=> ( ( ( some_a @ X22 )
= ( Plus2 @ A2 @ B2 ) )
=> ( ( some_a @ X2 )
= ( Plus2 @ X1 @ X22 ) ) ) ) ) ) ) ) ).
% logic.move_sum
thf(fact_280_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_281_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_282_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,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( smaller_interp_c_d_a @ Delta3 @ Delta3 ) ) ).
% logic.smaller_interp_refl
thf(fact_283_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,Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [S6: c > d,X3: a] :
( ( member_a @ X3 @ ( Delta3 @ S6 ) )
=> ( member_a @ X3 @ ( Delta4 @ S6 ) ) )
=> ( smaller_interp_c_d_a @ Delta3 @ Delta4 ) ) ) ).
% logic.smaller_interpI
thf(fact_284_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_285_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_286_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,Q2: b,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q2 @ B ) )
=> ( pre_compatible_a @ Plus2 @ A @ B ) ) ) ).
% logic.compatible_multiples
thf(fact_287_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_288_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_289_pre__logic_Ocompatible__def,axiom,
( pre_compatible_a
= ( ^ [Plus: a > a > option_a,A4: a,B4: a] :
( ( Plus @ A4 @ B4 )
!= none_a ) ) ) ).
% pre_logic.compatible_def
thf(fact_290_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,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a,B6: a] :
( ( ( pre_larger_a @ Plus2 @ A5 @ B6 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B6 @ S4 @ Delta3 @ A3 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A5 @ S4 @ Delta3 @ A3 ) )
=> ( intuit7508411120625971703_b_c_d @ Plus2 @ Mult @ Valid @ S4 @ Delta3 @ A3 ) ) ) ).
% logic.intuitionisticI
thf(fact_291_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,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( intuit7508411120625971703_b_c_d @ Plus2 @ Mult @ Valid @ S4 @ Delta3 @ A3 )
= ( ! [A4: a,B4: a] :
( ( ( pre_larger_a @ Plus2 @ A4 @ B4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B4 @ S4 @ Delta3 @ A3 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ) ).
% logic.intuitionistic_def
thf(fact_292_logic_Oequal__outside__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,S4: c > d,S7: c > d,S5: set_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( equal_outside_c_d @ S4 @ S7 @ S5 )
= ( ! [X: c] :
( ~ ( member_c @ X @ S5 )
=> ( ( S4 @ X )
= ( S7 @ X ) ) ) ) ) ) ).
% logic.equal_outside_def
thf(fact_293_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,Sigma3: a,P: b,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a] :
( ( Sigma3
= ( Mult @ P @ A5 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A5 @ S4 @ Delta3 @ A3 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ) ).
% logic.sat_mult
thf(fact_294_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,P: b,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( mult_b_a_d_c @ P @ A3 ) )
= ( ? [A4: a] :
( ( Sigma3
= ( Mult @ P @ A4 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ) ).
% logic.sat.simps(1)
thf(fact_295_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) )
= ( ? [A4: a,P3: b] :
( ( Sigma3
= ( Mult @ P3 @ A4 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ) ).
% logic.sat.simps(12)
thf(fact_296_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( and_a_b_d_c @ A3 @ B3 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ A3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ B3 ) ) ) ) ).
% logic.sat.simps(7)
thf(fact_297_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ B3 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.sat_imp
thf(fact_298_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( imp_a_b_d_c @ A3 @ B3 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ B3 ) ) ) ) ).
% logic.sat.simps(5)
thf(fact_299_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( or_a_b_d_c @ A3 @ B3 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ A3 )
| ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ B3 ) ) ) ) ).
% logic.sat.simps(6)
thf(fact_300_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S6: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ B3 ) )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ B3 ) ) ) ).
% logic.entailsI
thf(fact_301_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ B3 )
= ( ! [Sigma: a,S: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta3 @ B3 ) ) ) ) ) ).
% logic.entails_def
thf(fact_302_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( bounded_a_b_d_c @ A3 ) )
= ( ( Valid @ Sigma3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ A3 ) ) ) ) ).
% logic.sat.simps(11)
thf(fact_303_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,Sigma3: a,S4: c > d,Delta3: ( 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 @ Sigma3 @ S4 @ Delta3 @ ( sem_c_d_a_b @ B ) )
= ( B @ S4 @ Sigma3 ) ) ) ).
% logic.sat.simps(4)
thf(fact_304_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ pred_a_b_d_c )
= ( member_a @ Sigma3 @ ( Delta3 @ S4 ) ) ) ) ).
% logic.sat.simps(10)
thf(fact_305_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_306_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_307_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,X2: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ Y )
= ( Plus2 @ A @ B ) )
=> ( ( pre_larger_a @ Plus2 @ X2 @ Y )
=> ? [A6: a] :
( ( ( some_a @ X2 )
= ( Plus2 @ A6 @ B ) )
& ( pre_larger_a @ Plus2 @ A6 @ A ) ) ) ) ) ).
% logic.larger_first_sum
thf(fact_308_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,A7: a,B5: a,X2: a,A: a,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ X4 )
= ( Plus2 @ A7 @ B5 ) )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ A @ B ) )
=> ( ( pre_larger_a @ Plus2 @ A7 @ A )
=> ( ( pre_larger_a @ Plus2 @ B5 @ B )
=> ( pre_larger_a @ Plus2 @ X4 @ X2 ) ) ) ) ) ) ).
% logic.sum_both_larger
thf(fact_309_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S6: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ B3 ) )
=> ( ! [Sigma4: a,S6: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ B3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ A3 ) )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ B3 ) ) ) ) ).
% logic.equivalentI
thf(fact_310_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ B3 )
= ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ B3 )
& ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 @ Delta3 @ A3 ) ) ) ) ).
% logic.equivalent_def
thf(fact_311_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,F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ F2 )
= ( ! [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( smaller_interp_c_d_a @ ( F2 @ Delta ) @ ( F2 @ Delta2 ) ) ) ) ) ) ).
% logic.monotonic_def
thf(fact_312_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,F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [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_c_d_a @ F2 ) ) ) ).
% logic.monotonicI
thf(fact_313_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,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
= ( ! [Sigma: a,Sigma2: a,S: c > d,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta @ A3 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S @ Delta2 @ A3 ) ) ) ) ) ).
% logic.pure_def
thf(fact_314_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,X2: a,Y: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus2 @ X2 @ Y )
=> ( pre_compatible_a @ Plus2 @ X2 @ Y ) ) ) ).
% logic.larger_implies_compatible
thf(fact_315_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,X2: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus2 @ A @ B )
=> ( ( pre_compatible_a @ Plus2 @ X2 @ A )
=> ( pre_compatible_a @ Plus2 @ X2 @ B ) ) ) ) ).
% logic.compatible_smaller
thf(fact_316_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,Q: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q @ Delta3 )
= ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ P2 ) @ C @ Q @ Delta3 ) ) ) ).
% logic.hoare_triple_input
thf(fact_317_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,F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ F2 )
= ( ! [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( smaller_interp_c_d_a @ ( F2 @ Delta2 ) @ ( F2 @ Delta ) ) ) ) ) ) ).
% logic.non_increasing_def
thf(fact_318_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,F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [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_c_d_a @ F2 ) ) ) ).
% logic.non_increasingI
thf(fact_319_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,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( indep_interp_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
= ( ! [X: a,S: c > d,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S @ Delta @ A3 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S @ Delta2 @ A3 ) ) ) ) ) ).
% logic.indep_interp_def
thf(fact_320_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( star_a_b_d_c @ A3 @ B3 ) )
= ( ? [A4: a,B4: a] :
( ( ( some_a @ Sigma3 )
= ( Plus2 @ A4 @ B4 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S4 @ Delta3 @ A3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B4 @ S4 @ Delta3 @ B3 ) ) ) ) ) ).
% logic.sat.simps(2)
thf(fact_321_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,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,Sigma3: a,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a,Sigma5: a] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A5 @ S4 @ Delta3 @ A3 )
& ( ( some_a @ Sigma5 )
= ( Plus2 @ Sigma3 @ A5 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma5 @ S4 @ Delta3 @ B3 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.sat_wand
thf(fact_322_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( wand_a_b_d_c @ A3 @ B3 ) )
= ( ! [A4: a,Sigma2: a] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S4 @ Delta3 @ A3 )
& ( ( some_a @ Sigma2 )
= ( Plus2 @ Sigma3 @ A4 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S4 @ Delta3 @ B3 ) ) ) ) ) ).
% logic.sat.simps(3)
thf(fact_323_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,Sigma3: a,S4: a > option_a,Delta3: ( a > option_a ) > set_a,X2: a,A3: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( forall5484998627543102345tion_a @ X2 @ A3 ) )
= ( ! [V: option_a] : ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_a_option_a @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ) ).
% logic.sat.simps(9)
thf(fact_324_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,X2: c,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( forall_c_a_b_d @ X2 @ A3 ) )
= ( ! [V: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_c_d @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ) ).
% logic.sat.simps(9)
thf(fact_325_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,Sigma3: a,S4: a > option_a,X2: a,Delta3: ( a > option_a ) > set_a,A3: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [V2: option_a] : ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_a_option_a @ S4 @ X2 @ V2 ) @ Delta3 @ A3 )
=> ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( forall5484998627543102345tion_a @ X2 @ A3 ) ) ) ) ).
% logic.sat_forall
thf(fact_326_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,Sigma3: a,S4: c > d,X2: c,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [V2: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_c_d @ S4 @ X2 @ V2 ) @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( forall_c_a_b_d @ X2 @ A3 ) ) ) ) ).
% logic.sat_forall
thf(fact_327_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,Sigma3: a,S4: a > option_a,Delta3: ( a > option_a ) > set_a,X2: a,A3: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( exists7165000112504185261tion_a @ X2 @ A3 ) )
= ( ? [V: option_a] : ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_a_option_a @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ) ).
% logic.sat.simps(8)
thf(fact_328_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,Sigma3: a,S4: c > d,Delta3: ( c > d ) > set_a,X2: c,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S4 @ Delta3 @ ( exists_c_a_b_d @ X2 @ A3 ) )
= ( ? [V: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_c_d @ S4 @ X2 @ V ) @ Delta3 @ A3 ) ) ) ) ).
% logic.sat.simps(8)
thf(fact_329_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,A3: 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 @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A3 ) ) ) ) ) ).
% logic.mono_mult
thf(fact_330_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,A3: 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 @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A3 ) ) ) ) ) ).
% logic.mono_wild
thf(fact_331_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,X2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( smaller_interp_c_d_a @ empty_interp_c_d_a @ X2 ) ) ).
% logic.smaller_empty
thf(fact_332_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a,A: a,S4: 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 @ A3 @ Delta3 ) @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta4 ) )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S4 @ Delta3 @ A3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S4 @ Delta4 @ A3 ) ) ) ) ).
% logic.smaller_interp_applies_cons
thf(fact_333_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,A3: assertion_a_b_d_c,B3: 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 @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ) ) ).
% logic.mono_star
thf(fact_334_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,A3: assertion_a_b_d_c,V3: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( forall_c_a_b_d @ V3 @ A3 ) ) ) ) ) ).
% logic.mono_forall
thf(fact_335_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,A3: assertion_a_b_d_c,B3: 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 @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ) ) ) ).
% logic.mono_and
thf(fact_336_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,A3: assertion_a_b_d_c,V3: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( exists_c_a_b_d @ V3 @ A3 ) ) ) ) ) ).
% logic.mono_exists
thf(fact_337_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,A3: assertion_a_b_d_c,B3: 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 @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ A3 @ B3 ) ) ) ) ) ) ).
% logic.mono_or
thf(fact_338_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,A3: 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 @ A3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ A3 ) ) ) ) ) ).
% logic.mono_bounded
thf(fact_339_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,B3: ( 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 @ B3 ) ) ) ) ).
% logic.mono_sem
thf(fact_340_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_341_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,B4: a] :
( ( Plus @ A4 @ B4 )
= ( Plus @ B4 @ A4 ) )
& ! [A4: a,B4: a,Ab2: a,C2: a,Bc2: a] :
( ( ( ( Plus @ A4 @ B4 )
= ( some_a @ Ab2 ) )
& ( ( Plus @ B4 @ C2 )
= ( some_a @ Bc2 ) ) )
=> ( ( Plus @ Ab2 @ C2 )
= ( Plus @ A4 @ Bc2 ) ) )
& ! [A4: a,B4: a,Ab2: a,C2: a] :
( ( ( ( Plus @ A4 @ B4 )
= ( some_a @ Ab2 ) )
& ~ ( pre_compatible_a @ Plus @ B4 @ 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,B4: a,C2: a,P3: b] :
( ( ( some_a @ A4 )
= ( Plus @ B4 @ C2 ) )
=> ( ( some_a @ ( Mult2 @ P3 @ A4 ) )
= ( Plus @ ( Mult2 @ P3 @ B4 ) @ ( Mult2 @ P3 @ C2 ) ) ) )
& ! [P3: b,Q3: b,X: a] :
( ( some_a @ ( Mult2 @ ( Sadd2 @ P3 @ Q3 ) @ X ) )
= ( Plus @ ( Mult2 @ P3 @ X ) @ ( Mult2 @ Q3 @ X ) ) )
& ! [A4: a] :
( ( Mult2 @ One2 @ A4 )
= A4 )
& ! [A4: a,B4: a] :
( ( ( Valid2 @ A4 )
& ( pre_larger_a @ Plus @ A4 @ B4 ) )
=> ( Valid2 @ B4 ) ) ) ) ) ).
% logic_def
thf(fact_342_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,A3: assertion_a_b_d_c,X2: a,Delta3: ( c > d ) > set_a,S4: c > d,Delta4: ( 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 @ A3 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ S4 ) )
=> ( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta4 @ S4 ) ) ) ) ) ) ).
% logic.mono_instantiate
thf(fact_343_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,A3: assertion_a_b_d_c,B3: 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 @ A3 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ) ) ).
% logic.non_inc_star
thf(fact_344_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,A3: assertion_a_b_d_c,X2: a,Delta4: ( c > d ) > set_a,S4: c > d,Delta3: ( 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 @ A3 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta4 @ S4 ) )
=> ( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ S4 ) ) ) ) ) ) ).
% logic.non_increasing_instantiate
thf(fact_345_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,Q: assertion_a_b_d_c,Delta3: ( 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 @ Q @ Delta3 )
= ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ ( bounded_a_b_d_c @ Q ) @ Delta3 ) ) ) ) ).
% logic.hoare_triple_output
thf(fact_346_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,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( indep_interp_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 ) ) ) ) ).
% logic.indep_implies_non_increasing
thf(fact_347_fun__upd__idem__iff,axiom,
! [F2: c > d,X2: c,Y: d] :
( ( ( fun_upd_c_d @ F2 @ X2 @ Y )
= F2 )
= ( ( F2 @ X2 )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_348_fun__upd__idem__iff,axiom,
! [F2: a > option_a,X2: a,Y: option_a] :
( ( ( fun_upd_a_option_a @ F2 @ X2 @ Y )
= F2 )
= ( ( F2 @ X2 )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_349_fun__upd__twist,axiom,
! [A: c,C: c,M: c > d,B: d,D: d] :
( ( A != C )
=> ( ( fun_upd_c_d @ ( fun_upd_c_d @ M @ A @ B ) @ C @ D )
= ( fun_upd_c_d @ ( fun_upd_c_d @ M @ C @ D ) @ A @ B ) ) ) ).
% fun_upd_twist
thf(fact_350_fun__upd__twist,axiom,
! [A: a,C: a,M: a > option_a,B: option_a,D: option_a] :
( ( A != C )
=> ( ( fun_upd_a_option_a @ ( fun_upd_a_option_a @ M @ A @ B ) @ C @ D )
= ( fun_upd_a_option_a @ ( fun_upd_a_option_a @ M @ C @ D ) @ A @ B ) ) ) ).
% fun_upd_twist
thf(fact_351_fun__upd__other,axiom,
! [Z: c,X2: c,F2: c > d,Y: d] :
( ( Z != X2 )
=> ( ( fun_upd_c_d @ F2 @ X2 @ Y @ Z )
= ( F2 @ Z ) ) ) ).
% fun_upd_other
thf(fact_352_fun__upd__other,axiom,
! [Z: a,X2: a,F2: a > option_a,Y: option_a] :
( ( Z != X2 )
=> ( ( fun_upd_a_option_a @ F2 @ X2 @ Y @ Z )
= ( F2 @ Z ) ) ) ).
% fun_upd_other
thf(fact_353_fun__upd__same,axiom,
! [F2: c > d,X2: c,Y: d] :
( ( fun_upd_c_d @ F2 @ X2 @ Y @ X2 )
= Y ) ).
% fun_upd_same
thf(fact_354_fun__upd__same,axiom,
! [F2: a > option_a,X2: a,Y: option_a] :
( ( fun_upd_a_option_a @ F2 @ X2 @ Y @ X2 )
= Y ) ).
% fun_upd_same
thf(fact_355_fun__upd__idem,axiom,
! [F2: c > d,X2: c,Y: d] :
( ( ( F2 @ X2 )
= Y )
=> ( ( fun_upd_c_d @ F2 @ X2 @ Y )
= F2 ) ) ).
% fun_upd_idem
thf(fact_356_fun__upd__idem,axiom,
! [F2: a > option_a,X2: a,Y: option_a] :
( ( ( F2 @ X2 )
= Y )
=> ( ( fun_upd_a_option_a @ F2 @ X2 @ Y )
= F2 ) ) ).
% fun_upd_idem
thf(fact_357_fun__upd__eqD,axiom,
! [F2: c > d,X2: c,Y: d,G: c > d,Z: d] :
( ( ( fun_upd_c_d @ F2 @ X2 @ Y )
= ( fun_upd_c_d @ G @ X2 @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_358_fun__upd__eqD,axiom,
! [F2: a > option_a,X2: a,Y: option_a,G: a > option_a,Z: option_a] :
( ( ( fun_upd_a_option_a @ F2 @ X2 @ Y )
= ( fun_upd_a_option_a @ G @ X2 @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_359_fun__upd__def,axiom,
( fun_upd_c_d
= ( ^ [F: c > d,A4: c,B4: d,X: c] : ( if_d @ ( X = A4 ) @ B4 @ ( F @ X ) ) ) ) ).
% fun_upd_def
thf(fact_360_fun__upd__def,axiom,
( fun_upd_a_option_a
= ( ^ [F: a > option_a,A4: a,B4: option_a,X: a] : ( if_option_a @ ( X = A4 ) @ B4 @ ( F @ X ) ) ) ) ).
% fun_upd_def
thf(fact_361_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,A3: assertion_a_b_d_c,S5: set_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ S5 )
= ( ! [Sigma: a,S: c > d,Delta: ( c > d ) > set_a,S2: c > d] :
( ( equal_outside_c_d @ S @ S2 @ S5 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta @ A3 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S2 @ Delta @ A3 ) ) ) ) ) ) ).
% logic.not_in_fv_def
thf(fact_362_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,A3: assertion_a_b_d_c,B3: 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 @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ) ) ) ).
% logic.mono_wand
thf(fact_363_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,A3: assertion_a_b_d_c,B3: 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 @ A3 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B3 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ) ) ) ).
% logic.mono_imp
thf(fact_364_combinable__instantiate__one,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,A: a,S4: c > d,B: a,X2: a,P: b,Q2: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S4 @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S4 @ Delta3 @ A3 )
=> ( ( ( some_a @ X2 )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q2 @ B ) ) )
=> ( ( ( sadd @ P @ Q2 )
= one )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S4 @ Delta3 @ A3 ) ) ) ) ) ) ).
% combinable_instantiate_one
thf(fact_365_combinable__def,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
= ( ! [P3: b,Q3: b] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P3 @ A3 ) @ ( mult_b_a_d_c @ Q3 @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( sadd @ P3 @ Q3 ) @ A3 ) ) ) ) ).
% combinable_def
thf(fact_366_combinable__instantiate,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,A: a,S4: c > d,B: a,X2: a,P: b,Q2: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S4 @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S4 @ Delta3 @ A3 )
=> ( ( ( some_a @ X2 )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q2 @ B ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S4 @ Delta3 @ ( mult_b_a_d_c @ ( sadd @ P @ Q2 ) @ A3 ) ) ) ) ) ) ).
% combinable_instantiate
thf(fact_367_combinable__exists,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta3 @ A3 @ X2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( exists_c_a_b_d @ X2 @ A3 ) ) ) ) ).
% combinable_exists
thf(fact_368_combinable__imp,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% combinable_imp
thf(fact_369_combinableI__old,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ! [A5: a,B6: a,P6: b,Q4: b,X3: a,Sigma4: a,S6: c > d] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A5 @ S6 @ Delta3 @ A3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B6 @ S6 @ Delta3 @ A3 )
& ( ( some_a @ Sigma4 )
= ( plus @ ( mult @ P6 @ A5 ) @ ( mult @ Q4 @ B6 ) ) )
& ( Sigma4
= ( mult @ ( sadd @ P6 @ Q4 ) @ X3 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X3 @ S6 @ Delta3 @ A3 ) )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 ) ) ).
% combinableI_old
thf(fact_370_combinable__mult,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,Pi: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( mult_b_a_d_c @ Pi @ A3 ) ) ) ).
% combinable_mult
thf(fact_371_combinable__wildcard,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ) ).
% combinable_wildcard
thf(fact_372_combinable__star,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% combinable_star
thf(fact_373_combinable__forall,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( forall_c_a_b_d @ X2 @ A3 ) ) ) ).
% combinable_forall
thf(fact_374_combinable__and,axiom,
! [Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% combinable_and
thf(fact_375_combinable__wand,axiom,
! [Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c,A3: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ).
% combinable_wand
thf(fact_376_combinable__pure,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A3 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A3 ) ) ).
% combinable_pure
thf(fact_377_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,Delta3: ( a > option_a ) > set_a,A3: assert1556940916145061938on_a_a,X2: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambi704529886615442436tion_a @ Plus2 @ Mult @ Valid @ Delta3 @ A3 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: option_a,V22: option_a,S: a > option_a] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma_1 @ ( fun_upd_a_option_a @ S @ X2 @ V1 ) @ Delta3 @ A3 )
& ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma_2 @ ( fun_upd_a_option_a @ S @ X2 @ V22 ) @ Delta3 @ A3 ) )
=> ( V1 = V22 ) ) ) ) ) ).
% logic.unambiguous_def
thf(fact_378_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta3 @ A3 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: d,V22: d,S: c > d] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_1 @ ( fun_upd_c_d @ S @ X2 @ V1 ) @ Delta3 @ A3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_2 @ ( fun_upd_c_d @ S @ X2 @ V22 ) @ Delta3 @ A3 ) )
=> ( V1 = V22 ) ) ) ) ) ).
% logic.unambiguous_def
thf(fact_379_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,X2: a,Delta3: ( a > option_a ) > set_a,A3: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma_12: a,Sigma_22: a,V12: option_a,V23: option_a,S6: a > option_a] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma_12 @ ( fun_upd_a_option_a @ S6 @ X2 @ V12 ) @ Delta3 @ A3 )
& ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma_22 @ ( fun_upd_a_option_a @ S6 @ X2 @ V23 ) @ Delta3 @ A3 ) )
=> ( V12 = V23 ) )
=> ( unambi704529886615442436tion_a @ Plus2 @ Mult @ Valid @ Delta3 @ A3 @ X2 ) ) ) ).
