%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP127^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:46 AM UTC 2026
% Result : Theorem 2.76s 1.61s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 112 ( 7 ~; 0 |; 0 &; 105 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 72 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 38 ^; 7 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_6,type,
countable_Set_cset_c: $tType ).
thf(type_def_8,type,
monomo197243225tT_a_m: $tType ).
thf(type_def_9,type,
m: $tType ).
thf(type_def_10,type,
counta191869203tT_a_m: $tType ).
thf(func_def_0,type,
counta191869203tT_a_m: $tType ).
thf(func_def_1,type,
monomo197243225tT_a_m: $tType ).
thf(func_def_2,type,
countable_Set_cset_c: $tType ).
thf(func_def_3,type,
m: $tType ).
thf(func_def_4,type,
c: $tType ).
thf(func_def_5,type,
countable_Set_cin_c: c > countable_Set_cset_c > $o ).
thf(func_def_6,type,
counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).
thf(func_def_7,type,
comp_M864375327_a_m_c: ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c > monomo197243225tT_a_m ).
thf(func_def_8,type,
comp_M1062614966_m_c_c: ( monomo197243225tT_a_m > c ) > ( c > monomo197243225tT_a_m ) > c > c ).
thf(func_def_9,type,
comp_M1944986301tT_a_m: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).
thf(func_def_10,type,
comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).
thf(func_def_11,type,
comp_M750374454_m_m_m: ( monomo197243225tT_a_m > m ) > ( m > monomo197243225tT_a_m ) > m > m ).
thf(func_def_12,type,
comp_c1772230468_a_m_c: ( c > monomo197243225tT_a_m ) > ( c > c ) > c > monomo197243225tT_a_m ).
thf(func_def_13,type,
comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).
thf(func_def_14,type,
comp_c997395372tT_a_m: ( c > m ) > ( monomo197243225tT_a_m > c ) > monomo197243225tT_a_m > m ).
thf(func_def_15,type,
comp_c_m_c: ( c > m ) > ( c > c ) > c > m ).
thf(func_def_16,type,
comp_c_m_m: ( c > m ) > ( m > c ) > m > m ).
thf(func_def_17,type,
comp_m1038691662_a_m_c: ( m > monomo197243225tT_a_m ) > ( c > m ) > c > monomo197243225tT_a_m ).
thf(func_def_18,type,
comp_m_c_c: ( m > c ) > ( c > m ) > c > c ).
thf(func_def_19,type,
comp_m263856566tT_a_m: ( m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m > m ).
thf(func_def_20,type,
comp_m_m_c: ( m > m ) > ( c > m ) > c > m ).
thf(func_def_21,type,
comp_m_m_m: ( m > m ) > ( m > m ) > m > m ).
thf(func_def_22,type,
minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(func_def_23,type,
if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(func_def_24,type,
if_c: $o > c > c > c ).
thf(func_def_25,type,
monomo2081011572_m_m_a: ( counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m ) > counta191869203tT_a_m > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
thf(func_def_26,type,
monomo463139869_c_m_a: ( countable_Set_cset_c > ( c > m ) > m ) > countable_Set_cset_c > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
thf(func_def_27,type,
monomo412532791tT_m_a: m > monomo197243225tT_a_m ).
thf(func_def_28,type,
monomo624345106et_a_m: monomo197243225tT_a_m > m ).
thf(func_def_29,type,
bot_bo1320844070cset_c: countable_Set_cset_c ).
thf(func_def_30,type,
ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
thf(func_def_31,type,
ord_le1376176871cset_c: ( $o > countable_Set_cset_c ) > ( $o > countable_Set_cset_c ) > $o ).
thf(func_def_32,type,
ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
thf(func_def_33,type,
order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
thf(func_def_34,type,
f: c > monomo197243225tT_a_m ).
thf(func_def_35,type,
mergec: countable_Set_cset_c > ( c > m ) > m ).
thf(func_def_36,type,
x: c ).
