TPTP Problem File: SLH0585^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Separation_Logic_Unbounded/0003_FixedPoint/prob_00527_016638__6859828_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1134 ( 438 unt; 287 typ; 0 def)
% Number of atoms : 2377 ( 714 equ; 0 cnn)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 10710 ( 297 ~; 11 |; 129 &;9554 @)
% ( 0 <=>; 719 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 33 ( 32 usr)
% Number of type conns : 5289 (5289 >; 0 *; 0 +; 0 <<)
% Number of symbols : 258 ( 255 usr; 20 con; 0-13 aty)
% Number of variables : 4144 ( 112 ^;3994 !; 38 ?;4144 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 16:05:27.373
%------------------------------------------------------------------------------
% Could-be-implicit typings (32)
thf(ty_n_t__Set__Oset_It__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_J,type,
set_Pr1216123688828223200_a_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J_J,type,
produc5105196854009589546_a_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J_J,type,
set_Pr1275464188344874039_a_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J,type,
produc5278197477302038359_a_c_d: $tType ).
thf(ty_n_t__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,
option3890169911263941780_a_c_d: $tType ).
thf(ty_n_t__Set__Oset_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,
set_Pr336584576397674490_a_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J,type,
produc5213381314664832452_a_c_d: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mt__Option__Ooption_Itf__a_J_Mtf__a_J,type,
assert1556940916145061938on_a_a: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__d_Mtf__c_J,type,
assert3107445333071088380_a_d_c: $tType ).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
option6413918287372586467_a_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
set_as909545710669178647_b_d_c: $tType ).
thf(ty_n_t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
set_c_d_set_a: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
set_option_option_a: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
assertion_a_b_d_c: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__a_Mtf__d_Mtf__c_J,type,
assertion_a_a_d_c: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
set_Product_prod_a_a: $tType ).
thf(ty_n_t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
product_prod_a_c_d: $tType ).
thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
option_option_a: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__b_J_J,type,
set_option_b: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
set_option_a: $tType ).
thf(ty_n_t__Option__Ooption_I_062_Itf__c_Mtf__d_J_J,type,
option_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
product_prod_a_a: $tType ).
thf(ty_n_t__Option__Ooption_Itf__b_J,type,
option_b: $tType ).
thf(ty_n_t__Option__Ooption_Itf__a_J,type,
option_a: $tType ).
thf(ty_n_t__Set__Oset_Itf__d_J,type,
set_d: $tType ).
thf(ty_n_t__Set__Oset_Itf__c_J,type,
set_c: $tType ).
thf(ty_n_t__Set__Oset_Itf__b_J,type,
set_b: $tType ).
thf(ty_n_t__Set__Oset_Itf__a_J,type,
set_a: $tType ).
thf(ty_n_tf__d,type,
d: $tType ).
thf(ty_n_tf__c,type,
c: $tType ).
thf(ty_n_tf__b,type,
b: $tType ).
thf(ty_n_tf__a,type,
a: $tType ).
% Explicit typings (255)
thf(sy_c_BNF__Def_OGrp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
bNF_Gr8554578625086265742_b_d_c: set_as909545710669178647_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_BNF__Def_OGrp_001tf__b_001tf__b,type,
bNF_Grp_b_b: set_b > ( b > b ) > b > b > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_I_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5462665785578358557_b_d_c: ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > $o ) > ( ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__c_Mtf__d_J_M_062_Itf__a_M_Eo_J_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
bNF_re1770667264140748071_b_d_c: ( ( ( c > d ) > a > $o ) > ( ( c > d ) > a > $o ) > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5536568207858047837_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J,type,
bNF_re3555337462168811729_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J,type,
bNF_re5146714292400357853_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J,type,
bNF_re6312048780865235365_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J,type,
bNF_re3015297470480446045_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J,type,
bNF_re6606623624522348157_b_d_c: ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_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_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_It__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_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,type,
bNF_re7213484083391222185_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 ) > $o ) > ( ( 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 ) > 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_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re969776683416675581_b_d_c: ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_J,type,
bNF_re6697097071762359901_d_c_o: ( ( b > b > $o ) > ( b > b > $o ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > $o ) > ( ( b > b > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( b > b > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_Eo_J_001_062_Itf__b_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_Eo_J,type,
bNF_re3168247226632236905_d_c_o: ( ( b > $o ) > ( b > $o ) > $o ) > ( ( assertion_a_b_d_c > $o ) > ( assertion_a_b_d_c > $o ) > $o ) > ( ( b > $o ) > assertion_a_b_d_c > $o ) > ( ( b > $o ) > assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
bNF_re4457485704112703733_b_d_c: ( ( b > b ) > ( b > b ) > $o ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( b > b ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( b > b ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J_001_062_I_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_J,type,
bNF_re6171781090946898727_b_d_c: ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_Itf__c_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_J,type,
bNF_re4264221303238623901_b_d_c: ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_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_Itf__c_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_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_J_J_001_062_Itf__c_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_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_J_J,type,
bNF_re6482585556422379257_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 ) > 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 ) > $o ) > ( ( 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 ) > ( ( 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 ) > $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__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J_J_J,type,
bNF_re515523818749706873_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > ( ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ) > ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_M_062_It__UnboundedLogic__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_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_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_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_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_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_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_J,type,
bNF_re3899328378992105309_b_d_c: ( c > c > $o ) > ( ( ( 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 ) > 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 ) > ( 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_It__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_Itf__a_J,type,
finite1674126218327898605tion_a: set_option_a > $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_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_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_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__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_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_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_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_up7970115895444633960_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 ) > c > assertion_a_b_d_c > assertion_a_b_d_c ).
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__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__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_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_001tf__a,type,
lattic5961991414251573132_set_a: ( a > a > a ) > $o ).
thf(sy_c_Lattices__Big_Osemilattice__set_OF_001tf__a,type,
lattic5116578512385870296ce_F_a: ( a > a > a ) > set_a > 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_001tf__a_001tf__a,type,
dom_a_a: ( a > option_a ) > set_a ).
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__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_001tf__a,type,
graph_a_a: ( a > option_a ) > set_Product_prod_a_a ).
thf(sy_c_Map_Omap__add_001t__Option__Ooption_Itf__a_J_001tf__a,type,
map_add_option_a_a: ( option_a > option_a ) > ( option_a > option_a ) > option_a > option_a ).
thf(sy_c_Map_Omap__add_001tf__a_001tf__a,type,
map_add_a_a: ( a > option_a ) > ( a > option_a ) > a > option_a ).
thf(sy_c_Map_Omap__add_001tf__b_001tf__a,type,
map_add_b_a: ( b > option_a ) > ( b > option_a ) > b > option_a ).
thf(sy_c_Map_Omap__le_001tf__a_001tf__a,type,
map_le_a_a: ( a > option_a ) > ( a > option_a ) > $o ).
thf(sy_c_Map_Oran_001tf__a_001tf__a,type,
ran_a_a: ( a > option_a ) > set_a ).
thf(sy_c_Map_Orestrict__map_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_Itf__c_Mtf__d_J,type,
restri4474245042709046629_a_c_d: ( ( ( c > d ) > set_a ) > option_c_d ) > set_c_d_set_a > ( ( c > d ) > set_a ) > option_c_d ).
thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_Itf__a_J_001tf__a,type,
restri3984065703976872170on_a_a: ( option_a > option_a ) > set_option_a > option_a > option_a ).
thf(sy_c_Map_Orestrict__map_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,
restri3968632621895983051_a_c_d: ( assertion_a_b_d_c > option3890169911263941780_a_c_d ) > set_as909545710669178647_b_d_c > assertion_a_b_d_c > option3890169911263941780_a_c_d ).
thf(sy_c_Map_Orestrict__map_001tf__a_001tf__a,type,
restrict_map_a_a: ( a > option_a ) > set_a > a > option_a ).
thf(sy_c_Option_Obind_001tf__a_001tf__a,type,
bind_a_a: option_a > ( a > option_a ) > option_a ).
thf(sy_c_Option_Ocombine__options_001tf__a,type,
combine_options_a: ( a > a > a ) > option_a > option_a > option_a ).
thf(sy_c_Option_Ois__none_001tf__a,type,
is_none_a: option_a > $o ).
thf(sy_c_Option_Ooption_ONone_001_062_Itf__c_Mtf__d_J,type,
none_c_d: option_c_d ).
thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__a_J,type,
none_option_a: option_option_a ).
thf(sy_c_Option_Ooption_ONone_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,
none_P4438893274231186595_a_c_d: option3890169911263941780_a_c_d ).
thf(sy_c_Option_Ooption_ONone_001tf__a,type,
none_a: option_a ).
thf(sy_c_Option_Ooption_OSome_001_062_Itf__c_Mtf__d_J,type,
some_c_d: ( c > d ) > option_c_d ).
thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__a_J,type,
some_option_a: option_a > option_option_a ).
thf(sy_c_Option_Ooption_OSome_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,
some_P3194730542479778335_a_c_d: produc5213381314664832452_a_c_d > option3890169911263941780_a_c_d ).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
some_P1084500821511757806_a_c_d: product_prod_a_c_d > option6413918287372586467_a_c_d ).
thf(sy_c_Option_Ooption_OSome_001tf__a,type,
some_a: a > option_a ).
thf(sy_c_Option_Ooption_OSome_001tf__b,type,
some_b: b > option_b ).
thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001tf__a,type,
case_option_o_a: $o > ( a > $o ) > option_a > $o ).
thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_Itf__a_J_001tf__a,type,
case_o3148979394504432965on_a_a: option_a > ( a > option_a ) > option_a > option_a ).
thf(sy_c_Option_Ooption_Ocase__option_001tf__a_001tf__a,type,
case_option_a_a: a > ( a > a ) > option_a > a ).
thf(sy_c_Option_Ooption_Omap__option_001tf__a_001tf__a,type,
map_option_a_a: ( a > a ) > option_a > option_a ).
thf(sy_c_Option_Ooption_Opred__option_001tf__a,type,
pred_option_a: ( a > $o ) > option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__a_001tf__a,type,
rel_option_a_a: ( a > a > $o ) > option_a > option_a > $o ).
thf(sy_c_Option_Ooption_Oset__option_001t__Option__Ooption_Itf__a_J,type,
set_option_option_a2: option_option_a > set_option_a ).
thf(sy_c_Option_Ooption_Oset__option_001tf__a,type,
set_option_a2: option_a > set_a ).
thf(sy_c_Option_Ooption_Oset__option_001tf__b,type,
set_option_b2: option_b > set_b ).
thf(sy_c_Option_Ooption_Othe_001tf__a,type,
the_a: option_a > a ).
thf(sy_c_Option_Othese_001t__Option__Ooption_Itf__a_J,type,
these_option_a: set_option_option_a > set_option_a ).
thf(sy_c_Option_Othese_001tf__a,type,
these_a: set_option_a > set_a ).
thf(sy_c_Option_Othese_001tf__b,type,
these_b: set_option_b > set_b ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
bot_bot_set_option_a: set_option_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
bot_bot_set_a: set_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
bot_bot_set_b: set_b ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__c_J,type,
bot_bot_set_c: set_c ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
top_to1659475022456381882tion_a: set_option_option_a ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
top_top_set_option_a: set_option_a ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_J,type,
top_to5090759043282426983_b_d_c: set_as909545710669178647_b_d_c ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
top_top_set_a: set_a ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
top_top_set_b: set_b ).
thf(sy_c_Product__Type_OPair_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_Itf__c_Mtf__d_J,type,
produc7376592049607813182_a_c_d: ( ( c > d ) > set_a ) > ( c > d ) > produc5213381314664832452_a_c_d ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
produc8093790510458973071_a_c_d: product_prod_a_c_d > option6413918287372586467_a_c_d > produc5278197477302038359_a_c_d ).
thf(sy_c_Product__Type_OPair_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001t__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_Itf__c_Mtf__d_J_J,type,
produc8894421531525210148_a_c_d: assertion_a_b_d_c > produc5213381314664832452_a_c_d > produc5105196854009589546_a_c_d ).
thf(sy_c_Product__Type_OPair_001tf__a_001_062_Itf__c_Mtf__d_J,type,
product_Pair_a_c_d: a > ( c > d ) > product_prod_a_c_d ).
thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__a_J,type,
collect_option_a: ( option_a > $o ) > set_option_a ).
thf(sy_c_Set_OCollect_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,
collec2771355035510247705_a_c_d: ( produc5213381314664832452_a_c_d > $o ) > set_Pr336584576397674490_a_c_d ).
thf(sy_c_Set_OCollect_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,
collec4762846013371775487_a_c_d: ( produc5105196854009589546_a_c_d > $o ) > set_Pr1216123688828223200_a_c_d ).
thf(sy_c_Set_OCollect_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
collec7183461376620183714_b_d_c: ( assertion_a_b_d_c > $o ) > set_as909545710669178647_b_d_c ).
thf(sy_c_Set_OCollect_001tf__a,type,
collect_a: ( a > $o ) > set_a ).
thf(sy_c_Set_OCollect_001tf__b,type,
collect_b: ( b > $o ) > set_b ).
thf(sy_c_Set_OCollect_001tf__c,type,
collect_c: ( c > $o ) > set_c ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
image_2132136900116418507tion_a: ( option_a > option_option_a ) > set_option_a > set_option_option_a ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
image_7439109396645324421tion_a: ( option_a > option_a ) > set_option_a > set_option_a ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001tf__a,type,
image_option_a_a: ( option_a > a ) > set_option_a > set_a ).
thf(sy_c_Set_Oimage_001tf__a_001t__Option__Ooption_Itf__a_J,type,
image_a_option_a: ( a > option_a ) > set_a > set_option_a ).
thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(sy_c_Set_Oimage_001tf__b_001t__Option__Ooption_Itf__a_J,type,
image_b_option_a: ( b > option_a ) > set_b > set_option_a ).
thf(sy_c_Set_Oimage_001tf__b_001tf__a,type,
image_b_a: ( b > a ) > set_b > set_a ).
thf(sy_c_Set_Oimage_001tf__b_001tf__b,type,
image_b_b: ( b > b ) > set_b > set_b ).
thf(sy_c_Set_Oimage_001tf__c_001tf__d,type,
image_c_d: ( c > d ) > set_c > set_d ).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
insert605063979879581146tion_a: option_option_a > set_option_option_a > set_option_option_a ).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_Itf__a_J,type,
insert_option_a: option_a > set_option_a > set_option_a ).
thf(sy_c_Set_Oinsert_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,
insert9214331609911559156_a_c_d: produc5213381314664832452_a_c_d > set_Pr336584576397674490_a_c_d > set_Pr336584576397674490_a_c_d ).
thf(sy_c_Set_Oinsert_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,
insert1952503980790619482_a_c_d: produc5105196854009589546_a_c_d > set_Pr1216123688828223200_a_c_d > set_Pr1216123688828223200_a_c_d ).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
insert4534936382041156343od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(sy_c_Set_Oinsert_001tf__a,type,
insert_a: a > set_a > set_a ).
thf(sy_c_Set_Oinsert_001tf__b,type,
insert_b: b > set_b > set_b ).
thf(sy_c_Set_Oinsert_001tf__c,type,
insert_c: c > set_c > set_c ).
thf(sy_c_Set_Oinsert_001tf__d,type,
insert_d: d > set_d > set_d ).
thf(sy_c_Transfer_Obi__unique_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,
bi_uni8285078783686190927_b_d_c: ( assertion_a_b_d_c > assertion_a_b_d_c > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001tf__a_001tf__a,type,
bi_unique_a_a: ( a > a > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001tf__a_001tf__c,type,
bi_unique_a_c: ( a > c > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001tf__c_001tf__a,type,
bi_unique_c_a: ( c > a > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001tf__c_001tf__c,type,
bi_unique_c_c: ( c > c > $o ) > $o ).
thf(sy_c_UnboundedLogic_Oassertion_OAnd_001tf__a_001tf__b_001tf__d_001tf__c,type,
and_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OBounded_001tf__a_001tf__b_001tf__d_001tf__c,type,
bounded_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OExists_001tf__a_001tf__a_001tf__b_001t__Option__Ooption_Itf__a_J,type,
exists7165000112504185261tion_a: a > assert1556940916145061938on_a_a > assert1556940916145061938on_a_a ).
thf(sy_c_UnboundedLogic_Oassertion_OExists_001tf__c_001tf__a_001tf__b_001tf__d,type,
exists_c_a_b_d: c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OForall_001tf__a_001tf__a_001tf__b_001t__Option__Ooption_Itf__a_J,type,
forall5484998627543102345tion_a: a > assert1556940916145061938on_a_a > assert1556940916145061938on_a_a ).
thf(sy_c_UnboundedLogic_Oassertion_OForall_001tf__c_001tf__a_001tf__b_001tf__d,type,
forall_c_a_b_d: c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OImp_001tf__a_001tf__b_001tf__d_001tf__c,type,
imp_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OMult_001tf__b_001tf__a_001tf__d_001tf__c,type,
mult_b_a_d_c: b > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OOr_001tf__a_001tf__b_001tf__d_001tf__c,type,
or_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OPred_001tf__a_001tf__b_001tf__d_001tf__c,type,
pred_a_b_d_c: assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OSem_001tf__c_001tf__d_001tf__a_001tf__b,type,
sem_c_d_a_b: ( ( c > d ) > a > $o ) > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OStar_001tf__a_001tf__b_001tf__d_001tf__c,type,
star_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OWand_001tf__a_001tf__b_001tf__d_001tf__c,type,
wand_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_OWildcard_001tf__a_001tf__b_001tf__d_001tf__c,type,
wildcard_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_Ocase__assertion_001tf__c_001tf__d_001tf__a_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J_001tf__b,type,
case_a2736964712663357406_d_c_b: ( ( ( c > d ) > a > $o ) > assertion_a_b_d_c ) > ( b > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > ( c > assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_Omap__assertion_001tf__b_001tf__b_001tf__a_001tf__d_001tf__c,type,
map_as2132001898603344138_a_d_c: ( b > b ) > assertion_a_b_d_c > assertion_a_b_d_c ).
thf(sy_c_UnboundedLogic_Oassertion_Opred__assertion_001tf__b_001tf__a_001tf__d_001tf__c,type,
pred_a5408123710409757427_a_d_c: ( b > $o ) > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001t__Option__Ooption_Itf__a_J_001tf__b_001tf__a_001tf__d_001tf__c,type,
rel_as5306512150936529868_a_d_c: ( option_a > b > $o ) > assert3107445333071088380_a_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__a_001tf__b_001tf__a_001tf__d_001tf__c,type,
rel_as1194089545255703174_a_d_c: ( a > b > $o ) > assertion_a_a_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__d_001tf__c,type,
rel_as3901196536028962306_a_d_c: ( b > option_a > $o ) > assertion_a_b_d_c > assert3107445333071088380_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001tf__a_001tf__a_001tf__d_001tf__c,type,
rel_as373026983500813000_a_d_c: ( b > a > $o ) > assertion_a_b_d_c > assertion_a_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001tf__b_001tf__a_001tf__d_001tf__c,type,
rel_as1860989020795611527_a_d_c: ( b > b > $o ) > assertion_a_b_d_c > assertion_a_b_d_c > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_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_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_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_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_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__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_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_v,type,
v: c ).
thf(sy_v_valid,type,
valid: a > $o ).
thf(sy_v_x____,type,
x: a ).