% logic.unambiguousI
thf(fact_380_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,X2: c,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma_12: a,Sigma_22: a,V12: d,V23: d,S6: c > d] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_12 @ ( fun_upd_c_d @ S6 @ X2 @ V12 ) @ Delta3 @ A3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_22 @ ( fun_upd_c_d @ S6 @ X2 @ V23 ) @ Delta3 @ A3 ) )
=> ( V12 = V23 ) )
=> ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta3 @ A3 @ X2 ) ) ) ).
% logic.unambiguousI
thf(fact_381_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
= ( ! [P3: b,Q3: b] : ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P3 @ A3 ) @ ( mult_b_a_d_c @ Q3 @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( Sadd @ P3 @ Q3 ) @ A3 ) ) ) ) ) ).
% logic.combinable_def
thf(fact_382_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,A: a,S4: c > d,B: a,X2: a,P: b,Q2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S4 @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B @ S4 @ Delta3 @ A3 )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q2 @ B ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S4 @ Delta3 @ ( mult_b_a_d_c @ ( Sadd @ P @ Q2 ) @ A3 ) ) ) ) ) ) ) ).
% logic.combinable_instantiate
thf(fact_383_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta3 @ A3 @ X2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( exists_c_a_b_d @ X2 @ A3 ) ) ) ) ) ).
% logic.combinable_exists
thf(fact_384_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A3 ) @ Delta3 @ A3 ) ) ) ).
% logic.WildPure
thf(fact_385_logic_Ounambiguous_Ocong,axiom,
unambiguous_a_b_c_d = unambiguous_a_b_c_d ).
% logic.unambiguous.cong
thf(fact_386_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: 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 @ A3 @ Delta3 @ B3 )
= ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A3 ) @ Delta3 @ ( mult_b_a_d_c @ Pi @ B3 ) ) ) ) ).
% logic.DotPos
thf(fact_387_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,Q2: b,A3: assertion_a_b_d_c,Delta3: ( 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 @ Q2 @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( Smult @ P @ Q2 ) @ A3 ) ) ) ).
% logic.dot_mult1
thf(fact_388_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,Q2: b,A3: assertion_a_b_d_c,Delta3: ( 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 @ Q2 ) @ A3 ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q2 @ A3 ) ) ) ) ).
% logic.dot_mult2
thf(fact_389_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,A3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ Delta3 @ A3 ) ) ).
% logic.mult_one_same1
thf(fact_390_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ ( mult_b_a_d_c @ One @ A3 ) ) ) ).
% logic.mult_one_same2
thf(fact_391_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,Delta3: ( c > d ) > set_a,A3: 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 @ Delta3 @ A3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( mult_b_a_d_c @ Pi @ A3 ) ) ) ) ).
% logic.combinable_mult
thf(fact_392_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ B3 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A3 ) @ Delta3 @ ( wildcard_a_b_d_c @ B3 ) ) ) ) ).
% logic.WildPos
thf(fact_393_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,A3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ Delta3 @ A3 ) ) ).
% logic.DotFull
thf(fact_394_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,Q2: b,A3: assertion_a_b_d_c,Delta3: ( 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 @ Q2 @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( Smult @ P @ Q2 ) @ A3 ) ) ) ).
% logic.DotDot
thf(fact_395_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ) ) ).
% logic.combinable_wildcard
thf(fact_396_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% logic.combinable_star
thf(fact_397_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( forall_c_a_b_d @ X2 @ A3 ) ) ) ) ).
% logic.combinable_forall
thf(fact_398_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% logic.combinable_and
thf(fact_399_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,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.combinable_wand
thf(fact_400_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,A3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) ) @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ) ).
% logic.WildWild
thf(fact_401_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 ) ) ) ).
% logic.combinable_pure
thf(fact_402_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,X2: c,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta3 @ A3 @ X2 )
=> ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta3 @ ( star_a_b_d_c @ A3 @ B3 ) @ X2 ) ) ) ).
% logic.unambiguous_star
thf(fact_403_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a,B6: a,P6: b,Q4: b,X3: a,Sigma4: a,S6: c > d] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A5 @ S6 @ Delta3 @ A3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B6 @ S6 @ Delta3 @ A3 )
& ( ( some_a @ Sigma4 )
= ( Plus2 @ ( Mult @ P6 @ A5 ) @ ( Mult @ Q4 @ B6 ) ) )
& ( Sigma4
= ( Mult @ ( Sadd @ P6 @ Q4 ) @ X3 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X3 @ S6 @ Delta3 @ A3 ) )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 ) ) ) ).
% logic.combinableI_old
thf(fact_404_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,Delta3: ( c > d ) > set_a,A3: assertion_a_b_d_c,A: a,S4: c > d,B: a,X2: a,P: b,Q2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S4 @ Delta3 @ A3 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B @ S4 @ Delta3 @ A3 )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q2 @ B ) ) )
=> ( ( ( Sadd @ P @ Q2 )
= One )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S4 @ Delta3 @ A3 ) ) ) ) ) ) ) ).
% logic.combinable_instantiate_one
thf(fact_405_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.dot_star1
thf(fact_406_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.dot_star2
thf(fact_407_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,X2: c,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ A3 ) ) @ Delta3 @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ) ).
% logic.dot_forall1
thf(fact_408_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,X2: c,P: b,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A3 ) ) ) ) ).
% logic.dot_forall2
thf(fact_409_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.dot_and2
thf(fact_410_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.dot_and1
thf(fact_411_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.dot_wand1
thf(fact_412_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.dot_wand2
thf(fact_413_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,X2: c,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ A3 ) ) @ Delta3 @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ) ).
% logic.dot_exists1
thf(fact_414_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,X2: c,P: b,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A3 ) ) ) ) ).
% logic.dot_exists2
thf(fact_415_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.dot_imp2
thf(fact_416_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.dot_imp1
thf(fact_417_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.dot_or2
thf(fact_418_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.dot_or1
thf(fact_419_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,A3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) ) @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ) ).
% logic.WildDot
thf(fact_420_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,A3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) ) @ Delta3 @ ( wildcard_a_b_d_c @ A3 ) ) ) ).
% logic.DotWild
thf(fact_421_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( star_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) @ ( wildcard_a_b_d_c @ B3 ) ) ) ) ).
% logic.WildStar1
thf(fact_422_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.DotStar
thf(fact_423_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,X2: c,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ A3 ) ) @ Delta3 @ ( forall_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A3 ) ) ) ) ).
% logic.WildForall
thf(fact_424_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( and_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) @ ( wildcard_a_b_d_c @ B3 ) ) ) ) ).
% logic.WildAnd
thf(fact_425_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,X2: c,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ A3 ) ) @ Delta3 @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ) ).
% logic.DotForall
thf(fact_426_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) @ Delta3 @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A3 @ B3 ) ) ) ) ).
% logic.DotAnd
thf(fact_427_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,X2: c,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ A3 ) ) @ Delta3 @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ) ).
% logic.DotExists
thf(fact_428_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.DotWand
thf(fact_429_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.DotImp
thf(fact_430_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A3 ) @ ( mult_b_a_d_c @ P @ B3 ) ) ) ) ).
% logic.DotOr
thf(fact_431_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,X2: c,A3: assertion_a_b_d_c,Delta3: ( 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 @ X2 @ A3 ) ) @ Delta3 @ ( exists_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A3 ) ) ) ) ).
% logic.WildExists
thf(fact_432_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,A3: assertion_a_b_d_c,B3: assertion_a_b_d_c,Delta3: ( 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 @ A3 @ B3 ) ) @ Delta3 @ ( or_a_b_d_c @ ( wildcard_a_b_d_c @ A3 ) @ ( wildcard_a_b_d_c @ B3 ) ) ) ) ).
% logic.WildOr
thf(fact_433_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ ( mult_b_a_d_c @ P @ A3 ) ) ) ) ).
% logic.pure_mult2
thf(fact_434_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,A3: assertion_a_b_d_c,P: b,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ A3 ) @ Delta3 @ A3 ) ) ) ).
% logic.pure_mult1
thf(fact_435_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,A3: assertion_a_b_d_c,P: b,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ A3 ) @ Delta3 @ A3 ) ) ) ).
% logic.DotPure
thf(fact_436_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ B3 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta3 @ ( imp_a_b_d_c @ A3 @ B3 ) ) ) ) ) ).
% logic.combinable_imp
thf(fact_437_map__upd__nonempty,axiom,
! [T: a > option_a,K: a,X2: a] :
( ( fun_upd_a_option_a @ T @ K @ ( some_a @ X2 ) )
!= ( ^ [X: a] : none_a ) ) ).
% map_upd_nonempty
thf(fact_438_not__in__fv__mod,axiom,
! [A3: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma3: a,S4: c > d,Sigma6: a,S7: c > d,X2: a,Delta3: ( c > d ) > set_a] :
( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A3 @ ( modified_a_c_d @ C ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S4 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S7 ) ) ) @ C )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S4 @ Delta3 @ A3 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S7 @ Delta3 @ A3 ) ) ) ) ).
% not_in_fv_mod
thf(fact_439_safety__monotonicity__def,axiom,
! [C: set_Pr1275464188344874039_a_c_d] :
( ( safety844553430189520448_a_c_d @ plus @ valid @ C )
= ( ! [Sigma: a,Sigma2: a,S: c > d] :
( ( ( valid @ Sigma2 )
& ( pre_larger_a @ plus @ Sigma2 @ Sigma )
& ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S ) ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma2 @ S ) ) ) ) ) ).
% safety_monotonicity_def
thf(fact_440_empty__interp__def,axiom,
( empty_interp_c_d_a
= ( ^ [S: c > d] : bot_bot_set_a ) ) ).
% empty_interp_def
thf(fact_441_safe__def,axiom,
( safe_a_c_d
= ( ^ [C2: set_Pr1275464188344874039_a_c_d,Sigma: product_prod_a_c_d] :
~ ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ Sigma @ none_P2239999354720063602_a_c_d ) @ C2 ) ) ) ).
% safe_def
thf(fact_442_smaller__interp__def,axiom,
( smaller_interp_c_d_a
= ( ^ [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
! [S: c > d] : ( ord_less_eq_set_a @ ( Delta @ S ) @ ( Delta2 @ S ) ) ) ) ).
% smaller_interp_def
thf(fact_443_valid__command__def,axiom,
! [C: set_Pr1275464188344874039_a_c_d] :
( ( valid_command_a_c_d @ valid @ C )
= ( ! [A4: a,B4: a,Sa: c > d,Sb: c > d] :
( ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ A4 @ Sa ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ B4 @ Sb ) ) ) @ C )
& ( valid @ A4 ) )
=> ( valid @ B4 ) ) ) ) ).
% valid_command_def
thf(fact_444_frame__property__def,axiom,
! [C: set_Pr1275464188344874039_a_c_d] :
( ( frame_property_a_c_d @ plus @ valid @ C )
= ( ! [Sigma: a,Sigma_0: a,R4: a,Sigma2: a,S: c > d,S2: c > d] :
( ( ( valid @ Sigma )
& ( valid @ Sigma2 )
& ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma_0 @ S ) )
& ( ( some_a @ Sigma )
= ( plus @ Sigma_0 @ R4 ) )
& ( 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 @ Sigma2 @ S2 ) ) ) @ C ) )
=> ? [Sigma_02: a] :
( ( ( some_a @ Sigma2 )
= ( plus @ Sigma_02 @ R4 ) )
& ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma_0 @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma_02 @ S2 ) ) ) @ C ) ) ) ) ) ).
% frame_property_def
thf(fact_445_valid__hoare__triple__def,axiom,
! [P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q @ Delta3 )
= ( ! [Sigma: a,S: c > d] :
( ( ( valid @ Sigma )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta3 @ P2 ) )
=> ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S ) )
& ! [Sigma2: a,S2: c > d] :
( ( 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 @ Sigma2 @ S2 ) ) ) @ C )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S2 @ Delta3 @ Q ) ) ) ) ) ) ).
% valid_hoare_triple_def
thf(fact_446_valid__hoare__tripleI,axiom,
! [Delta3: ( c > d ) > set_a,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q: assertion_a_b_d_c] :
( ! [Sigma4: a,S6: c > d] :
( ( ( valid @ Sigma4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ P2 ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma4 @ S6 ) ) )
=> ( ! [Sigma4: a,S6: c > d,Sigma5: a,S8: c > d] :
( ( ( valid @ Sigma4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S6 @ Delta3 @ P2 ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S6 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S8 ) ) ) @ C )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S8 @ Delta3 @ Q ) ) )
=> ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q @ Delta3 ) ) ) ).
% valid_hoare_tripleI
thf(fact_447_logic_Osafe__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,C: set_Pr1275464188344874039_a_c_d,Sigma3: product_prod_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( safe_a_c_d @ C @ Sigma3 )
= ( ~ ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ Sigma3 @ none_P2239999354720063602_a_c_d ) @ C ) ) ) ) ).
% logic.safe_def
thf(fact_448_logic_Ovalid__command__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,C: set_Pr1275464188344874039_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_c_d @ Valid @ C )
= ( ! [A4: a,B4: a,Sa: c > d,Sb: c > d] :
( ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ A4 @ Sa ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ B4 @ Sb ) ) ) @ C )
& ( Valid @ A4 ) )
=> ( Valid @ B4 ) ) ) ) ) ).
% logic.valid_command_def
thf(fact_449_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,Delta3: ( c > d ) > set_a,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S6: c > d] :
( ( ( Valid @ Sigma4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ P2 ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma4 @ S6 ) ) )
=> ( ! [Sigma4: a,S6: c > d,Sigma5: a,S8: c > d] :
( ( ( Valid @ Sigma4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S6 @ Delta3 @ P2 ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S6 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S8 ) ) ) @ C )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma5 @ S8 @ Delta3 @ Q ) ) )
=> ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q @ Delta3 ) ) ) ) ).
% logic.valid_hoare_tripleI
thf(fact_450_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,Q: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q @ Delta3 )
= ( ! [Sigma: a,S: c > d] :
( ( ( Valid @ Sigma )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S @ Delta3 @ P2 ) )
=> ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S ) )
& ! [Sigma2: a,S2: c > d] :
( ( 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 @ Sigma2 @ S2 ) ) ) @ C )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S2 @ Delta3 @ Q ) ) ) ) ) ) ) ).
% logic.valid_hoare_triple_def
thf(fact_451_logic_Oframe__property__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,C: set_Pr1275464188344874039_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( frame_property_a_c_d @ Plus2 @ Valid @ C )
= ( ! [Sigma: a,Sigma_0: a,R4: a,Sigma2: a,S: c > d,S2: c > d] :
( ( ( Valid @ Sigma )
& ( Valid @ Sigma2 )
& ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma_0 @ S ) )
& ( ( some_a @ Sigma )
= ( Plus2 @ Sigma_0 @ R4 ) )
& ( 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 @ Sigma2 @ S2 ) ) ) @ C ) )
=> ? [Sigma_02: a] :
( ( ( some_a @ Sigma2 )
= ( Plus2 @ Sigma_02 @ R4 ) )
& ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma_0 @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma_02 @ S2 ) ) ) @ C ) ) ) ) ) ) ).
% logic.frame_property_def
thf(fact_452_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,A3: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma3: a,S4: c > d,Sigma6: a,S7: c > d,X2: a,Delta3: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ ( modified_a_c_d @ C ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S4 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S7 ) ) ) @ C )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S4 @ Delta3 @ A3 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S7 @ Delta3 @ A3 ) ) ) ) ) ).
% logic.not_in_fv_mod
thf(fact_453_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,Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
= ( ! [S: c > d] : ( ord_less_eq_set_a @ ( Delta3 @ S ) @ ( Delta4 @ S ) ) ) ) ) ).
% logic.smaller_interp_def
thf(fact_454_logic_Osafety__monotonicity__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,C: set_Pr1275464188344874039_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( safety844553430189520448_a_c_d @ Plus2 @ Valid @ C )
= ( ! [Sigma: a,Sigma2: a,S: c > d] :
( ( ( Valid @ Sigma2 )
& ( pre_larger_a @ Plus2 @ Sigma2 @ Sigma )
& ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S ) ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma2 @ S ) ) ) ) ) ) ).
% logic.safety_monotonicity_def
thf(fact_455_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,S4: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( empty_interp_c_d_a @ S4 )
= bot_bot_set_a ) ) ).
% logic.empty_interp_def
thf(fact_456_map__upd__eqD1,axiom,
! [M: a > option_a,A: a,X2: a,N: a > option_a,Y: a] :
( ( ( fun_upd_a_option_a @ M @ A @ ( some_a @ X2 ) )
= ( fun_upd_a_option_a @ N @ A @ ( some_a @ Y ) ) )
=> ( X2 = Y ) ) ).
% map_upd_eqD1
thf(fact_457_map__upd__triv,axiom,
! [T: a > option_a,K: a,X2: a] :
( ( ( T @ K )
= ( some_a @ X2 ) )
=> ( ( fun_upd_a_option_a @ T @ K @ ( some_a @ X2 ) )
= T ) ) ).
% map_upd_triv
thf(fact_458_map__upd__Some__unfold,axiom,
! [M: a > option_a,A: a,B: a,X2: a,Y: a] :
( ( ( fun_upd_a_option_a @ M @ A @ ( some_a @ B ) @ X2 )
= ( some_a @ Y ) )
= ( ( ( X2 = A )
& ( B = Y ) )
| ( ( X2 != A )
& ( ( M @ X2 )
= ( some_a @ Y ) ) ) ) ) ).
% map_upd_Some_unfold
thf(fact_459_map__le__imp__upd__le,axiom,
! [M1: a > option_a,M2: a > option_a,X2: a,Y: a] :
( ( map_le_a_a @ M1 @ M2 )
=> ( map_le_a_a @ ( fun_upd_a_option_a @ M1 @ X2 @ none_a ) @ ( fun_upd_a_option_a @ M2 @ X2 @ ( some_a @ Y ) ) ) ) ).
% map_le_imp_upd_le
thf(fact_460_option_Ocollapse,axiom,
! [Option: option6413918287372586467_a_c_d] :
( ( Option != none_P2239999354720063602_a_c_d )
=> ( ( some_P1084500821511757806_a_c_d @ ( the_Pr7316212213771180927_a_c_d @ Option ) )
= Option ) ) ).
% option.collapse
thf(fact_461_option_Ocollapse,axiom,
! [Option: option_a] :
( ( Option != none_a )
=> ( ( some_a @ ( the_a @ Option ) )
= Option ) ) ).
% option.collapse
thf(fact_462_map__add__upd,axiom,
! [F2: a > option_a,G: a > option_a,X2: a,Y: a] :
( ( map_add_a_a @ F2 @ ( fun_upd_a_option_a @ G @ X2 @ ( some_a @ Y ) ) )
= ( fun_upd_a_option_a @ ( map_add_a_a @ F2 @ G ) @ X2 @ ( some_a @ Y ) ) ) ).
% map_add_upd
thf(fact_463_map__add__find__right,axiom,
! [N: a > option_a,K: a,Xx: a,M: a > option_a] :
( ( ( N @ K )
= ( some_a @ Xx ) )
=> ( ( map_add_a_a @ M @ N @ K )
= ( some_a @ Xx ) ) ) ).
% map_add_find_right
thf(fact_464_option_Osel,axiom,
! [X22: product_prod_a_c_d] :
( ( the_Pr7316212213771180927_a_c_d @ ( some_P1084500821511757806_a_c_d @ X22 ) )
= X22 ) ).
% option.sel
thf(fact_465_option_Osel,axiom,
! [X22: a] :
( ( the_a @ ( some_a @ X22 ) )
= X22 ) ).
% option.sel
thf(fact_466_map__add__SomeD,axiom,
! [M: a > option_a,N: a > option_a,K: a,X2: a] :
( ( ( map_add_a_a @ M @ N @ K )
= ( some_a @ X2 ) )
=> ( ( ( N @ K )
= ( some_a @ X2 ) )
| ( ( ( N @ K )
= none_a )
& ( ( M @ K )
= ( some_a @ X2 ) ) ) ) ) ).
% map_add_SomeD
thf(fact_467_map__add__Some__iff,axiom,
! [M: a > option_a,N: a > option_a,K: a,X2: a] :
( ( ( map_add_a_a @ M @ N @ K )
= ( some_a @ X2 ) )
= ( ( ( N @ K )
= ( some_a @ X2 ) )
| ( ( ( N @ K )
= none_a )
& ( ( M @ K )
= ( some_a @ X2 ) ) ) ) ) ).
% map_add_Some_iff
thf(fact_468_option_Oexhaust__sel,axiom,
! [Option: option6413918287372586467_a_c_d] :
( ( Option != none_P2239999354720063602_a_c_d )
=> ( Option
= ( some_P1084500821511757806_a_c_d @ ( the_Pr7316212213771180927_a_c_d @ Option ) ) ) ) ).
% option.exhaust_sel
thf(fact_469_option_Oexhaust__sel,axiom,
! [Option: option_a] :
( ( Option != none_a )
=> ( Option
= ( some_a @ ( the_a @ Option ) ) ) ) ).