thf(func_def_48,type,
sK0: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_49,type,
sK1: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_50,type,
sK2: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_51,type,
sK3: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_52,type,
sK4: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_53,type,
sK5: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_54,type,
sK6: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_55,type,
sK7: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_56,type,
sK8: countable_Set_cset_c > c ).
thf(func_def_57,type,
sK9: ( c > m ) > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).
thf(func_def_58,type,
sK10: ( c > m ) > ( c > monomo197243225tT_a_m ) > c ).
thf(func_def_59,type,
sK11: ( c > m ) > ( c > monomo197243225tT_a_m ) > c ).
thf(func_def_60,type,
sK12: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_61,type,
sK13: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_62,type,
sK14: c > ( monomo197243225tT_a_m > m ) > ( c > m ) > monomo197243225tT_a_m ).
thf(func_def_63,type,
sK15: ( monomo197243225tT_a_m > m ) > ( c > m ) > c > monomo197243225tT_a_m ).
thf(func_def_64,type,
sK16: ( monomo197243225tT_a_m > m ) > ( c > m ) > c ).
thf(func_def_65,type,
sK17: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_66,type,
sK18: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_67,type,
sK19: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_68,type,
sK20: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_69,type,
sK21: monomo197243225tT_a_m > m ).
thf(func_def_70,type,
sK22: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_71,type,
sK23: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_72,type,
sK24: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_73,type,
sK25: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_74,type,
sK26: countable_Set_cset_c > c ).
thf(func_def_75,type,
sK27: ( monomo197243225tT_a_m > $o ) > m ).
thf(func_def_76,type,
sK28: countable_Set_cset_c > c ).
thf(func_def_77,type,
sK29: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_78,type,
sK30: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_79,type,
sK31: countable_Set_cset_c > countable_Set_cset_c > c ).
thf(func_def_80,type,
sK32: c > countable_Set_cset_c > countable_Set_cset_c ).
thf(func_def_81,type,
sK33: countable_Set_cset_c > c > countable_Set_cset_c ).
thf(func_def_82,type,
sK34: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_83,type,
sK35: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_84,type,
sK36: countable_Set_cset_c > countable_Set_cset_c > c ).
thf(func_def_85,type,
sK37: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_86,type,
sK38: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).
thf(func_def_88,type,
ph40:
!>[X0: $tType] : X0 ).
thf(f1268,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1267,f999]) ).
thf(f999,plain,
! [X0: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f711]) ).
thf(f711,plain,
! [X0: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ X0 ) )
= X0 ),
inference(rectify,[status(thm)],[f87]) ).
thf(f87,axiom,
! [X8: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ X8 ) )
= X8 ),
file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_86_nondetT_Oexhaust__sel) ).
thf(f1267,plain,
( ( f @ x )
!= ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( f @ x ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1266]) ).
thf(f1266,plain,
( ( f @ x )
!= ( monomo412532791tT_m_a
@ ( ^ [Y0: c] : ( monomo624345106et_a_m @ ( f @ Y0 ) )
@ x ) ) ),
inference(forward_demodulation,[status(thm)],[f1265,f1057]) ).
thf(f1057,plain,
! [X0: c,X1: c > m] :
( ( mergec @ ( counta472291938sert_c @ X0 @ bot_bo1320844070cset_c ) @ X1 )
= ( X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: c,X1: c > m] :
( ( mergec @ ( counta472291938sert_c @ X0 @ bot_bo1320844070cset_c ) @ X1 )
= ( X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_0_mergec__single) ).
thf(f1265,plain,
( ( f @ x )
!= ( monomo412532791tT_m_a
@ ( mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c )
@ ^ [Y0: c] : ( monomo624345106et_a_m @ ( f @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1180]) ).