% Relevant facts (841)
thf(fact_0_smaller__interpI,axiom,
! [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ! [S: c > d,X: a] :
( ( member_a @ X @ ( Delta @ S ) )
=> ( member_a @ X @ ( Delta2 @ S ) ) )
=> ( smaller_interp_c_d_a @ Delta @ Delta2 ) ) ).
% smaller_interpI
thf(fact_1_smaller__interp__refl,axiom,
! [Delta: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ Delta @ Delta ) ).
% smaller_interp_refl
thf(fact_2_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_3_commutative,axiom,
! [A: a,B: a] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ) ).
% commutative
thf(fact_4_can__divide,axiom,
! [P: b,A: a,B: a] :
( ( ( mult @ P @ A )
= ( mult @ P @ B ) )
=> ( A = B ) ) ).
% can_divide
thf(fact_5_asm0,axiom,
smaller_interp_c_d_a @ delta @ delta2 ).
% asm0
thf(fact_6_non__increasingI,axiom,
! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta4 ) @ ( F @ Delta3 ) ) )
=> ( non_increasing_c_d_a @ F ) ) ).
% non_increasingI
thf(fact_7_smaller__interp__applies__cons,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a,A: a,S2: c > d] :
( ( smaller_interp_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta ) @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 ) )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S2 @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S2 @ Delta2 @ A2 ) ) ) ).
% smaller_interp_applies_cons
thf(fact_8_assms,axiom,
non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ a2 ) ).
% assms
thf(fact_9_asm1,axiom,
member_a @ x @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ v @ a2 ) @ delta2 @ s ) ).
% asm1
thf(fact_10_unique__inv,axiom,
! [A: a,P: b,B: a] :
( ( A
= ( mult @ P @ B ) )
= ( B
= ( mult @ ( sinv @ P ) @ A ) ) ) ).
% unique_inv
thf(fact_11_non__increasing__instantiate,axiom,
! [A2: assertion_a_b_d_c,X2: a,Delta2: ( c > d ) > set_a,S2: c > d,Delta: ( c > d ) > set_a] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ S2 ) )
=> ( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ S2 ) ) ) ) ) ).
% non_increasing_instantiate
thf(fact_12_logic_Oapplies__eq_Ocong,axiom,
applies_eq_a_b_d_c = applies_eq_a_b_d_c ).
% logic.applies_eq.cong
thf(fact_13_indep__implies__non__increasing,axiom,
! [A2: assertion_a_b_d_c] :
( ( indep_interp_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) ) ) ).
% indep_implies_non_increasing
thf(fact_14_indep__interp__def,axiom,
! [A2: assertion_a_b_d_c] :
( ( indep_interp_a_b_d_c @ plus @ mult @ valid @ A2 )
= ( ! [X3: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ X3 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ X3 @ S3 @ Delta6 @ A2 ) ) ) ) ).
% indep_interp_def
thf(fact_15_mono__exists,axiom,
! [A2: assertion_a_b_d_c,V: c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ V @ A2 ) ) ) ) ).
% mono_exists
thf(fact_16_valid__mono,axiom,
! [A: a,B: a] :
( ( ( valid @ A )
& ( pre_larger_a @ plus @ A @ B ) )
=> ( valid @ B ) ) ).
% valid_mono
thf(fact_17_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_18_pure__def,axiom,
! [A2: assertion_a_b_d_c] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
= ( ! [Sigma: a,Sigma2: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta6 @ A2 ) ) ) ) ).
% pure_def
thf(fact_19_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_20_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_21_compatible__multiples,axiom,
! [P: b,A: a,Q: b,B: a] :
( ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) )
=> ( pre_compatible_a @ plus @ A @ B ) ) ).
% compatible_multiples
thf(fact_22_one__neutral,axiom,
! [A: a] :
( ( mult @ one @ A )
= A ) ).
% one_neutral
thf(fact_23_smaller__empty,axiom,
! [X2: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ empty_interp_c_d_a @ X2 ) ).
% smaller_empty
thf(fact_24_sat_Osimps_I8_J,axiom,
! [Sigma3: a,S2: a > option_a,Delta: ( a > option_a ) > set_a,X2: a,A2: assert1556940916145061938on_a_a] :
( ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( exists7165000112504185261tion_a @ X2 @ A2 ) )
= ( ? [V2: option_a] : ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_a_option_a @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ).
% sat.simps(8)
thf(fact_25_sat_Osimps_I8_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,X2: c,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( exists_c_a_b_d @ X2 @ A2 ) )
= ( ? [V2: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_c_d @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ).
% sat.simps(8)
thf(fact_26_non__increasing__def,axiom,
( non_increasing_c_d_a
= ( ^ [F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F2 @ Delta6 ) @ ( F2 @ Delta5 ) ) ) ) ) ).
% non_increasing_def
thf(fact_27_monotonicI,axiom,
! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta3 ) @ ( F @ Delta4 ) ) )
=> ( monotonic_c_d_a @ F ) ) ).
% monotonicI
thf(fact_28_monotonic__def,axiom,
( monotonic_c_d_a
= ( ^ [F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F2 @ Delta5 ) @ ( F2 @ Delta6 ) ) ) ) ) ).
% monotonic_def
thf(fact_29_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_30_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_31_mono__instantiate,axiom,
! [A2: assertion_a_b_d_c,X2: a,Delta: ( c > d ) > set_a,S2: c > d,Delta2: ( c > d ) > set_a] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ S2 ) )
=> ( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta2 @ S2 ) ) ) ) ) ).
% mono_instantiate
thf(fact_32_intuitionistic__def,axiom,
! [S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S2 @ Delta @ A2 )
= ( ! [A3: a,B2: a] :
( ( ( pre_larger_a @ plus @ A3 @ B2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B2 @ S2 @ Delta @ A2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ).
% intuitionistic_def
thf(fact_33_intuitionisticI,axiom,
! [S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [A4: a,B3: a] :
( ( ( pre_larger_a @ plus @ A4 @ B3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B3 @ S2 @ Delta @ A2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S2 @ Delta @ A2 ) )
=> ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S2 @ Delta @ A2 ) ) ).
% intuitionisticI
thf(fact_34_not__in__fv__def,axiom,
! [A2: assertion_a_b_d_c,S4: set_c] :
( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A2 @ S4 )
= ( ! [Sigma: a,S3: c > d,Delta5: ( c > d ) > set_a,S5: c > d] :
( ( equal_outside_c_d @ S3 @ S5 @ S4 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S5 @ Delta5 @ A2 ) ) ) ) ) ).
% not_in_fv_def
thf(fact_35_logic_Oindep__interp_Ocong,axiom,
indep_interp_a_b_d_c = indep_interp_a_b_d_c ).
% logic.indep_interp.cong
thf(fact_36_unambiguous__def,axiom,
! [Delta: ( a > option_a ) > set_a,A2: assert1556940916145061938on_a_a,X2: a] :
( ( unambi704529886615442436tion_a @ plus @ mult @ valid @ Delta @ A2 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: option_a,V22: option_a,S3: 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 @ S3 @ X2 @ V1 ) @ Delta @ A2 )
& ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma_2 @ ( fun_upd_a_option_a @ S3 @ X2 @ V22 ) @ Delta @ A2 ) )
=> ( V1 = V22 ) ) ) ) ).
% unambiguous_def
thf(fact_37_unambiguous__def,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,X2: c] :
( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta @ A2 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: d,V22: d,S3: c > d] :
( ( ( pre_compatible_a @ plus @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_1 @ ( fun_upd_c_d @ S3 @ X2 @ V1 ) @ Delta @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_2 @ ( fun_upd_c_d @ S3 @ X2 @ V22 ) @ Delta @ A2 ) )
=> ( V1 = V22 ) ) ) ) ).
% unambiguous_def
thf(fact_38_unambiguousI,axiom,
! [X2: a,Delta: ( a > option_a ) > set_a,A2: assert1556940916145061938on_a_a] :
( ! [Sigma_12: a,Sigma_22: a,V12: option_a,V23: option_a,S: 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 @ S @ X2 @ V12 ) @ Delta @ A2 )
& ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma_22 @ ( fun_upd_a_option_a @ S @ X2 @ V23 ) @ Delta @ A2 ) )
=> ( V12 = V23 ) )
=> ( unambi704529886615442436tion_a @ plus @ mult @ valid @ Delta @ A2 @ X2 ) ) ).
% unambiguousI
thf(fact_39_unambiguousI,axiom,
! [X2: c,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [Sigma_12: a,Sigma_22: a,V12: d,V23: d,S: c > d] :
( ( ( pre_compatible_a @ plus @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_12 @ ( fun_upd_c_d @ S @ X2 @ V12 ) @ Delta @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma_22 @ ( fun_upd_c_d @ S @ X2 @ V23 ) @ Delta @ A2 ) )
=> ( V12 = V23 ) )
=> ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta @ A2 @ X2 ) ) ).
% unambiguousI
thf(fact_40_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_41_sat_Osimps_I10_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ pred_a_b_d_c )
= ( member_a @ Sigma3 @ ( Delta @ S2 ) ) ) ).
% sat.simps(10)
thf(fact_42_non__increasing__wand,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% non_increasing_wand
thf(fact_43_non__increasing__imp,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% non_increasing_imp
thf(fact_44_mono__wand,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% mono_wand
thf(fact_45_mem__Collect__eq,axiom,
! [A: b,P2: b > $o] :
( ( member_b @ A @ ( collect_b @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_46_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_47_mem__Collect__eq,axiom,
! [A: a,P2: a > $o] :
( ( member_a @ A @ ( collect_a @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_48_Collect__mem__eq,axiom,
! [A2: set_b] :
( ( collect_b
@ ^ [X3: b] : ( member_b @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_49_Collect__mem__eq,axiom,
! [A2: set_option_a] :
( ( collect_option_a
@ ^ [X3: option_a] : ( member_option_a @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_50_Collect__mem__eq,axiom,
! [A2: set_a] :
( ( collect_a
@ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_51_Collect__cong,axiom,
! [P2: a > $o,Q2: a > $o] :
( ! [X: a] :
( ( P2 @ X )
= ( Q2 @ X ) )
=> ( ( collect_a @ P2 )
= ( collect_a @ Q2 ) ) ) ).
% Collect_cong
thf(fact_52_Collect__cong,axiom,
! [P2: option_a > $o,Q2: option_a > $o] :
( ! [X: option_a] :
( ( P2 @ X )
= ( Q2 @ X ) )
=> ( ( collect_option_a @ P2 )
= ( collect_option_a @ Q2 ) ) ) ).
% Collect_cong
thf(fact_53_mono__imp,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% mono_imp
thf(fact_54_non__increasing__bounded,axiom,
! [A2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ).
% non_increasing_bounded
thf(fact_55_mono__bounded,axiom,
! [A2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ).
% mono_bounded
thf(fact_56_non__increasing__or,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% non_increasing_or
thf(fact_57_sat_Osimps_I6_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( or_a_b_d_c @ A2 @ B4 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ A2 )
| ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ B4 ) ) ) ).
% sat.simps(6)
thf(fact_58_sat_Osimps_I5_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( imp_a_b_d_c @ A2 @ B4 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ B4 ) ) ) ).
% sat.simps(5)
thf(fact_59_sat__imp,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ B4 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ).
% sat_imp
thf(fact_60_sat_Osimps_I11_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( bounded_a_b_d_c @ A2 ) )
= ( ( valid @ Sigma3 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ A2 ) ) ) ).
% sat.simps(11)
thf(fact_61_mono__or,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% mono_or
thf(fact_62_hoare__triple__input,axiom,
! [P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta )
= ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ ( bounded_a_b_d_c @ P2 ) @ C @ Q2 @ Delta ) ) ).
% hoare_triple_input
thf(fact_63_equivalentI,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ! [Sigma4: a,S: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ B4 ) )
=> ( ! [Sigma4: a,S: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ B4 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ A2 ) )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 ) ) ) ).
% equivalentI
thf(fact_64_mono__forall,axiom,
! [A2: assertion_a_b_d_c,V: c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( forall_c_a_b_d @ V @ A2 ) ) ) ) ).
% mono_forall
thf(fact_65_non__increasing__and,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% non_increasing_and
thf(fact_66_mono__and,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% mono_and
thf(fact_67_sat_Osimps_I3_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( wand_a_b_d_c @ A2 @ B4 ) )
= ( ! [A3: a,Sigma2: a] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta @ A2 )
& ( ( some_a @ Sigma2 )
= ( plus @ Sigma3 @ A3 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S2 @ Delta @ B4 ) ) ) ) ).
% sat.simps(3)
thf(fact_68_sat__wand,axiom,
! [S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,Sigma3: a,B4: assertion_a_b_d_c] :
( ! [A4: a,Sigma5: a] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S2 @ Delta @ A2 )
& ( ( some_a @ Sigma5 )
= ( plus @ Sigma3 @ A4 ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S2 @ Delta @ B4 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ).
% sat_wand
thf(fact_69_sat_Osimps_I9_J,axiom,
! [Sigma3: a,S2: a > option_a,Delta: ( a > option_a ) > set_a,X2: a,A2: assert1556940916145061938on_a_a] :
( ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( forall5484998627543102345tion_a @ X2 @ A2 ) )
= ( ! [V2: option_a] : ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_a_option_a @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ).
% sat.simps(9)
thf(fact_70_sat_Osimps_I9_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,X2: c,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( forall_c_a_b_d @ X2 @ A2 ) )
= ( ! [V2: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_c_d @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ).
% sat.simps(9)
thf(fact_71_sat__forall,axiom,
! [Sigma3: a,S2: a > option_a,X2: a,Delta: ( a > option_a ) > set_a,A2: assert1556940916145061938on_a_a] :
( ! [V3: option_a] : ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_a_option_a @ S2 @ X2 @ V3 ) @ Delta @ A2 )
=> ( sat_a_b_a_option_a @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( forall5484998627543102345tion_a @ X2 @ A2 ) ) ) ).
% sat_forall
thf(fact_72_sat__forall,axiom,
! [Sigma3: a,S2: c > d,X2: c,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [V3: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ ( fun_upd_c_d @ S2 @ X2 @ V3 ) @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( forall_c_a_b_d @ X2 @ A2 ) ) ) ).
% sat_forall
thf(fact_73_non__increasing__mult,axiom,
! [A2: assertion_a_b_d_c,Pi: b] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ).
% non_increasing_mult
thf(fact_74_local_Omono__mult,axiom,
! [A2: assertion_a_b_d_c,Pi: b] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ).
% local.mono_mult
thf(fact_75_move__sum,axiom,
! [A: a,A1: a,A22: a,B: a,B1: a,B22: a,X2: a,X1: a,X22: a] :
( ( ( some_a @ A )
= ( plus @ A1 @ A22 ) )
=> ( ( ( some_a @ B )
= ( plus @ B1 @ B22 ) )
=> ( ( ( some_a @ X2 )
= ( plus @ A @ B ) )
=> ( ( ( some_a @ X1 )
= ( plus @ A1 @ B1 ) )
=> ( ( ( some_a @ X22 )
= ( plus @ A22 @ B22 ) )
=> ( ( some_a @ X2 )
= ( plus @ X1 @ X22 ) ) ) ) ) ) ) ).