% option.exhaust_sel
thf(fact_470_option_Osplit__sel,axiom,
! [P2: $o > $o,F1: $o,F22: a > $o,Option: option_a] :
( ( P2 @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( ( ( Option = none_a )
=> ( P2 @ F1 ) )
& ( ( Option
= ( some_a @ ( the_a @ Option ) ) )
=> ( P2 @ ( F22 @ ( the_a @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_471_option_Osplit__sel,axiom,
! [P2: option_a > $o,F1: option_a,F22: a > option_a,Option: option_a] :
( ( P2 @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( ( ( Option = none_a )
=> ( P2 @ F1 ) )
& ( ( Option
= ( some_a @ ( the_a @ Option ) ) )
=> ( P2 @ ( F22 @ ( the_a @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_472_option_Osplit__sel,axiom,
! [P2: a > $o,F1: a,F22: a > a,Option: option_a] :
( ( P2 @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( ( ( Option = none_a )
=> ( P2 @ F1 ) )
& ( ( Option
= ( some_a @ ( the_a @ Option ) ) )
=> ( P2 @ ( F22 @ ( the_a @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_473_option_Osplit__sel__asm,axiom,
! [P2: $o > $o,F1: $o,F22: a > $o,Option: option_a] :
( ( P2 @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( ~ ( ( ( Option = none_a )
& ~ ( P2 @ F1 ) )
| ( ( Option
= ( some_a @ ( the_a @ Option ) ) )
& ~ ( P2 @ ( F22 @ ( the_a @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_474_option_Osplit__sel__asm,axiom,
! [P2: option_a > $o,F1: option_a,F22: a > option_a,Option: option_a] :
( ( P2 @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( ~ ( ( ( Option = none_a )
& ~ ( P2 @ F1 ) )
| ( ( Option
= ( some_a @ ( the_a @ Option ) ) )
& ~ ( P2 @ ( F22 @ ( the_a @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_475_option_Osplit__sel__asm,axiom,
! [P2: a > $o,F1: a,F22: a > a,Option: option_a] :
( ( P2 @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( ~ ( ( ( Option = none_a )
& ~ ( P2 @ F1 ) )
| ( ( Option
= ( some_a @ ( the_a @ Option ) ) )
& ~ ( P2 @ ( F22 @ ( the_a @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_476_map__add__upd__left,axiom,
! [M: produc5278197477302038359_a_c_d,E2: produc5278197477302038359_a_c_d > option_a,E1: produc5278197477302038359_a_c_d > option_a,U1: a] :
( ~ ( member1180172933830803072_a_c_d @ M @ ( dom_Pr210953022859676729_c_d_a @ E2 ) )
=> ( ( map_ad5220634294393796252_c_d_a @ ( fun_up7463025390225626410tion_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_up7463025390225626410tion_a @ ( map_ad5220634294393796252_c_d_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_477_map__add__upd__left,axiom,
! [M: option_a,E2: option_a > option_a,E1: option_a > option_a,U1: a] :
( ~ ( member_option_a @ M @ ( dom_option_a_a @ E2 ) )
=> ( ( map_add_option_a_a @ ( fun_up1079276522633388797tion_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_up1079276522633388797tion_a @ ( map_add_option_a_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_478_map__add__upd__left,axiom,
! [M: b,E2: b > option_a,E1: b > option_a,U1: a] :
( ~ ( member_b @ M @ ( dom_b_a @ E2 ) )
=> ( ( map_add_b_a @ ( fun_upd_b_option_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_upd_b_option_a @ ( map_add_b_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_479_map__add__upd__left,axiom,
! [M: a,E2: a > option6413918287372586467_a_c_d,E1: a > option6413918287372586467_a_c_d,U1: product_prod_a_c_d] :
( ~ ( member_a @ M @ ( dom_a_3529858286862933695_a_c_d @ E2 ) )
=> ( ( map_ad2004115526166715036_a_c_d @ ( fun_up6642239869823773348_a_c_d @ E1 @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) @ E2 )
= ( fun_up6642239869823773348_a_c_d @ ( map_ad2004115526166715036_a_c_d @ E1 @ E2 ) @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_480_map__add__upd__left,axiom,
! [M: produc5278197477302038359_a_c_d,E2: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d,E1: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d,U1: product_prod_a_c_d] :
( ~ ( member1180172933830803072_a_c_d @ M @ ( dom_Pr2275460399045561368_a_c_d @ E2 ) )
=> ( ( map_ad4724009413847597045_a_c_d @ ( fun_up4007221454163596925_a_c_d @ E1 @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) @ E2 )
= ( fun_up4007221454163596925_a_c_d @ ( map_ad4724009413847597045_a_c_d @ E1 @ E2 ) @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_481_map__add__upd__left,axiom,
! [M: option_a,E2: option_a > option6413918287372586467_a_c_d,E1: option_a > option6413918287372586467_a_c_d,U1: product_prod_a_c_d] :
( ~ ( member_option_a @ M @ ( dom_op6156779764657312645_a_c_d @ E2 ) )
=> ( ( map_ad3766086351437021154_a_c_d @ ( fun_up5969202740897331946_a_c_d @ E1 @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) @ E2 )
= ( fun_up5969202740897331946_a_c_d @ ( map_ad3766086351437021154_a_c_d @ E1 @ E2 ) @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_482_map__add__upd__left,axiom,
! [M: b,E2: b > option6413918287372586467_a_c_d,E1: b > option6413918287372586467_a_c_d,U1: product_prod_a_c_d] :
( ~ ( member_b @ M @ ( dom_b_1825636403396063168_a_c_d @ E2 ) )
=> ( ( map_ad299893642699844509_a_c_d @ ( fun_up6513502963972302373_a_c_d @ E1 @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) @ E2 )
= ( fun_up6513502963972302373_a_c_d @ ( map_ad299893642699844509_a_c_d @ E1 @ E2 ) @ M @ ( some_P1084500821511757806_a_c_d @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_483_map__add__upd__left,axiom,
! [M: a,E2: a > option_a,E1: a > option_a,U1: a] :
( ~ ( member_a @ M @ ( dom_a_a @ E2 ) )
=> ( ( map_add_a_a @ ( fun_upd_a_option_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_upd_a_option_a @ ( map_add_a_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_484_in__graphI,axiom,
! [M: product_prod_a_c_d > option6212624336325788467_a_c_d,K: product_prod_a_c_d,V3: option6413918287372586467_a_c_d] :
( ( ( M @ K )
= ( some_o8886552288663794750_a_c_d @ V3 ) )
=> ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ K @ V3 ) @ ( graph_7244981646656495094_a_c_d @ M ) ) ) ).
% in_graphI
thf(fact_485_in__graphI,axiom,
! [M: a > option_c_d,K: a,V3: c > d] :
( ( ( M @ K )
= ( some_c_d @ V3 ) )
=> ( member8846983874477766826_a_c_d @ ( product_Pair_a_c_d @ K @ V3 ) @ ( graph_a_c_d @ M ) ) ) ).
% in_graphI
thf(fact_486_in__graphI,axiom,
! [M: assertion_a_b_d_c > option3890169911263941780_a_c_d,K: assertion_a_b_d_c,V3: produc5213381314664832452_a_c_d] :
( ( ( M @ K )
= ( some_P3194730542479778335_a_c_d @ V3 ) )
=> ( member537768723423446209_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V3 ) @ ( graph_7603009230766167293_a_c_d @ M ) ) ) ).
% in_graphI
thf(fact_487_in__graphI,axiom,
! [M: ( ( c > d ) > set_a ) > option_c_d,K: ( c > d ) > set_a,V3: c > d] :
( ( ( M @ K )
= ( some_c_d @ V3 ) )
=> ( member1642667639779969243_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V3 ) @ ( graph_c_d_set_a_c_d @ M ) ) ) ).
% in_graphI
thf(fact_488_in__graphD,axiom,
! [K: product_prod_a_c_d,V3: option6413918287372586467_a_c_d,M: product_prod_a_c_d > option6212624336325788467_a_c_d] :
( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ K @ V3 ) @ ( graph_7244981646656495094_a_c_d @ M ) )
=> ( ( M @ K )
= ( some_o8886552288663794750_a_c_d @ V3 ) ) ) ).
% in_graphD
thf(fact_489_in__graphD,axiom,
! [K: a,V3: c > d,M: a > option_c_d] :
( ( member8846983874477766826_a_c_d @ ( product_Pair_a_c_d @ K @ V3 ) @ ( graph_a_c_d @ M ) )
=> ( ( M @ K )
= ( some_c_d @ V3 ) ) ) ).
% in_graphD
thf(fact_490_in__graphD,axiom,
! [K: assertion_a_b_d_c,V3: produc5213381314664832452_a_c_d,M: assertion_a_b_d_c > option3890169911263941780_a_c_d] :
( ( member537768723423446209_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V3 ) @ ( graph_7603009230766167293_a_c_d @ M ) )
=> ( ( M @ K )
= ( some_P3194730542479778335_a_c_d @ V3 ) ) ) ).
% in_graphD
thf(fact_491_in__graphD,axiom,
! [K: ( c > d ) > set_a,V3: c > d,M: ( ( c > d ) > set_a ) > option_c_d] :
( ( member1642667639779969243_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V3 ) @ ( graph_c_d_set_a_c_d @ M ) )
=> ( ( M @ K )
= ( some_c_d @ V3 ) ) ) ).
% in_graphD
thf(fact_492_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,X2: produc5105196854009589546_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ~ ! [A8: assertion_a_b_d_c,Delta5: ( c > d ) > set_a,S6: c > d] :
( X2
!= ( produc8894421531525210148_a_c_d @ A8 @ ( produc7376592049607813182_a_c_d @ Delta5 @ S6 ) ) ) ) ).
% logic.applies_eq.cases
thf(fact_493_domD,axiom,
! [A: produc5278197477302038359_a_c_d,M: produc5278197477302038359_a_c_d > option_a] :
( ( member1180172933830803072_a_c_d @ A @ ( dom_Pr210953022859676729_c_d_a @ M ) )
=> ? [B6: a] :
( ( M @ A )
= ( some_a @ B6 ) ) ) ).
% domD
thf(fact_494_domD,axiom,
! [A: option_a,M: option_a > option_a] :
( ( member_option_a @ A @ ( dom_option_a_a @ M ) )
=> ? [B6: a] :
( ( M @ A )
= ( some_a @ B6 ) ) ) ).
% domD
thf(fact_495_domD,axiom,
! [A: b,M: b > option_a] :
( ( member_b @ A @ ( dom_b_a @ M ) )
=> ? [B6: a] :
( ( M @ A )
= ( some_a @ B6 ) ) ) ).
% domD
thf(fact_496_domD,axiom,
! [A: a,M: a > option6413918287372586467_a_c_d] :
( ( member_a @ A @ ( dom_a_3529858286862933695_a_c_d @ M ) )
=> ? [B6: product_prod_a_c_d] :
( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B6 ) ) ) ).
% domD
thf(fact_497_domD,axiom,
! [A: produc5278197477302038359_a_c_d,M: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d] :
( ( member1180172933830803072_a_c_d @ A @ ( dom_Pr2275460399045561368_a_c_d @ M ) )
=> ? [B6: product_prod_a_c_d] :
( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B6 ) ) ) ).
% domD
thf(fact_498_domD,axiom,
! [A: option_a,M: option_a > option6413918287372586467_a_c_d] :
( ( member_option_a @ A @ ( dom_op6156779764657312645_a_c_d @ M ) )
=> ? [B6: product_prod_a_c_d] :
( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B6 ) ) ) ).
% domD
thf(fact_499_domD,axiom,
! [A: b,M: b > option6413918287372586467_a_c_d] :
( ( member_b @ A @ ( dom_b_1825636403396063168_a_c_d @ M ) )
=> ? [B6: product_prod_a_c_d] :
( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B6 ) ) ) ).
% domD
thf(fact_500_domD,axiom,
! [A: a,M: a > option_a] :
( ( member_a @ A @ ( dom_a_a @ M ) )
=> ? [B6: a] :
( ( M @ A )
= ( some_a @ B6 ) ) ) ).
% domD
thf(fact_501_domI,axiom,
! [M: produc5278197477302038359_a_c_d > option_a,A: produc5278197477302038359_a_c_d,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member1180172933830803072_a_c_d @ A @ ( dom_Pr210953022859676729_c_d_a @ M ) ) ) ).
% domI
thf(fact_502_domI,axiom,
! [M: option_a > option_a,A: option_a,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member_option_a @ A @ ( dom_option_a_a @ M ) ) ) ).
% domI
thf(fact_503_domI,axiom,
! [M: b > option_a,A: b,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member_b @ A @ ( dom_b_a @ M ) ) ) ).
% domI
thf(fact_504_domI,axiom,
! [M: a > option6413918287372586467_a_c_d,A: a,B: product_prod_a_c_d] :
( ( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B ) )
=> ( member_a @ A @ ( dom_a_3529858286862933695_a_c_d @ M ) ) ) ).
% domI
thf(fact_505_domI,axiom,
! [M: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d,A: produc5278197477302038359_a_c_d,B: product_prod_a_c_d] :
( ( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B ) )
=> ( member1180172933830803072_a_c_d @ A @ ( dom_Pr2275460399045561368_a_c_d @ M ) ) ) ).
% domI
thf(fact_506_domI,axiom,
! [M: option_a > option6413918287372586467_a_c_d,A: option_a,B: product_prod_a_c_d] :
( ( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B ) )
=> ( member_option_a @ A @ ( dom_op6156779764657312645_a_c_d @ M ) ) ) ).
% domI
thf(fact_507_domI,axiom,
! [M: b > option6413918287372586467_a_c_d,A: b,B: product_prod_a_c_d] :
( ( ( M @ A )
= ( some_P1084500821511757806_a_c_d @ B ) )
=> ( member_b @ A @ ( dom_b_1825636403396063168_a_c_d @ M ) ) ) ).
% domI
thf(fact_508_domI,axiom,
! [M: a > option_a,A: a,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member_a @ A @ ( dom_a_a @ M ) ) ) ).
% domI
thf(fact_509_option_Osimps_I5_J,axiom,
! [F1: $o,F22: a > $o,X22: a] :
( ( case_option_o_a @ F1 @ F22 @ ( some_a @ X22 ) )
= ( F22 @ X22 ) ) ).
% option.simps(5)
thf(fact_510_option_Osimps_I5_J,axiom,
! [F1: option_a,F22: a > option_a,X22: a] :
( ( case_o3148979394504432965on_a_a @ F1 @ F22 @ ( some_a @ X22 ) )
= ( F22 @ X22 ) ) ).
% option.simps(5)
thf(fact_511_option_Osimps_I5_J,axiom,
! [F1: a,F22: a > a,X22: a] :
( ( case_option_a_a @ F1 @ F22 @ ( some_a @ X22 ) )
= ( F22 @ X22 ) ) ).
% option.simps(5)
thf(fact_512_graph__map__upd,axiom,
! [M: product_prod_a_c_d > option6212624336325788467_a_c_d,K: product_prod_a_c_d,V3: option6413918287372586467_a_c_d] :
( ( graph_7244981646656495094_a_c_d @ ( fun_up3914643275129436357_a_c_d @ M @ K @ ( some_o8886552288663794750_a_c_d @ V3 ) ) )
= ( insert4072338954160766247_a_c_d @ ( produc8093790510458973071_a_c_d @ K @ V3 ) @ ( graph_7244981646656495094_a_c_d @ ( fun_up3914643275129436357_a_c_d @ M @ K @ none_o2262236386069974722_a_c_d ) ) ) ) ).
% graph_map_upd
thf(fact_513_graph__map__upd,axiom,
! [M: a > option_c_d,K: a,V3: c > d] :
( ( graph_a_c_d @ ( fun_upd_a_option_c_d @ M @ K @ ( some_c_d @ V3 ) ) )
= ( insert2748062992969704259_a_c_d @ ( product_Pair_a_c_d @ K @ V3 ) @ ( graph_a_c_d @ ( fun_upd_a_option_c_d @ M @ K @ none_c_d ) ) ) ) ).
% graph_map_upd
thf(fact_514_graph__map__upd,axiom,
! [M: assertion_a_b_d_c > option3890169911263941780_a_c_d,K: assertion_a_b_d_c,V3: produc5213381314664832452_a_c_d] :
( ( graph_7603009230766167293_a_c_d @ ( fun_up8563802042059451790_a_c_d @ M @ K @ ( some_P3194730542479778335_a_c_d @ V3 ) ) )
= ( insert1952503980790619482_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V3 ) @ ( graph_7603009230766167293_a_c_d @ ( fun_up8563802042059451790_a_c_d @ M @ K @ none_P4438893274231186595_a_c_d ) ) ) ) ).
% graph_map_upd
thf(fact_515_graph__map__upd,axiom,
! [M: ( ( c > d ) > set_a ) > option_c_d,K: ( c > d ) > set_a,V3: c > d] :
( ( graph_c_d_set_a_c_d @ ( fun_up2820008246124789800on_c_d @ M @ K @ ( some_c_d @ V3 ) ) )
= ( insert9214331609911559156_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V3 ) @ ( graph_c_d_set_a_c_d @ ( fun_up2820008246124789800on_c_d @ M @ K @ none_c_d ) ) ) ) ).
% graph_map_upd
thf(fact_516_graph__map__upd,axiom,
! [M: a > option_a,K: a,V3: a] :
( ( graph_a_a @ ( fun_upd_a_option_a @ M @ K @ ( some_a @ V3 ) ) )
= ( insert4534936382041156343od_a_a @ ( product_Pair_a_a @ K @ V3 ) @ ( graph_a_a @ ( fun_upd_a_option_a @ M @ K @ none_a ) ) ) ) ).
% graph_map_upd
thf(fact_517_graph__restrictD_I2_J,axiom,
! [K: product_prod_a_c_d,V3: option6413918287372586467_a_c_d,M: product_prod_a_c_d > option6212624336325788467_a_c_d,A3: set_Pr334309860168054345_a_c_d] :
( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ K @ V3 ) @ ( graph_7244981646656495094_a_c_d @ ( restri3000517089388389544_a_c_d @ M @ A3 ) ) )
=> ( ( M @ K )
= ( some_o8886552288663794750_a_c_d @ V3 ) ) ) ).
% graph_restrictD(2)
thf(fact_518_graph__restrictD_I2_J,axiom,
! [K: a,V3: c > d,M: a > option_c_d,A3: set_a] :
( ( member8846983874477766826_a_c_d @ ( product_Pair_a_c_d @ K @ V3 ) @ ( graph_a_c_d @ ( restrict_map_a_c_d @ M @ A3 ) ) )
=> ( ( M @ K )
= ( some_c_d @ V3 ) ) ) ).
% graph_restrictD(2)
thf(fact_519_graph__restrictD_I2_J,axiom,
! [K: assertion_a_b_d_c,V3: produc5213381314664832452_a_c_d,M: assertion_a_b_d_c > option3890169911263941780_a_c_d,A3: set_as909545710669178647_b_d_c] :
( ( member537768723423446209_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V3 ) @ ( graph_7603009230766167293_a_c_d @ ( restri3968632621895983051_a_c_d @ M @ A3 ) ) )
=> ( ( M @ K )
= ( some_P3194730542479778335_a_c_d @ V3 ) ) ) ).
% graph_restrictD(2)
thf(fact_520_graph__restrictD_I2_J,axiom,
! [K: ( c > d ) > set_a,V3: c > d,M: ( ( c > d ) > set_a ) > option_c_d,A3: set_c_d_set_a] :
( ( member1642667639779969243_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V3 ) @ ( graph_c_d_set_a_c_d @ ( restri4474245042709046629_a_c_d @ M @ A3 ) ) )
=> ( ( M @ K )
= ( some_c_d @ V3 ) ) ) ).
% graph_restrictD(2)
thf(fact_521_bind__split__asm,axiom,
! [P2: option_a > $o,M: option6413918287372586467_a_c_d,F2: product_prod_a_c_d > option_a] :
( ( P2 @ ( bind_P2911691133002111467_c_d_a @ M @ F2 ) )
= ( ~ ( ( ( M = none_P2239999354720063602_a_c_d )
& ~ ( P2 @ none_a ) )
| ? [X: product_prod_a_c_d] :
( ( M
= ( some_P1084500821511757806_a_c_d @ X ) )
& ~ ( P2 @ ( F2 @ X ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_522_bind__split__asm,axiom,
! [P2: option_a > $o,M: option_a,F2: a > option_a] :
( ( P2 @ ( bind_a_a @ M @ F2 ) )
= ( ~ ( ( ( M = none_a )
& ~ ( P2 @ none_a ) )
| ? [X: a] :
( ( M
= ( some_a @ X ) )
& ~ ( P2 @ ( F2 @ X ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_523_bind__split,axiom,
! [P2: option_a > $o,M: option6413918287372586467_a_c_d,F2: product_prod_a_c_d > option_a] :
( ( P2 @ ( bind_P2911691133002111467_c_d_a @ M @ F2 ) )
= ( ( ( M = none_P2239999354720063602_a_c_d )
=> ( P2 @ none_a ) )
& ! [V: product_prod_a_c_d] :
( ( M
= ( some_P1084500821511757806_a_c_d @ V ) )
=> ( P2 @ ( F2 @ V ) ) ) ) ) ).
% bind_split
thf(fact_524_bind__split,axiom,
! [P2: option_a > $o,M: option_a,F2: a > option_a] :
( ( P2 @ ( bind_a_a @ M @ F2 ) )
= ( ( ( M = none_a )
=> ( P2 @ none_a ) )
& ! [V: a] :
( ( M
= ( some_a @ V ) )
=> ( P2 @ ( F2 @ V ) ) ) ) ) ).
% bind_split
thf(fact_525_image__map__upd,axiom,
! [X2: produc5278197477302038359_a_c_d,A3: set_Pr1275464188344874039_a_c_d,M: produc5278197477302038359_a_c_d > option_a,Y: a] :
( ~ ( member1180172933830803072_a_c_d @ X2 @ A3 )
=> ( ( image_158748266322232498tion_a @ ( fun_up7463025390225626410tion_a @ M @ X2 @ ( some_a @ Y ) ) @ A3 )
= ( image_158748266322232498tion_a @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_526_image__map__upd,axiom,
! [X2: option_a,A3: set_option_a,M: option_a > option_a,Y: a] :
( ~ ( member_option_a @ X2 @ A3 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ M @ X2 @ ( some_a @ Y ) ) @ A3 )
= ( image_7439109396645324421tion_a @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_527_image__map__upd,axiom,
! [X2: b,A3: set_b,M: b > option_a,Y: a] :
( ~ ( member_b @ X2 @ A3 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ M @ X2 @ ( some_a @ Y ) ) @ A3 )
= ( image_b_option_a @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_528_image__map__upd,axiom,
! [X2: a,A3: set_a,M: a > option6413918287372586467_a_c_d,Y: product_prod_a_c_d] :
( ~ ( member_a @ X2 @ A3 )
=> ( ( image_3786525410991915292_a_c_d @ ( fun_up6642239869823773348_a_c_d @ M @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) ) @ A3 )
= ( image_3786525410991915292_a_c_d @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_529_image__map__upd,axiom,
! [X2: produc5278197477302038359_a_c_d,A3: set_Pr1275464188344874039_a_c_d,M: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d,Y: product_prod_a_c_d] :
( ~ ( member1180172933830803072_a_c_d @ X2 @ A3 )
=> ( ( image_1524162552056343797_a_c_d @ ( fun_up4007221454163596925_a_c_d @ M @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) ) @ A3 )
= ( image_1524162552056343797_a_c_d @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_530_image__map__upd,axiom,
! [X2: option_a,A3: set_option_a,M: option_a > option6413918287372586467_a_c_d,Y: product_prod_a_c_d] :
( ~ ( member_option_a @ X2 @ A3 )
=> ( ( image_3697009332183072098_a_c_d @ ( fun_up5969202740897331946_a_c_d @ M @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) ) @ A3 )
= ( image_3697009332183072098_a_c_d @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_531_image__map__upd,axiom,
! [X2: b,A3: set_b,M: b > option6413918287372586467_a_c_d,Y: product_prod_a_c_d] :
( ~ ( member_b @ X2 @ A3 )
=> ( ( image_3657788505140444317_a_c_d @ ( fun_up6513502963972302373_a_c_d @ M @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) ) @ A3 )
= ( image_3657788505140444317_a_c_d @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_532_image__map__upd,axiom,
! [X2: a,A3: set_a,M: a > option_a,Y: a] :
( ~ ( member_a @ X2 @ A3 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ M @ X2 @ ( some_a @ Y ) ) @ A3 )
= ( image_a_option_a @ M @ A3 ) ) ) ).
% image_map_upd
thf(fact_533_bind__runit,axiom,
! [X2: option6413918287372586467_a_c_d] :
( ( bind_P5476543181312113638_a_c_d @ X2 @ some_P1084500821511757806_a_c_d )
= X2 ) ).
% bind_runit
thf(fact_534_bind__runit,axiom,
! [X2: option_a] :
( ( bind_a_a @ X2 @ some_a )
= X2 ) ).