thf(f1180,plain,
( ( f @ x )
!= ( ^ [Y0: countable_Set_cset_c > ( c > m ) > m,Y1: countable_Set_cset_c,Y2: c > monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( Y0 @ Y1
@ ( ^ [Y3: monomo197243225tT_a_m > m,Y4: c > monomo197243225tT_a_m,Y5: c] : ( Y3 @ ( Y4 @ Y5 ) )
@ monomo624345106et_a_m
@ Y2 ) ) )
@ mergec
@ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c )
@ f ) ),
inference(definition_unfolding,[status(thm)],[f1095,f1154]) ).
thf(f1154,plain,
( monomo463139869_c_m_a
= ( ^ [Y0: countable_Set_cset_c > ( c > m ) > m,Y1: countable_Set_cset_c,Y2: c > monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( Y0 @ Y1
@ ( ^ [Y3: monomo197243225tT_a_m > m,Y4: c > monomo197243225tT_a_m,Y5: c] : ( Y3 @ ( Y4 @ Y5 ) )
@ monomo624345106et_a_m
@ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1009,f1012]) ).
thf(f1012,plain,
( comp_M750374444_m_m_c
= ( ^ [Y0: monomo197243225tT_a_m > m,Y1: c > monomo197243225tT_a_m,Y2: c] : ( Y0 @ ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f602]) ).
thf(f602,plain,
( comp_M750374444_m_m_c
= ( ^ [Y0: monomo197243225tT_a_m > m,Y1: c > monomo197243225tT_a_m,Y2: c] : ( Y0 @ ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f601]) ).
thf(f601,plain,
( comp_M750374444_m_m_c
= ( ^ [X0: monomo197243225tT_a_m > m,X1: c > monomo197243225tT_a_m,X2: c] : ( X0 @ ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
( comp_M750374444_m_m_c
= ( ^ [X11: monomo197243225tT_a_m > m,X12: c > monomo197243225tT_a_m,X13: c] : ( X11 @ ( X12 @ X13 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_17_comp__apply) ).
thf(f1009,plain,
( monomo463139869_c_m_a
= ( ^ [Y0: countable_Set_cset_c > ( c > m ) > m,Y1: countable_Set_cset_c,Y2: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Y0 @ Y1 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
thf(f334,plain,
( monomo463139869_c_m_a
= ( ^ [Y0: countable_Set_cset_c > ( c > m ) > m,Y1: countable_Set_cset_c,Y2: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Y0 @ Y1 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f333]) ).
thf(f333,plain,
( monomo463139869_c_m_a
= ( ^ [X0: countable_Set_cset_c > ( c > m ) > m,X1: countable_Set_cset_c,X2: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( X0 @ X1 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
( monomo463139869_c_m_a
= ( ^ [X14: countable_Set_cset_c > ( c > m ) > m,X15: countable_Set_cset_c,X11: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( X14 @ X15 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ X11 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_19_cset__nondetM__base_Oaltc__nondet__def) ).
thf(f1095,plain,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
!= ( f @ x ) ),
inference(cnf_transformation,[status(thm)],[f667]) ).
thf(f667,plain,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
!= ( f @ x ) ),
inference(flattening,[status(thm)],[f317]) ).
thf(f317,negated_conjecture,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
!= ( f @ x ) ),
inference(negated_conjecture,[status(cth)],[f316]) ).