% move_sum
thf(fact_76_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_77_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_78_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_79_sum__both__larger,axiom,
! [X4: a,A5: a,B5: a,X2: a,A: a,B: a] :
( ( ( some_a @ X4 )
= ( plus @ A5 @ B5 ) )
=> ( ( ( some_a @ X2 )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ A5 @ A )
=> ( ( pre_larger_a @ plus @ B5 @ B )
=> ( pre_larger_a @ plus @ X4 @ X2 ) ) ) ) ) ).
% sum_both_larger
thf(fact_80_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_81_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_82_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_83_sat__mult,axiom,
! [Sigma3: a,P: b,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [A4: a] :
( ( Sigma3
= ( mult @ P @ A4 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S2 @ Delta @ A2 ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% sat_mult
thf(fact_84_sat_Osimps_I1_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,P: b,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( mult_b_a_d_c @ P @ A2 ) )
= ( ? [A3: a] :
( ( Sigma3
= ( mult @ P @ A3 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ).
% sat.simps(1)
thf(fact_85_sat_Osimps_I7_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( and_a_b_d_c @ A2 @ B4 ) )
= ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ B4 ) ) ) ).
% sat.simps(7)
thf(fact_86_DotAnd,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ).
% DotAnd
thf(fact_87_DotForall,axiom,
! [P: b,X2: c,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A2 ) ) @ Delta @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% DotForall
thf(fact_88_DotExists,axiom,
! [P: b,X2: c,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A2 ) ) @ Delta @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% DotExists
thf(fact_89_DotWand,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% DotWand
thf(fact_90_DotOr,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% DotOr
thf(fact_91_DotImp,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% DotImp
thf(fact_92_DotPure,axiom,
! [A2: assertion_a_b_d_c,P: b,Delta: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta @ A2 ) ) ).
% DotPure
thf(fact_93_DotFull,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ one @ A2 ) @ Delta @ A2 ) ).
% DotFull
thf(fact_94_hoare__triple__output,axiom,
! [C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( valid_command_a_c_d @ valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta )
= ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ ( bounded_a_b_d_c @ Q2 ) @ Delta ) ) ) ).
% hoare_triple_output
thf(fact_95_DotDot,axiom,
! [P: b,Q: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ ( smult @ P @ Q ) @ A2 ) ) ).
% DotDot
thf(fact_96_mult__one__same2,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ ( mult_b_a_d_c @ one @ A2 ) ) ).
% mult_one_same2
thf(fact_97_mult__one__same1,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ one @ A2 ) @ Delta @ A2 ) ).
% mult_one_same1
thf(fact_98_DotStar,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% DotStar
thf(fact_99_non__inc__star,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% non_inc_star
thf(fact_100_mono__star,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% mono_star
thf(fact_101_sat_Osimps_I2_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( star_a_b_d_c @ A2 @ B4 ) )
= ( ? [A3: a,B2: a] :
( ( ( some_a @ Sigma3 )
= ( plus @ A3 @ B2 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B2 @ S2 @ Delta @ B4 ) ) ) ) ).
% sat.simps(2)
thf(fact_102_WildPure,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta @ A2 ) ) ).
% WildPure
thf(fact_103_non__increasing__sem,axiom,
! [B4: ( c > d ) > a > $o] : ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( sem_c_d_a_b @ B4 ) ) ) ).
% non_increasing_sem
thf(fact_104_mono__sem,axiom,
! [B4: ( c > d ) > a > $o] : ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( sem_c_d_a_b @ B4 ) ) ) ).
% mono_sem
thf(fact_105_can__factorize,axiom,
! [Q: b,P: b] :
? [R: b] :
( Q
= ( smult @ R @ P ) ) ).
% can_factorize
thf(fact_106_smult__asso,axiom,
! [P: b,Q: b,R2: b] :
( ( smult @ ( smult @ P @ Q ) @ R2 )
= ( smult @ P @ ( smult @ Q @ R2 ) ) ) ).
% smult_asso
thf(fact_107_smult__comm,axiom,
! [P: b,Q: b] :
( ( smult @ P @ Q )
= ( smult @ Q @ P ) ) ).
% smult_comm
thf(fact_108_double__mult,axiom,
! [P: b,Q: b,A: a] :
( ( mult @ P @ ( mult @ Q @ A ) )
= ( mult @ ( smult @ P @ Q ) @ A ) ) ).
% double_mult
thf(fact_109_sone__neutral,axiom,
! [P: b] :
( ( smult @ one @ P )
= P ) ).
% sone_neutral
thf(fact_110_sinv__inverse,axiom,
! [P: b] :
( ( smult @ P @ ( sinv @ P ) )
= one ) ).
% sinv_inverse
thf(fact_111_DotPos,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c,Pi: b] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 )
= ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ Pi @ A2 ) @ Delta @ ( mult_b_a_d_c @ Pi @ B4 ) ) ) ).
% DotPos
thf(fact_112_entailsI,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ! [Sigma4: a,S: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ B4 ) )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 ) ) ).
% entailsI
thf(fact_113_entails__def,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 )
= ( ! [Sigma: a,S3: c > d] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S3 @ Delta @ A2 )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S3 @ Delta @ B4 ) ) ) ) ).
% entails_def
thf(fact_114_sat_Osimps_I12_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( wildcard_a_b_d_c @ A2 ) )
= ( ? [A3: a,P3: b] :
( ( Sigma3
= ( mult @ P3 @ A3 ) )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ).
% sat.simps(12)
thf(fact_115_WildPos,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta @ ( wildcard_a_b_d_c @ B4 ) ) ) ).
% WildPos
thf(fact_116_equivalent__def,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( equivalent_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 )
= ( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ B4 )
& ( entails_a_b_d_c @ plus @ mult @ valid @ B4 @ Delta @ A2 ) ) ) ).
% equivalent_def
thf(fact_117_WildWild,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ).
% WildWild
thf(fact_118_unambiguous__star,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,X2: c,B4: assertion_a_b_d_c] :
( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta @ A2 @ X2 )
=> ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta @ ( star_a_b_d_c @ A2 @ B4 ) @ X2 ) ) ).
% unambiguous_star
thf(fact_119_sat_Osimps_I4_J,axiom,
! [Sigma3: a,S2: c > d,Delta: ( c > d ) > set_a,B: ( c > d ) > a > $o] :
( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta @ ( sem_c_d_a_b @ B ) )
= ( B @ S2 @ Sigma3 ) ) ).
% sat.simps(4)
thf(fact_120_mono__wild,axiom,
! [A2: assertion_a_b_d_c] :
( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% mono_wild
thf(fact_121_non__increasing__wild,axiom,
! [A2: assertion_a_b_d_c] :
( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% non_increasing_wild
thf(fact_122_dot__star1,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% dot_star1
thf(fact_123_dot__star2,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ).
% dot_star2
thf(fact_124_DotWild,axiom,
! [P: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ).
% DotWild
thf(fact_125_WildDot,axiom,
! [P: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ).
% WildDot
thf(fact_126_dot__exists1,axiom,
! [P: b,X2: c,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A2 ) ) @ Delta @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% dot_exists1
thf(fact_127_dot__exists2,axiom,
! [X2: c,P: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A2 ) ) ) ).
% dot_exists2
thf(fact_128_dot__forall1,axiom,
! [P: b,X2: c,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A2 ) ) @ Delta @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% dot_forall1
thf(fact_129_dot__forall2,axiom,
! [X2: c,P: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A2 ) ) ) ).
% dot_forall2
thf(fact_130_dot__and1,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% dot_and1
thf(fact_131_dot__and2,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ).
% dot_and2
thf(fact_132_dot__imp1,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ).
% dot_imp1
thf(fact_133_dot__imp2,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% dot_imp2
thf(fact_134_dot__or1,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% dot_or1
thf(fact_135_dot__or2,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B4 ) ) ) ).
% dot_or2
thf(fact_136_dot__wand1,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ).
% dot_wand1
thf(fact_137_dot__wand2,axiom,
! [P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ).
% dot_wand2
thf(fact_138_WildStar1,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( star_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( star_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B4 ) ) ) ).
% WildStar1
thf(fact_139_WildForall,axiom,
! [X2: c,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( forall_c_a_b_d @ X2 @ A2 ) ) @ Delta @ ( forall_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% WildForall
thf(fact_140_WildAnd,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( and_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( and_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B4 ) ) ) ).
% WildAnd
thf(fact_141_pure__mult1,axiom,
! [A2: assertion_a_b_d_c,P: b,Delta: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta @ A2 ) ) ).
% pure_mult1
thf(fact_142_pure__mult2,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,P: b] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).
% pure_mult2
thf(fact_143_WildExists,axiom,
! [X2: c,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( exists_c_a_b_d @ X2 @ A2 ) ) @ Delta @ ( exists_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% WildExists
thf(fact_144_WildOr,axiom,
! [A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( equivalent_a_b_d_c @ plus @ mult @ valid @ ( wildcard_a_b_d_c @ ( or_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( or_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B4 ) ) ) ).
% WildOr
thf(fact_145_dot__mult1,axiom,
! [P: b,Q: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ ( smult @ P @ Q ) @ A2 ) ) ).
% dot_mult1
thf(fact_146_dot__mult2,axiom,
! [P: b,Q: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( mult_b_a_d_c @ ( smult @ P @ Q ) @ A2 ) @ Delta @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) ) ).
% dot_mult2
thf(fact_147_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_148_frame__rule,axiom,
! [C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,R3: assertion_a_b_d_c] :
( ( valid_command_a_c_d @ valid @ C )
=> ( ( safety844553430189520448_a_c_d @ plus @ valid @ C )
=> ( ( frame_property_a_c_d @ plus @ valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta )
=> ( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ R3 @ ( modified_a_c_d @ C ) )
=> ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ P2 @ R3 ) @ C @ ( star_a_b_d_c @ Q2 @ R3 ) @ Delta ) ) ) ) ) ) ).
% frame_rule
thf(fact_149_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_150_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_151_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_152_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_153_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_154_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_155_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_156_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_157_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_158_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_159_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_160_logic_Osat_Ocong,axiom,
sat_a_b_c_d = sat_a_b_c_d ).
% logic.sat.cong
thf(fact_161_logic_Oentails_Ocong,axiom,
entails_a_b_d_c = entails_a_b_d_c ).
% logic.entails.cong
thf(fact_162_logic_Oequivalent_Ocong,axiom,
equivalent_a_b_d_c = equivalent_a_b_d_c ).
% logic.equivalent.cong
thf(fact_163_pre__logic_Ocompatible_Ocong,axiom,
pre_compatible_a = pre_compatible_a ).
% pre_logic.compatible.cong
thf(fact_164_pre__logic_Olarger_Ocong,axiom,
pre_larger_a = pre_larger_a ).
% pre_logic.larger.cong
thf(fact_165_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_166_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_167_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_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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_179_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_180_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_181_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_182_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_183_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_184_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_185_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_186_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_187_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_188_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_189_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_190_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_191_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_192_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_193_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_194_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_195_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_196_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_197_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_198_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_199_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_200_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_201_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_202_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_203_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_204_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_205_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_206_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_207_pre__logic_Olarger__def,axiom,
( pre_larger_a
= ( ^ [Plus: a > a > option_a,A3: a,B2: a] :
? [C2: a] :
( ( some_a @ A3 )
= ( Plus @ B2 @ C2 ) ) ) ) ).
% pre_logic.larger_def
thf(fact_208_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_209_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_210_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_211_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_212_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_213_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_214_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_215_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_216_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_217_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_218_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_219_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_220_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_221_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_222_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_223_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_224_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_225_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_226_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_227_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_228_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_229_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_230_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_231_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_232_fun__upd__upd,axiom,
! [F: c > d,X2: c,Y: d,Z: d] :
( ( fun_upd_c_d @ ( fun_upd_c_d @ F @ X2 @ Y ) @ X2 @ Z )
= ( fun_upd_c_d @ F @ X2 @ Z ) ) ).
% fun_upd_upd
thf(fact_233_fun__upd__upd,axiom,
! [F: a > option_a,X2: a,Y: option_a,Z: option_a] :
( ( fun_upd_a_option_a @ ( fun_upd_a_option_a @ F @ X2 @ Y ) @ X2 @ Z )
= ( fun_upd_a_option_a @ F @ X2 @ Z ) ) ).
% fun_upd_upd
thf(fact_234_fun__upd__triv,axiom,
! [F: c > d,X2: c] :
( ( fun_upd_c_d @ F @ X2 @ ( F @ X2 ) )
= F ) ).
% fun_upd_triv
thf(fact_235_fun__upd__triv,axiom,
! [F: a > option_a,X2: a] :
( ( fun_upd_a_option_a @ F @ X2 @ ( F @ X2 ) )
= F ) ).
% fun_upd_triv
thf(fact_236_fun__upd__apply,axiom,
( fun_upd_c_d
= ( ^ [F2: c > d,X3: c,Y2: d,Z2: c] : ( if_d @ ( Z2 = X3 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_237_fun__upd__apply,axiom,
( fun_upd_a_option_a
= ( ^ [F2: a > option_a,X3: a,Y2: option_a,Z2: a] : ( if_option_a @ ( Z2 = X3 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_238_logic__axioms,axiom,
logic_a_b @ plus @ mult @ smult @ sadd @ sinv @ one @ valid ).
% logic_axioms
thf(fact_239_option_Oinject,axiom,
! [X22: a,Y23: a] :
( ( ( some_a @ X22 )
= ( some_a @ Y23 ) )
= ( X22 = Y23 ) ) ).
% option.inject
thf(fact_240_logic_Oframe__rule,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,R3: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_c_d @ Valid @ C )
=> ( ( safety844553430189520448_a_c_d @ Plus2 @ Valid @ C )
=> ( ( frame_property_a_c_d @ Plus2 @ Valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ R3 @ ( modified_a_c_d @ C ) )
=> ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ P2 @ R3 ) @ C @ ( star_a_b_d_c @ Q2 @ R3 ) @ Delta ) ) ) ) ) ) ) ).
% logic.frame_rule
thf(fact_241_compatible__def,axiom,
! [A: a,B: a] :
( ( pre_compatible_a @ plus @ A @ B )
= ( ( plus @ A @ B )
!= none_a ) ) ).
% compatible_def
thf(fact_242_distrib__mult,axiom,
! [P: b,Q: b,X2: a] :
( ( some_a @ ( mult @ ( sadd @ P @ Q ) @ X2 ) )
= ( plus @ ( mult @ P @ X2 ) @ ( mult @ Q @ X2 ) ) ) ).
% distrib_mult
thf(fact_243_sadd__comm,axiom,
! [P: b,Q: b] :
( ( sadd @ P @ Q )
= ( sadd @ Q @ P ) ) ).
% sadd_comm
thf(fact_244_smult__distrib,axiom,
! [P: b,Q: b,R2: b] :
( ( smult @ P @ ( sadd @ Q @ R2 ) )
= ( sadd @ ( smult @ P @ Q ) @ ( smult @ P @ R2 ) ) ) ).
% smult_distrib
thf(fact_245_not__Some__eq,axiom,
! [X2: option_a] :
( ( ! [Y2: a] :
( X2
!= ( some_a @ Y2 ) ) )
= ( X2 = none_a ) ) ).
% not_Some_eq
thf(fact_246_not__None__eq,axiom,
! [X2: option_a] :
( ( X2 != none_a )
= ( ? [Y2: a] :
( X2
= ( some_a @ Y2 ) ) ) ) ).
% not_None_eq
thf(fact_247_logic_Osadd__comm,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Sadd @ P @ Q )
= ( Sadd @ Q @ P ) ) ) ).
% logic.sadd_comm
thf(fact_248_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_249_logic_Osmult__asso,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ ( Smult @ P @ Q ) @ R2 )
= ( Smult @ P @ ( Smult @ Q @ R2 ) ) ) ) ).
% logic.smult_asso
thf(fact_250_logic_Osmult__comm,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ Q )
= ( Smult @ Q @ P ) ) ) ).
% logic.smult_comm
thf(fact_251_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_252_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_253_logic_Odouble__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Mult @ P @ ( Mult @ Q @ A ) )
= ( Mult @ ( Smult @ P @ Q ) @ A ) ) ) ).
% logic.double_mult
thf(fact_254_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_255_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_256_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_257_logic_Osmult__distrib,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R2: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ ( Sadd @ Q @ R2 ) )
= ( Sadd @ ( Smult @ P @ Q ) @ ( Smult @ P @ R2 ) ) ) ) ).
% logic.smult_distrib
thf(fact_258_option_Odistinct_I1_J,axiom,
! [X22: a] :
( none_a
!= ( some_a @ X22 ) ) ).
% option.distinct(1)
thf(fact_259_option_OdiscI,axiom,
! [Option: option_a,X22: a] :
( ( Option
= ( some_a @ X22 ) )
=> ( Option != none_a ) ) ).
% option.discI
thf(fact_260_option_Oexhaust,axiom,
! [Y: option_a] :
( ( Y != none_a )
=> ~ ! [X23: a] :
( Y
!= ( some_a @ X23 ) ) ) ).
% option.exhaust
thf(fact_261_split__option__ex,axiom,
( ( ^ [P4: option_a > $o] :
? [X5: option_a] : ( P4 @ X5 ) )
= ( ^ [P5: option_a > $o] :
( ( P5 @ none_a )
| ? [X3: a] : ( P5 @ ( some_a @ X3 ) ) ) ) ) ).
% split_option_ex
thf(fact_262_split__option__all,axiom,
( ( ^ [P4: option_a > $o] :
! [X5: option_a] : ( P4 @ X5 ) )
= ( ^ [P5: option_a > $o] :
( ( P5 @ none_a )
& ! [X3: a] : ( P5 @ ( some_a @ X3 ) ) ) ) ) ).