% bind_runit
thf(fact_535_bind_Obind__lunit,axiom,
! [X2: a,F2: a > option_a] :
( ( bind_a_a @ ( some_a @ X2 ) @ F2 )
= ( F2 @ X2 ) ) ).
% bind.bind_lunit
thf(fact_536_Option_Obind__cong,axiom,
! [X2: option_a,Y: option_a,F2: a > option_a,G: a > option_a] :
( ( X2 = Y )
=> ( ! [A5: a] :
( ( Y
= ( some_a @ A5 ) )
=> ( ( F2 @ A5 )
= ( G @ A5 ) ) )
=> ( ( bind_a_a @ X2 @ F2 )
= ( bind_a_a @ Y @ G ) ) ) ) ).
% Option.bind_cong
thf(fact_537_bind__eq__Some__conv,axiom,
! [F2: option6413918287372586467_a_c_d,G: product_prod_a_c_d > option_a,X2: a] :
( ( ( bind_P2911691133002111467_c_d_a @ F2 @ G )
= ( some_a @ X2 ) )
= ( ? [Y2: product_prod_a_c_d] :
( ( F2
= ( some_P1084500821511757806_a_c_d @ Y2 ) )
& ( ( G @ Y2 )
= ( some_a @ X2 ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_538_bind__eq__Some__conv,axiom,
! [F2: option_a,G: a > option6413918287372586467_a_c_d,X2: product_prod_a_c_d] :
( ( ( bind_a4598251245030301523_a_c_d @ F2 @ G )
= ( some_P1084500821511757806_a_c_d @ X2 ) )
= ( ? [Y2: a] :
( ( F2
= ( some_a @ Y2 ) )
& ( ( G @ Y2 )
= ( some_P1084500821511757806_a_c_d @ X2 ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_539_bind__eq__Some__conv,axiom,
! [F2: option6413918287372586467_a_c_d,G: product_prod_a_c_d > option6413918287372586467_a_c_d,X2: product_prod_a_c_d] :
( ( ( bind_P5476543181312113638_a_c_d @ F2 @ G )
= ( some_P1084500821511757806_a_c_d @ X2 ) )
= ( ? [Y2: product_prod_a_c_d] :
( ( F2
= ( some_P1084500821511757806_a_c_d @ Y2 ) )
& ( ( G @ Y2 )
= ( some_P1084500821511757806_a_c_d @ X2 ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_540_bind__eq__Some__conv,axiom,
! [F2: option_a,G: a > option_a,X2: a] :
( ( ( bind_a_a @ F2 @ G )
= ( some_a @ X2 ) )
= ( ? [Y2: a] :
( ( F2
= ( some_a @ Y2 ) )
& ( ( G @ Y2 )
= ( some_a @ X2 ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_541_None__notin__image__Some,axiom,
! [A3: set_Pr334309860168054345_a_c_d] :
~ ( member5926479794665358074_a_c_d @ none_P2239999354720063602_a_c_d @ ( image_5741706613785127421_a_c_d @ some_P1084500821511757806_a_c_d @ A3 ) ) ).
% None_notin_image_Some
thf(fact_542_None__notin__image__Some,axiom,
! [A3: set_a] :
~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A3 ) ) ).
% None_notin_image_Some
thf(fact_543_insert__dom,axiom,
! [F2: option_a > option_a,X2: option_a,Y: a] :
( ( ( F2 @ X2 )
= ( some_a @ Y ) )
=> ( ( insert_option_a @ X2 @ ( dom_option_a_a @ F2 ) )
= ( dom_option_a_a @ F2 ) ) ) ).
% insert_dom
thf(fact_544_insert__dom,axiom,
! [F2: a > option_a,X2: a,Y: a] :
( ( ( F2 @ X2 )
= ( some_a @ Y ) )
=> ( ( insert_a @ X2 @ ( dom_a_a @ F2 ) )
= ( dom_a_a @ F2 ) ) ) ).
% insert_dom
thf(fact_545_insert__dom,axiom,
! [F2: option_a > option6413918287372586467_a_c_d,X2: option_a,Y: product_prod_a_c_d] :
( ( ( F2 @ X2 )
= ( some_P1084500821511757806_a_c_d @ Y ) )
=> ( ( insert_option_a @ X2 @ ( dom_op6156779764657312645_a_c_d @ F2 ) )
= ( dom_op6156779764657312645_a_c_d @ F2 ) ) ) ).
% insert_dom
thf(fact_546_insert__dom,axiom,
! [F2: a > option6413918287372586467_a_c_d,X2: a,Y: product_prod_a_c_d] :
( ( ( F2 @ X2 )
= ( some_P1084500821511757806_a_c_d @ Y ) )
=> ( ( insert_a @ X2 @ ( dom_a_3529858286862933695_a_c_d @ F2 ) )
= ( dom_a_3529858286862933695_a_c_d @ F2 ) ) ) ).
% insert_dom
thf(fact_547_ran__map__upd,axiom,
! [M: a > option_a,A: a,B: a] :
( ( ( M @ A )
= none_a )
=> ( ( ran_a_a @ ( fun_upd_a_option_a @ M @ A @ ( some_a @ B ) ) )
= ( insert_a @ B @ ( ran_a_a @ M ) ) ) ) ).
% ran_map_upd
thf(fact_548_restrict__upd__same,axiom,
! [M: option_a > option_a,X2: option_a,Y: a] :
( ( restri3984065703976872170on_a_a @ ( fun_up1079276522633388797tion_a @ M @ X2 @ ( some_a @ Y ) ) @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) )
= ( restri3984065703976872170on_a_a @ M @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ) ).
% restrict_upd_same
thf(fact_549_restrict__upd__same,axiom,
! [M: option_a > option6413918287372586467_a_c_d,X2: option_a,Y: product_prod_a_c_d] :
( ( restri9088203652661596199_a_c_d @ ( fun_up5969202740897331946_a_c_d @ M @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) ) @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) )
= ( restri9088203652661596199_a_c_d @ M @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ) ).
% restrict_upd_same
thf(fact_550_restrict__upd__same,axiom,
! [M: a > option_a,X2: a,Y: a] :
( ( restrict_map_a_a @ ( fun_upd_a_option_a @ M @ X2 @ ( some_a @ Y ) ) @ ( uminus_uminus_set_a @ ( insert_a @ X2 @ bot_bot_set_a ) ) )
= ( restrict_map_a_a @ M @ ( uminus_uminus_set_a @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ).
% restrict_upd_same
thf(fact_551_restrict__upd__same,axiom,
! [M: a > option6413918287372586467_a_c_d,X2: a,Y: product_prod_a_c_d] :
( ( restri776808000187872865_a_c_d @ ( fun_up6642239869823773348_a_c_d @ M @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) ) @ ( uminus_uminus_set_a @ ( insert_a @ X2 @ bot_bot_set_a ) ) )
= ( restri776808000187872865_a_c_d @ M @ ( uminus_uminus_set_a @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ).
% restrict_upd_same
thf(fact_552_these__image__Some__eq,axiom,
! [A3: set_Pr334309860168054345_a_c_d] :
( ( these_5134989223866396566_a_c_d @ ( image_5741706613785127421_a_c_d @ some_P1084500821511757806_a_c_d @ A3 ) )
= A3 ) ).
% these_image_Some_eq
thf(fact_553_these__image__Some__eq,axiom,
! [A3: set_a] :
( ( these_a @ ( image_a_option_a @ some_a @ A3 ) )
= A3 ) ).
% these_image_Some_eq
thf(fact_554_these__insert__Some,axiom,
! [X2: option_a,A3: set_option_option_a] :
( ( these_option_a @ ( insert605063979879581146tion_a @ ( some_option_a @ X2 ) @ A3 ) )
= ( insert_option_a @ X2 @ ( these_option_a @ A3 ) ) ) ).
% these_insert_Some
thf(fact_555_these__insert__Some,axiom,
! [X2: product_prod_a_c_d,A3: set_op3383557829362473625_a_c_d] :
( ( these_5134989223866396566_a_c_d @ ( insert6629875870486991891_a_c_d @ ( some_P1084500821511757806_a_c_d @ X2 ) @ A3 ) )
= ( insert2748062992969704259_a_c_d @ X2 @ ( these_5134989223866396566_a_c_d @ A3 ) ) ) ).
% these_insert_Some
thf(fact_556_these__insert__Some,axiom,
! [X2: a,A3: set_option_a] :
( ( these_a @ ( insert_option_a @ ( some_a @ X2 ) @ A3 ) )
= ( insert_a @ X2 @ ( these_a @ A3 ) ) ) ).
% these_insert_Some
thf(fact_557_in__these__eq,axiom,
! [X2: produc5278197477302038359_a_c_d,A3: set_op7411283011066580861_a_c_d] :
( ( member1180172933830803072_a_c_d @ X2 @ ( these_5855049757122979476_a_c_d @ A3 ) )
= ( member7124857669314633414_a_c_d @ ( some_P7564561949935391804_a_c_d @ X2 ) @ A3 ) ) ).
% in_these_eq
thf(fact_558_in__these__eq,axiom,
! [X2: option_a,A3: set_option_option_a] :
( ( member_option_a @ X2 @ ( these_option_a @ A3 ) )
= ( member5113800082084363315tion_a @ ( some_option_a @ X2 ) @ A3 ) ) ).
% in_these_eq
thf(fact_559_in__these__eq,axiom,
! [X2: b,A3: set_option_b] :
( ( member_b @ X2 @ ( these_b @ A3 ) )
= ( member_option_b @ ( some_b @ X2 ) @ A3 ) ) ).
% in_these_eq
thf(fact_560_in__these__eq,axiom,
! [X2: product_prod_a_c_d,A3: set_op3383557829362473625_a_c_d] :
( ( member8846983874477766826_a_c_d @ X2 @ ( these_5134989223866396566_a_c_d @ A3 ) )
= ( member5926479794665358074_a_c_d @ ( some_P1084500821511757806_a_c_d @ X2 ) @ A3 ) ) ).
% in_these_eq
thf(fact_561_in__these__eq,axiom,
! [X2: a,A3: set_option_a] :
( ( member_a @ X2 @ ( these_a @ A3 ) )
= ( member_option_a @ ( some_a @ X2 ) @ A3 ) ) ).
% in_these_eq
thf(fact_562_override__on__insert_H,axiom,
! [F2: c > d,G: c > d,X2: c,X6: set_c] :
( ( override_on_c_d @ F2 @ G @ ( insert_c @ X2 @ X6 ) )
= ( override_on_c_d @ ( fun_upd_c_d @ F2 @ X2 @ ( G @ X2 ) ) @ G @ X6 ) ) ).
% override_on_insert'
thf(fact_563_override__on__insert_H,axiom,
! [F2: a > option_a,G: a > option_a,X2: a,X6: set_a] :
( ( overri633547075744967556tion_a @ F2 @ G @ ( insert_a @ X2 @ X6 ) )
= ( overri633547075744967556tion_a @ ( fun_upd_a_option_a @ F2 @ X2 @ ( G @ X2 ) ) @ G @ X6 ) ) ).
% override_on_insert'
thf(fact_564_override__on__insert,axiom,
! [F2: c > d,G: c > d,X2: c,X6: set_c] :
( ( override_on_c_d @ F2 @ G @ ( insert_c @ X2 @ X6 ) )
= ( fun_upd_c_d @ ( override_on_c_d @ F2 @ G @ X6 ) @ X2 @ ( G @ X2 ) ) ) ).
% override_on_insert
thf(fact_565_override__on__insert,axiom,
! [F2: a > option_a,G: a > option_a,X2: a,X6: set_a] :
( ( overri633547075744967556tion_a @ F2 @ G @ ( insert_a @ X2 @ X6 ) )
= ( fun_upd_a_option_a @ ( overri633547075744967556tion_a @ F2 @ G @ X6 ) @ X2 @ ( G @ X2 ) ) ) ).
% override_on_insert
thf(fact_566_fun__upd__image,axiom,
! [X2: produc5278197477302038359_a_c_d,A3: set_Pr1275464188344874039_a_c_d,F2: produc5278197477302038359_a_c_d > option_a,Y: option_a] :
( ( ( member1180172933830803072_a_c_d @ X2 @ A3 )
=> ( ( image_158748266322232498tion_a @ ( fun_up7463025390225626410tion_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_option_a @ Y @ ( image_158748266322232498tion_a @ F2 @ ( minus_4271488753454470558_a_c_d @ A3 @ ( insert4072338954160766247_a_c_d @ X2 @ bot_bo4027597737525728931_a_c_d ) ) ) ) ) )
& ( ~ ( member1180172933830803072_a_c_d @ X2 @ A3 )
=> ( ( image_158748266322232498tion_a @ ( fun_up7463025390225626410tion_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_158748266322232498tion_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_567_fun__upd__image,axiom,
! [X2: produc5278197477302038359_a_c_d,A3: set_Pr1275464188344874039_a_c_d,F2: produc5278197477302038359_a_c_d > a,Y: a] :
( ( ( member1180172933830803072_a_c_d @ X2 @ A3 )
=> ( ( image_8636529855994272620_c_d_a @ ( fun_up2227350886784581604_c_d_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_a @ Y @ ( image_8636529855994272620_c_d_a @ F2 @ ( minus_4271488753454470558_a_c_d @ A3 @ ( insert4072338954160766247_a_c_d @ X2 @ bot_bo4027597737525728931_a_c_d ) ) ) ) ) )
& ( ~ ( member1180172933830803072_a_c_d @ X2 @ A3 )
=> ( ( image_8636529855994272620_c_d_a @ ( fun_up2227350886784581604_c_d_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_8636529855994272620_c_d_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_568_fun__upd__image,axiom,
! [X2: option_a,A3: set_option_a,F2: option_a > option_a,Y: option_a] :
( ( ( member_option_a @ X2 @ A3 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_option_a @ Y @ ( image_7439109396645324421tion_a @ F2 @ ( minus_1574173051537231627tion_a @ A3 @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ) ) )
& ( ~ ( member_option_a @ X2 @ A3 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_7439109396645324421tion_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_569_fun__upd__image,axiom,
! [X2: option_a,A3: set_option_a,F2: option_a > a,Y: a] :
( ( ( member_option_a @ X2 @ A3 )
=> ( ( image_option_a_a @ ( fun_upd_option_a_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_a @ Y @ ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ A3 @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ) ) )
& ( ~ ( member_option_a @ X2 @ A3 )
=> ( ( image_option_a_a @ ( fun_upd_option_a_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_option_a_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_570_fun__upd__image,axiom,
! [X2: b,A3: set_b,F2: b > option_a,Y: option_a] :
( ( ( member_b @ X2 @ A3 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_option_a @ Y @ ( image_b_option_a @ F2 @ ( minus_minus_set_b @ A3 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) )
& ( ~ ( member_b @ X2 @ A3 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_b_option_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_571_fun__upd__image,axiom,
! [X2: b,A3: set_b,F2: b > a,Y: a] :
( ( ( member_b @ X2 @ A3 )
=> ( ( image_b_a @ ( fun_upd_b_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_a @ Y @ ( image_b_a @ F2 @ ( minus_minus_set_b @ A3 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) )
& ( ~ ( member_b @ X2 @ A3 )
=> ( ( image_b_a @ ( fun_upd_b_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_b_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_572_fun__upd__image,axiom,
! [X2: c,A3: set_c,F2: c > d,Y: d] :
( ( ( member_c @ X2 @ A3 )
=> ( ( image_c_d @ ( fun_upd_c_d @ F2 @ X2 @ Y ) @ A3 )
= ( insert_d @ Y @ ( image_c_d @ F2 @ ( minus_minus_set_c @ A3 @ ( insert_c @ X2 @ bot_bot_set_c ) ) ) ) ) )
& ( ~ ( member_c @ X2 @ A3 )
=> ( ( image_c_d @ ( fun_upd_c_d @ F2 @ X2 @ Y ) @ A3 )
= ( image_c_d @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_573_fun__upd__image,axiom,
! [X2: a,A3: set_a,F2: a > a,Y: a] :
( ( ( member_a @ X2 @ A3 )
=> ( ( image_a_a @ ( fun_upd_a_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_a @ Y @ ( image_a_a @ F2 @ ( minus_minus_set_a @ A3 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) )
& ( ~ ( member_a @ X2 @ A3 )
=> ( ( image_a_a @ ( fun_upd_a_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_a_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_574_fun__upd__image,axiom,
! [X2: a,A3: set_a,F2: a > option_a,Y: option_a] :
( ( ( member_a @ X2 @ A3 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ F2 @ X2 @ Y ) @ A3 )
= ( insert_option_a @ Y @ ( image_a_option_a @ F2 @ ( minus_minus_set_a @ A3 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) )
& ( ~ ( member_a @ X2 @ A3 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ F2 @ X2 @ Y ) @ A3 )
= ( image_a_option_a @ F2 @ A3 ) ) ) ) ).
% fun_upd_image
thf(fact_575_option_Osimps_I15_J,axiom,
! [X22: option_a] :
( ( set_option_option_a2 @ ( some_option_a @ X22 ) )
= ( insert_option_a @ X22 @ bot_bot_set_option_a ) ) ).
% option.simps(15)
thf(fact_576_option_Osimps_I15_J,axiom,
! [X22: product_prod_a_c_d] :
( ( set_op7017632568034097669_a_c_d @ ( some_P1084500821511757806_a_c_d @ X22 ) )
= ( insert2748062992969704259_a_c_d @ X22 @ bot_bo110114171885311197_a_c_d ) ) ).
% option.simps(15)
thf(fact_577_option_Osimps_I15_J,axiom,
! [X22: a] :
( ( set_option_a2 @ ( some_a @ X22 ) )
= ( insert_a @ X22 @ bot_bot_set_a ) ) ).
% option.simps(15)
thf(fact_578_elem__set,axiom,
! [X2: produc5278197477302038359_a_c_d,Xo: option6736415434736681245_a_c_d] :
( ( member1180172933830803072_a_c_d @ X2 @ ( set_op1238738513205398757_a_c_d @ Xo ) )
= ( Xo
= ( some_P7564561949935391804_a_c_d @ X2 ) ) ) ).
% elem_set
thf(fact_579_elem__set,axiom,
! [X2: option_a,Xo: option_option_a] :
( ( member_option_a @ X2 @ ( set_option_option_a2 @ Xo ) )
= ( Xo
= ( some_option_a @ X2 ) ) ) ).
% elem_set
thf(fact_580_elem__set,axiom,
! [X2: b,Xo: option_b] :
( ( member_b @ X2 @ ( set_option_b2 @ Xo ) )
= ( Xo
= ( some_b @ X2 ) ) ) ).
% elem_set
thf(fact_581_elem__set,axiom,
! [X2: product_prod_a_c_d,Xo: option6413918287372586467_a_c_d] :
( ( member8846983874477766826_a_c_d @ X2 @ ( set_op7017632568034097669_a_c_d @ Xo ) )
= ( Xo
= ( some_P1084500821511757806_a_c_d @ X2 ) ) ) ).
% elem_set
thf(fact_582_elem__set,axiom,
! [X2: a,Xo: option_a] :
( ( member_a @ X2 @ ( set_option_a2 @ Xo ) )
= ( Xo
= ( some_a @ X2 ) ) ) ).
% elem_set
thf(fact_583_option_Oset__cases,axiom,
! [E: produc5278197477302038359_a_c_d,A: option6736415434736681245_a_c_d] :
( ( member1180172933830803072_a_c_d @ E @ ( set_op1238738513205398757_a_c_d @ A ) )
=> ( A
= ( some_P7564561949935391804_a_c_d @ E ) ) ) ).
% option.set_cases
thf(fact_584_option_Oset__cases,axiom,
! [E: option_a,A: option_option_a] :
( ( member_option_a @ E @ ( set_option_option_a2 @ A ) )
=> ( A
= ( some_option_a @ E ) ) ) ).
% option.set_cases
thf(fact_585_option_Oset__cases,axiom,
! [E: b,A: option_b] :
( ( member_b @ E @ ( set_option_b2 @ A ) )
=> ( A
= ( some_b @ E ) ) ) ).
% option.set_cases
thf(fact_586_option_Oset__cases,axiom,
! [E: product_prod_a_c_d,A: option6413918287372586467_a_c_d] :
( ( member8846983874477766826_a_c_d @ E @ ( set_op7017632568034097669_a_c_d @ A ) )
=> ( A
= ( some_P1084500821511757806_a_c_d @ E ) ) ) ).
% option.set_cases
thf(fact_587_option_Oset__cases,axiom,
! [E: a,A: option_a] :
( ( member_a @ E @ ( set_option_a2 @ A ) )
=> ( A
= ( some_a @ E ) ) ) ).
% option.set_cases
thf(fact_588_option_Oset__intros,axiom,
! [X22: produc5278197477302038359_a_c_d] : ( member1180172933830803072_a_c_d @ X22 @ ( set_op1238738513205398757_a_c_d @ ( some_P7564561949935391804_a_c_d @ X22 ) ) ) ).
% option.set_intros
thf(fact_589_option_Oset__intros,axiom,
! [X22: option_a] : ( member_option_a @ X22 @ ( set_option_option_a2 @ ( some_option_a @ X22 ) ) ) ).
% option.set_intros
thf(fact_590_option_Oset__intros,axiom,
! [X22: b] : ( member_b @ X22 @ ( set_option_b2 @ ( some_b @ X22 ) ) ) ).
% option.set_intros
thf(fact_591_option_Oset__intros,axiom,
! [X22: product_prod_a_c_d] : ( member8846983874477766826_a_c_d @ X22 @ ( set_op7017632568034097669_a_c_d @ ( some_P1084500821511757806_a_c_d @ X22 ) ) ) ).
% option.set_intros
thf(fact_592_option_Oset__intros,axiom,
! [X22: a] : ( member_a @ X22 @ ( set_option_a2 @ ( some_a @ X22 ) ) ) ).
% option.set_intros
thf(fact_593_ospec,axiom,
! [A3: option6413918287372586467_a_c_d,P2: product_prod_a_c_d > $o,X2: product_prod_a_c_d] :
( ! [X3: product_prod_a_c_d] :
( ( member8846983874477766826_a_c_d @ X3 @ ( set_op7017632568034097669_a_c_d @ A3 ) )
=> ( P2 @ X3 ) )
=> ( ( A3
= ( some_P1084500821511757806_a_c_d @ X2 ) )
=> ( P2 @ X2 ) ) ) ).
% ospec
thf(fact_594_ospec,axiom,
! [A3: option_a,P2: a > $o,X2: a] :
( ! [X3: a] :
( ( member_a @ X3 @ ( set_option_a2 @ A3 ) )
=> ( P2 @ X3 ) )
=> ( ( A3
= ( some_a @ X2 ) )
=> ( P2 @ X2 ) ) ) ).
% ospec
thf(fact_595_notin__range__Some,axiom,
! [X2: option6413918287372586467_a_c_d] :
( ( ~ ( member5926479794665358074_a_c_d @ X2 @ ( image_5741706613785127421_a_c_d @ some_P1084500821511757806_a_c_d @ top_to5543414004138509561_a_c_d ) ) )
= ( X2 = none_P2239999354720063602_a_c_d ) ) ).