thf(f316,conjecture,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
= ( f @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP127^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:27:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP127^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Monomorphic_Monad problem prob_2789__7122292_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Monomorphic_Monad/prob_2789__7122292_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 353 ( 116 unt; 37 typ; 0 def)
% 0.30/0.46 % Number of atoms : 769 ( 436 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 5 ( 2 avg)
% 0.30/0.46 % Number of connectives : 2537 ( 60 ~; 9 |; 23 &;2121 @)
% 0.30/0.46 % ( 0 <=>; 324 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 14 ( 6 avg)
% 0.30/0.46 % Number of types : 6 ( 5 usr)
% 0.30/0.46 % Number of type conns : 702 ( 702 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 35 ( 32 usr; 4 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 1106 ( 82 ^;1003 !; 21 ?;1106 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:37:01.423
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (5)
% 0.30/0.46 thf(ty_n_t__Countable____Set____Type__Ocset_It__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_J,type,
% 0.30/0.46 counta191869203tT_a_m: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 0.30/0.46 monomo197243225tT_a_m: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 countable_Set_cset_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__m,type,
% 0.30/0.46 m: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__c,type,
% 0.30/0.46 c: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (32)
% 0.30/0.46 thf(sy_c_Countable__Set__Type_Ocin_001tf__c,type,
% 0.30/0.46 countable_Set_cin_c: c > countable_Set_cset_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Countable__Set__Type_Ocinsert_001tf__c,type,
% 0.30/0.46 counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
% 0.30/0.46 comp_M864375327_a_m_c: ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c_001tf__c,type,
% 0.30/0.46 comp_M1062614966_m_c_c: ( monomo197243225tT_a_m > c ) > ( c > monomo197243225tT_a_m ) > c > c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 0.30/0.46 comp_M1944986301tT_a_m: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__c,type,
% 0.30/0.46 comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__m,type,
% 0.30/0.46 comp_M750374454_m_m_m: ( monomo197243225tT_a_m > m ) > ( m > monomo197243225tT_a_m ) > m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__c_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
% 0.30/0.46 comp_c1772230468_a_m_c: ( c > monomo197243225tT_a_m ) > ( c > c ) > c > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__c_001tf__c_001tf__c,type,
% 0.30/0.46 comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 0.30/0.46 comp_c997395372tT_a_m: ( c > m ) > ( monomo197243225tT_a_m > c ) > monomo197243225tT_a_m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001tf__c,type,
% 0.30/0.46 comp_c_m_c: ( c > m ) > ( c > c ) > c > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001tf__m,type,
% 0.30/0.46 comp_c_m_m: ( c > m ) > ( m > c ) > m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
% 0.30/0.46 comp_m1038691662_a_m_c: ( m > monomo197243225tT_a_m ) > ( c > m ) > c > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__m_001tf__c_001tf__c,type,
% 0.30/0.46 comp_m_c_c: ( m > c ) > ( c > m ) > c > c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 0.30/0.46 comp_m263856566tT_a_m: ( m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001tf__c,type,
% 0.30/0.46 comp_m_m_c: ( m > m ) > ( c > m ) > c > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001tf__m,type,
% 0.30/0.46 comp_m_m_m: ( m > m ) > ( m > m ) > m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If_001tf__c,type,
% 0.30/0.46 if_c: $o > c > c > c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_Ocset__nondetM__base_Oaltc__nondet_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__a,type,
% 0.30/0.46 monomo2081011572_m_m_a: ( counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m ) > counta191869203tT_a_m > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_Ocset__nondetM__base_Oaltc__nondet_001tf__c_001tf__m_001tf__a,type,
% 0.30/0.46 monomo463139869_c_m_a: ( countable_Set_cset_c > ( c > m ) > m ) > countable_Set_cset_c > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_OnondetT_ONondetT_001tf__m_001tf__a,type,
% 0.30/0.46 monomo412532791tT_m_a: m > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_OnondetT_Orun__nondet_001tf__a_001tf__m,type,
% 0.30/0.46 monomo624345106et_a_m: monomo197243225tT_a_m > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 bot_bo1320844070cset_c: countable_Set_cset_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Countable____Set____Type__Ocset_Itf__c_J_J,type,
% 0.30/0.46 ord_le1376176871cset_c: ( $o > countable_Set_cset_c ) > ( $o > countable_Set_cset_c ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 0.30/0.46 order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_f____,type,
% 0.30/0.46 f: c > monomo197243225tT_a_m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_mergec,type,
% 0.30/0.46 mergec: countable_Set_cset_c > ( c > m ) > m ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_x____,type,
% 0.30/0.46 x: c ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (310)
% 0.30/0.46 thf(fact_0_mergec__single,axiom,
% 0.30/0.46 ! [X: c,F: c > m] :
% 0.30/0.46 ( ( mergec @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) @ F )
% 0.30/0.46 = ( F @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % mergec_single
% 0.30/0.46 thf(fact_1_cset__nondetM__base_Oaltc__nondet_Ocong,axiom,
% 0.30/0.46 monomo463139869_c_m_a = monomo463139869_c_m_a ).