% split_option_all
thf(fact_263_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 ) )
=> ( ! [A4: a,B3: a] :
( ( X2
= ( some_a @ A4 ) )
=> ( ( Y
= ( some_a @ B3 ) )
=> ( P2 @ X2 @ Y ) ) )
=> ( P2 @ X2 @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_264_logic_Odistrib__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,X2: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( some_a @ ( Mult @ ( Sadd @ P @ Q ) @ X2 ) )
= ( Plus2 @ ( Mult @ P @ X2 ) @ ( Mult @ Q @ X2 ) ) ) ) ).
% logic.distrib_mult
thf(fact_265_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_266_logic_Omove__sum,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,A1: a,A22: a,B: a,B1: a,B22: a,X2: a,X1: a,X22: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ A )
= ( Plus2 @ A1 @ A22 ) )
=> ( ( ( some_a @ B )
= ( Plus2 @ B1 @ B22 ) )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ A @ B ) )
=> ( ( ( some_a @ X1 )
= ( Plus2 @ A1 @ B1 ) )
=> ( ( ( some_a @ X22 )
= ( Plus2 @ A22 @ B22 ) )
=> ( ( some_a @ X2 )
= ( Plus2 @ X1 @ X22 ) ) ) ) ) ) ) ) ).
% logic.move_sum
thf(fact_267_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_268_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_269_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,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( smaller_interp_c_d_a @ Delta @ Delta ) ) ).
% logic.smaller_interp_refl
thf(fact_270_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,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [S: c > d,X: a] :
( ( member_a @ X @ ( Delta @ S ) )
=> ( member_a @ X @ ( Delta2 @ S ) ) )
=> ( smaller_interp_c_d_a @ Delta @ Delta2 ) ) ) ).
% logic.smaller_interpI
thf(fact_271_logic_Ocompatible__multiples,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,Q: b,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) )
=> ( pre_compatible_a @ Plus2 @ A @ B ) ) ) ).
% logic.compatible_multiples
thf(fact_272_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_273_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_274_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_275_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_276_pre__logic_Ocompatible__def,axiom,
( pre_compatible_a
= ( ^ [Plus: a > a > option_a,A3: a,B2: a] :
( ( Plus @ A3 @ B2 )
!= none_a ) ) ) ).
% pre_logic.compatible_def
thf(fact_277_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,S2: c > d,Delta: ( c > d ) > set_a,P: b,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( mult_b_a_d_c @ P @ A2 ) )
= ( ? [A3: a] :
( ( Sigma3
= ( Mult @ P @ A3 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ) ).
% logic.sat.simps(1)
thf(fact_278_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A4: a] :
( ( Sigma3
= ( Mult @ P @ A4 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S2 @ Delta @ A2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.sat_mult
thf(fact_279_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( wildcard_a_b_d_c @ A2 ) )
= ( ? [A3: a,P3: b] :
( ( Sigma3
= ( Mult @ P3 @ A3 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ) ).
% logic.sat.simps(12)
thf(fact_280_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( and_a_b_d_c @ A2 @ B4 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ B4 ) ) ) ) ).
% logic.sat.simps(7)
thf(fact_281_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( or_a_b_d_c @ A2 @ B4 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ A2 )
| ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ B4 ) ) ) ) ).
% logic.sat.simps(6)
thf(fact_282_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( imp_a_b_d_c @ A2 @ B4 ) )
= ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ B4 ) ) ) ) ).
% logic.sat.simps(5)
thf(fact_283_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ B4 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.sat_imp
thf(fact_284_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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ B4 ) )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 ) ) ) ).
% logic.entailsI
thf(fact_285_logic_Oentails__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 )
= ( ! [Sigma: a,S3: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S3 @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S3 @ Delta @ B4 ) ) ) ) ) ).
% logic.entails_def
thf(fact_286_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( bounded_a_b_d_c @ A2 ) )
= ( ( Valid @ Sigma3 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(11)
thf(fact_287_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,S2: c > d,Delta: ( 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 @ S2 @ Delta @ ( sem_c_d_a_b @ B ) )
= ( B @ S2 @ Sigma3 ) ) ) ).
% logic.sat.simps(4)
thf(fact_288_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,S2: c > d,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ pred_a_b_d_c )
= ( member_a @ Sigma3 @ ( Delta @ S2 ) ) ) ) ).
% logic.sat.simps(10)
thf(fact_289_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_290_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_291_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,A5: a,B5: a,X2: a,A: a,B: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ X4 )
= ( Plus2 @ A5 @ B5 ) )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ A @ B ) )
=> ( ( pre_larger_a @ Plus2 @ A5 @ A )
=> ( ( pre_larger_a @ Plus2 @ B5 @ B )
=> ( pre_larger_a @ Plus2 @ X4 @ X2 ) ) ) ) ) ) ).
% logic.sum_both_larger
thf(fact_292_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_293_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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ B4 ) )
=> ( ! [Sigma4: a,S: c > d] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ B4 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ A2 ) )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 ) ) ) ) ).
% logic.equivalentI
thf(fact_294_logic_Oequivalent__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 )
= ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 )
& ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 @ Delta @ A2 ) ) ) ) ).
% logic.equivalent_def
thf(fact_295_logic_Omonotonic__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ F )
= ( ! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F @ Delta5 ) @ ( F @ Delta6 ) ) ) ) ) ) ).
% logic.monotonic_def
thf(fact_296_logic_OmonotonicI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta3 ) @ ( F @ Delta4 ) ) )
=> ( monotonic_c_d_a @ F ) ) ) ).
% logic.monotonicI
thf(fact_297_logic_Onon__increasing__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ F )
= ( ! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
=> ( smaller_interp_c_d_a @ ( F @ Delta6 ) @ ( F @ Delta5 ) ) ) ) ) ) ).
% logic.non_increasing_def
thf(fact_298_logic_Onon__increasingI,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
( ( smaller_interp_c_d_a @ Delta3 @ Delta4 )
=> ( smaller_interp_c_d_a @ ( F @ Delta4 ) @ ( F @ Delta3 ) ) )
=> ( non_increasing_c_d_a @ F ) ) ) ).
% logic.non_increasingI
thf(fact_299_logic_Opure__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
= ( ! [Sigma: a,Sigma2: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S3 @ Delta6 @ A2 ) ) ) ) ) ).
% logic.pure_def
thf(fact_300_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_301_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_302_logic_Ohoare__triple__input,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta )
= ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ P2 ) @ C @ Q2 @ Delta ) ) ) ).
% logic.hoare_triple_input
thf(fact_303_logic_Oindep__interp__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( indep_interp_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
= ( ! [X3: a,S3: c > d,Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X3 @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X3 @ S3 @ Delta6 @ A2 ) ) ) ) ) ).
% logic.indep_interp_def
thf(fact_304_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( star_a_b_d_c @ A2 @ B4 ) )
= ( ? [A3: a,B2: a] :
( ( ( some_a @ Sigma3 )
= ( Plus2 @ A3 @ B2 ) )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B2 @ S2 @ Delta @ B4 ) ) ) ) ) ).
% logic.sat.simps(2)
thf(fact_305_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( wand_a_b_d_c @ A2 @ B4 ) )
= ( ! [A3: a,Sigma2: a] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta @ A2 )
& ( ( some_a @ Sigma2 )
= ( Plus2 @ Sigma3 @ A3 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S2 @ Delta @ B4 ) ) ) ) ) ).
% logic.sat.simps(3)
thf(fact_306_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,Sigma3: a,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A4: a,Sigma5: a] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S2 @ Delta @ A2 )
& ( ( some_a @ Sigma5 )
= ( Plus2 @ Sigma3 @ A4 ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma5 @ S2 @ Delta @ B4 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.sat_wand
thf(fact_307_logic_Omono__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ) ).
% logic.mono_mult
thf(fact_308_logic_Onon__increasing__mult,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ) ).
% logic.non_increasing_mult
thf(fact_309_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,S2: a > option_a,X2: a,Delta: ( a > option_a ) > set_a,A2: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [V3: option_a] : ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_a_option_a @ S2 @ X2 @ V3 ) @ Delta @ A2 )
=> ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( forall5484998627543102345tion_a @ X2 @ A2 ) ) ) ) ).
% logic.sat_forall
thf(fact_310_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,S2: c > d,X2: c,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [V3: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_c_d @ S2 @ X2 @ V3 ) @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( forall_c_a_b_d @ X2 @ A2 ) ) ) ) ).
% logic.sat_forall
thf(fact_311_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,S2: a > option_a,Delta: ( a > option_a ) > set_a,X2: a,A2: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( forall5484998627543102345tion_a @ X2 @ A2 ) )
= ( ! [V2: option_a] : ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_a_option_a @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(9)
thf(fact_312_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,S2: c > d,Delta: ( c > d ) > set_a,X2: c,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( forall_c_a_b_d @ X2 @ A2 ) )
= ( ! [V2: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_c_d @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(9)
thf(fact_313_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,S2: a > option_a,Delta: ( a > option_a ) > set_a,X2: a,A2: assert1556940916145061938on_a_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( exists7165000112504185261tion_a @ X2 @ A2 ) )
= ( ? [V2: option_a] : ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_a_option_a @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(8)
thf(fact_314_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,S2: c > d,Delta: ( c > d ) > set_a,X2: c,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ S2 @ Delta @ ( exists_c_a_b_d @ X2 @ A2 ) )
= ( ? [V2: d] : ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma3 @ ( fun_upd_c_d @ S2 @ X2 @ V2 ) @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(8)
thf(fact_315_logic_Omono__wild,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.mono_wild
thf(fact_316_logic_Onon__increasing__wild,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.non_increasing_wild
thf(fact_317_logic_Omono__star,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.mono_star
thf(fact_318_logic_Osmaller__interp__applies__cons,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a,A: a,S2: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( smaller_interp_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta ) @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 ) )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S2 @ Delta @ A2 )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S2 @ Delta2 @ A2 ) ) ) ) ).
% logic.smaller_interp_applies_cons
thf(fact_319_logic_Omono__and,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.mono_and
thf(fact_320_logic_Omono__forall,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,V: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( forall_c_a_b_d @ V @ A2 ) ) ) ) ) ).
% logic.mono_forall
thf(fact_321_logic_Omono__or,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.mono_or
thf(fact_322_logic_Omono__exists,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,V: c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( exists_c_a_b_d @ V @ A2 ) ) ) ) ) ).
% logic.mono_exists
thf(fact_323_logic_Onon__inc__star,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.non_inc_star
thf(fact_324_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_325_logic_Onon__increasing__and,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.non_increasing_and
thf(fact_326_logic_Onon__increasing__or,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.non_increasing_or
thf(fact_327_logic_Omono__bounded,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.mono_bounded
thf(fact_328_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,B4: ( 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 @ B4 ) ) ) ) ).
% logic.mono_sem
thf(fact_329_logic_Onon__increasing__bounded,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( bounded_a_b_d_c @ A2 ) ) ) ) ) ).
% logic.non_increasing_bounded
thf(fact_330_logic_Onon__increasing__sem,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,B4: ( c > d ) > a > $o] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( sem_c_d_a_b @ B4 ) ) ) ) ).
% logic.non_increasing_sem
thf(fact_331_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_332_logic_Omono__instantiate,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,X2: a,Delta: ( c > d ) > set_a,S2: c > d,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ S2 ) )
=> ( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ S2 ) ) ) ) ) ) ).
% logic.mono_instantiate
thf(fact_333_logic_Onon__increasing__instantiate,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,X2: a,Delta2: ( c > d ) > set_a,S2: c > d,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta2 @ S2 ) )
=> ( ( smaller_interp_c_d_a @ Delta @ Delta2 )
=> ( member_a @ X2 @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ S2 ) ) ) ) ) ) ).
% logic.non_increasing_instantiate
thf(fact_334_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] :
( ! [A3: a,B2: a] :
( ( Plus @ A3 @ B2 )
= ( Plus @ B2 @ A3 ) )
& ! [A3: a,B2: a,Ab2: a,C2: a,Bc2: a] :
( ( ( ( Plus @ A3 @ B2 )
= ( some_a @ Ab2 ) )
& ( ( Plus @ B2 @ C2 )
= ( some_a @ Bc2 ) ) )
=> ( ( Plus @ Ab2 @ C2 )
= ( Plus @ A3 @ Bc2 ) ) )
& ! [A3: a,B2: a,Ab2: a,C2: a] :
( ( ( ( Plus @ A3 @ B2 )
= ( some_a @ Ab2 ) )
& ~ ( pre_compatible_a @ Plus @ B2 @ 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,A3: a] :
( ( Mult2 @ P3 @ ( Mult2 @ Q3 @ A3 ) )
= ( Mult2 @ ( Smult2 @ P3 @ Q3 ) @ A3 ) )
& ! [A3: a,B2: a,C2: a,P3: b] :
( ( ( some_a @ A3 )
= ( Plus @ B2 @ C2 ) )
=> ( ( some_a @ ( Mult2 @ P3 @ A3 ) )
= ( Plus @ ( Mult2 @ P3 @ B2 ) @ ( Mult2 @ P3 @ C2 ) ) ) )
& ! [P3: b,Q3: b,X3: a] :
( ( some_a @ ( Mult2 @ ( Sadd2 @ P3 @ Q3 ) @ X3 ) )
= ( Plus @ ( Mult2 @ P3 @ X3 ) @ ( Mult2 @ Q3 @ X3 ) ) )
& ! [A3: a] :
( ( Mult2 @ One2 @ A3 )
= A3 )
& ! [A3: a,B2: a] :
( ( ( Valid2 @ A3 )
& ( pre_larger_a @ Plus @ A3 @ B2 ) )
=> ( Valid2 @ B2 ) ) ) ) ) ).
% logic_def
thf(fact_335_logic_Oindep__implies__non__increasing,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( indep_interp_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) ) ) ) ).
% logic.indep_implies_non_increasing
thf(fact_336_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( intuit7508411120625971703_b_c_d @ Plus2 @ Mult @ Valid @ S2 @ Delta @ A2 )
= ( ! [A3: a,B2: a] :
( ( ( pre_larger_a @ Plus2 @ A3 @ B2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B2 @ S2 @ Delta @ A2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ) ).
% logic.intuitionistic_def
thf(fact_337_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,S2: c > d,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A4: a,B3: a] :
( ( ( pre_larger_a @ Plus2 @ A4 @ B3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B3 @ S2 @ Delta @ A2 ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S2 @ Delta @ A2 ) )
=> ( intuit7508411120625971703_b_c_d @ Plus2 @ Mult @ Valid @ S2 @ Delta @ A2 ) ) ) ).
% logic.intuitionisticI
thf(fact_338_logic_Ohoare__triple__output,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,C: set_Pr1275464188344874039_a_c_d,P2: assertion_a_b_d_c,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_c_d @ Valid @ C )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta )
= ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ ( bounded_a_b_d_c @ Q2 ) @ Delta ) ) ) ) ).
% logic.hoare_triple_output
thf(fact_339_fun__upd__idem__iff,axiom,
! [F: c > d,X2: c,Y: d] :
( ( ( fun_upd_c_d @ F @ X2 @ Y )
= F )
= ( ( F @ X2 )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_340_fun__upd__idem__iff,axiom,
! [F: a > option_a,X2: a,Y: option_a] :
( ( ( fun_upd_a_option_a @ F @ X2 @ Y )
= F )
= ( ( F @ X2 )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_341_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_342_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_343_fun__upd__other,axiom,
! [Z: c,X2: c,F: c > d,Y: d] :
( ( Z != X2 )
=> ( ( fun_upd_c_d @ F @ X2 @ Y @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_344_fun__upd__other,axiom,
! [Z: a,X2: a,F: a > option_a,Y: option_a] :
( ( Z != X2 )
=> ( ( fun_upd_a_option_a @ F @ X2 @ Y @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_345_fun__upd__same,axiom,
! [F: c > d,X2: c,Y: d] :
( ( fun_upd_c_d @ F @ X2 @ Y @ X2 )
= Y ) ).
% fun_upd_same
thf(fact_346_fun__upd__same,axiom,
! [F: a > option_a,X2: a,Y: option_a] :
( ( fun_upd_a_option_a @ F @ X2 @ Y @ X2 )
= Y ) ).
% fun_upd_same
thf(fact_347_fun__upd__idem,axiom,
! [F: c > d,X2: c,Y: d] :
( ( ( F @ X2 )
= Y )
=> ( ( fun_upd_c_d @ F @ X2 @ Y )
= F ) ) ).
% fun_upd_idem
thf(fact_348_fun__upd__idem,axiom,
! [F: a > option_a,X2: a,Y: option_a] :
( ( ( F @ X2 )
= Y )
=> ( ( fun_upd_a_option_a @ F @ X2 @ Y )
= F ) ) ).
% fun_upd_idem
thf(fact_349_fun__upd__eqD,axiom,
! [F: c > d,X2: c,Y: d,G: c > d,Z: d] :
( ( ( fun_upd_c_d @ F @ X2 @ Y )
= ( fun_upd_c_d @ G @ X2 @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_350_fun__upd__eqD,axiom,
! [F: a > option_a,X2: a,Y: option_a,G: a > option_a,Z: option_a] :
( ( ( fun_upd_a_option_a @ F @ X2 @ Y )
= ( fun_upd_a_option_a @ G @ X2 @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_351_fun__upd__def,axiom,
( fun_upd_c_d
= ( ^ [F2: c > d,A3: c,B2: d,X3: c] : ( if_d @ ( X3 = A3 ) @ B2 @ ( F2 @ X3 ) ) ) ) ).