% notin_range_Some
thf(fact_596_notin__range__Some,axiom,
! [X2: option_option_a] :
( ( ~ ( member5113800082084363315tion_a @ X2 @ ( image_2132136900116418507tion_a @ some_option_a @ top_top_set_option_a ) ) )
= ( X2 = none_option_a ) ) ).
% notin_range_Some
thf(fact_597_notin__range__Some,axiom,
! [X2: option_a] :
( ( ~ ( member_option_a @ X2 @ ( image_a_option_a @ some_a @ top_top_set_a ) ) )
= ( X2 = none_a ) ) ).
% notin_range_Some
thf(fact_598_ran__map__upd__Some,axiom,
! [M: a > option_a,X2: a,Y: a,Z: a] :
( ( ( M @ X2 )
= ( some_a @ Y ) )
=> ( ( inj_on_a_option_a @ M @ ( dom_a_a @ M ) )
=> ( ~ ( member_a @ Z @ ( ran_a_a @ M ) )
=> ( ( ran_a_a @ ( fun_upd_a_option_a @ M @ X2 @ ( some_a @ Z ) ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( ran_a_a @ M ) @ ( insert_a @ Y @ bot_bot_set_a ) ) @ ( insert_a @ Z @ bot_bot_set_a ) ) ) ) ) ) ).
% ran_map_upd_Some
thf(fact_599_dom__eq__singleton__conv,axiom,
! [F2: option_a > option_a,X2: option_a] :
( ( ( dom_option_a_a @ F2 )
= ( insert_option_a @ X2 @ bot_bot_set_option_a ) )
= ( ? [V: a] :
( F2
= ( fun_up1079276522633388797tion_a
@ ^ [X: option_a] : none_a
@ X2
@ ( some_a @ V ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_600_dom__eq__singleton__conv,axiom,
! [F2: option_a > option6413918287372586467_a_c_d,X2: option_a] :
( ( ( dom_op6156779764657312645_a_c_d @ F2 )
= ( insert_option_a @ X2 @ bot_bot_set_option_a ) )
= ( ? [V: product_prod_a_c_d] :
( F2
= ( fun_up5969202740897331946_a_c_d
@ ^ [X: option_a] : none_P2239999354720063602_a_c_d
@ X2
@ ( some_P1084500821511757806_a_c_d @ V ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_601_dom__eq__singleton__conv,axiom,
! [F2: a > option_a,X2: a] :
( ( ( dom_a_a @ F2 )
= ( insert_a @ X2 @ bot_bot_set_a ) )
= ( ? [V: a] :
( F2
= ( fun_upd_a_option_a
@ ^ [X: a] : none_a
@ X2
@ ( some_a @ V ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_602_dom__eq__singleton__conv,axiom,
! [F2: a > option6413918287372586467_a_c_d,X2: a] :
( ( ( dom_a_3529858286862933695_a_c_d @ F2 )
= ( insert_a @ X2 @ bot_bot_set_a ) )
= ( ? [V: product_prod_a_c_d] :
( F2
= ( fun_up6642239869823773348_a_c_d
@ ^ [X: a] : none_P2239999354720063602_a_c_d
@ X2
@ ( some_P1084500821511757806_a_c_d @ V ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_603_dom__const,axiom,
! [F2: a > a] :
( ( dom_a_a
@ ^ [X: a] : ( some_a @ ( F2 @ X ) ) )
= top_top_set_a ) ).
% dom_const
thf(fact_604_dom__const,axiom,
! [F2: a > product_prod_a_c_d] :
( ( dom_a_3529858286862933695_a_c_d
@ ^ [X: a] : ( some_P1084500821511757806_a_c_d @ ( F2 @ X ) ) )
= top_top_set_a ) ).
% dom_const
thf(fact_605_dom__const,axiom,
! [F2: option_a > a] :
( ( dom_option_a_a
@ ^ [X: option_a] : ( some_a @ ( F2 @ X ) ) )
= top_top_set_option_a ) ).
% dom_const
thf(fact_606_dom__const,axiom,
! [F2: option_a > product_prod_a_c_d] :
( ( dom_op6156779764657312645_a_c_d
@ ^ [X: option_a] : ( some_P1084500821511757806_a_c_d @ ( F2 @ X ) ) )
= top_top_set_option_a ) ).
% dom_const
thf(fact_607_inj__Some,axiom,
! [A3: set_Pr334309860168054345_a_c_d] : ( inj_on7837763817969280361_a_c_d @ some_P1084500821511757806_a_c_d @ A3 ) ).
% inj_Some
thf(fact_608_inj__Some,axiom,
! [A3: set_a] : ( inj_on_a_option_a @ some_a @ A3 ) ).
% inj_Some
thf(fact_609_case__optionE,axiom,
! [P2: $o,Q: product_prod_a_c_d > $o,X2: option6413918287372586467_a_c_d] :
( ( case_o6877627483922084448_a_c_d @ P2 @ Q @ X2 )
=> ( ( ( X2 = none_P2239999354720063602_a_c_d )
=> ~ P2 )
=> ~ ! [Y3: product_prod_a_c_d] :
( ( X2
= ( some_P1084500821511757806_a_c_d @ Y3 ) )
=> ~ ( Q @ Y3 ) ) ) ) ).
% case_optionE
thf(fact_610_case__optionE,axiom,
! [P2: $o,Q: a > $o,X2: option_a] :
( ( case_option_o_a @ P2 @ Q @ X2 )
=> ( ( ( X2 = none_a )
=> ~ P2 )
=> ~ ! [Y3: a] :
( ( X2
= ( some_a @ Y3 ) )
=> ~ ( Q @ Y3 ) ) ) ) ).
% case_optionE
thf(fact_611_map__add__def,axiom,
( map_add_a_a
= ( ^ [M12: a > option_a,M22: a > option_a,X: a] : ( case_o3148979394504432965on_a_a @ ( M12 @ X ) @ some_a @ ( M22 @ X ) ) ) ) ).
% map_add_def
thf(fact_612_inj__on__fun__updI,axiom,
! [F2: c > d,A3: set_c,Y: d,X2: c] :
( ( inj_on_c_d @ F2 @ A3 )
=> ( ~ ( member_d @ Y @ ( image_c_d @ F2 @ A3 ) )
=> ( inj_on_c_d @ ( fun_upd_c_d @ F2 @ X2 @ Y ) @ A3 ) ) ) ).
% inj_on_fun_updI
thf(fact_613_inj__on__fun__updI,axiom,
! [F2: a > option_a,A3: set_a,Y: option_a,X2: a] :
( ( inj_on_a_option_a @ F2 @ A3 )
=> ( ~ ( member_option_a @ Y @ ( image_a_option_a @ F2 @ A3 ) )
=> ( inj_on_a_option_a @ ( fun_upd_a_option_a @ F2 @ X2 @ Y ) @ A3 ) ) ) ).
% inj_on_fun_updI
thf(fact_614_Some__image__these__eq,axiom,
! [A3: set_op3383557829362473625_a_c_d] :
( ( image_5741706613785127421_a_c_d @ some_P1084500821511757806_a_c_d @ ( these_5134989223866396566_a_c_d @ A3 ) )
= ( collec8541501982283775800_a_c_d
@ ^ [X: option6413918287372586467_a_c_d] :
( ( member5926479794665358074_a_c_d @ X @ A3 )
& ( X != none_P2239999354720063602_a_c_d ) ) ) ) ).
% Some_image_these_eq
thf(fact_615_Some__image__these__eq,axiom,
! [A3: set_option_a] :
( ( image_a_option_a @ some_a @ ( these_a @ A3 ) )
= ( collect_option_a
@ ^ [X: option_a] :
( ( member_option_a @ X @ A3 )
& ( X != none_a ) ) ) ) ).
% Some_image_these_eq
thf(fact_616_UNIV__option__conv,axiom,
( top_to2846071696153141577_a_c_d
= ( insert6629875870486991891_a_c_d @ none_P2239999354720063602_a_c_d @ ( image_5741706613785127421_a_c_d @ some_P1084500821511757806_a_c_d @ top_to5543414004138509561_a_c_d ) ) ) ).
% UNIV_option_conv
thf(fact_617_UNIV__option__conv,axiom,
( top_to1659475022456381882tion_a
= ( insert605063979879581146tion_a @ none_option_a @ ( image_2132136900116418507tion_a @ some_option_a @ top_top_set_option_a ) ) ) ).
% UNIV_option_conv
thf(fact_618_UNIV__option__conv,axiom,
( top_top_set_option_a
= ( insert_option_a @ none_a @ ( image_a_option_a @ some_a @ top_top_set_a ) ) ) ).
% UNIV_option_conv
thf(fact_619_applies__eq_Osimps,axiom,
! [A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,S4: c > d] :
( ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A3 @ Delta3 @ S4 )
= ( collect_a
@ ^ [Uu: a] :
? [A4: a] :
( ( Uu = A4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ).
% applies_eq.simps
thf(fact_620_applies__eq_Oelims,axiom,
! [X2: 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 @ X2 @ Xa @ Xb )
= Y )
=> ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ plus @ mult @ valid @ Uu @ Xb @ Xa @ X2 ) ) ) ) ).
% applies_eq.elims
thf(fact_621_finite__Map__induct,axiom,
! [M: produc5278197477302038359_a_c_d > option_a,P2: ( produc5278197477302038359_a_c_d > option_a ) > $o] :
( ( finite5665696198532655488_a_c_d @ ( dom_Pr210953022859676729_c_d_a @ M ) )
=> ( ( P2
@ ^ [X: produc5278197477302038359_a_c_d] : none_a )
=> ( ! [K2: produc5278197477302038359_a_c_d,V2: a,M3: produc5278197477302038359_a_c_d > option_a] :
( ( finite5665696198532655488_a_c_d @ ( dom_Pr210953022859676729_c_d_a @ M3 ) )
=> ( ~ ( member1180172933830803072_a_c_d @ K2 @ ( dom_Pr210953022859676729_c_d_a @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_up7463025390225626410tion_a @ M3 @ K2 @ ( some_a @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_622_finite__Map__induct,axiom,
! [M: b > option_a,P2: ( b > option_a ) > $o] :
( ( finite_finite_b @ ( dom_b_a @ M ) )
=> ( ( P2
@ ^ [X: b] : none_a )
=> ( ! [K2: b,V2: a,M3: b > option_a] :
( ( finite_finite_b @ ( dom_b_a @ M3 ) )
=> ( ~ ( member_b @ K2 @ ( dom_b_a @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_upd_b_option_a @ M3 @ K2 @ ( some_a @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_623_finite__Map__induct,axiom,
! [M: option_a > option_a,P2: ( option_a > option_a ) > $o] :
( ( finite1674126218327898605tion_a @ ( dom_option_a_a @ M ) )
=> ( ( P2
@ ^ [X: option_a] : none_a )
=> ( ! [K2: option_a,V2: a,M3: option_a > option_a] :
( ( finite1674126218327898605tion_a @ ( dom_option_a_a @ M3 ) )
=> ( ~ ( member_option_a @ K2 @ ( dom_option_a_a @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_up1079276522633388797tion_a @ M3 @ K2 @ ( some_a @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_624_finite__Map__induct,axiom,
! [M: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d,P2: ( produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d ) > $o] :
( ( finite5665696198532655488_a_c_d @ ( dom_Pr2275460399045561368_a_c_d @ M ) )
=> ( ( P2
@ ^ [X: produc5278197477302038359_a_c_d] : none_P2239999354720063602_a_c_d )
=> ( ! [K2: produc5278197477302038359_a_c_d,V2: product_prod_a_c_d,M3: produc5278197477302038359_a_c_d > option6413918287372586467_a_c_d] :
( ( finite5665696198532655488_a_c_d @ ( dom_Pr2275460399045561368_a_c_d @ M3 ) )
=> ( ~ ( member1180172933830803072_a_c_d @ K2 @ ( dom_Pr2275460399045561368_a_c_d @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_up4007221454163596925_a_c_d @ M3 @ K2 @ ( some_P1084500821511757806_a_c_d @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_625_finite__Map__induct,axiom,
! [M: b > option6413918287372586467_a_c_d,P2: ( b > option6413918287372586467_a_c_d ) > $o] :
( ( finite_finite_b @ ( dom_b_1825636403396063168_a_c_d @ M ) )
=> ( ( P2
@ ^ [X: b] : none_P2239999354720063602_a_c_d )
=> ( ! [K2: b,V2: product_prod_a_c_d,M3: b > option6413918287372586467_a_c_d] :
( ( finite_finite_b @ ( dom_b_1825636403396063168_a_c_d @ M3 ) )
=> ( ~ ( member_b @ K2 @ ( dom_b_1825636403396063168_a_c_d @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_up6513502963972302373_a_c_d @ M3 @ K2 @ ( some_P1084500821511757806_a_c_d @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_626_finite__Map__induct,axiom,
! [M: a > option6413918287372586467_a_c_d,P2: ( a > option6413918287372586467_a_c_d ) > $o] :
( ( finite_finite_a @ ( dom_a_3529858286862933695_a_c_d @ M ) )
=> ( ( P2
@ ^ [X: a] : none_P2239999354720063602_a_c_d )
=> ( ! [K2: a,V2: product_prod_a_c_d,M3: a > option6413918287372586467_a_c_d] :
( ( finite_finite_a @ ( dom_a_3529858286862933695_a_c_d @ M3 ) )
=> ( ~ ( member_a @ K2 @ ( dom_a_3529858286862933695_a_c_d @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_up6642239869823773348_a_c_d @ M3 @ K2 @ ( some_P1084500821511757806_a_c_d @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_627_finite__Map__induct,axiom,
! [M: option_a > option6413918287372586467_a_c_d,P2: ( option_a > option6413918287372586467_a_c_d ) > $o] :
( ( finite1674126218327898605tion_a @ ( dom_op6156779764657312645_a_c_d @ M ) )
=> ( ( P2
@ ^ [X: option_a] : none_P2239999354720063602_a_c_d )
=> ( ! [K2: option_a,V2: product_prod_a_c_d,M3: option_a > option6413918287372586467_a_c_d] :
( ( finite1674126218327898605tion_a @ ( dom_op6156779764657312645_a_c_d @ M3 ) )
=> ( ~ ( member_option_a @ K2 @ ( dom_op6156779764657312645_a_c_d @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_up5969202740897331946_a_c_d @ M3 @ K2 @ ( some_P1084500821511757806_a_c_d @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_628_finite__Map__induct,axiom,
! [M: a > option_a,P2: ( a > option_a ) > $o] :
( ( finite_finite_a @ ( dom_a_a @ M ) )
=> ( ( P2
@ ^ [X: a] : none_a )
=> ( ! [K2: a,V2: a,M3: a > option_a] :
( ( finite_finite_a @ ( dom_a_a @ M3 ) )
=> ( ~ ( member_a @ K2 @ ( dom_a_a @ M3 ) )
=> ( ( P2 @ M3 )
=> ( P2 @ ( fun_upd_a_option_a @ M3 @ K2 @ ( some_a @ V2 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_629_modified__def,axiom,
( modified_a_c_d
= ( ^ [C2: set_Pr1275464188344874039_a_c_d] :
( collect_c
@ ^ [Uu: c] :
? [X: c] :
( ( Uu = X )
& ? [Sigma: a,S: c > d,Sigma2: a,S2: c > d] :
( ( 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 @ Sigma2 @ S2 ) ) ) @ C2 )
& ( ( S @ X )
!= ( S2 @ X ) ) ) ) ) ) ) ).
% modified_def
thf(fact_630_finite__range__Some,axiom,
( ( finite3027439597799462906_a_c_d @ ( image_5741706613785127421_a_c_d @ some_P1084500821511757806_a_c_d @ top_to5543414004138509561_a_c_d ) )
= ( finite6487500827408305578_a_c_d @ top_to5543414004138509561_a_c_d ) ) ).
% finite_range_Some
thf(fact_631_finite__range__Some,axiom,
( ( finite8114217219359860531tion_a @ ( image_2132136900116418507tion_a @ some_option_a @ top_top_set_option_a ) )
= ( finite1674126218327898605tion_a @ top_top_set_option_a ) ) ).
% finite_range_Some
thf(fact_632_finite__range__Some,axiom,
( ( finite1674126218327898605tion_a @ ( image_a_option_a @ some_a @ top_top_set_a ) )
= ( finite_finite_a @ top_top_set_a ) ) ).
% finite_range_Some
thf(fact_633_logic_Omodified__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,C: set_Pr1275464188344874039_a_c_d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( modified_a_c_d @ C )
= ( collect_c
@ ^ [Uu: c] :
? [X: c] :
( ( Uu = X )
& ? [Sigma: a,S: c > d,Sigma2: a,S2: c > d] :
( ( 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 @ Sigma2 @ S2 ) ) ) @ C )
& ( ( S @ X )
!= ( S2 @ X ) ) ) ) ) ) ) ).
% logic.modified_def
thf(fact_634_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,A3: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,S4: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A3 @ Delta3 @ S4 )
= ( collect_a
@ ^ [Uu: a] :
? [A4: a] :
( ( Uu = A4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S4 @ Delta3 @ A3 ) ) ) ) ) ).
% logic.applies_eq.simps
thf(fact_635_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,X2: 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 @ X2 @ Xa @ Xb )
= Y )
=> ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Uu @ Xb @ Xa @ X2 ) ) ) ) ) ).
% logic.applies_eq.elims
thf(fact_636_graph__def,axiom,
( graph_7244981646656495094_a_c_d
= ( ^ [M4: product_prod_a_c_d > option6212624336325788467_a_c_d] :
( collec245936426562692802_a_c_d
@ ^ [Uu: produc5278197477302038359_a_c_d] :
? [A4: product_prod_a_c_d,B4: option6413918287372586467_a_c_d] :
( ( Uu
= ( produc8093790510458973071_a_c_d @ A4 @ B4 ) )
& ( ( M4 @ A4 )
= ( some_o8886552288663794750_a_c_d @ B4 ) ) ) ) ) ) ).
% graph_def
thf(fact_637_graph__def,axiom,
( graph_a_c_d
= ( ^ [M4: a > option_c_d] :
( collec793421012733635048_a_c_d
@ ^ [Uu: product_prod_a_c_d] :
? [A4: a,B4: c > d] :
( ( Uu
= ( product_Pair_a_c_d @ A4 @ B4 ) )
& ( ( M4 @ A4 )
= ( some_c_d @ B4 ) ) ) ) ) ) ).
% graph_def
thf(fact_638_graph__def,axiom,
( graph_7603009230766167293_a_c_d
= ( ^ [M4: assertion_a_b_d_c > option3890169911263941780_a_c_d] :
( collec4762846013371775487_a_c_d
@ ^ [Uu: produc5105196854009589546_a_c_d] :
? [A4: assertion_a_b_d_c,B4: produc5213381314664832452_a_c_d] :
( ( Uu
= ( produc8894421531525210148_a_c_d @ A4 @ B4 ) )
& ( ( M4 @ A4 )
= ( some_P3194730542479778335_a_c_d @ B4 ) ) ) ) ) ) ).
% graph_def
thf(fact_639_graph__def,axiom,
( graph_c_d_set_a_c_d
= ( ^ [M4: ( ( c > d ) > set_a ) > option_c_d] :
( collec2771355035510247705_a_c_d
@ ^ [Uu: produc5213381314664832452_a_c_d] :
? [A4: ( c > d ) > set_a,B4: c > d] :
( ( Uu
= ( produc7376592049607813182_a_c_d @ A4 @ B4 ) )
& ( ( M4 @ A4 )
= ( some_c_d @ B4 ) ) ) ) ) ) ).
% graph_def
thf(fact_640_finite__range__updI,axiom,
! [F2: a > option_a,A: a,B: a] :
( ( finite1674126218327898605tion_a @ ( image_a_option_a @ F2 @ top_top_set_a ) )
=> ( finite1674126218327898605tion_a @ ( image_a_option_a @ ( fun_upd_a_option_a @ F2 @ A @ ( some_a @ B ) ) @ top_top_set_a ) ) ) ).
% finite_range_updI
thf(fact_641_finite__range__updI,axiom,
! [F2: a > option6413918287372586467_a_c_d,A: a,B: product_prod_a_c_d] :
( ( finite3027439597799462906_a_c_d @ ( image_3786525410991915292_a_c_d @ F2 @ top_top_set_a ) )
=> ( finite3027439597799462906_a_c_d @ ( image_3786525410991915292_a_c_d @ ( fun_up6642239869823773348_a_c_d @ F2 @ A @ ( some_P1084500821511757806_a_c_d @ B ) ) @ top_top_set_a ) ) ) ).
% finite_range_updI
thf(fact_642_finite__range__updI,axiom,
! [F2: option_a > option_a,A: option_a,B: a] :
( ( finite1674126218327898605tion_a @ ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a ) )
=> ( finite1674126218327898605tion_a @ ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F2 @ A @ ( some_a @ B ) ) @ top_top_set_option_a ) ) ) ).
% finite_range_updI
thf(fact_643_finite__range__updI,axiom,
! [F2: option_a > option6413918287372586467_a_c_d,A: option_a,B: product_prod_a_c_d] :
( ( finite3027439597799462906_a_c_d @ ( image_3697009332183072098_a_c_d @ F2 @ top_top_set_option_a ) )
=> ( finite3027439597799462906_a_c_d @ ( image_3697009332183072098_a_c_d @ ( fun_up5969202740897331946_a_c_d @ F2 @ A @ ( some_P1084500821511757806_a_c_d @ B ) ) @ top_top_set_option_a ) ) ) ).
% finite_range_updI
thf(fact_644_applies__eq_Opelims,axiom,
! [X2: 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 @ X2 @ Xa @ Xb )
= Y )
=> ( ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X2 @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) )
=> ~ ( ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ plus @ mult @ valid @ Uu @ Xb @ Xa @ X2 ) ) )
=> ~ ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X2 @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) ) ) ) ) ).
% applies_eq.pelims
thf(fact_645_finite__update__induct,axiom,
! [F2: c > d,C: d,P2: ( c > d ) > $o] :
( ( finite_finite_c
@ ( collect_c
@ ^ [A4: c] :
( ( F2 @ A4 )
!= C ) ) )
=> ( ( P2
@ ^ [A4: c] : C )
=> ( ! [A5: c,B6: d,F3: c > d] :
( ( finite_finite_c
@ ( collect_c
@ ^ [C2: c] :
( ( F3 @ C2 )
!= C ) ) )
=> ( ( ( F3 @ A5 )
= C )
=> ( ( B6 != C )
=> ( ( P2 @ F3 )
=> ( P2 @ ( fun_upd_c_d @ F3 @ A5 @ B6 ) ) ) ) ) )
=> ( P2 @ F2 ) ) ) ) ).
% finite_update_induct
thf(fact_646_finite__update__induct,axiom,
! [F2: a > option_a,C: option_a,P2: ( a > option_a ) > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [A4: a] :
( ( F2 @ A4 )
!= C ) ) )
=> ( ( P2
@ ^ [A4: a] : C )
=> ( ! [A5: a,B6: option_a,F3: a > option_a] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C2: a] :
( ( F3 @ C2 )
!= C ) ) )
=> ( ( ( F3 @ A5 )
= C )
=> ( ( B6 != C )
=> ( ( P2 @ F3 )
=> ( P2 @ ( fun_upd_a_option_a @ F3 @ A5 @ B6 ) ) ) ) ) )
=> ( P2 @ F2 ) ) ) ) ).