% 0.30/0.46
% 0.30/0.46 % cset_nondetM_base.altc_nondet.cong
% 0.30/0.46 thf(fact_2_cinsert__absorb2,axiom,
% 0.30/0.46 ! [X: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( counta472291938sert_c @ X @ ( counta472291938sert_c @ X @ A ) )
% 0.30/0.46 = ( counta472291938sert_c @ X @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_absorb2
% 0.30/0.46 thf(fact_3_cdoubleton__eq__iff,axiom,
% 0.30/0.46 ! [A2: c,B: c,C: c,D: c] :
% 0.30/0.46 ( ( ( counta472291938sert_c @ A2 @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
% 0.30/0.46 = ( counta472291938sert_c @ C @ ( counta472291938sert_c @ D @ bot_bo1320844070cset_c ) ) )
% 0.30/0.46 = ( ( ( A2 = C )
% 0.30/0.46 & ( B = D ) )
% 0.30/0.46 | ( ( A2 = D )
% 0.30/0.46 & ( B = C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cdoubleton_eq_iff
% 0.30/0.46 thf(fact_4_csingleton__inject,axiom,
% 0.30/0.46 ! [A2: c,B: c] :
% 0.30/0.46 ( ( ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c )
% 0.30/0.46 = ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
% 0.30/0.46 => ( A2 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % csingleton_inject
% 0.30/0.46 thf(fact_5_cinsert__not__cempty,axiom,
% 0.30/0.46 ! [A2: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( counta472291938sert_c @ A2 @ A )
% 0.30/0.46 != bot_bo1320844070cset_c ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_not_cempty
% 0.30/0.46 thf(fact_6_cinsert__commute,axiom,
% 0.30/0.46 ! [X: c,Y: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( counta472291938sert_c @ X @ ( counta472291938sert_c @ Y @ A ) )
% 0.30/0.46 = ( counta472291938sert_c @ Y @ ( counta472291938sert_c @ X @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_commute
% 0.30/0.46 thf(fact_7_run__altc__nondet,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ mergec @ A @ F ) )
% 0.30/0.46 = ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % run_altc_nondet
% 0.30/0.46 thf(fact_8_nondetT_Oexpand,axiom,
% 0.30/0.46 ! [NondetT: monomo197243225tT_a_m,NondetT2: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( monomo624345106et_a_m @ NondetT )
% 0.30/0.46 = ( monomo624345106et_a_m @ NondetT2 ) )
% 0.30/0.46 => ( NondetT = NondetT2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.expand
% 0.30/0.46 thf(fact_9_cset__nondetM__base_Orun__altc__nondet,axiom,
% 0.30/0.46 ! [Mergec: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,A: counta191869203tT_a_m,F: monomo197243225tT_a_m > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ Mergec @ A @ F ) )
% 0.30/0.46 = ( Mergec @ A @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cset_nondetM_base.run_altc_nondet
% 0.30/0.46 thf(fact_10_cset__nondetM__base_Orun__altc__nondet,axiom,
% 0.30/0.46 ! [Mergec: countable_Set_cset_c > ( c > m ) > m,A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ Mergec @ A @ F ) )
% 0.30/0.46 = ( Mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cset_nondetM_base.run_altc_nondet
% 0.30/0.46 thf(fact_11_altc__nondet__def,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( monomo463139869_c_m_a @ mergec @ A @ F )
% 0.30/0.46 = ( monomo412532791tT_m_a @ ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % altc_nondet_def
% 0.30/0.46 thf(fact_12_comp__apply,axiom,
% 0.30/0.46 ( comp_M1944986301tT_a_m
% 0.30/0.46 = ( ^ [F2: monomo197243225tT_a_m > m,G: monomo197243225tT_a_m > monomo197243225tT_a_m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_13_comp__apply,axiom,
% 0.30/0.46 ( comp_m263856566tT_a_m
% 0.30/0.46 = ( ^ [F2: m > m,G: monomo197243225tT_a_m > m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_14_comp__apply,axiom,