% fun_upd_def
thf(fact_352_fun__upd__def,axiom,
( fun_upd_a_option_a
= ( ^ [F2: a > option_a,A3: a,B2: option_a,X3: a] : ( if_option_a @ ( X3 = A3 ) @ B2 @ ( F2 @ X3 ) ) ) ) ).
% fun_upd_def
thf(fact_353_logic_Onot__in__fv__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,S4: set_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ S4 )
= ( ! [Sigma: a,S3: c > d,Delta5: ( c > d ) > set_a,S5: c > d] :
( ( equal_outside_c_d @ S3 @ S5 @ S4 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S3 @ Delta5 @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S5 @ Delta5 @ A2 ) ) ) ) ) ) ).
% logic.not_in_fv_def
thf(fact_354_logic_Onon__increasing__wand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.non_increasing_wand
thf(fact_355_logic_Onon__increasing__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.non_increasing_imp
thf(fact_356_logic_Omono__wand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.mono_wand
thf(fact_357_logic_Omono__imp,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( non_increasing_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 ) )
=> ( ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ B4 ) )
=> ( monotonic_c_d_a @ ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ) ) ).
% logic.mono_imp
thf(fact_358_combinable__instantiate__one,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S2: c > d,B: a,X2: a,P: b,Q: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S2 @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S2 @ Delta @ A2 )
=> ( ( ( some_a @ X2 )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
=> ( ( ( sadd @ P @ Q )
= one )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S2 @ Delta @ A2 ) ) ) ) ) ) ).
% combinable_instantiate_one
thf(fact_359_not__in__fv__mod,axiom,
! [A2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma3: a,S2: c > d,Sigma6: a,S6: c > d,X2: a,Delta: ( c > d ) > set_a] :
( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A2 @ ( modified_a_c_d @ C ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S2 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S6 ) ) ) @ C )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S2 @ Delta @ A2 )
= ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S6 @ Delta @ A2 ) ) ) ) ).
% not_in_fv_mod
thf(fact_360_combinable__def,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
= ( ! [P3: b,Q3: b] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P3 @ A2 ) @ ( mult_b_a_d_c @ Q3 @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ ( sadd @ P3 @ Q3 ) @ A2 ) ) ) ) ).
% combinable_def
thf(fact_361_valid__hoare__tripleI,axiom,
! [Delta: ( c > d ) > set_a,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c] :
( ! [Sigma4: a,S: c > d] :
( ( ( valid @ Sigma4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ P2 ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma4 @ S ) ) )
=> ( ! [Sigma4: a,S: c > d,Sigma5: a,S7: c > d] :
( ( ( valid @ Sigma4 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ P2 ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S7 ) ) ) @ C )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S7 @ Delta @ Q2 ) ) )
=> ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta ) ) ) ).
% valid_hoare_tripleI
thf(fact_362_valid__hoare__triple__def,axiom,
! [P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P2 @ C @ Q2 @ Delta )
= ( ! [Sigma: a,S3: c > d] :
( ( ( valid @ Sigma )
& ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S3 @ Delta @ P2 ) )
=> ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S3 ) )
& ! [Sigma2: a,S5: c > d] :
( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma @ S3 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma2 @ S5 ) ) ) @ C )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S5 @ Delta @ Q2 ) ) ) ) ) ) ).
% valid_hoare_triple_def
thf(fact_363_combinable__instantiate,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S2: c > d,B: a,X2: a,P: b,Q: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S2 @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S2 @ Delta @ A2 )
=> ( ( ( some_a @ X2 )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X2 @ S2 @ Delta @ ( mult_b_a_d_c @ ( sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ).
% combinable_instantiate
thf(fact_364_combinable__mult,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,Pi: b] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ).
% combinable_mult
thf(fact_365_combinable__wildcard,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% combinable_wildcard
thf(fact_366_combinable__star,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% combinable_star
thf(fact_367_combinable__and,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% combinable_and
thf(fact_368_combinable__forall,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,X2: c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( forall_c_a_b_d @ X2 @ A2 ) ) ) ).
% combinable_forall
thf(fact_369_combinable__wand,axiom,
! [Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c,A2: assertion_a_b_d_c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ).
% combinable_wand
thf(fact_370_combinable__pure,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 ) ) ).
% combinable_pure
thf(fact_371_combinableI__old,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ! [A4: a,B3: a,P6: b,Q4: b,X: a,Sigma4: a,S: c > d] :
( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S @ Delta @ A2 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ B3 @ S @ Delta @ A2 )
& ( ( some_a @ Sigma4 )
= ( plus @ ( mult @ P6 @ A4 ) @ ( mult @ Q4 @ B3 ) ) )
& ( Sigma4
= ( mult @ ( sadd @ P6 @ Q4 ) @ X ) ) )
=> ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S @ Delta @ A2 ) )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 ) ) ).
% combinableI_old
thf(fact_372_combinable__imp,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
=> ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% combinable_imp
thf(fact_373_combinable__exists,axiom,
! [Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,X2: c] :
( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( unambiguous_a_b_c_d @ plus @ mult @ valid @ Delta @ A2 @ X2 )
=> ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta @ ( exists_c_a_b_d @ X2 @ A2 ) ) ) ) ).
% combinable_exists
thf(fact_374_logic_Ovalid__hoare__triple__def,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta )
= ( ! [Sigma: a,S3: c > d] :
( ( ( Valid @ Sigma )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma @ S3 @ Delta @ P2 ) )
=> ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S3 ) )
& ! [Sigma2: a,S5: c > d] :
( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma @ S3 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma2 @ S5 ) ) ) @ C )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma2 @ S5 @ Delta @ Q2 ) ) ) ) ) ) ) ).
% logic.valid_hoare_triple_def
thf(fact_375_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,Delta: ( c > d ) > set_a,P2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma4: a,S: c > d] :
( ( ( Valid @ Sigma4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ P2 ) )
=> ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma4 @ S ) ) )
=> ( ! [Sigma4: a,S: c > d,Sigma5: a,S7: c > d] :
( ( ( Valid @ Sigma4 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma4 @ S @ Delta @ P2 ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S7 ) ) ) @ C )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma5 @ S7 @ Delta @ Q2 ) ) )
=> ( valid_6037315502795721655_b_d_c @ Plus2 @ Mult @ Valid @ P2 @ C @ Q2 @ Delta ) ) ) ) ).
% logic.valid_hoare_tripleI
thf(fact_376_logic_Onot__in__fv__mod,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma3: a,S2: c > d,Sigma6: a,S6: c > d,X2: a,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ ( modified_a_c_d @ C ) )
=> ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S2 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S6 ) ) ) @ C )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S2 @ Delta @ A2 )
= ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S6 @ Delta @ A2 ) ) ) ) ) ).
% logic.not_in_fv_mod
thf(fact_377_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,Delta: ( a > option_a ) > set_a,A2: 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,S: 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 @ S @ X2 @ V12 ) @ Delta @ A2 )
& ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma_22 @ ( fun_upd_a_option_a @ S @ X2 @ V23 ) @ Delta @ A2 ) )
=> ( V12 = V23 ) )
=> ( unambi704529886615442436tion_a @ Plus2 @ Mult @ Valid @ Delta @ A2 @ X2 ) ) ) ).
% logic.unambiguousI
thf(fact_378_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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma_12: a,Sigma_22: a,V12: d,V23: d,S: c > d] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_12 @ ( fun_upd_c_d @ S @ X2 @ V12 ) @ Delta @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_22 @ ( fun_upd_c_d @ S @ X2 @ V23 ) @ Delta @ A2 ) )
=> ( V12 = V23 ) )
=> ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta @ A2 @ X2 ) ) ) ).
% logic.unambiguousI
thf(fact_379_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,Delta: ( a > option_a ) > set_a,A2: assert1556940916145061938on_a_a,X2: a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambi704529886615442436tion_a @ Plus2 @ Mult @ Valid @ Delta @ A2 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: option_a,V22: option_a,S3: 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 @ S3 @ X2 @ V1 ) @ Delta @ A2 )
& ( sat_a_b_a_option_a @ Plus2 @ Mult @ Valid @ Sigma_2 @ ( fun_upd_a_option_a @ S3 @ X2 @ V22 ) @ Delta @ A2 ) )
=> ( V1 = V22 ) ) ) ) ) ).
% logic.unambiguous_def
thf(fact_380_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,Delta: ( c > d ) > set_a,A2: 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 @ Delta @ A2 @ X2 )
= ( ! [Sigma_1: a,Sigma_2: a,V1: d,V22: d,S3: c > d] :
( ( ( pre_compatible_a @ Plus2 @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_1 @ ( fun_upd_c_d @ S3 @ X2 @ V1 ) @ Delta @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ Sigma_2 @ ( fun_upd_c_d @ S3 @ X2 @ V22 ) @ Delta @ A2 ) )
=> ( V1 = V22 ) ) ) ) ) ).
% logic.unambiguous_def
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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
= ( ! [P3: b,Q3: b] : ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P3 @ A2 ) @ ( mult_b_a_d_c @ Q3 @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ ( Sadd @ P3 @ Q3 ) @ A2 ) ) ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S2: c > d,B: a,X2: a,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S2 @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B @ S2 @ Delta @ A2 )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S2 @ Delta @ ( mult_b_a_d_c @ ( Sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: 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 @ Delta @ A2 )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta @ A2 @ X2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( exists_c_a_b_d @ X2 @ A2 ) ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta @ A2 ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 )
= ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ Pi @ A2 ) @ Delta @ ( mult_b_a_d_c @ Pi @ B4 ) ) ) ) ).
% 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,Q: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ ( Smult @ P @ Q ) @ A2 ) ) ) ).
% 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,Q: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ ( Smult @ P @ Q ) @ A2 ) @ Delta @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ One @ A2 ) @ Delta @ A2 ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ ( mult_b_a_d_c @ One @ A2 ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,Pi: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( mult_b_a_d_c @ Pi @ A2 ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ B4 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ A2 ) @ Delta @ ( wildcard_a_b_d_c @ B4 ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ One @ A2 ) @ Delta @ A2 ) ) ).
% 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,Q: b,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( mult_b_a_d_c @ Q @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ ( Smult @ P @ Q ) @ A2 ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% logic.combinable_star
thf(fact_397_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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% logic.combinable_and
thf(fact_398_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,Delta: ( c > d ) > set_a,A2: 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 @ Delta @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( forall_c_a_b_d @ X2 @ A2 ) ) ) ) ).
% logic.combinable_forall
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,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,X2: c,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta @ A2 @ X2 )
=> ( unambiguous_a_b_c_d @ Plus2 @ Mult @ Valid @ Delta @ ( star_a_b_d_c @ A2 @ B4 ) @ 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A4: a,B3: a,P6: b,Q4: b,X: a,Sigma4: a,S: c > d] :
( ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A4 @ S @ Delta @ A2 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B3 @ S @ Delta @ A2 )
& ( ( some_a @ Sigma4 )
= ( Plus2 @ ( Mult @ P6 @ A4 ) @ ( Mult @ Q4 @ B3 ) ) )
& ( Sigma4
= ( Mult @ ( Sadd @ P6 @ Q4 ) @ X ) ) )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X @ S @ Delta @ A2 ) )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 ) ) ) ).
% 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,Delta: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S2: c > d,B: a,X2: a,P: b,Q: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A @ S2 @ Delta @ A2 )
=> ( ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ B @ S2 @ Delta @ A2 )
=> ( ( ( some_a @ X2 )
= ( Plus2 @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
=> ( ( ( Sadd @ P @ Q )
= One )
=> ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ X2 @ S2 @ Delta @ A2 ) ) ) ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.dot_star2
thf(fact_407_logic_Odot__and2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.dot_and2
thf(fact_408_logic_Odot__and1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.dot_and1
thf(fact_409_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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( forall_c_a_b_d @ X2 @ A2 ) ) ) ) ).
% logic.dot_forall2
thf(fact_410_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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.dot_forall1
thf(fact_411_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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.dot_exists1
thf(fact_412_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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( exists_c_a_b_d @ X2 @ A2 ) ) ) ) ).
% logic.dot_exists2
thf(fact_413_logic_Odot__or1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.dot_or1
thf(fact_414_logic_Odot__or2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.dot_or2
thf(fact_415_logic_Odot__imp1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.dot_imp1
thf(fact_416_logic_Odot__imp2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.dot_imp2
thf(fact_417_logic_Odot__wand1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.dot_wand1
thf(fact_418_logic_Odot__wand2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.dot_wand2
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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) ) @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( wildcard_a_b_d_c @ A2 ) ) @ Delta @ ( wildcard_a_b_d_c @ A2 ) ) ) ).
% 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,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( star_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( star_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B4 ) ) ) ) ).
% logic.WildStar1
thf(fact_422_logic_OWildAnd,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( and_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( and_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B4 ) ) ) ) ).
% logic.WildAnd
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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( forall_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% logic.WildForall
thf(fact_424_logic_ODotStar,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( star_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.DotStar
thf(fact_425_logic_ODotAnd,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( and_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) @ Delta @ ( mult_b_a_d_c @ P @ ( and_a_b_d_c @ A2 @ B4 ) ) ) ) ).
% logic.DotAnd
thf(fact_426_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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( forall_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.DotForall
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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( exists_c_a_b_d @ X2 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.DotExists
thf(fact_428_logic_ODotOr,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( or_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( or_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.DotOr
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,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( imp_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( imp_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.DotImp
thf(fact_430_logic_ODotWand,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ ( wand_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( wand_a_b_d_c @ ( mult_b_a_d_c @ P @ A2 ) @ ( mult_b_a_d_c @ P @ B4 ) ) ) ) ).
% logic.DotWand
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,A2: assertion_a_b_d_c,Delta: ( 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 @ A2 ) ) @ Delta @ ( exists_c_a_b_d @ X2 @ ( wildcard_a_b_d_c @ A2 ) ) ) ) ).
% 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,A2: assertion_a_b_d_c,B4: assertion_a_b_d_c,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( wildcard_a_b_d_c @ ( or_a_b_d_c @ A2 @ B4 ) ) @ Delta @ ( or_a_b_d_c @ ( wildcard_a_b_d_c @ A2 ) @ ( wildcard_a_b_d_c @ B4 ) ) ) ) ).
% logic.WildOr
thf(fact_433_logic_Opure__mult1,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,P: b,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta @ A2 ) ) ) ).
% logic.pure_mult1
thf(fact_434_logic_Opure__mult2,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,P: b] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( entails_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).
% logic.pure_mult2
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,A2: assertion_a_b_d_c,P: b,Delta: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( equivalent_a_b_d_c @ Plus2 @ Mult @ Valid @ ( mult_b_a_d_c @ P @ A2 ) @ Delta @ A2 ) ) ) ).
% 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,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,B4: assertion_a_b_d_c] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 )
=> ( ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ B4 )
=> ( combinable_a_b_c_d @ Plus2 @ Mult @ Sadd @ Valid @ Delta @ ( imp_a_b_d_c @ A2 @ B4 ) ) ) ) ) ).
% 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 ) )
!= ( ^ [X3: a] : none_a ) ) ).
% map_upd_nonempty
thf(fact_438_empty__interp__def,axiom,
( empty_interp_c_d_a
= ( ^ [S3: c > d] : bot_bot_set_a ) ) ).
% empty_interp_def
thf(fact_439_smaller__interp__def,axiom,
( smaller_interp_c_d_a
= ( ^ [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
! [S3: c > d] : ( ord_less_eq_set_a @ ( Delta5 @ S3 ) @ ( Delta6 @ S3 ) ) ) ) ).
% smaller_interp_def
thf(fact_440_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,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( smaller_interp_c_d_a @ Delta @ Delta2 )
= ( ! [S3: c > d] : ( ord_less_eq_set_a @ ( Delta @ S3 ) @ ( Delta2 @ S3 ) ) ) ) ) ).
% logic.smaller_interp_def
thf(fact_441_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,S2: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( empty_interp_c_d_a @ S2 )
= bot_bot_set_a ) ) ).
% logic.empty_interp_def
thf(fact_442_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_443_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_444_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_445_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_446_option_Ocollapse,axiom,
! [Option: option_a] :
( ( Option != none_a )
=> ( ( some_a @ ( the_a @ Option ) )
= Option ) ) ).
% option.collapse
thf(fact_447_map__add__upd,axiom,
! [F: a > option_a,G: a > option_a,X2: a,Y: a] :
( ( map_add_a_a @ F @ ( fun_upd_a_option_a @ G @ X2 @ ( some_a @ Y ) ) )
= ( fun_upd_a_option_a @ ( map_add_a_a @ F @ G ) @ X2 @ ( some_a @ Y ) ) ) ).
% map_add_upd
thf(fact_448_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_449_option_Osel,axiom,
! [X22: a] :
( ( the_a @ ( some_a @ X22 ) )
= X22 ) ).
% option.sel
thf(fact_450_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_451_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_452_option_Oexhaust__sel,axiom,
! [Option: option_a] :
( ( Option != none_a )
=> ( Option
= ( some_a @ ( the_a @ Option ) ) ) ) ).