% finite_update_induct
thf(fact_647_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,X2: 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 @ X2 @ Xa @ Xb )
= Y )
=> ( ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X2 @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) )
=> ~ ( ( Y
= ( collect_a
@ ^ [Uu: a] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Uu @ Xb @ Xa @ X2 ) ) )
=> ~ ( accp_P5381461700908302305_a_c_d @ applie8886407701077375079_b_d_c @ ( produc8894421531525210148_a_c_d @ X2 @ ( produc7376592049607813182_a_c_d @ Xa @ Xb ) ) ) ) ) ) ) ).
% logic.applies_eq.pelims
thf(fact_648_combine__options__def,axiom,
( combin3634409207779412564_a_c_d
= ( ^ [F: product_prod_a_c_d > product_prod_a_c_d > product_prod_a_c_d,X: option6413918287372586467_a_c_d,Y2: option6413918287372586467_a_c_d] :
( case_o2693460655523628675_a_c_d @ Y2
@ ^ [Z2: product_prod_a_c_d] :
( case_o2693460655523628675_a_c_d @ ( some_P1084500821511757806_a_c_d @ Z2 )
@ ^ [Aa: product_prod_a_c_d] : ( some_P1084500821511757806_a_c_d @ ( F @ Z2 @ Aa ) )
@ Y2 )
@ X ) ) ) ).
% combine_options_def
thf(fact_649_combine__options__def,axiom,
( combine_options_a
= ( ^ [F: a > a > a,X: option_a,Y2: option_a] :
( case_o3148979394504432965on_a_a @ Y2
@ ^ [Z2: a] :
( case_o3148979394504432965on_a_a @ ( some_a @ Z2 )
@ ^ [Aa: a] : ( some_a @ ( F @ Z2 @ Aa ) )
@ Y2 )
@ X ) ) ) ).
% combine_options_def
thf(fact_650_applies__eq_Ocases,axiom,
! [X2: produc5105196854009589546_a_c_d] :
~ ! [A8: assertion_a_b_d_c,Delta5: ( c > d ) > set_a,S6: c > d] :
( X2
!= ( produc8894421531525210148_a_c_d @ A8 @ ( produc7376592049607813182_a_c_d @ Delta5 @ S6 ) ) ) ).
% applies_eq.cases
thf(fact_651_combine__options__simps_I3_J,axiom,
! [F2: product_prod_a_c_d > product_prod_a_c_d > product_prod_a_c_d,A: product_prod_a_c_d,B: product_prod_a_c_d] :
( ( combin3634409207779412564_a_c_d @ F2 @ ( some_P1084500821511757806_a_c_d @ A ) @ ( some_P1084500821511757806_a_c_d @ B ) )
= ( some_P1084500821511757806_a_c_d @ ( F2 @ A @ B ) ) ) ).
% combine_options_simps(3)
thf(fact_652_combine__options__simps_I3_J,axiom,
! [F2: a > a > a,A: a,B: a] :
( ( combine_options_a @ F2 @ ( some_a @ A ) @ ( some_a @ B ) )
= ( some_a @ ( F2 @ A @ B ) ) ) ).
% combine_options_simps(3)
thf(fact_653_map__option__case,axiom,
( map_option_a_a
= ( ^ [F: a > a] :
( case_o3148979394504432965on_a_a @ none_a
@ ^ [X: a] : ( some_a @ ( F @ X ) ) ) ) ) ).
% map_option_case
thf(fact_654_assertion_Osimps_I325_J,axiom,
! [X212: b,X223: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( mult_b_a_d_c @ X212 @ X223 ) )
= ( insert_b @ X212 @ ( set_as7232682317586342732_b_d_c @ X223 ) ) ) ).
% assertion.simps(325)
thf(fact_655_Sup__fin_Oeq__fold_H,axiom,
( lattic2918178361130032022_set_b
= ( ^ [A9: set_set_b] :
( the_set_b
@ ( finite4684332809091328718_set_b
@ ^ [X: set_b,Y2: option_set_b] : ( some_set_b @ ( case_o6570817238820213323_set_b @ X @ ( sup_sup_set_b @ X ) @ Y2 ) )
@ none_set_b
@ A9 ) ) ) ) ).
% Sup_fin.eq_fold'
thf(fact_656_is__none__code_I2_J,axiom,
! [X2: product_prod_a_c_d] :
~ ( is_non1375147668126617655_a_c_d @ ( some_P1084500821511757806_a_c_d @ X2 ) ) ).
% is_none_code(2)
thf(fact_657_is__none__code_I2_J,axiom,
! [X2: a] :
~ ( is_none_a @ ( some_a @ X2 ) ) ).
% is_none_code(2)
thf(fact_658_map__option__eq__Some,axiom,
! [F2: product_prod_a_c_d > a,Xo: option6413918287372586467_a_c_d,Y: a] :
( ( ( map_op5913999614919751774_c_d_a @ F2 @ Xo )
= ( some_a @ Y ) )
= ( ? [Z2: product_prod_a_c_d] :
( ( Xo
= ( some_P1084500821511757806_a_c_d @ Z2 ) )
& ( ( F2 @ Z2 )
= Y ) ) ) ) ).
% map_option_eq_Some
thf(fact_659_map__option__eq__Some,axiom,
! [F2: a > product_prod_a_c_d,Xo: option_a,Y: product_prod_a_c_d] :
( ( ( map_op7600559726947941830_a_c_d @ F2 @ Xo )
= ( some_P1084500821511757806_a_c_d @ Y ) )
= ( ? [Z2: a] :
( ( Xo
= ( some_a @ Z2 ) )
& ( ( F2 @ Z2 )
= Y ) ) ) ) ).
% map_option_eq_Some
thf(fact_660_map__option__eq__Some,axiom,
! [F2: product_prod_a_c_d > product_prod_a_c_d,Xo: option6413918287372586467_a_c_d,Y: product_prod_a_c_d] :
( ( ( map_op989909284770252723_a_c_d @ F2 @ Xo )
= ( some_P1084500821511757806_a_c_d @ Y ) )
= ( ? [Z2: product_prod_a_c_d] :
( ( Xo
= ( some_P1084500821511757806_a_c_d @ Z2 ) )
& ( ( F2 @ Z2 )
= Y ) ) ) ) ).
% map_option_eq_Some
thf(fact_661_map__option__eq__Some,axiom,
! [F2: a > a,Xo: option_a,Y: a] :
( ( ( map_option_a_a @ F2 @ Xo )
= ( some_a @ Y ) )
= ( ? [Z2: a] :
( ( Xo
= ( some_a @ Z2 ) )
& ( ( F2 @ Z2 )
= Y ) ) ) ) ).
% map_option_eq_Some
thf(fact_662_assertion_Oset__intros_I2_J,axiom,
! [Yb: b,X223: assertion_a_b_d_c,X212: b] :
( ( member_b @ Yb @ ( set_as7232682317586342732_b_d_c @ X223 ) )
=> ( member_b @ Yb @ ( set_as7232682317586342732_b_d_c @ ( mult_b_a_d_c @ X212 @ X223 ) ) ) ) ).
% assertion.set_intros(2)
thf(fact_663_assertion_Oset__intros_I1_J,axiom,
! [X212: b,X223: assertion_a_b_d_c] : ( member_b @ X212 @ ( set_as7232682317586342732_b_d_c @ ( mult_b_a_d_c @ X212 @ X223 ) ) ) ).
% assertion.set_intros(1)
thf(fact_664_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_665_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_666_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_667_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_668_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_669_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_670_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_671_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_672_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_673_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_674_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_675_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_676_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_677_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_678_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_679_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_680_assertion_Osimps_I335_J,axiom,
! [X123: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( wildcard_a_b_d_c @ X123 ) )
= ( set_as7232682317586342732_b_d_c @ X123 ) ) ).
% assertion.simps(335)
thf(fact_681_assertion_Oset__intros_I16_J,axiom,
! [Yp: b,X123: assertion_a_b_d_c] :
( ( member_b @ Yp @ ( set_as7232682317586342732_b_d_c @ X123 ) )
=> ( member_b @ Yp @ ( set_as7232682317586342732_b_d_c @ ( wildcard_a_b_d_c @ X123 ) ) ) ) ).
% assertion.set_intros(16)
thf(fact_682_option_Osimps_I9_J,axiom,
! [F2: a > product_prod_a_c_d,X22: a] :
( ( map_op7600559726947941830_a_c_d @ F2 @ ( some_a @ X22 ) )
= ( some_P1084500821511757806_a_c_d @ ( F2 @ X22 ) ) ) ).
% option.simps(9)
thf(fact_683_option_Osimps_I9_J,axiom,
! [F2: product_prod_a_c_d > a,X22: product_prod_a_c_d] :
( ( map_op5913999614919751774_c_d_a @ F2 @ ( some_P1084500821511757806_a_c_d @ X22 ) )
= ( some_a @ ( F2 @ X22 ) ) ) ).
% option.simps(9)
thf(fact_684_option_Osimps_I9_J,axiom,
! [F2: product_prod_a_c_d > product_prod_a_c_d,X22: product_prod_a_c_d] :
( ( map_op989909284770252723_a_c_d @ F2 @ ( some_P1084500821511757806_a_c_d @ X22 ) )
= ( some_P1084500821511757806_a_c_d @ ( F2 @ X22 ) ) ) ).
% option.simps(9)
thf(fact_685_option_Osimps_I9_J,axiom,
! [F2: a > a,X22: a] :
( ( map_option_a_a @ F2 @ ( some_a @ X22 ) )
= ( some_a @ ( F2 @ X22 ) ) ) ).
% option.simps(9)
thf(fact_686_map__option__cong,axiom,
! [X2: option_a,Y: option_a,F2: a > a,G: a > a] :
( ( X2 = Y )
=> ( ! [A5: a] :
( ( Y
= ( some_a @ A5 ) )
=> ( ( F2 @ A5 )
= ( G @ A5 ) ) )
=> ( ( map_option_a_a @ F2 @ X2 )
= ( map_option_a_a @ G @ Y ) ) ) ) ).
% map_option_cong
thf(fact_687_is__none__simps_I2_J,axiom,
! [X2: product_prod_a_c_d] :
~ ( is_non1375147668126617655_a_c_d @ ( some_P1084500821511757806_a_c_d @ X2 ) ) ).
% is_none_simps(2)
thf(fact_688_is__none__simps_I2_J,axiom,
! [X2: a] :
~ ( is_none_a @ ( some_a @ X2 ) ) ).
% is_none_simps(2)
thf(fact_689_assertion_Osimps_I324_J,axiom,
! [X1: ( c > d ) > a > $o] :
( ( set_as7232682317586342732_b_d_c @ ( sem_c_d_a_b @ X1 ) )
= bot_bot_set_b ) ).
% assertion.simps(324)
thf(fact_690_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_691_assertion_Osimps_I333_J,axiom,
( ( set_as7232682317586342732_b_d_c @ pred_a_b_d_c )
= bot_bot_set_b ) ).
% assertion.simps(333)
thf(fact_692_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_693_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_694_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_695_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_696_map__option__o__map__upd,axiom,
! [F2: a > product_prod_a_c_d,M: a > option_a,A: a,B: a] :
( ( comp_o5508582540435784312_c_d_a @ ( map_op7600559726947941830_a_c_d @ F2 ) @ ( fun_upd_a_option_a @ M @ A @ ( some_a @ B ) ) )
= ( fun_up6642239869823773348_a_c_d @ ( comp_o5508582540435784312_c_d_a @ ( map_op7600559726947941830_a_c_d @ F2 ) @ M ) @ A @ ( some_P1084500821511757806_a_c_d @ ( F2 @ B ) ) ) ) ).
% map_option_o_map_upd
thf(fact_697_map__option__o__map__upd,axiom,
! [F2: product_prod_a_c_d > a,M: a > option6413918287372586467_a_c_d,A: a,B: product_prod_a_c_d] :
( ( comp_o5927112796044265472on_a_a @ ( map_op5913999614919751774_c_d_a @ F2 ) @ ( fun_up6642239869823773348_a_c_d @ M @ A @ ( some_P1084500821511757806_a_c_d @ B ) ) )
= ( fun_upd_a_option_a @ ( comp_o5927112796044265472on_a_a @ ( map_op5913999614919751774_c_d_a @ F2 ) @ M ) @ A @ ( some_a @ ( F2 @ B ) ) ) ) ).
% map_option_o_map_upd
thf(fact_698_map__option__o__map__upd,axiom,
! [F2: a > a,M: a > option_a,A: a,B: a] :
( ( comp_o6087033147929006299on_a_a @ ( map_option_a_a @ F2 ) @ ( fun_upd_a_option_a @ M @ A @ ( some_a @ B ) ) )
= ( fun_upd_a_option_a @ ( comp_o6087033147929006299on_a_a @ ( map_option_a_a @ F2 ) @ M ) @ A @ ( some_a @ ( F2 @ B ) ) ) ) ).
% map_option_o_map_upd
thf(fact_699_semilattice__set_Oeq__fold_H,axiom,
! [F2: product_prod_a_c_d > product_prod_a_c_d > product_prod_a_c_d,A3: set_Pr334309860168054345_a_c_d] :
( ( lattic4068221337090480901_a_c_d @ F2 )
=> ( ( lattic8819272484393134521_a_c_d @ F2 @ A3 )
= ( the_Pr7316212213771180927_a_c_d
@ ( finite125887116680883648_a_c_d
@ ^ [X: product_prod_a_c_d,Y2: option6413918287372586467_a_c_d] : ( some_P1084500821511757806_a_c_d @ ( case_o2371922091259498419_a_c_d @ X @ ( F2 @ X ) @ Y2 ) )
@ none_P2239999354720063602_a_c_d
@ A3 ) ) ) ) ).
% semilattice_set.eq_fold'
thf(fact_700_semilattice__set_Oeq__fold_H,axiom,
! [F2: a > a > a,A3: set_a] :
( ( lattic5961991414251573132_set_a @ F2 )
=> ( ( lattic5116578512385870296ce_F_a @ F2 @ A3 )
= ( the_a
@ ( finite6501707464432451470tion_a
@ ^ [X: a,Y2: option_a] : ( some_a @ ( case_option_a_a @ X @ ( F2 @ X ) @ Y2 ) )
@ none_a
@ A3 ) ) ) ) ).
% semilattice_set.eq_fold'
thf(fact_701_map__conv__bind__option,axiom,
( map_option_a_a
= ( ^ [F: a > a,X: option_a] : ( bind_a_a @ X @ ( comp_a_option_a_a @ some_a @ F ) ) ) ) ).
% map_conv_bind_option
thf(fact_702_fun__upd__comp,axiom,
! [F2: d > d,G: c > d,X2: c,Y: d] :
( ( comp_d_d_c @ F2 @ ( fun_upd_c_d @ G @ X2 @ Y ) )
= ( fun_upd_c_d @ ( comp_d_d_c @ F2 @ G ) @ X2 @ ( F2 @ Y ) ) ) ).
% fun_upd_comp
thf(fact_703_fun__upd__comp,axiom,
! [F2: option_a > a,G: a > option_a,X2: a,Y: option_a] :
( ( comp_option_a_a_a @ F2 @ ( fun_upd_a_option_a @ G @ X2 @ Y ) )
= ( fun_upd_a_a @ ( comp_option_a_a_a @ F2 @ G ) @ X2 @ ( F2 @ Y ) ) ) ).
% fun_upd_comp
thf(fact_704_fun__upd__comp,axiom,
! [F2: option_a > option_a,G: a > option_a,X2: a,Y: option_a] :
( ( comp_o6087033147929006299on_a_a @ F2 @ ( fun_upd_a_option_a @ G @ X2 @ Y ) )
= ( fun_upd_a_option_a @ ( comp_o6087033147929006299on_a_a @ F2 @ G ) @ X2 @ ( F2 @ Y ) ) ) ).
% fun_upd_comp
thf(fact_705_comp__the__Some,axiom,
( ( comp_o6230065071311576686_a_c_d @ the_Pr7316212213771180927_a_c_d @ some_P1084500821511757806_a_c_d )
= id_Pro4866527663230331490_a_c_d ) ).
% comp_the_Some
thf(fact_706_comp__the__Some,axiom,
( ( comp_option_a_a_a @ the_a @ some_a )
= id_a ) ).
% comp_the_Some
thf(fact_707_assertion_Orel__distinct_I18_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(18)
thf(fact_708_assertion_Orel__inject_I2_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( mult_b_a_d_c @ Y21 @ Y22 ) )
= ( ( R3 @ X212 @ Y21 )
& ( rel_as1860989020795611527_a_d_c @ R3 @ X223 @ Y22 ) ) ) ).
% assertion.rel_inject(2)
thf(fact_709_assertion_Orel__intros_I2_J,axiom,
! [R3: b > b > $o,X212: b,Y21: b,X223: assertion_a_b_d_c,Y22: assertion_a_b_d_c] :
( ( R3 @ X212 @ Y21 )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X223 @ Y22 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X223 ) @ ( mult_b_a_d_c @ Y21 @ Y22 ) ) ) ) ).
% assertion.rel_intros(2)
thf(fact_710_assertion_Orel__inject_I12_J,axiom,
! [R3: b > b > $o,X123: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ X123 ) @ ( wildcard_a_b_d_c @ Y12 ) )
= ( rel_as1860989020795611527_a_d_c @ R3 @ X123 @ Y12 ) ) ).
% assertion.rel_inject(12)
thf(fact_711_assertion_Orel__intros_I12_J,axiom,
! [R3: b > b > $o,X123: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X123 @ Y12 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ X123 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ) ).
% assertion.rel_intros(12)
thf(fact_712_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_713_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_714_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_715_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_716_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_717_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_718_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_719_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_720_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_721_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_722_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_723_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_724_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_725_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_726_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_727_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_728_assertion_Orel__inject_I1_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o,Y1: ( c > d ) > a > $o] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( sem_c_d_a_b @ Y1 ) )
= ( X1 = Y1 ) ) ).
% assertion.rel_inject(1)
thf(fact_729_assertion_Orel__intros_I1_J,axiom,
! [X1: ( c > d ) > a > $o,Y1: ( c > d ) > a > $o,R3: b > b > $o] :
( ( X1 = Y1 )
=> ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( sem_c_d_a_b @ Y1 ) ) ) ).
% assertion.rel_intros(1)
thf(fact_730_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_731_assertion_Orel__eq,axiom,
( ( rel_as1860989020795611527_a_d_c
@ ^ [Y4: b,Z3: b] : ( Y4 = Z3 ) )
= ( ^ [Y4: assertion_a_b_d_c,Z3: assertion_a_b_d_c] : ( Y4 = Z3 ) ) ) ).
% assertion.rel_eq
thf(fact_732_assertion_Orel__refl,axiom,
! [Ra: b > b > $o,X2: assertion_a_b_d_c] :
( ! [X3: b] : ( Ra @ X3 @ X3 )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X2 @ X2 ) ) ).
% assertion.rel_refl
thf(fact_733_assertion_Orel__refl__strong,axiom,
! [X2: assertion_a_b_d_c,Ra: b > b > $o] :
( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( Ra @ Z4 @ Z4 ) )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X2 @ X2 ) ) ).
% assertion.rel_refl_strong
thf(fact_734_assertion_Orel__mono__strong,axiom,
! [R3: a > b > $o,X2: assertion_a_a_d_c,Y: assertion_a_b_d_c,Ra: a > b > $o] :
( ( rel_as1194089545255703174_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: a,Yb2: b] :
( ( member_a @ Z4 @ ( set_as1636463702398212043_a_d_c @ X2 ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as1194089545255703174_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_735_assertion_Orel__mono__strong,axiom,
! [R3: produc5278197477302038359_a_c_d > b > $o,X2: assert7138933933671473679_d_d_c,Y: assertion_a_b_d_c,Ra: produc5278197477302038359_a_c_d > b > $o] :
( ( rel_as4509594154181250527_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: produc5278197477302038359_a_c_d,Yb2: b] :
( ( member1180172933830803072_a_c_d @ Z4 @ ( set_as6006471827460666276_d_d_c @ X2 ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as4509594154181250527_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_736_assertion_Orel__mono__strong,axiom,
! [R3: option_a > b > $o,X2: assert3107445333071088380_a_d_c,Y: assertion_a_b_d_c,Ra: option_a > b > $o] :
( ( rel_as5306512150936529868_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: option_a,Yb2: b] :
( ( member_option_a @ Z4 @ ( set_as971186299496371729_a_d_c @ X2 ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as5306512150936529868_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_737_assertion_Orel__mono__strong,axiom,
! [R3: b > a > $o,X2: assertion_a_b_d_c,Y: assertion_a_a_d_c,Ra: b > a > $o] :
( ( rel_as373026983500813000_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: b,Yb2: a] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( member_a @ Yb2 @ ( set_as1636463702398212043_a_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as373026983500813000_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_738_assertion_Orel__mono__strong,axiom,
! [R3: b > produc5278197477302038359_a_c_d > $o,X2: assertion_a_b_d_c,Y: assert7138933933671473679_d_d_c,Ra: b > produc5278197477302038359_a_c_d > $o] :
( ( rel_as8965792146747367215_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: b,Yb2: produc5278197477302038359_a_c_d] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( member1180172933830803072_a_c_d @ Yb2 @ ( set_as6006471827460666276_d_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as8965792146747367215_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_739_assertion_Orel__mono__strong,axiom,
! [R3: b > option_a > $o,X2: assertion_a_b_d_c,Y: assert3107445333071088380_a_d_c,Ra: b > option_a > $o] :
( ( rel_as3901196536028962306_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: b,Yb2: option_a] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( member_option_a @ Yb2 @ ( set_as971186299496371729_a_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as3901196536028962306_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_740_assertion_Orel__mono__strong,axiom,
! [R3: b > b > $o,X2: assertion_a_b_d_c,Y: assertion_a_b_d_c,Ra: b > b > $o] :
( ( rel_as1860989020795611527_a_d_c @ R3 @ X2 @ Y )
=> ( ! [Z4: b,Yb2: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Y ) )
=> ( ( R3 @ Z4 @ Yb2 )
=> ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X2 @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_741_assertion_Orel__cong,axiom,
! [X2: 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] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: a,Yb2: b] :
( ( member_a @ Z4 @ ( set_as1636463702398212043_a_d_c @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as1194089545255703174_a_d_c @ R3 @ X2 @ Y )
= ( rel_as1194089545255703174_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_742_assertion_Orel__cong,axiom,
! [X2: assert7138933933671473679_d_d_c,Ya: assert7138933933671473679_d_d_c,Y: assertion_a_b_d_c,Xa: assertion_a_b_d_c,R3: produc5278197477302038359_a_c_d > b > $o,Ra: produc5278197477302038359_a_c_d > b > $o] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: produc5278197477302038359_a_c_d,Yb2: b] :
( ( member1180172933830803072_a_c_d @ Z4 @ ( set_as6006471827460666276_d_d_c @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as4509594154181250527_a_d_c @ R3 @ X2 @ Y )
= ( rel_as4509594154181250527_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_743_assertion_Orel__cong,axiom,
! [X2: assert3107445333071088380_a_d_c,Ya: assert3107445333071088380_a_d_c,Y: assertion_a_b_d_c,Xa: assertion_a_b_d_c,R3: option_a > b > $o,Ra: option_a > b > $o] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: option_a,Yb2: b] :
( ( member_option_a @ Z4 @ ( set_as971186299496371729_a_d_c @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as5306512150936529868_a_d_c @ R3 @ X2 @ Y )
= ( rel_as5306512150936529868_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_744_assertion_Orel__cong,axiom,
! [X2: 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] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: b,Yb2: a] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( member_a @ Yb2 @ ( set_as1636463702398212043_a_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as373026983500813000_a_d_c @ R3 @ X2 @ Y )
= ( rel_as373026983500813000_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_745_assertion_Orel__cong,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,Y: assert7138933933671473679_d_d_c,Xa: assert7138933933671473679_d_d_c,R3: b > produc5278197477302038359_a_c_d > $o,Ra: b > produc5278197477302038359_a_c_d > $o] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: b,Yb2: produc5278197477302038359_a_c_d] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( member1180172933830803072_a_c_d @ Yb2 @ ( set_as6006471827460666276_d_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as8965792146747367215_a_d_c @ R3 @ X2 @ Y )
= ( rel_as8965792146747367215_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_746_assertion_Orel__cong,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,Y: assert3107445333071088380_a_d_c,Xa: assert3107445333071088380_a_d_c,R3: b > option_a > $o,Ra: b > option_a > $o] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: b,Yb2: option_a] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( member_option_a @ Yb2 @ ( set_as971186299496371729_a_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as3901196536028962306_a_d_c @ R3 @ X2 @ Y )
= ( rel_as3901196536028962306_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_747_assertion_Orel__cong,axiom,
! [X2: 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] :
( ( X2 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z4: b,Yb2: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( R3 @ Z4 @ Yb2 )
= ( Ra @ Z4 @ Yb2 ) ) ) )
=> ( ( rel_as1860989020795611527_a_d_c @ R3 @ X2 @ Y )
= ( rel_as1860989020795611527_a_d_c @ Ra @ Ya @ Xa ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_748_assertion_Orel__distinct_I42_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(42)
thf(fact_749_assertion_Orel__distinct_I41_J,axiom,
! [R3: b > b > $o,X212: b,X223: assertion_a_b_d_c,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X223 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(41)
thf(fact_750_assertion_Orel__distinct_I24_J,axiom,
! [R3: b > b > $o,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ Y31 @ Y32 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(24)
thf(fact_751_assertion_Orel__distinct_I23_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( star_a_b_d_c @ Y31 @ Y32 ) ) ).