% option.exhaust_sel
thf(fact_453_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_454_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_455_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_456_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_457_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_458_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_459_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_460_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_461_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_462_in__graphD,axiom,
! [K: assertion_a_b_d_c,V: produc5213381314664832452_a_c_d,M: assertion_a_b_d_c > option3890169911263941780_a_c_d] :
( ( member537768723423446209_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V ) @ ( graph_7603009230766167293_a_c_d @ M ) )
=> ( ( M @ K )
= ( some_P3194730542479778335_a_c_d @ V ) ) ) ).
% in_graphD
thf(fact_463_in__graphD,axiom,
! [K: ( c > d ) > set_a,V: c > d,M: ( ( c > d ) > set_a ) > option_c_d] :
( ( member1642667639779969243_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V ) @ ( graph_c_d_set_a_c_d @ M ) )
=> ( ( M @ K )
= ( some_c_d @ V ) ) ) ).
% in_graphD
thf(fact_464_in__graphI,axiom,
! [M: assertion_a_b_d_c > option3890169911263941780_a_c_d,K: assertion_a_b_d_c,V: produc5213381314664832452_a_c_d] :
( ( ( M @ K )
= ( some_P3194730542479778335_a_c_d @ V ) )
=> ( member537768723423446209_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V ) @ ( graph_7603009230766167293_a_c_d @ M ) ) ) ).
% in_graphI
thf(fact_465_in__graphI,axiom,
! [M: ( ( c > d ) > set_a ) > option_c_d,K: ( c > d ) > set_a,V: c > d] :
( ( ( M @ K )
= ( some_c_d @ V ) )
=> ( member1642667639779969243_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V ) @ ( graph_c_d_set_a_c_d @ M ) ) ) ).
% in_graphI
thf(fact_466_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 )
=> ~ ! [A7: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,S: c > d] :
( X2
!= ( produc8894421531525210148_a_c_d @ A7 @ ( produc7376592049607813182_a_c_d @ Delta3 @ S ) ) ) ) ).
% logic.applies_eq.cases
thf(fact_467_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_468_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_469_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_470_domD,axiom,
! [A: option_a,M: option_a > option_a] :
( ( member_option_a @ A @ ( dom_option_a_a @ M ) )
=> ? [B3: a] :
( ( M @ A )
= ( some_a @ B3 ) ) ) ).
% domD
thf(fact_471_domD,axiom,
! [A: b,M: b > option_a] :
( ( member_b @ A @ ( dom_b_a @ M ) )
=> ? [B3: a] :
( ( M @ A )
= ( some_a @ B3 ) ) ) ).
% domD
thf(fact_472_domD,axiom,
! [A: a,M: a > option_a] :
( ( member_a @ A @ ( dom_a_a @ M ) )
=> ? [B3: a] :
( ( M @ A )
= ( some_a @ B3 ) ) ) ).
% domD
thf(fact_473_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_474_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_475_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_476_graph__map__upd,axiom,
! [M: assertion_a_b_d_c > option3890169911263941780_a_c_d,K: assertion_a_b_d_c,V: produc5213381314664832452_a_c_d] :
( ( graph_7603009230766167293_a_c_d @ ( fun_up8563802042059451790_a_c_d @ M @ K @ ( some_P3194730542479778335_a_c_d @ V ) ) )
= ( insert1952503980790619482_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V ) @ ( graph_7603009230766167293_a_c_d @ ( fun_up8563802042059451790_a_c_d @ M @ K @ none_P4438893274231186595_a_c_d ) ) ) ) ).
% graph_map_upd
thf(fact_477_graph__map__upd,axiom,
! [M: ( ( c > d ) > set_a ) > option_c_d,K: ( c > d ) > set_a,V: c > d] :
( ( graph_c_d_set_a_c_d @ ( fun_up2820008246124789800on_c_d @ M @ K @ ( some_c_d @ V ) ) )
= ( insert9214331609911559156_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V ) @ ( graph_c_d_set_a_c_d @ ( fun_up2820008246124789800on_c_d @ M @ K @ none_c_d ) ) ) ) ).
% graph_map_upd
thf(fact_478_graph__map__upd,axiom,
! [M: a > option_a,K: a,V: a] :
( ( graph_a_a @ ( fun_upd_a_option_a @ M @ K @ ( some_a @ V ) ) )
= ( insert4534936382041156343od_a_a @ ( product_Pair_a_a @ K @ V ) @ ( graph_a_a @ ( fun_upd_a_option_a @ M @ K @ none_a ) ) ) ) ).
% graph_map_upd
thf(fact_479_graph__restrictD_I2_J,axiom,
! [K: assertion_a_b_d_c,V: produc5213381314664832452_a_c_d,M: assertion_a_b_d_c > option3890169911263941780_a_c_d,A2: set_as909545710669178647_b_d_c] :
( ( member537768723423446209_a_c_d @ ( produc8894421531525210148_a_c_d @ K @ V ) @ ( graph_7603009230766167293_a_c_d @ ( restri3968632621895983051_a_c_d @ M @ A2 ) ) )
=> ( ( M @ K )
= ( some_P3194730542479778335_a_c_d @ V ) ) ) ).
% graph_restrictD(2)
thf(fact_480_graph__restrictD_I2_J,axiom,
! [K: ( c > d ) > set_a,V: c > d,M: ( ( c > d ) > set_a ) > option_c_d,A2: set_c_d_set_a] :
( ( member1642667639779969243_a_c_d @ ( produc7376592049607813182_a_c_d @ K @ V ) @ ( graph_c_d_set_a_c_d @ ( restri4474245042709046629_a_c_d @ M @ A2 ) ) )
=> ( ( M @ K )
= ( some_c_d @ V ) ) ) ).
% graph_restrictD(2)
thf(fact_481_bind__split__asm,axiom,
! [P2: option_a > $o,M: option_a,F: a > option_a] :
( ( P2 @ ( bind_a_a @ M @ F ) )
= ( ~ ( ( ( M = none_a )
& ~ ( P2 @ none_a ) )
| ? [X3: a] :
( ( M
= ( some_a @ X3 ) )
& ~ ( P2 @ ( F @ X3 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_482_bind__split,axiom,
! [P2: option_a > $o,M: option_a,F: a > option_a] :
( ( P2 @ ( bind_a_a @ M @ F ) )
= ( ( ( M = none_a )
=> ( P2 @ none_a ) )
& ! [V2: a] :
( ( M
= ( some_a @ V2 ) )
=> ( P2 @ ( F @ V2 ) ) ) ) ) ).
% bind_split
thf(fact_483_bind__runit,axiom,
! [X2: option_a] :
( ( bind_a_a @ X2 @ some_a )
= X2 ) ).
% bind_runit
thf(fact_484_bind__eq__Some__conv,axiom,
! [F: option_a,G: a > option_a,X2: a] :
( ( ( bind_a_a @ F @ G )
= ( some_a @ X2 ) )
= ( ? [Y2: a] :
( ( F
= ( some_a @ Y2 ) )
& ( ( G @ Y2 )
= ( some_a @ X2 ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_485_Option_Obind__cong,axiom,
! [X2: option_a,Y: option_a,F: a > option_a,G: a > option_a] :
( ( X2 = Y )
=> ( ! [A4: a] :
( ( Y
= ( some_a @ A4 ) )
=> ( ( F @ A4 )
= ( G @ A4 ) ) )
=> ( ( bind_a_a @ X2 @ F )
= ( bind_a_a @ Y @ G ) ) ) ) ).
% Option.bind_cong
thf(fact_486_bind_Obind__lunit,axiom,
! [X2: a,F: a > option_a] :
( ( bind_a_a @ ( some_a @ X2 ) @ F )
= ( F @ X2 ) ) ).
% bind.bind_lunit
thf(fact_487_insert__dom,axiom,
! [F: option_a > option_a,X2: option_a,Y: a] :
( ( ( F @ X2 )
= ( some_a @ Y ) )
=> ( ( insert_option_a @ X2 @ ( dom_option_a_a @ F ) )
= ( dom_option_a_a @ F ) ) ) ).
% insert_dom
thf(fact_488_insert__dom,axiom,
! [F: a > option_a,X2: a,Y: a] :
( ( ( F @ X2 )
= ( some_a @ Y ) )
=> ( ( insert_a @ X2 @ ( dom_a_a @ F ) )
= ( dom_a_a @ F ) ) ) ).
% insert_dom
thf(fact_489_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_490_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_491_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_492_these__insert__Some,axiom,
! [X2: option_a,A2: set_option_option_a] :
( ( these_option_a @ ( insert605063979879581146tion_a @ ( some_option_a @ X2 ) @ A2 ) )
= ( insert_option_a @ X2 @ ( these_option_a @ A2 ) ) ) ).
% these_insert_Some
thf(fact_493_these__insert__Some,axiom,
! [X2: a,A2: set_option_a] :
( ( these_a @ ( insert_option_a @ ( some_a @ X2 ) @ A2 ) )
= ( insert_a @ X2 @ ( these_a @ A2 ) ) ) ).
% these_insert_Some
thf(fact_494_override__on__insert,axiom,
! [F: c > d,G: c > d,X2: c,X6: set_c] :
( ( override_on_c_d @ F @ G @ ( insert_c @ X2 @ X6 ) )
= ( fun_upd_c_d @ ( override_on_c_d @ F @ G @ X6 ) @ X2 @ ( G @ X2 ) ) ) ).
% override_on_insert
thf(fact_495_override__on__insert,axiom,
! [F: a > option_a,G: a > option_a,X2: a,X6: set_a] :
( ( overri633547075744967556tion_a @ F @ G @ ( insert_a @ X2 @ X6 ) )
= ( fun_upd_a_option_a @ ( overri633547075744967556tion_a @ F @ G @ X6 ) @ X2 @ ( G @ X2 ) ) ) ).
% override_on_insert
thf(fact_496_in__these__eq,axiom,
! [X2: option_a,A2: set_option_option_a] :
( ( member_option_a @ X2 @ ( these_option_a @ A2 ) )
= ( member5113800082084363315tion_a @ ( some_option_a @ X2 ) @ A2 ) ) ).
% in_these_eq
thf(fact_497_in__these__eq,axiom,
! [X2: b,A2: set_option_b] :
( ( member_b @ X2 @ ( these_b @ A2 ) )
= ( member_option_b @ ( some_b @ X2 ) @ A2 ) ) ).
% in_these_eq
thf(fact_498_in__these__eq,axiom,
! [X2: a,A2: set_option_a] :
( ( member_a @ X2 @ ( these_a @ A2 ) )
= ( member_option_a @ ( some_a @ X2 ) @ A2 ) ) ).
% in_these_eq
thf(fact_499_override__on__insert_H,axiom,
! [F: c > d,G: c > d,X2: c,X6: set_c] :
( ( override_on_c_d @ F @ G @ ( insert_c @ X2 @ X6 ) )
= ( override_on_c_d @ ( fun_upd_c_d @ F @ X2 @ ( G @ X2 ) ) @ G @ X6 ) ) ).
% override_on_insert'
thf(fact_500_override__on__insert_H,axiom,
! [F: a > option_a,G: a > option_a,X2: a,X6: set_a] :
( ( overri633547075744967556tion_a @ F @ G @ ( insert_a @ X2 @ X6 ) )
= ( overri633547075744967556tion_a @ ( fun_upd_a_option_a @ F @ X2 @ ( G @ X2 ) ) @ G @ X6 ) ) ).
% override_on_insert'
thf(fact_501_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_502_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_503_these__image__Some__eq,axiom,
! [A2: set_a] :
( ( these_a @ ( image_a_option_a @ some_a @ A2 ) )
= A2 ) ).
% these_image_Some_eq
thf(fact_504_dom__eq__singleton__conv,axiom,
! [F: option_a > option_a,X2: option_a] :
( ( ( dom_option_a_a @ F )
= ( insert_option_a @ X2 @ bot_bot_set_option_a ) )
= ( ? [V2: a] :
( F
= ( fun_up1079276522633388797tion_a
@ ^ [X3: option_a] : none_a
@ X2
@ ( some_a @ V2 ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_505_dom__eq__singleton__conv,axiom,
! [F: a > option_a,X2: a] :
( ( ( dom_a_a @ F )
= ( insert_a @ X2 @ bot_bot_set_a ) )
= ( ? [V2: a] :
( F
= ( fun_upd_a_option_a
@ ^ [X3: a] : none_a
@ X2
@ ( some_a @ V2 ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_506_image__map__upd,axiom,
! [X2: option_a,A2: set_option_a,M: option_a > option_a,Y: a] :
( ~ ( member_option_a @ X2 @ A2 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ M @ X2 @ ( some_a @ Y ) ) @ A2 )
= ( image_7439109396645324421tion_a @ M @ A2 ) ) ) ).
% image_map_upd
thf(fact_507_image__map__upd,axiom,
! [X2: b,A2: set_b,M: b > option_a,Y: a] :
( ~ ( member_b @ X2 @ A2 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ M @ X2 @ ( some_a @ Y ) ) @ A2 )
= ( image_b_option_a @ M @ A2 ) ) ) ).
% image_map_upd
thf(fact_508_image__map__upd,axiom,
! [X2: a,A2: set_a,M: a > option_a,Y: a] :
( ~ ( member_a @ X2 @ A2 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ M @ X2 @ ( some_a @ Y ) ) @ A2 )
= ( image_a_option_a @ M @ A2 ) ) ) ).
% image_map_upd
thf(fact_509_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_510_elem__set,axiom,
! [X2: b,Xo: option_b] :
( ( member_b @ X2 @ ( set_option_b2 @ Xo ) )
= ( Xo
= ( some_b @ X2 ) ) ) ).
% elem_set
thf(fact_511_elem__set,axiom,
! [X2: a,Xo: option_a] :
( ( member_a @ X2 @ ( set_option_a2 @ Xo ) )
= ( Xo
= ( some_a @ X2 ) ) ) ).
% elem_set
thf(fact_512_Some__image__these__eq,axiom,
! [A2: set_option_a] :
( ( image_a_option_a @ some_a @ ( these_a @ A2 ) )
= ( collect_option_a
@ ^ [X3: option_a] :
( ( member_option_a @ X3 @ A2 )
& ( X3 != none_a ) ) ) ) ).
% Some_image_these_eq
thf(fact_513_map__add__def,axiom,
( map_add_a_a
= ( ^ [M12: a > option_a,M22: a > option_a,X3: a] : ( case_o3148979394504432965on_a_a @ ( M12 @ X3 ) @ some_a @ ( M22 @ X3 ) ) ) ) ).
% map_add_def
thf(fact_514_case__optionE,axiom,
! [P2: $o,Q2: a > $o,X2: option_a] :
( ( case_option_o_a @ P2 @ Q2 @ X2 )
=> ( ( ( X2 = none_a )
=> ~ P2 )
=> ~ ! [Y3: a] :
( ( X2
= ( some_a @ Y3 ) )
=> ~ ( Q2 @ Y3 ) ) ) ) ).
% case_optionE
thf(fact_515_ospec,axiom,
! [A2: option_a,P2: a > $o,X2: a] :
( ! [X: a] :
( ( member_a @ X @ ( set_option_a2 @ A2 ) )
=> ( P2 @ X ) )
=> ( ( A2
= ( some_a @ X2 ) )
=> ( P2 @ X2 ) ) ) ).
% ospec
thf(fact_516_option_Oset__intros,axiom,
! [X22: option_a] : ( member_option_a @ X22 @ ( set_option_option_a2 @ ( some_option_a @ X22 ) ) ) ).
% option.set_intros
thf(fact_517_option_Oset__intros,axiom,
! [X22: b] : ( member_b @ X22 @ ( set_option_b2 @ ( some_b @ X22 ) ) ) ).
% option.set_intros
thf(fact_518_option_Oset__intros,axiom,
! [X22: a] : ( member_a @ X22 @ ( set_option_a2 @ ( some_a @ X22 ) ) ) ).
% option.set_intros
thf(fact_519_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_520_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_521_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_522_None__notin__image__Some,axiom,
! [A2: set_a] :
~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A2 ) ) ).
% None_notin_image_Some
thf(fact_523_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_524_applies__eq_Osimps,axiom,
! [A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,S2: c > d] :
( ( applies_eq_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta @ S2 )
= ( collect_a
@ ^ [Uu: a] :
? [A3: a] :
( ( Uu = A3 )
& ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ).
% applies_eq.simps
thf(fact_525_finite__Map__induct,axiom,
! [M: b > option_a,P2: ( b > option_a ) > $o] :
( ( finite_finite_b @ ( dom_b_a @ M ) )
=> ( ( P2
@ ^ [X3: b] : none_a )
=> ( ! [K2: b,V3: 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 @ V3 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_526_finite__Map__induct,axiom,
! [M: option_a > option_a,P2: ( option_a > option_a ) > $o] :
( ( finite1674126218327898605tion_a @ ( dom_option_a_a @ M ) )
=> ( ( P2
@ ^ [X3: option_a] : none_a )
=> ( ! [K2: option_a,V3: 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 @ V3 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_527_finite__Map__induct,axiom,
! [M: a > option_a,P2: ( a > option_a ) > $o] :
( ( finite_finite_a @ ( dom_a_a @ M ) )
=> ( ( P2
@ ^ [X3: a] : none_a )
=> ( ! [K2: a,V3: 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 @ V3 ) ) ) ) ) )
=> ( P2 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_528_fun__upd__image,axiom,
! [X2: option_a,A2: set_option_a,F: option_a > option_a,Y: option_a] :
( ( ( member_option_a @ X2 @ A2 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F @ X2 @ Y ) @ A2 )
= ( insert_option_a @ Y @ ( image_7439109396645324421tion_a @ F @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ) ) )
& ( ~ ( member_option_a @ X2 @ A2 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F @ X2 @ Y ) @ A2 )
= ( image_7439109396645324421tion_a @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_529_fun__upd__image,axiom,
! [X2: option_a,A2: set_option_a,F: option_a > a,Y: a] :
( ( ( member_option_a @ X2 @ A2 )
=> ( ( image_option_a_a @ ( fun_upd_option_a_a @ F @ X2 @ Y ) @ A2 )
= ( insert_a @ Y @ ( image_option_a_a @ F @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ) ) )
& ( ~ ( member_option_a @ X2 @ A2 )
=> ( ( image_option_a_a @ ( fun_upd_option_a_a @ F @ X2 @ Y ) @ A2 )
= ( image_option_a_a @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_530_fun__upd__image,axiom,
! [X2: b,A2: set_b,F: b > option_a,Y: option_a] :
( ( ( member_b @ X2 @ A2 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ F @ X2 @ Y ) @ A2 )
= ( insert_option_a @ Y @ ( image_b_option_a @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) )
& ( ~ ( member_b @ X2 @ A2 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ F @ X2 @ Y ) @ A2 )
= ( image_b_option_a @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_531_fun__upd__image,axiom,
! [X2: b,A2: set_b,F: b > a,Y: a] :
( ( ( member_b @ X2 @ A2 )
=> ( ( image_b_a @ ( fun_upd_b_a @ F @ X2 @ Y ) @ A2 )
= ( insert_a @ Y @ ( image_b_a @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) )
& ( ~ ( member_b @ X2 @ A2 )
=> ( ( image_b_a @ ( fun_upd_b_a @ F @ X2 @ Y ) @ A2 )
= ( image_b_a @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_532_fun__upd__image,axiom,
! [X2: c,A2: set_c,F: c > d,Y: d] :
( ( ( member_c @ X2 @ A2 )
=> ( ( image_c_d @ ( fun_upd_c_d @ F @ X2 @ Y ) @ A2 )
= ( insert_d @ Y @ ( image_c_d @ F @ ( minus_minus_set_c @ A2 @ ( insert_c @ X2 @ bot_bot_set_c ) ) ) ) ) )
& ( ~ ( member_c @ X2 @ A2 )
=> ( ( image_c_d @ ( fun_upd_c_d @ F @ X2 @ Y ) @ A2 )
= ( image_c_d @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_533_fun__upd__image,axiom,
! [X2: a,A2: set_a,F: a > a,Y: a] :
( ( ( member_a @ X2 @ A2 )
=> ( ( image_a_a @ ( fun_upd_a_a @ F @ X2 @ Y ) @ A2 )
= ( insert_a @ Y @ ( image_a_a @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) )
& ( ~ ( member_a @ X2 @ A2 )
=> ( ( image_a_a @ ( fun_upd_a_a @ F @ X2 @ Y ) @ A2 )
= ( image_a_a @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_534_fun__upd__image,axiom,
! [X2: a,A2: set_a,F: a > option_a,Y: option_a] :
( ( ( member_a @ X2 @ A2 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ F @ X2 @ Y ) @ A2 )
= ( insert_option_a @ Y @ ( image_a_option_a @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) )
& ( ~ ( member_a @ X2 @ A2 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ F @ X2 @ Y ) @ A2 )
= ( image_a_option_a @ F @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_535_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_536_logic_Oapplies__eq_Osimps,axiom,
! [Plus2: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta: ( c > d ) > set_a,S2: c > d] :
( ( logic_a_b @ Plus2 @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( applies_eq_a_b_d_c @ Plus2 @ Mult @ Valid @ A2 @ Delta @ S2 )
= ( collect_a
@ ^ [Uu: a] :
? [A3: a] :
( ( Uu = A3 )
& ( sat_a_b_c_d @ Plus2 @ Mult @ Valid @ A3 @ S2 @ Delta @ A2 ) ) ) ) ) ).
% logic.applies_eq.simps
thf(fact_537_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] :
? [A3: assertion_a_b_d_c,B2: produc5213381314664832452_a_c_d] :
( ( Uu
= ( produc8894421531525210148_a_c_d @ A3 @ B2 ) )
& ( ( M4 @ A3 )
= ( some_P3194730542479778335_a_c_d @ B2 ) ) ) ) ) ) ).
% graph_def
thf(fact_538_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] :
? [A3: ( c > d ) > set_a,B2: c > d] :
( ( Uu
= ( produc7376592049607813182_a_c_d @ A3 @ B2 ) )
& ( ( M4 @ A3 )
= ( some_c_d @ B2 ) ) ) ) ) ) ).
% graph_def
thf(fact_539_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_540_finite__update__induct,axiom,
! [F: c > d,C: d,P2: ( c > d ) > $o] :
( ( finite_finite_c
@ ( collect_c
@ ^ [A3: c] :
( ( F @ A3 )
!= C ) ) )
=> ( ( P2
@ ^ [A3: c] : C )
=> ( ! [A4: c,B3: d,F3: c > d] :
( ( finite_finite_c
@ ( collect_c
@ ^ [C2: c] :
( ( F3 @ C2 )
!= C ) ) )
=> ( ( ( F3 @ A4 )
= C )
=> ( ( B3 != C )
=> ( ( P2 @ F3 )
=> ( P2 @ ( fun_upd_c_d @ F3 @ A4 @ B3 ) ) ) ) ) )
=> ( P2 @ F ) ) ) ) ).
% finite_update_induct
thf(fact_541_finite__update__induct,axiom,
! [F: a > option_a,C: option_a,P2: ( a > option_a ) > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [A3: a] :
( ( F @ A3 )
!= C ) ) )
=> ( ( P2
@ ^ [A3: a] : C )
=> ( ! [A4: a,B3: option_a,F3: a > option_a] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C2: a] :
( ( F3 @ C2 )
!= C ) ) )
=> ( ( ( F3 @ A4 )
= C )
=> ( ( B3 != C )
=> ( ( P2 @ F3 )
=> ( P2 @ ( fun_upd_a_option_a @ F3 @ A4 @ B3 ) ) ) ) ) )
=> ( P2 @ F ) ) ) ) ).
% finite_update_induct
thf(fact_542_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_543_combine__options__def,axiom,
( combine_options_a
= ( ^ [F2: a > a > a,X3: option_a,Y2: option_a] :
( case_o3148979394504432965on_a_a @ Y2
@ ^ [Z2: a] :
( case_o3148979394504432965on_a_a @ ( some_a @ Z2 )
@ ^ [Aa: a] : ( some_a @ ( F2 @ Z2 @ Aa ) )
@ Y2 )
@ X3 ) ) ) ).
% combine_options_def
thf(fact_544_applies__eq_Ocases,axiom,
! [X2: produc5105196854009589546_a_c_d] :
~ ! [A7: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,S: c > d] :
( X2
!= ( produc8894421531525210148_a_c_d @ A7 @ ( produc7376592049607813182_a_c_d @ Delta3 @ S ) ) ) ).
% applies_eq.cases
thf(fact_545_combine__options__simps_I3_J,axiom,
! [F: a > a > a,A: a,B: a] :
( ( combine_options_a @ F @ ( some_a @ A ) @ ( some_a @ B ) )
= ( some_a @ ( F @ A @ B ) ) ) ).
% combine_options_simps(3)
thf(fact_546_finite__range__updI,axiom,
! [F: a > option_a,A: a,B: a] :
( ( finite1674126218327898605tion_a @ ( image_a_option_a @ F @ top_top_set_a ) )
=> ( finite1674126218327898605tion_a @ ( image_a_option_a @ ( fun_upd_a_option_a @ F @ A @ ( some_a @ B ) ) @ top_top_set_a ) ) ) ).
% finite_range_updI
thf(fact_547_finite__range__updI,axiom,
! [F: option_a > option_a,A: option_a,B: a] :
( ( finite1674126218327898605tion_a @ ( image_7439109396645324421tion_a @ F @ top_top_set_option_a ) )
=> ( finite1674126218327898605tion_a @ ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F @ A @ ( some_a @ B ) ) @ top_top_set_option_a ) ) ) ).
% finite_range_updI
thf(fact_548_map__option__case,axiom,
( map_option_a_a
= ( ^ [F2: a > a] :
( case_o3148979394504432965on_a_a @ none_a
@ ^ [X3: a] : ( some_a @ ( F2 @ X3 ) ) ) ) ) ).
% map_option_case
thf(fact_549_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_550_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_551_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_552_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_553_map__option__eq__Some,axiom,
! [F: a > a,Xo: option_a,Y: a] :
( ( ( map_option_a_a @ F @ Xo )
= ( some_a @ Y ) )
= ( ? [Z2: a] :
( ( Xo
= ( some_a @ Z2 ) )
& ( ( F @ Z2 )
= Y ) ) ) ) ).
% map_option_eq_Some
thf(fact_554_dom__const,axiom,
! [F: a > a] :
( ( dom_a_a
@ ^ [X3: a] : ( some_a @ ( F @ X3 ) ) )
= top_top_set_a ) ).
% dom_const
thf(fact_555_dom__const,axiom,
! [F: option_a > a] :
( ( dom_option_a_a
@ ^ [X3: option_a] : ( some_a @ ( F @ X3 ) ) )
= top_top_set_option_a ) ).
% dom_const
thf(fact_556_option_Osimps_I9_J,axiom,
! [F: a > a,X22: a] :
( ( map_option_a_a @ F @ ( some_a @ X22 ) )
= ( some_a @ ( F @ X22 ) ) ) ).
% option.simps(9)
thf(fact_557_map__option__cong,axiom,
! [X2: option_a,Y: option_a,F: a > a,G: a > a] :
( ( X2 = Y )
=> ( ! [A4: a] :
( ( Y
= ( some_a @ A4 ) )
=> ( ( F @ A4 )
= ( G @ A4 ) ) )
=> ( ( map_option_a_a @ F @ X2 )
= ( map_option_a_a @ G @ Y ) ) ) ) ).
% map_option_cong
thf(fact_558_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_559_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_560_map__option__o__map__upd,axiom,
! [F: a > a,M: a > option_a,A: a,B: a] :
( ( comp_o6087033147929006299on_a_a @ ( map_option_a_a @ F ) @ ( fun_upd_a_option_a @ M @ A @ ( some_a @ B ) ) )
= ( fun_upd_a_option_a @ ( comp_o6087033147929006299on_a_a @ ( map_option_a_a @ F ) @ M ) @ A @ ( some_a @ ( F @ B ) ) ) ) ).
% map_option_o_map_upd
thf(fact_561_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_562_map__conv__bind__option,axiom,
( map_option_a_a
= ( ^ [F2: a > a,X3: option_a] : ( bind_a_a @ X3 @ ( comp_a_option_a_a @ some_a @ F2 ) ) ) ) ).
% map_conv_bind_option
thf(fact_563_fun__upd__comp,axiom,
! [F: d > d,G: c > d,X2: c,Y: d] :
( ( comp_d_d_c @ F @ ( fun_upd_c_d @ G @ X2 @ Y ) )
= ( fun_upd_c_d @ ( comp_d_d_c @ F @ G ) @ X2 @ ( F @ Y ) ) ) ).
% fun_upd_comp
thf(fact_564_fun__upd__comp,axiom,
! [F: option_a > a,G: a > option_a,X2: a,Y: option_a] :
( ( comp_option_a_a_a @ F @ ( fun_upd_a_option_a @ G @ X2 @ Y ) )
= ( fun_upd_a_a @ ( comp_option_a_a_a @ F @ G ) @ X2 @ ( F @ Y ) ) ) ).
% fun_upd_comp
thf(fact_565_fun__upd__comp,axiom,
! [F: option_a > option_a,G: a > option_a,X2: a,Y: option_a] :
( ( comp_o6087033147929006299on_a_a @ F @ ( fun_upd_a_option_a @ G @ X2 @ Y ) )
= ( fun_upd_a_option_a @ ( comp_o6087033147929006299on_a_a @ F @ G ) @ X2 @ ( F @ Y ) ) ) ).
% fun_upd_comp
thf(fact_566_inj__Some,axiom,
! [A2: set_a] : ( inj_on_a_option_a @ some_a @ A2 ) ).
% inj_Some
thf(fact_567_inj__on__fun__updI,axiom,
! [F: c > d,A2: set_c,Y: d,X2: c] :
( ( inj_on_c_d @ F @ A2 )
=> ( ~ ( member_d @ Y @ ( image_c_d @ F @ A2 ) )
=> ( inj_on_c_d @ ( fun_upd_c_d @ F @ X2 @ Y ) @ A2 ) ) ) ).
% inj_on_fun_updI
thf(fact_568_inj__on__fun__updI,axiom,
! [F: a > option_a,A2: set_a,Y: option_a,X2: a] :
( ( inj_on_a_option_a @ F @ A2 )
=> ( ~ ( member_option_a @ Y @ ( image_a_option_a @ F @ A2 ) )
=> ( inj_on_a_option_a @ ( fun_upd_a_option_a @ F @ X2 @ Y ) @ A2 ) ) ) ).
% inj_on_fun_updI
thf(fact_569_comp__the__Some,axiom,
( ( comp_option_a_a_a @ the_a @ some_a )
= id_a ) ).
% comp_the_Some
thf(fact_570_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_571_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_572_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_573_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_574_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_575_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_576_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_577_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_578_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_579_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_580_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_581_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_582_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_583_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_584_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_585_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_586_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_587_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_588_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_589_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_590_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_591_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_592_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_593_assertion_Osimps_I333_J,axiom,
( ( set_as7232682317586342732_b_d_c @ pred_a_b_d_c )
= bot_bot_set_b ) ).
% assertion.simps(333)
thf(fact_594_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_595_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_596_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_597_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_598_semilattice__set_Oeq__fold_H,axiom,
! [F: a > a > a,A2: set_a] :
( ( lattic5961991414251573132_set_a @ F )
=> ( ( lattic5116578512385870296ce_F_a @ F @ A2 )
= ( the_a
@ ( finite6501707464432451470tion_a
@ ^ [X3: a,Y2: option_a] : ( some_a @ ( case_option_a_a @ X3 @ ( F @ X3 ) @ Y2 ) )
@ none_a
@ A2 ) ) ) ) ).
% semilattice_set.eq_fold'
thf(fact_599_is__none__code_I2_J,axiom,
! [X2: a] :
~ ( is_none_a @ ( some_a @ X2 ) ) ).
% is_none_code(2)
thf(fact_600_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_601_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_602_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_603_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_604_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_605_assertion_Orel__refl,axiom,
! [Ra: b > b > $o,X2: assertion_a_b_d_c] :
( ! [X: b] : ( Ra @ X @ X )
=> ( rel_as1860989020795611527_a_d_c @ Ra @ X2 @ X2 ) ) ).
% assertion.rel_refl
thf(fact_606_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_607_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_608_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_609_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_610_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_611_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_612_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_613_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_614_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_615_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_616_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_617_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_618_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_619_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_620_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_621_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_622_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_623_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_624_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_625_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_626_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_627_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_628_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_629_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_630_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_631_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_632_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_633_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_634_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_635_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_636_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_637_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_638_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_639_is__none__simps_I2_J,axiom,
! [X2: a] :
~ ( is_none_a @ ( some_a @ X2 ) ) ).
% is_none_simps(2)
thf(fact_640_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_641_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_642_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_643_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_644_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_645_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_646_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_647_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_648_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_649_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_650_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_651_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_652_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_653_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_654_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_655_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_656_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_657_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_658_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_659_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_660_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_661_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_662_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_663_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_664_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_665_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_666_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_667_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_668_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_669_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_670_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_671_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_672_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_673_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_674_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_675_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_676_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_677_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_678_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_679_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_680_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_681_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_682_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_683_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_684_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_685_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_686_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_687_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_688_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_689_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_690_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_691_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_692_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_693_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_694_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_695_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_696_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_697_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_698_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_699_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_700_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_701_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_702_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_703_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_704_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_705_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_706_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_707_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_708_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_709_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_710_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_711_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_712_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_713_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_714_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_715_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_716_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_717_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_718_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_719_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_720_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_721_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_722_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_723_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_724_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_725_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_726_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_727_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_728_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_729_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_730_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_731_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_732_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_733_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_734_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_735_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_736_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_737_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_738_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_739_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_740_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_741_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_742_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_743_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_744_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_745_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_746_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_747_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_748_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_749_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_750_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_751_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_752_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_753_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_754_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_755_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_756_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_757_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_758_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_759_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_760_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_761_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_762_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_763_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_764_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_765_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_766_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_767_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_768_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_769_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_770_assertion_Oset__map,axiom,
! [F: b > b,V: assertion_a_b_d_c] :
( ( set_as7232682317586342732_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ V ) )
= ( image_b_b @ F @ ( set_as7232682317586342732_b_d_c @ V ) ) ) ).
% assertion.set_map
thf(fact_771_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_772_option_Orel__induct,axiom,
! [R3: a > a > $o,X2: option_a,Y: option_a,Q2: option_a > option_a > $o] :
( ( rel_option_a_a @ R3 @ X2 @ Y )
=> ( ( Q2 @ none_a @ none_a )
=> ( ! [A23: a,B23: a] :
( ( R3 @ A23 @ B23 )
=> ( Q2 @ ( some_a @ A23 ) @ ( some_a @ B23 ) ) )
=> ( Q2 @ X2 @ Y ) ) ) ) ).