% assertion.rel_distinct(23)
thf(fact_752_assertion_Orel__distinct_I36_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(36)
thf(fact_753_assertion_Orel__distinct_I35_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(35)
thf(fact_754_assertion_Orel__distinct_I29_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(29)
thf(fact_755_assertion_Orel__distinct_I30_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(30)
thf(fact_756_assertion_Orel__distinct_I34_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(34)
thf(fact_757_assertion_Orel__distinct_I33_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(33)
thf(fact_758_assertion_Orel__distinct_I26_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ Y41 @ Y42 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(26)
thf(fact_759_assertion_Orel__distinct_I25_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(25)
thf(fact_760_assertion_Orel__distinct_I27_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(27)
thf(fact_761_assertion_Orel__distinct_I28_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ Y51 @ Y52 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(28)
thf(fact_762_assertion_Orel__distinct_I31_J,axiom,
! [R3: b > b > $o,X212: b,X223: 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 @ X223 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(31)
thf(fact_763_assertion_Orel__distinct_I32_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(32)
thf(fact_764_assertion_Orel__distinct_I39_J,axiom,
! [R3: b > b > $o,X212: b,X223: assertion_a_b_d_c,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X223 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(39)
thf(fact_765_assertion_Orel__distinct_I40_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(40)
thf(fact_766_assertion_Orel__distinct_I1_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o,Y21: b,Y22: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( mult_b_a_d_c @ Y21 @ Y22 ) ) ).
% assertion.rel_distinct(1)
thf(fact_767_assertion_Orel__distinct_I2_J,axiom,
! [R3: b > b > $o,Y21: b,Y22: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ Y21 @ Y22 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(2)
thf(fact_768_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_769_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_770_assertion_Orel__distinct_I37_J,axiom,
! [R3: b > b > $o,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( mult_b_a_d_c @ X212 @ X223 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(37)
thf(fact_771_assertion_Orel__distinct_I38_J,axiom,
! [R3: b > b > $o,X212: b,X223: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ pred_a_b_d_c @ ( mult_b_a_d_c @ X212 @ X223 ) ) ).
% assertion.rel_distinct(38)
thf(fact_772_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_773_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_774_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_775_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_776_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_777_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_778_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_779_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_780_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_781_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_782_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_783_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_784_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_785_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_786_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_787_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_788_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_789_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_790_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_791_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_792_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_793_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_794_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_795_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_796_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_797_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_798_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_799_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_800_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_801_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_802_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_803_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_804_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_805_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_806_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_807_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_808_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_809_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_810_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_811_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_812_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_813_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_814_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_815_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_816_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_817_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_818_assertion_Orel__distinct_I22_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wildcard_a_b_d_c @ Y12 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(22)
thf(fact_819_assertion_Orel__distinct_I21_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o,Y12: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( wildcard_a_b_d_c @ Y12 ) ) ).
% assertion.rel_distinct(21)
thf(fact_820_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_821_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_822_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_823_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_824_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_825_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_826_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_827_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_828_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_829_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_830_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_831_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_832_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_833_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_834_assertion_Orel__distinct_I4_J,axiom,
! [R3: b > b > $o,Y31: assertion_a_b_d_c,Y32: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( star_a_b_d_c @ Y31 @ Y32 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(4)
thf(fact_835_assertion_Orel__distinct_I3_J,axiom,
! [R3: b > b > $o,X1: ( 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 @ X1 ) @ ( star_a_b_d_c @ Y31 @ Y32 ) ) ).
% assertion.rel_distinct(3)
thf(fact_836_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_837_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_838_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_839_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_840_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_841_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_842_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_843_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_844_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_845_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_846_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_847_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_848_assertion_Orel__distinct_I16_J,axiom,
! [R3: b > b > $o,Y91: c,Y92: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( forall_c_a_b_d @ Y91 @ Y92 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(16)
thf(fact_849_assertion_Orel__distinct_I15_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o,Y91: c,Y92: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( forall_c_a_b_d @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(15)
thf(fact_850_assertion_Orel__distinct_I9_J,axiom,
! [R3: b > b > $o,X1: ( 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 @ X1 ) @ ( and_a_b_d_c @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(9)
thf(fact_851_assertion_Orel__distinct_I10_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_d_c,Y62: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( and_a_b_d_c @ Y61 @ Y62 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(10)
thf(fact_852_assertion_Orel__distinct_I14_J,axiom,
! [R3: b > b > $o,Y81: c,Y82: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( exists_c_a_b_d @ Y81 @ Y82 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(14)
thf(fact_853_assertion_Orel__distinct_I13_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o,Y81: c,Y82: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( exists_c_a_b_d @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(13)
thf(fact_854_assertion_Orel__distinct_I6_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( wand_a_b_d_c @ Y41 @ Y42 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(6)
thf(fact_855_assertion_Orel__distinct_I5_J,axiom,
! [R3: b > b > $o,X1: ( 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 @ X1 ) @ ( wand_a_b_d_c @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(5)
thf(fact_856_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_857_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_858_assertion_Orel__distinct_I7_J,axiom,
! [R3: b > b > $o,X1: ( 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 @ X1 ) @ ( or_a_b_d_c @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(7)
thf(fact_859_assertion_Orel__distinct_I8_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_d_c,Y52: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( or_a_b_d_c @ Y51 @ Y52 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(8)
thf(fact_860_assertion_Orel__distinct_I11_J,axiom,
! [R3: b > b > $o,X1: ( 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 @ X1 ) @ ( imp_a_b_d_c @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(11)
thf(fact_861_assertion_Orel__distinct_I12_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_d_c,Y72: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( imp_a_b_d_c @ Y71 @ Y72 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(12)
thf(fact_862_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_863_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_864_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_865_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_866_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_867_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_868_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_869_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_870_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_871_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_872_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_873_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_874_assertion_Orel__distinct_I19_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o,Y11: assertion_a_b_d_c] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ ( bounded_a_b_d_c @ Y11 ) ) ).
% assertion.rel_distinct(19)
thf(fact_875_assertion_Orel__distinct_I20_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_d_c,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( bounded_a_b_d_c @ Y11 ) @ ( sem_c_d_a_b @ X1 ) ) ).
% assertion.rel_distinct(20)
thf(fact_876_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_877_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_878_assertion_Orel__distinct_I17_J,axiom,
! [R3: b > b > $o,X1: ( c > d ) > a > $o] :
~ ( rel_as1860989020795611527_a_d_c @ R3 @ ( sem_c_d_a_b @ X1 ) @ pred_a_b_d_c ) ).
% assertion.rel_distinct(17)
thf(fact_879_option_Opred__inject_I2_J,axiom,
! [P2: product_prod_a_c_d > $o,A: product_prod_a_c_d] :
( ( pred_o8515923536274941648_a_c_d @ P2 @ ( some_P1084500821511757806_a_c_d @ A ) )
= ( P2 @ A ) ) ).
% option.pred_inject(2)
thf(fact_880_option_Opred__inject_I2_J,axiom,
! [P2: a > $o,A: a] :
( ( pred_option_a @ P2 @ ( some_a @ A ) )
= ( P2 @ A ) ) ).
% option.pred_inject(2)
thf(fact_881_assertion_Oset__map,axiom,
! [F2: b > b,V3: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ V3 ) )
= ( image_b_b @ F2 @ ( set_as7232682317586342732_b_d_c @ V3 ) ) ) ).
% assertion.set_map
thf(fact_882_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_883_option_Orel__distinct_I2_J,axiom,
! [R3: product_prod_a_c_d > a > $o,Y23: product_prod_a_c_d] :
~ ( rel_op4189142500506136609_c_d_a @ R3 @ ( some_P1084500821511757806_a_c_d @ Y23 ) @ none_a ) ).
% option.rel_distinct(2)
thf(fact_884_option_Orel__distinct_I2_J,axiom,
! [R3: a > a > $o,Y23: a] :
~ ( rel_option_a_a @ R3 @ ( some_a @ Y23 ) @ none_a ) ).
% option.rel_distinct(2)
thf(fact_885_assertion_Omap__comp,axiom,
! [G: b > b,F2: b > b,V3: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ G @ ( map_as2132001898603344138_a_d_c @ F2 @ V3 ) )
= ( map_as2132001898603344138_a_d_c @ ( comp_b_b_b @ G @ F2 ) @ V3 ) ) ).
% assertion.map_comp
thf(fact_886_assertion_Orel__map_I2_J,axiom,
! [Sa2: b > b > $o,X2: assertion_a_b_d_c,G: b > b,Y: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ Sa2 @ X2 @ ( map_as2132001898603344138_a_d_c @ G @ Y ) )
= ( rel_as1860989020795611527_a_d_c
@ ^ [X: b,Y2: b] : ( Sa2 @ X @ ( G @ Y2 ) )
@ X2
@ Y ) ) ).
% assertion.rel_map(2)
thf(fact_887_assertion_Orel__map_I1_J,axiom,
! [Sb2: b > b > $o,I: b > b,X2: assertion_a_b_d_c,Y: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ Sb2 @ ( map_as2132001898603344138_a_d_c @ I @ X2 ) @ Y )
= ( rel_as1860989020795611527_a_d_c
@ ^ [X: b] : ( Sb2 @ ( I @ X ) )
@ X2
@ Y ) ) ).
% assertion.rel_map(1)
thf(fact_888_assertion_Omap__id,axiom,
! [T: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ id_b @ T )
= T ) ).
% assertion.map_id
thf(fact_889_assertion_Omap__id0,axiom,
( ( map_as2132001898603344138_a_d_c @ id_b )
= id_assertion_a_b_d_c ) ).
% assertion.map_id0
thf(fact_890_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_891_assertion_Omap__cong,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,F2: b > b,G: b > b] :
( ( X2 = Ya )
=> ( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( F2 @ Z4 )
= ( G @ Z4 ) ) )
=> ( ( map_as2132001898603344138_a_d_c @ F2 @ X2 )
= ( map_as2132001898603344138_a_d_c @ G @ Ya ) ) ) ) ).
% assertion.map_cong
thf(fact_892_assertion_Omap__cong0,axiom,
! [X2: assertion_a_b_d_c,F2: b > b,G: b > b] :
( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( F2 @ Z4 )
= ( G @ Z4 ) ) )
=> ( ( map_as2132001898603344138_a_d_c @ F2 @ X2 )
= ( map_as2132001898603344138_a_d_c @ G @ X2 ) ) ) ).
% assertion.map_cong0
thf(fact_893_assertion_Oinj__map__strong,axiom,
! [X2: assertion_a_b_d_c,Xa: assertion_a_b_d_c,F2: b > b,Fa: b > b] :
( ! [Z4: b,Za: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( member_b @ Za @ ( set_as7232682317586342732_b_d_c @ Xa ) )
=> ( ( ( F2 @ Z4 )
= ( Fa @ Za ) )
=> ( Z4 = Za ) ) ) )
=> ( ( ( map_as2132001898603344138_a_d_c @ F2 @ X2 )
= ( map_as2132001898603344138_a_d_c @ Fa @ Xa ) )
=> ( X2 = Xa ) ) ) ).
% assertion.inj_map_strong
thf(fact_894_assertion_Omap__ident__strong,axiom,
! [T: assertion_a_b_d_c,F2: b > b] :
( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ T ) )
=> ( ( F2 @ Z4 )
= Z4 ) )
=> ( ( map_as2132001898603344138_a_d_c @ F2 @ T )
= T ) ) ).
% assertion.map_ident_strong
thf(fact_895_option__rel__Some2,axiom,
! [A3: product_prod_a_c_d > a > $o,X2: option6413918287372586467_a_c_d,Y: a] :
( ( rel_op4189142500506136609_c_d_a @ A3 @ X2 @ ( some_a @ Y ) )
= ( ? [X7: product_prod_a_c_d] :
( ( X2
= ( some_P1084500821511757806_a_c_d @ X7 ) )
& ( A3 @ X7 @ Y ) ) ) ) ).
% option_rel_Some2
thf(fact_896_option__rel__Some2,axiom,
! [A3: a > product_prod_a_c_d > $o,X2: option_a,Y: product_prod_a_c_d] :
( ( rel_op5875702612534326665_a_c_d @ A3 @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) )
= ( ? [X7: a] :
( ( X2
= ( some_a @ X7 ) )
& ( A3 @ X7 @ Y ) ) ) ) ).
% option_rel_Some2
thf(fact_897_option__rel__Some2,axiom,
! [A3: product_prod_a_c_d > product_prod_a_c_d > $o,X2: option6413918287372586467_a_c_d,Y: product_prod_a_c_d] :
( ( rel_op4656678800532059696_a_c_d @ A3 @ X2 @ ( some_P1084500821511757806_a_c_d @ Y ) )
= ( ? [X7: product_prod_a_c_d] :
( ( X2
= ( some_P1084500821511757806_a_c_d @ X7 ) )
& ( A3 @ X7 @ Y ) ) ) ) ).
% option_rel_Some2
thf(fact_898_option__rel__Some2,axiom,
! [A3: a > a > $o,X2: option_a,Y: a] :
( ( rel_option_a_a @ A3 @ X2 @ ( some_a @ Y ) )
= ( ? [X7: a] :
( ( X2
= ( some_a @ X7 ) )
& ( A3 @ X7 @ Y ) ) ) ) ).
% option_rel_Some2
thf(fact_899_option__rel__Some1,axiom,
! [A3: a > product_prod_a_c_d > $o,X2: a,Y: option6413918287372586467_a_c_d] :
( ( rel_op5875702612534326665_a_c_d @ A3 @ ( some_a @ X2 ) @ Y )
= ( ? [Y5: product_prod_a_c_d] :
( ( Y
= ( some_P1084500821511757806_a_c_d @ Y5 ) )
& ( A3 @ X2 @ Y5 ) ) ) ) ).
% option_rel_Some1
thf(fact_900_option__rel__Some1,axiom,
! [A3: product_prod_a_c_d > a > $o,X2: product_prod_a_c_d,Y: option_a] :
( ( rel_op4189142500506136609_c_d_a @ A3 @ ( some_P1084500821511757806_a_c_d @ X2 ) @ Y )
= ( ? [Y5: a] :
( ( Y
= ( some_a @ Y5 ) )
& ( A3 @ X2 @ Y5 ) ) ) ) ).
% option_rel_Some1
thf(fact_901_option__rel__Some1,axiom,
! [A3: product_prod_a_c_d > product_prod_a_c_d > $o,X2: product_prod_a_c_d,Y: option6413918287372586467_a_c_d] :
( ( rel_op4656678800532059696_a_c_d @ A3 @ ( some_P1084500821511757806_a_c_d @ X2 ) @ Y )
= ( ? [Y5: product_prod_a_c_d] :
( ( Y
= ( some_P1084500821511757806_a_c_d @ Y5 ) )
& ( A3 @ X2 @ Y5 ) ) ) ) ).
% option_rel_Some1
thf(fact_902_option__rel__Some1,axiom,
! [A3: a > a > $o,X2: a,Y: option_a] :
( ( rel_option_a_a @ A3 @ ( some_a @ X2 ) @ Y )
= ( ? [Y5: a] :
( ( Y
= ( some_a @ Y5 ) )
& ( A3 @ X2 @ Y5 ) ) ) ) ).
% option_rel_Some1
thf(fact_903_option_Orel__intros_I2_J,axiom,
! [R3: a > product_prod_a_c_d > $o,X22: a,Y23: product_prod_a_c_d] :
( ( R3 @ X22 @ Y23 )
=> ( rel_op5875702612534326665_a_c_d @ R3 @ ( some_a @ X22 ) @ ( some_P1084500821511757806_a_c_d @ Y23 ) ) ) ).
% option.rel_intros(2)
thf(fact_904_option_Orel__intros_I2_J,axiom,
! [R3: product_prod_a_c_d > a > $o,X22: product_prod_a_c_d,Y23: a] :
( ( R3 @ X22 @ Y23 )
=> ( rel_op4189142500506136609_c_d_a @ R3 @ ( some_P1084500821511757806_a_c_d @ X22 ) @ ( some_a @ Y23 ) ) ) ).
% option.rel_intros(2)
thf(fact_905_option_Orel__intros_I2_J,axiom,
! [R3: product_prod_a_c_d > product_prod_a_c_d > $o,X22: product_prod_a_c_d,Y23: product_prod_a_c_d] :
( ( R3 @ X22 @ Y23 )
=> ( rel_op4656678800532059696_a_c_d @ R3 @ ( some_P1084500821511757806_a_c_d @ X22 ) @ ( some_P1084500821511757806_a_c_d @ Y23 ) ) ) ).
% option.rel_intros(2)
thf(fact_906_option_Orel__intros_I2_J,axiom,
! [R3: a > a > $o,X22: a,Y23: a] :
( ( R3 @ X22 @ Y23 )
=> ( rel_option_a_a @ R3 @ ( some_a @ X22 ) @ ( some_a @ Y23 ) ) ) ).
% option.rel_intros(2)
thf(fact_907_option_Orel__inject_I2_J,axiom,
! [R3: a > product_prod_a_c_d > $o,X22: a,Y23: product_prod_a_c_d] :
( ( rel_op5875702612534326665_a_c_d @ R3 @ ( some_a @ X22 ) @ ( some_P1084500821511757806_a_c_d @ Y23 ) )
= ( R3 @ X22 @ Y23 ) ) ).
% option.rel_inject(2)
thf(fact_908_option_Orel__inject_I2_J,axiom,
! [R3: product_prod_a_c_d > a > $o,X22: product_prod_a_c_d,Y23: a] :
( ( rel_op4189142500506136609_c_d_a @ R3 @ ( some_P1084500821511757806_a_c_d @ X22 ) @ ( some_a @ Y23 ) )
= ( R3 @ X22 @ Y23 ) ) ).
% option.rel_inject(2)
thf(fact_909_option_Orel__inject_I2_J,axiom,
! [R3: product_prod_a_c_d > product_prod_a_c_d > $o,X22: product_prod_a_c_d,Y23: product_prod_a_c_d] :
( ( rel_op4656678800532059696_a_c_d @ R3 @ ( some_P1084500821511757806_a_c_d @ X22 ) @ ( some_P1084500821511757806_a_c_d @ Y23 ) )
= ( R3 @ X22 @ Y23 ) ) ).
% option.rel_inject(2)
thf(fact_910_option_Orel__inject_I2_J,axiom,
! [R3: a > a > $o,X22: a,Y23: a] :
( ( rel_option_a_a @ R3 @ ( some_a @ X22 ) @ ( some_a @ Y23 ) )
= ( R3 @ X22 @ Y23 ) ) ).
% option.rel_inject(2)
thf(fact_911_assertion_Osimps_I176_J,axiom,
! [F2: b > b,X912: c,X922: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( forall_c_a_b_d @ X912 @ X922 ) )
= ( forall_c_a_b_d @ X912 @ ( map_as2132001898603344138_a_d_c @ F2 @ X922 ) ) ) ).
% assertion.simps(176)
thf(fact_912_assertion_Osimps_I173_J,axiom,
! [F2: b > b,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( and_a_b_d_c @ X612 @ X622 ) )
= ( and_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X612 ) @ ( map_as2132001898603344138_a_d_c @ F2 @ X622 ) ) ) ).
% assertion.simps(173)
thf(fact_913_assertion_Osimps_I171_J,axiom,
! [F2: b > b,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( wand_a_b_d_c @ X412 @ X422 ) )
= ( wand_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X412 ) @ ( map_as2132001898603344138_a_d_c @ F2 @ X422 ) ) ) ).
% assertion.simps(171)
thf(fact_914_assertion_Osimps_I175_J,axiom,
! [F2: b > b,X812: c,X822: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( exists_c_a_b_d @ X812 @ X822 ) )
= ( exists_c_a_b_d @ X812 @ ( map_as2132001898603344138_a_d_c @ F2 @ X822 ) ) ) ).
% assertion.simps(175)
thf(fact_915_assertion_Osimps_I172_J,axiom,
! [F2: b > b,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( or_a_b_d_c @ X512 @ X522 ) )
= ( or_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X512 ) @ ( map_as2132001898603344138_a_d_c @ F2 @ X522 ) ) ) ).
% assertion.simps(172)
thf(fact_916_assertion_Osimps_I174_J,axiom,
! [F2: b > b,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( imp_a_b_d_c @ X712 @ X722 ) )
= ( imp_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X712 ) @ ( map_as2132001898603344138_a_d_c @ F2 @ X722 ) ) ) ).