% option.rel_induct
thf(fact_773_assertion_Orel__map_I1_J,axiom,
! [Sb: b > b > $o,I: b > b,X2: assertion_a_b_d_c,Y: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ Sb @ ( map_as2132001898603344138_a_d_c @ I @ X2 ) @ Y )
= ( rel_as1860989020795611527_a_d_c
@ ^ [X3: b] : ( Sb @ ( I @ X3 ) )
@ X2
@ Y ) ) ).
% assertion.rel_map(1)
thf(fact_774_assertion_Orel__map_I2_J,axiom,
! [Sa: b > b > $o,X2: assertion_a_b_d_c,G: b > b,Y: assertion_a_b_d_c] :
( ( rel_as1860989020795611527_a_d_c @ Sa @ X2 @ ( map_as2132001898603344138_a_d_c @ G @ Y ) )
= ( rel_as1860989020795611527_a_d_c
@ ^ [X3: b,Y2: b] : ( Sa @ X3 @ ( G @ Y2 ) )
@ X2
@ Y ) ) ).
% assertion.rel_map(2)
thf(fact_775_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_776_assertion_Omap__comp,axiom,
! [G: b > b,F: b > b,V: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ G @ ( map_as2132001898603344138_a_d_c @ F @ V ) )
= ( map_as2132001898603344138_a_d_c @ ( comp_b_b_b @ G @ F ) @ V ) ) ).
% assertion.map_comp
thf(fact_777_assertion_Omap__ident__strong,axiom,
! [T: assertion_a_b_d_c,F: b > b] :
( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ T ) )
=> ( ( F @ Z4 )
= Z4 ) )
=> ( ( map_as2132001898603344138_a_d_c @ F @ T )
= T ) ) ).
% assertion.map_ident_strong
thf(fact_778_assertion_Oinj__map__strong,axiom,
! [X2: assertion_a_b_d_c,Xa: assertion_a_b_d_c,F: 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 ) )
=> ( ( ( F @ Z4 )
= ( Fa @ Za ) )
=> ( Z4 = Za ) ) ) )
=> ( ( ( map_as2132001898603344138_a_d_c @ F @ X2 )
= ( map_as2132001898603344138_a_d_c @ Fa @ Xa ) )
=> ( X2 = Xa ) ) ) ).
% assertion.inj_map_strong
thf(fact_779_assertion_Omap__cong0,axiom,
! [X2: assertion_a_b_d_c,F: b > b,G: b > b] :
( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ X2 ) )
=> ( ( F @ Z4 )
= ( G @ Z4 ) ) )
=> ( ( map_as2132001898603344138_a_d_c @ F @ X2 )
= ( map_as2132001898603344138_a_d_c @ G @ X2 ) ) ) ).
% assertion.map_cong0
thf(fact_780_assertion_Omap__cong,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,F: b > b,G: b > b] :
( ( X2 = Ya )
=> ( ! [Z4: b] :
( ( member_b @ Z4 @ ( set_as7232682317586342732_b_d_c @ Ya ) )
=> ( ( F @ Z4 )
= ( G @ Z4 ) ) )
=> ( ( map_as2132001898603344138_a_d_c @ F @ X2 )
= ( map_as2132001898603344138_a_d_c @ G @ Ya ) ) ) ) ).
% assertion.map_cong
thf(fact_781_assertion_Omap__id0,axiom,
( ( map_as2132001898603344138_a_d_c @ id_b )
= id_assertion_a_b_d_c ) ).
% assertion.map_id0
thf(fact_782_assertion_Omap__id,axiom,
! [T: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ id_b @ T )
= T ) ).
% assertion.map_id
thf(fact_783_assertion_Osimps_I169_J,axiom,
! [F: b > b,X212: b,X223: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( mult_b_a_d_c @ X212 @ X223 ) )
= ( mult_b_a_d_c @ ( F @ X212 ) @ ( map_as2132001898603344138_a_d_c @ F @ X223 ) ) ) ).
% assertion.simps(169)
thf(fact_784_assertion_Osimps_I179_J,axiom,
! [F: b > b,X123: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( wildcard_a_b_d_c @ X123 ) )
= ( wildcard_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X123 ) ) ) ).
% assertion.simps(179)
thf(fact_785_assertion_Osimps_I170_J,axiom,
! [F: b > b,X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( star_a_b_d_c @ X312 @ X322 ) )
= ( star_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X312 ) @ ( map_as2132001898603344138_a_d_c @ F @ X322 ) ) ) ).
% assertion.simps(170)
thf(fact_786_assertion_Osimps_I173_J,axiom,
! [F: b > b,X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( and_a_b_d_c @ X612 @ X622 ) )
= ( and_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X612 ) @ ( map_as2132001898603344138_a_d_c @ F @ X622 ) ) ) ).
% assertion.simps(173)
thf(fact_787_assertion_Osimps_I176_J,axiom,
! [F: b > b,X912: c,X922: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( forall_c_a_b_d @ X912 @ X922 ) )
= ( forall_c_a_b_d @ X912 @ ( map_as2132001898603344138_a_d_c @ F @ X922 ) ) ) ).
% assertion.simps(176)
thf(fact_788_assertion_Osimps_I175_J,axiom,
! [F: b > b,X812: c,X822: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( exists_c_a_b_d @ X812 @ X822 ) )
= ( exists_c_a_b_d @ X812 @ ( map_as2132001898603344138_a_d_c @ F @ X822 ) ) ) ).
% assertion.simps(175)
thf(fact_789_assertion_Osimps_I174_J,axiom,
! [F: b > b,X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( imp_a_b_d_c @ X712 @ X722 ) )
= ( imp_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X712 ) @ ( map_as2132001898603344138_a_d_c @ F @ X722 ) ) ) ).
% assertion.simps(174)
thf(fact_790_assertion_Osimps_I172_J,axiom,
! [F: b > b,X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( or_a_b_d_c @ X512 @ X522 ) )
= ( or_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X512 ) @ ( map_as2132001898603344138_a_d_c @ F @ X522 ) ) ) ).
% assertion.simps(172)
thf(fact_791_assertion_Osimps_I171_J,axiom,
! [F: b > b,X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( wand_a_b_d_c @ X412 @ X422 ) )
= ( wand_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X412 ) @ ( map_as2132001898603344138_a_d_c @ F @ X422 ) ) ) ).
% assertion.simps(171)
thf(fact_792_assertion_Osimps_I178_J,axiom,
! [F: b > b,X112: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c @ F @ ( bounded_a_b_d_c @ X112 ) )
= ( bounded_a_b_d_c @ ( map_as2132001898603344138_a_d_c @ F @ X112 ) ) ) ).
% assertion.simps(178)
thf(fact_793_assertion_Osimps_I168_J,axiom,
! [F: b > b,X1: ( c > d ) > a > $o] :
( ( map_as2132001898603344138_a_d_c @ F @ ( sem_c_d_a_b @ X1 ) )
= ( sem_c_d_a_b @ X1 ) ) ).
% assertion.simps(168)
thf(fact_794_assertion_Osimps_I177_J,axiom,
! [F: b > b] :
( ( map_as2132001898603344138_a_d_c @ F @ pred_a_b_d_c )
= pred_a_b_d_c ) ).
% assertion.simps(177)
thf(fact_795_option__rel__Some2,axiom,
! [A2: a > a > $o,X2: option_a,Y: a] :
( ( rel_option_a_a @ A2 @ X2 @ ( some_a @ Y ) )
= ( ? [X7: a] :
( ( X2
= ( some_a @ X7 ) )
& ( A2 @ X7 @ Y ) ) ) ) ).
% option_rel_Some2
thf(fact_796_option__rel__Some1,axiom,
! [A2: a > a > $o,X2: a,Y: option_a] :
( ( rel_option_a_a @ A2 @ ( some_a @ X2 ) @ Y )
= ( ? [Y5: a] :
( ( Y
= ( some_a @ Y5 ) )
& ( A2 @ X2 @ Y5 ) ) ) ) ).
% option_rel_Some1
thf(fact_797_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_798_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_799_assertion_Omap__ident,axiom,
! [T: assertion_a_b_d_c] :
( ( map_as2132001898603344138_a_d_c
@ ^ [X3: b] : X3
@ T )
= T ) ).
% assertion.map_ident
thf(fact_800_assertion_Oinj__map,axiom,
! [F: b > b] :
( ( inj_on_b_b @ F @ top_top_set_b )
=> ( inj_on3926713243670117681_b_d_c @ ( map_as2132001898603344138_a_d_c @ F ) @ top_to5090759043282426983_b_d_c ) ) ).
% assertion.inj_map
thf(fact_801_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_802_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_803_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_804_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 ) )
=> ~ ! [X: a] :
( ( A
= ( some_a @ X ) )
=> ! [Y3: a] :
( ( B
= ( some_a @ Y3 ) )
=> ~ ( R3 @ X @ Y3 ) ) ) ) ) ).
% option.rel_cases
thf(fact_805_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_806_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_807_assertion_Orel__transfer,axiom,
! [Sa: b > b > $o,Sc: b > b > $o] :
( bNF_re6697097071762359901_d_c_o
@ ( bNF_re4413358128099268379_o_b_o @ Sa
@ ( bNF_rel_fun_b_b_o_o @ Sc
@ ^ [Y4: $o,Z3: $o] : ( Y4 = Z3 ) ) )
@ ( bNF_re7564741212224818219_d_c_o @ ( rel_as1860989020795611527_a_d_c @ Sa )
@ ( 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_808_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_809_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_810_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_811_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_812_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_813_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_814_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_815_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_816_assertion_Ocase__transfer,axiom,
! [S4: assertion_a_b_d_c > assertion_a_b_d_c > $o,R3: b > b > $o] :
( bNF_re5462665785578358557_b_d_c
@ ( bNF_re1770667264140748071_b_d_c
@ ^ [Y4: ( c > d ) > a > $o,Z3: ( c > d ) > a > $o] : ( Y4 = Z3 )
@ S4 )
@ ( bNF_re969776683416675581_b_d_c @ ( bNF_re377125674677652585_b_d_c @ R3 @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re5536568207858047837_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re3555337462168811729_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re5146714292400357853_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re6312048780865235365_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re3015297470480446045_b_d_c @ ( bNF_re8872988018146346089_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( bNF_re6171781090946898727_b_d_c
@ ( bNF_re133962660596780713_b_d_c
@ ^ [Y4: c,Z3: c] : ( Y4 = Z3 )
@ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) )
@ ( 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 ) @ S4 ) )
@ ( bNF_re515523818749706873_b_d_c @ S4 @ ( bNF_re6606623624522348157_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) @ ( bNF_re8402442907184412917_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) @ ( bNF_re5048873211533932509_b_d_c @ ( rel_as1860989020795611527_a_d_c @ R3 ) @ S4 ) ) ) ) ) ) ) ) ) ) ) )
@ case_a2736964712663357406_d_c_b
@ case_a2736964712663357406_d_c_b ) ).
% assertion.case_transfer
thf(fact_817_fun__upd__transfer,axiom,
! [A2: c > c > $o,B4: d > d > $o] :
( ( bi_unique_c_c @ A2 )
=> ( bNF_re4162436072719156391_d_c_d @ ( bNF_rel_fun_c_c_d_d @ A2 @ B4 ) @ ( bNF_re6283605750710864861_d_c_d @ A2 @ ( bNF_re2118925435710938475_d_c_d @ B4 @ ( bNF_rel_fun_c_c_d_d @ A2 @ B4 ) ) ) @ fun_upd_c_d @ fun_upd_c_d ) ) ).
% fun_upd_transfer
thf(fact_818_fun__upd__transfer,axiom,
! [A2: c > a > $o,B4: d > option_a > $o] :
( ( bi_unique_c_a @ A2 )
=> ( bNF_re5308688359564752758tion_a @ ( bNF_re2367443474453270238tion_a @ A2 @ B4 ) @ ( bNF_re2730572489753928035tion_a @ A2 @ ( bNF_re4105512943801057267tion_a @ B4 @ ( bNF_re2367443474453270238tion_a @ A2 @ B4 ) ) ) @ fun_upd_c_d @ fun_upd_a_option_a ) ) ).
% fun_upd_transfer
thf(fact_819_fun__upd__transfer,axiom,
! [A2: a > c > $o,B4: option_a > d > $o] :
( ( bi_unique_a_c @ A2 )
=> ( bNF_re3817954351838466806_d_c_d @ ( bNF_re3628769949165654428on_a_d @ A2 @ B4 ) @ ( bNF_re7925548642511003351_d_c_d @ A2 @ ( bNF_re6291851909076488365_a_c_d @ B4 @ ( bNF_re3628769949165654428on_a_d @ A2 @ B4 ) ) ) @ fun_upd_a_option_a @ fun_upd_c_d ) ) ).
% fun_upd_transfer
thf(fact_820_fun__upd__transfer,axiom,
! [A2: a > a > $o,B4: option_a > option_a > $o] :
( ( bi_unique_a_a @ A2 )
=> ( bNF_re4933961146405920325tion_a @ ( bNF_re1187871780581372509tion_a @ A2 @ B4 ) @ ( bNF_re845666378725559389tion_a @ A2 @ ( bNF_re8162217253061806133tion_a @ B4 @ ( bNF_re1187871780581372509tion_a @ A2 @ B4 ) ) ) @ fun_upd_a_option_a @ fun_upd_a_option_a ) ) ).
% fun_upd_transfer
thf(fact_821_fun__upd__transfer,axiom,
! [A2: c > c > $o,B4: ( assertion_a_b_d_c > assertion_a_b_d_c ) > ( assertion_a_b_d_c > assertion_a_b_d_c ) > $o] :
( ( bi_unique_c_c @ A2 )
=> ( bNF_re6482585556422379257_b_d_c @ ( bNF_re133962660596780713_b_d_c @ A2 @ B4 ) @ ( bNF_re3899328378992105309_b_d_c @ A2 @ ( bNF_re7213484083391222185_b_d_c @ B4 @ ( bNF_re133962660596780713_b_d_c @ A2 @ B4 ) ) ) @ fun_up7970115895444633960_b_d_c @ fun_up7970115895444633960_b_d_c ) ) ).
% fun_upd_transfer
thf(fact_822_fun__upd__transfer,axiom,
! [A2: assertion_a_b_d_c > assertion_a_b_d_c > $o,B4: assertion_a_b_d_c > assertion_a_b_d_c > $o] :
( ( bi_uni8285078783686190927_b_d_c @ A2 )
=> ( bNF_re8313538116629745697_b_d_c @ ( bNF_re5048873211533932509_b_d_c @ A2 @ B4 ) @ ( bNF_re39574443744948061_b_d_c @ A2 @ ( bNF_re8872988018146346089_b_d_c @ B4 @ ( bNF_re5048873211533932509_b_d_c @ A2 @ B4 ) ) ) @ fun_up5644072878873480765_b_d_c @ fun_up5644072878873480765_b_d_c ) ) ).
% fun_upd_transfer
thf(fact_823_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_824_assertion_Orel__Grp,axiom,
! [A2: set_b,F: b > b] :
( ( rel_as1860989020795611527_a_d_c @ ( bNF_Grp_b_b @ A2 @ F ) )
= ( bNF_Gr8554578625086265742_b_d_c
@ ( collec7183461376620183714_b_d_c
@ ^ [X3: assertion_a_b_d_c] : ( ord_less_eq_set_b @ ( set_as7232682317586342732_b_d_c @ X3 ) @ A2 ) )
@ ( map_as2132001898603344138_a_d_c @ F ) ) ) ).
% assertion.rel_Grp
thf(fact_825_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_826_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_827_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_828_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_829_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_830_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_831_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_832_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_833_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_834_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_835_assertion_Opred__True,axiom,
( ( pred_a5408123710409757427_a_d_c
@ ^ [Uu: b] : $true )
= ( ^ [Uu: assertion_a_b_d_c] : $true ) ) ).
% assertion.pred_True
thf(fact_836_assertion_Omap__cong__pred,axiom,
! [X2: assertion_a_b_d_c,Ya: assertion_a_b_d_c,F: b > b,G: b > b] :
( ( X2 = Ya )
=> ( ( pred_a5408123710409757427_a_d_c
@ ^ [Z2: b] :
( ( F @ Z2 )
= ( G @ Z2 ) )
@ Ya )
=> ( ( map_as2132001898603344138_a_d_c @ F @ X2 )
= ( map_as2132001898603344138_a_d_c @ G @ Ya ) ) ) ) ).
% assertion.map_cong_pred
thf(fact_837_assertion_Opred__map,axiom,
! [Q2: b > $o,F: b > b,X2: assertion_a_b_d_c] :
( ( pred_a5408123710409757427_a_d_c @ Q2 @ ( map_as2132001898603344138_a_d_c @ F @ X2 ) )
= ( pred_a5408123710409757427_a_d_c @ ( comp_b_o_b @ Q2 @ F ) @ X2 ) ) ).
% assertion.pred_map
thf(fact_838_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_839_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
thf(fact_840_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
% 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,
member_a @ x @ ( applies_eq_a_b_d_c @ plus @ mult @ valid @ ( exists_c_a_b_d @ v @ a2 ) @ delta @ s ) ).
%------------------------------------------------------------------------------