% assertion.simps(174)
thf(fact_917_assertion_Osimps_I178_J,axiom,
! [F2: b > b,X112: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( bounded_a_b_d_c @ X112 ) )
= ( bounded_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X112 ) ) ) ).
% assertion.simps(178)
thf(fact_918_assertion_Osimps_I168_J,axiom,
! [F2: b > b,X1: ( c > d ) > a > $o] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( sem_c_d_a_b @ X1 ) )
= ( sem_c_d_a_b @ X1 ) ) ).
% assertion.simps(168)
thf(fact_919_assertion_Osimps_I177_J,axiom,
! [F2: b > b] :
( ( map_as2132001898603344138_a_d_c @ F2 @ pred_a_b_d_c )
= pred_a_b_d_c ) ).
% assertion.simps(177)
thf(fact_920_assertion_Osimps_I170_J,axiom,
! [F2: b > b,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( star_a_b_d_c @ X312 @ X322 ) )
= ( star_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X312 ) @ ( map_as2132001898603344138_a_d_c @ F2 @ X322 ) ) ) ).
% assertion.simps(170)
thf(fact_921_assertion_Osimps_I179_J,axiom,
! [F2: b > b,X123: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( wildcard_a_b_d_c @ X123 ) )
= ( wildcard_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 @ X123 ) ) ) ).
% assertion.simps(179)
thf(fact_922_assertion_Osimps_I169_J,axiom,
! [F2: b > b,X212: b,X223: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F2 @ ( mult_b_a_d_c @ X212 @ X223 ) )
= ( mult_b_a_d_c @ ( F2 @ X212 ) @ ( map_as2132001898603344138_a_d_c @ F2 @ X223 ) ) ) ).
% assertion.simps(169)
thf(fact_923_assertion_Omap__ident,axiom,
! [T: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c
@ ^ [X: b] : X
@ T )
= T ) ).
% assertion.map_ident
thf(fact_924_assertion_Oinj__map,axiom,
! [F2: b > b] :
( ( inj_on_b_b @ F2 @ top_top_set_b )
=> ( inj_on3926713243670117681_b_d_c @ ( map_as2132001898603344138_a_d_c @ F2 ) @ top_to5090759043282426983_b_d_c ) ) ).
% assertion.inj_map
thf(fact_925_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_926_option_Orel__induct,axiom,
! [R3: a > product_prod_a_c_d > $o,X2: option_a,Y: option6413918287372586467_a_c_d,Q: option_a > option6413918287372586467_a_c_d > $o] :
( ( rel_op5875702612534326665_a_c_d @ R3 @ X2 @ Y )
=> ( ( Q @ none_a @ none_P2239999354720063602_a_c_d )
=> ( ! [A22: a,B22: product_prod_a_c_d] :
( ( R3 @ A22 @ B22 )
=> ( Q @ ( some_a @ A22 ) @ ( some_P1084500821511757806_a_c_d @ B22 ) ) )
=> ( Q @ X2 @ Y ) ) ) ) ).
% option.rel_induct
thf(fact_927_option_Orel__induct,axiom,
! [R3: product_prod_a_c_d > a > $o,X2: option6413918287372586467_a_c_d,Y: option_a,Q: option6413918287372586467_a_c_d > option_a > $o] :
( ( rel_op4189142500506136609_c_d_a @ R3 @ X2 @ Y )
=> ( ( Q @ none_P2239999354720063602_a_c_d @ none_a )
=> ( ! [A22: product_prod_a_c_d,B22: a] :
( ( R3 @ A22 @ B22 )
=> ( Q @ ( some_P1084500821511757806_a_c_d @ A22 ) @ ( some_a @ B22 ) ) )
=> ( Q @ X2 @ Y ) ) ) ) ).
% option.rel_induct
thf(fact_928_option_Orel__induct,axiom,
! [R3: product_prod_a_c_d > product_prod_a_c_d > $o,X2: option6413918287372586467_a_c_d,Y: option6413918287372586467_a_c_d,Q: option6413918287372586467_a_c_d > option6413918287372586467_a_c_d > $o] :
( ( rel_op4656678800532059696_a_c_d @ R3 @ X2 @ Y )
=> ( ( Q @ none_P2239999354720063602_a_c_d @ none_P2239999354720063602_a_c_d )
=> ( ! [A22: product_prod_a_c_d,B22: product_prod_a_c_d] :
( ( R3 @ A22 @ B22 )
=> ( Q @ ( some_P1084500821511757806_a_c_d @ A22 ) @ ( some_P1084500821511757806_a_c_d @ B22 ) ) )
=> ( Q @ X2 @ Y ) ) ) ) ).
% option.rel_induct
thf(fact_929_option_Orel__induct,axiom,
! [R3: a > a > $o,X2: option_a,Y: option_a,Q: option_a > option_a > $o] :
( ( rel_option_a_a @ R3 @ X2 @ Y )
=> ( ( Q @ none_a @ none_a )
=> ( ! [A22: a,B22: a] :
( ( R3 @ A22 @ B22 )
=> ( Q @ ( some_a @ A22 ) @ ( some_a @ B22 ) ) )
=> ( Q @ X2 @ Y ) ) ) ) ).
% option.rel_induct
thf(fact_930_option_Orel__cases,axiom,
! [R3: a > product_prod_a_c_d > $o,A: option_a,B: option6413918287372586467_a_c_d] :
( ( rel_op5875702612534326665_a_c_d @ R3 @ A @ B )
=> ( ( ( A = none_a )
=> ( B != none_P2239999354720063602_a_c_d ) )
=> ~ ! [X3: a] :
( ( A
= ( some_a @ X3 ) )
=> ! [Y3: product_prod_a_c_d] :
( ( B
= ( some_P1084500821511757806_a_c_d @ Y3 ) )
=> ~ ( R3 @ X3 @ Y3 ) ) ) ) ) ).
% option.rel_cases
thf(fact_931_option_Orel__cases,axiom,
! [R3: product_prod_a_c_d > a > $o,A: option6413918287372586467_a_c_d,B: option_a] :
( ( rel_op4189142500506136609_c_d_a @ R3 @ A @ B )
=> ( ( ( A = none_P2239999354720063602_a_c_d )
=> ( B != none_a ) )
=> ~ ! [X3: product_prod_a_c_d] :
( ( A
= ( some_P1084500821511757806_a_c_d @ X3 ) )
=> ! [Y3: a] :
( ( B
= ( some_a @ Y3 ) )
=> ~ ( R3 @ X3 @ Y3 ) ) ) ) ) ).
% option.rel_cases
thf(fact_932_option_Orel__cases,axiom,
! [R3: product_prod_a_c_d > product_prod_a_c_d > $o,A: option6413918287372586467_a_c_d,B: option6413918287372586467_a_c_d] :
( ( rel_op4656678800532059696_a_c_d @ R3 @ A @ B )
=> ( ( ( A = none_P2239999354720063602_a_c_d )
=> ( B != none_P2239999354720063602_a_c_d ) )
=> ~ ! [X3: product_prod_a_c_d] :
( ( A
= ( some_P1084500821511757806_a_c_d @ X3 ) )
=> ! [Y3: product_prod_a_c_d] :
( ( B
= ( some_P1084500821511757806_a_c_d @ Y3 ) )
=> ~ ( R3 @ X3 @ Y3 ) ) ) ) ) ).
% option.rel_cases
thf(fact_933_option_Orel__cases,axiom,
! [R3: a > a > $o,A: option_a,B: option_a] :
( ( rel_option_a_a @ R3 @ A @ B )
=> ( ( ( A = none_a )
=> ( B != none_a ) )
=> ~ ! [X3: a] :
( ( A
= ( some_a @ X3 ) )
=> ! [Y3: a] :
( ( B
= ( some_a @ Y3 ) )
=> ~ ( R3 @ X3 @ Y3 ) ) ) ) ) ).
% option.rel_cases
thf(fact_934_option_Orel__distinct_I1_J,axiom,
! [R3: a > product_prod_a_c_d > $o,Y23: product_prod_a_c_d] :
~ ( rel_op5875702612534326665_a_c_d @ R3 @ none_a @ ( some_P1084500821511757806_a_c_d @ Y23 ) ) ).
% option.rel_distinct(1)
thf(fact_935_option_Orel__distinct_I1_J,axiom,
! [R3: a > a > $o,Y23: a] :
~ ( rel_option_a_a @ R3 @ none_a @ ( some_a @ Y23 ) ) ).
% option.rel_distinct(1)
thf(fact_936_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_937_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_938_assertion_Orel__transfer,axiom,
! [Sa2: b > b > $o,Sc: b > b > $o] :
( bNF_re6697097071762359901_d_c_o
@ ( bNF_re4413358128099268379_o_b_o @ Sa2
@ ( bNF_rel_fun_b_b_o_o @ Sc
@ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
@ ( bNF_re7564741212224818219_d_c_o @ ( rel_as1860989020795611527_a_d_c @ Sa2 )
@ ( bNF_re7425909319474424221_c_o_o @ ( rel_as1860989020795611527_a_d_c @ Sc )
@ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
@ rel_as1860989020795611527_a_d_c
@ rel_as1860989020795611527_a_d_c ) ).
% assertion.rel_transfer
thf(fact_939_option_Octr__transfer_I2_J,axiom,
! [R3: a > product_prod_a_c_d > $o] : ( bNF_re9155705077389660979_a_c_d @ R3 @ ( rel_op5875702612534326665_a_c_d @ R3 ) @ some_a @ some_P1084500821511757806_a_c_d ) ).
% option.ctr_transfer(2)
thf(fact_940_option_Octr__transfer_I2_J,axiom,
! [R3: product_prod_a_c_d > a > $o] : ( bNF_re3106999726094018323tion_a @ R3 @ ( rel_op4189142500506136609_c_d_a @ R3 ) @ some_P1084500821511757806_a_c_d @ some_a ) ).
% option.ctr_transfer(2)
thf(fact_941_option_Octr__transfer_I2_J,axiom,
! [R3: product_prod_a_c_d > product_prod_a_c_d > $o] : ( bNF_re7631950180739184205_a_c_d @ R3 @ ( rel_op4656678800532059696_a_c_d @ R3 ) @ some_P1084500821511757806_a_c_d @ some_P1084500821511757806_a_c_d ) ).
% option.ctr_transfer(2)
thf(fact_942_option_Octr__transfer_I2_J,axiom,
! [R3: a > a > $o] : ( bNF_re1187871780581372509tion_a @ R3 @ ( rel_option_a_a @ R3 ) @ some_a @ some_a ) ).
% option.ctr_transfer(2)
thf(fact_943_assertion_Octr__transfer_I1_J,axiom,
! [R3: b > b > $o] :
( bNF_re1770667264140748071_b_d_c
@ ^ [Y4: ( c > d ) > a > $o,Z3: ( c > d ) > a > $o] : ( Y4 = Z3 )
@ ( rel_as1860989020795611527_a_d_c @ R3 )
@ sem_c_d_a_b
@ sem_c_d_a_b ) ).
% assertion.ctr_transfer(1)
thf(fact_944_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_945_assertion_Octr__transfer_I9_J,axiom,
! [R3: b > b > $o] :
( bNF_re133962660596780713_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( 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_946_assertion_Octr__transfer_I8_J,axiom,
! [R3: b > b > $o] :
( bNF_re133962660596780713_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( 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_947_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_948_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_949_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_950_assertion_Ocase__transfer,axiom,
! [S5: ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o,R3: b > b > $o] :
( bNF_re2658820731495178543_b_d_c
@ ( bNF_re7112637536428693683_b_d_c
@ ^ [Y4: ( c > d ) > a > $o,Z3: ( c > d ) > a > $o] : ( Y4 = Z3 )
@ S5 )
@ ( bNF_re8066222765365709061_b_d_c @ ( bNF_re7963540674472851293_b_d_c @ R3 @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re1913961672366121877_b_d_c @ ( bNF_re39574443744948061_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re251176583891200149_b_d_c @ ( bNF_re39574443744948061_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re8060521475475539349_b_d_c @ ( bNF_re39574443744948061_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re3682814332405119637_b_d_c @ ( bNF_re39574443744948061_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re4121371422775248789_b_d_c @ ( bNF_re39574443744948061_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re4985889110256990915_b_d_c
@ ( bNF_re6592304143361956253_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re672856011677040387_b_d_c
@ ( bNF_re6592304143361956253_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re3297605885130694505_b_d_c @ S5 @ ( bNF_re8482286197440273641_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) @ ( bNF_re9183090372639188701_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) ) ) ) ) ) ) ) ) ) ) )
@ case_a2494328633001133122_d_c_b
@ case_a2494328633001133122_d_c_b ) ).
% assertion.case_transfer
thf(fact_951_assertion_Ocase__transfer,axiom,
! [S5: 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
@ ^ [Y4: ( c > d ) > a > $o,Z3: ( c > d ) > a > $o] : ( Y4 = Z3 )
@ S5 )
@ ( bNF_re969776683416675581_b_d_c @ ( bNF_re377125674677652585_b_d_c @ R3 @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( 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 ) @ S5 ) )
@ ( 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 ) @ S5 ) )
@ ( 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 ) @ S5 ) )
@ ( 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 ) @ S5 ) )
@ ( 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 ) @ S5 ) )
@ ( bNF_re6171781090946898727_b_d_c
@ ( bNF_re133962660596780713_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re4264221303238623901_b_d_c
@ ( bNF_re133962660596780713_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) )
@ ( bNF_re515523818749706873_b_d_c @ S5 @ ( bNF_re6606623624522348157_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) @ ( bNF_re8402442907184412917_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S5 ) ) ) ) ) ) ) ) ) ) ) )
@ case_a2736964712663357406_d_c_b
@ case_a2736964712663357406_d_c_b ) ).
% assertion.case_transfer
thf(fact_952_fun__upd__transfer,axiom,
! [A3: c > c > $o,B3: d > d > $o] :
( ( bi_unique_c_c @ A3 )
=> ( bNF_re4162436072719156391_d_c_d @ ( bNF_rel_fun_c_c_d_d @ A3 @ B3 ) @ ( bNF_re6283605750710864861_d_c_d @ A3 @ ( bNF_re2118925435710938475_d_c_d @ B3 @ ( bNF_rel_fun_c_c_d_d @ A3 @ B3 ) ) ) @ fun_upd_c_d @ fun_upd_c_d ) ) ).
% fun_upd_transfer
thf(fact_953_fun__upd__transfer,axiom,
! [A3: c > a > $o,B3: d > option_a > $o] :
( ( bi_unique_c_a @ A3 )
=> ( bNF_re5308688359564752758tion_a @ ( bNF_re2367443474453270238tion_a @ A3 @ B3 ) @ ( bNF_re2730572489753928035tion_a @ A3 @ ( bNF_re4105512943801057267tion_a @ B3 @ ( bNF_re2367443474453270238tion_a @ A3 @ B3 ) ) ) @ fun_upd_c_d @ fun_upd_a_option_a ) ) ).
% fun_upd_transfer
thf(fact_954_fun__upd__transfer,axiom,
! [A3: a > c > $o,B3: option_a > d > $o] :
( ( bi_unique_a_c @ A3 )
=> ( bNF_re3817954351838466806_d_c_d @ ( bNF_re3628769949165654428on_a_d @ A3 @ B3 ) @ ( bNF_re7925548642511003351_d_c_d @ A3 @ ( bNF_re6291851909076488365_a_c_d @ B3 @ ( bNF_re3628769949165654428on_a_d @ A3 @ B3 ) ) ) @ fun_upd_a_option_a @ fun_upd_c_d ) ) ).
% fun_upd_transfer
thf(fact_955_fun__upd__transfer,axiom,
! [A3: a > a > $o,B3: option_a > option_a > $o] :
( ( bi_unique_a_a @ A3 )
=> ( bNF_re4933961146405920325tion_a @ ( bNF_re1187871780581372509tion_a @ A3 @ B3 ) @ ( bNF_re845666378725559389tion_a @ A3 @ ( bNF_re8162217253061806133tion_a @ B3 @ ( bNF_re1187871780581372509tion_a @ A3 @ B3 ) ) ) @ fun_upd_a_option_a @ fun_upd_a_option_a ) ) ).
% fun_upd_transfer
thf(fact_956_fun__upd__transfer,axiom,
! [A3: assertion_a_b_d_c > assertion_a_b_d_c > $o,B3: ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o] :
( ( bi_uni8285078783686190927_b_d_c @ A3 )
=> ( bNF_re4842871906108351673_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ A3 @ B3 ) @ ( bNF_re5290459592999203293_b_d_c @ A3 @ ( bNF_re2031598785229489641_b_d_c @ B3 @ ( bNF_re8872988018146346089_b_d_c @ A3 @ B3 ) ) ) @ fun_up8437948482231556639_b_d_c @ fun_up8437948482231556639_b_d_c ) ) ).
% fun_upd_transfer
thf(fact_957_fun__upd__transfer,axiom,
! [A3: assertion_a_b_d_c > assertion_a_b_d_c > $o,B3: assertion_a_b_d_c > assertion_a_b_d_c > $o] :
( ( bi_uni8285078783686190927_b_d_c @ A3 )
=> ( bNF_re8313538116629745697_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ A3 @ B3 ) @ ( bNF_re39574443744948061_b_d_c @ A3 @ ( bNF_re8872988018146346089_b_d_c @ B3 @ ( bNF_re5048873211533932509_b_d_c @ A3 @ B3 ) ) ) @ fun_up5644072878873480765_b_d_c @ fun_up5644072878873480765_b_d_c ) ) ).
% fun_upd_transfer
thf(fact_958_assertion_Opred__transfer,axiom,
! [R3: b > b > $o] :
( bNF_re3168247226632236905_d_c_o
@ ( bNF_rel_fun_b_b_o_o @ R3
@ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) )
@ ( bNF_re7425909319474424221_c_o_o @ ( rel_as1860989020795611527_a_d_c @ R3 )
@ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) )
@ pred_a5408123710409757427_a_d_c
@ pred_a5408123710409757427_a_d_c ) ).
% assertion.pred_transfer
thf(fact_959_assertion_Orel__Grp,axiom,
! [A3: set_b,F2: b > b] :
( ( rel_as1860989020795611527_a_d_c @ ( bNF_Grp_b_b @ A3 @ F2 ) )
= ( bNF_Gr8554578625086265742_b_d_c
@ ( collec7183461376620183714_b_d_c
@ ^ [X: assertion_a_b_d_c] : ( ord_less_eq_set_b @ ( set_as7232682317586342732_b_d_c @ X ) @ A3 ) )
@ ( map_as2132001898603344138_a_d_c @ F2 ) ) ) ).
% assertion.rel_Grp
thf(fact_960_assertion_Opred__inject_I2_J,axiom,
! [P2: b > $o,A: b,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( mult_b_a_d_c @ A @ Aa2 ) )
= ( ( P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ) ).
% assertion.pred_inject(2)
thf(fact_961_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_962_assertion_Opred__inject_I3_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( star_a_b_d_c @ A @ Aa2 ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ) ).
% assertion.pred_inject(3)
thf(fact_963_assertion_Opred__inject_I9_J,axiom,
! [P2: b > $o,A: c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( forall_c_a_b_d @ A @ Aa2 ) )
= ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ).
% assertion.pred_inject(9)
thf(fact_964_assertion_Opred__inject_I6_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( and_a_b_d_c @ A @ Aa2 ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ) ).
% assertion.pred_inject(6)
thf(fact_965_assertion_Opred__inject_I8_J,axiom,
! [P2: b > $o,A: c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( exists_c_a_b_d @ A @ Aa2 ) )
= ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ).
% assertion.pred_inject(8)
thf(fact_966_assertion_Opred__inject_I4_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( wand_a_b_d_c @ A @ Aa2 ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ) ).
% assertion.pred_inject(4)
thf(fact_967_assertion_Opred__inject_I7_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( imp_a_b_d_c @ A @ Aa2 ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ) ).
% assertion.pred_inject(7)
thf(fact_968_assertion_Opred__inject_I5_J,axiom,
! [P2: b > $o,A: assertion_a_b_d_c,Aa2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ ( or_a_b_d_c @ A @ Aa2 ) )
= ( ( pred_a5408123710409757427_a_d_c @ P2 @ A )
& ( pred_a5408123710409757427_a_d_c @ P2 @ Aa2 ) ) ) ).
% assertion.pred_inject(5)
thf(fact_969_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_970_assertion_Opred__True,axiom,
( ( pred_a5408123710409757427_a_d_c
@ ^ [Uu: b] : $true )
= ( ^ [Uu: assertion_a_b_d_c] : $true ) ) ).
% assertion.pred_True
thf(fact_971_assertion_Omap__cong__pred,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,F2: b > b,G: b > b] :
( ( X2 = Ya )
=> ( ( pred_a5408123710409757427_a_d_c
@ ^ [Z2: b] :
( ( F2 @ Z2 )
= ( G @ Z2 ) )
@ Ya )
=> ( ( map_as2132001898603344138_a_d_c @ F2 @ X2 )
= ( map_as2132001898603344138_a_d_c @ G @ Ya ) ) ) ) ).
% assertion.map_cong_pred
thf(fact_972_assertion_Opred__map,axiom,
! [Q: b > $o,F2: b > b,X2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ Q @ ( map_as2132001898603344138_a_d_c @ F2 @ X2 ) )
= ( pred_a5408123710409757427_a_d_c @ ( comp_b_o_b @ Q @ F2 ) @ X2 ) ) ).
% assertion.pred_map
thf(fact_973_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_974_assertion_Opred__mono__strong,axiom,
! [P2: b > $o,X2: assertion_a_b_d_c,Pa: b > $o] :
( ( pred_a5408123710409757427_a_d_c @ P2 @ X2 )
=> ( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( P2 @ Z4 )
=> ( Pa @ Z4 ) ) )
=> ( pred_a5408123710409757427_a_d_c @ Pa @ X2 ) ) ) ).
% assertion.pred_mono_strong
thf(fact_975_assertion_Opred__cong,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,P2: b > $o,Pa: b > $o] :
( ( X2 = Ya )
=> ( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( P2 @ Z4 )
= ( Pa @ Z4 ) ) )
=> ( ( pred_a5408123710409757427_a_d_c @ P2 @ X2 )
= ( pred_a5408123710409757427_a_d_c @ Pa @ Ya ) ) ) ) ).
% assertion.pred_cong
% Helper facts (5)
thf(help_If_2_1_If_001tf__d_T,axiom,
! [X2: d,Y: d] :
( ( if_d @ $false @ X2 @ Y )
= Y ) ).
thf(help_If_1_1_If_001tf__d_T,axiom,
! [X2: d,Y: d] :
( ( if_d @ $true @ X2 @ Y )
= X2 ) ).
thf(help_If_3_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
! [P2: $o] :
( ( P2 = $true )
| ( P2 = $false ) ) ).
thf(help_If_2_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
! [X2: option_a,Y: option_a] :
( ( if_option_a @ $false @ X2 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
! [X2: option_a,Y: option_a] :
( ( if_option_a @ $true @ X2 @ Y )
= X2 ) ).
% Conjectures (1)
thf(conj_0,conjecture,
sat_a_b_c_d @ plus @ mult @ valid @ a3 @ s @ delta @ a2 ).
%------------------------------------------------------------------------------