% 0.30/0.46 ( comp_m_m_c
% 0.30/0.46 = ( ^ [F2: m > m,G: c > m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_15_comp__apply,axiom,
% 0.30/0.46 ( comp_c1772230468_a_m_c
% 0.30/0.46 = ( ^ [F2: c > monomo197243225tT_a_m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_16_comp__apply,axiom,
% 0.30/0.46 ( comp_c_m_c
% 0.30/0.46 = ( ^ [F2: c > m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_17_comp__apply,axiom,
% 0.30/0.46 ( comp_M750374444_m_m_c
% 0.30/0.46 = ( ^ [F2: monomo197243225tT_a_m > m,G: c > monomo197243225tT_a_m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_18_cset__nondetM__base_Oaltc__nondet__def,axiom,
% 0.30/0.46 ( monomo2081011572_m_m_a
% 0.30/0.46 = ( ^ [Mergec2: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,A3: counta191869203tT_a_m,F2: monomo197243225tT_a_m > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Mergec2 @ A3 @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ F2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cset_nondetM_base.altc_nondet_def
% 0.30/0.46 thf(fact_19_cset__nondetM__base_Oaltc__nondet__def,axiom,
% 0.30/0.46 ( monomo463139869_c_m_a
% 0.30/0.46 = ( ^ [Mergec2: countable_Set_cset_c > ( c > m ) > m,A3: countable_Set_cset_c,F2: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Mergec2 @ A3 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cset_nondetM_base.altc_nondet_def
% 0.30/0.46 thf(fact_20_comp__def,axiom,
% 0.30/0.46 ( comp_M1944986301tT_a_m
% 0.30/0.46 = ( ^ [F2: monomo197243225tT_a_m > m,G: monomo197243225tT_a_m > monomo197243225tT_a_m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_21_comp__def,axiom,
% 0.30/0.46 ( comp_m263856566tT_a_m
% 0.30/0.46 = ( ^ [F2: m > m,G: monomo197243225tT_a_m > m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_22_comp__def,axiom,
% 0.30/0.46 ( comp_m_m_c
% 0.30/0.46 = ( ^ [F2: m > m,G: c > m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_23_comp__def,axiom,
% 0.30/0.46 ( comp_c1772230468_a_m_c
% 0.30/0.46 = ( ^ [F2: c > monomo197243225tT_a_m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_24_comp__def,axiom,
% 0.30/0.46 ( comp_c_m_c
% 0.30/0.46 = ( ^ [F2: c > m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_25_comp__def,axiom,
% 0.30/0.46 ( comp_M750374444_m_m_c
% 0.30/0.46 = ( ^ [F2: monomo197243225tT_a_m > m,G: c > monomo197243225tT_a_m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_26_comp__assoc,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,H: c > c] :
% 0.30/0.46 ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_27_comp__assoc,axiom,
% 0.30/0.46 ! [F: m > m,G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_28_comp__assoc,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_29_comp__assoc,axiom,
% 0.30/0.46 ! [F: m > m,G2: m > m,H: c > m] :
% 0.30/0.46 ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_30_comp__assoc,axiom,
% 0.30/0.46 ! [F: c > m,G2: m > c,H: c > m] :
% 0.30/0.46 ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_31_comp__assoc,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,H: c > c] :
% 0.30/0.46 ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_32_comp__assoc,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,H: c > c] :
% 0.30/0.46 ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_33_comp__assoc,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,H: monomo197243225tT_a_m > c] :
% 0.30/0.46 ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ F @ ( comp_c997395372tT_a_m @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_34_comp__assoc,axiom,
% 0.30/0.46 ! [F: c > m,G2: monomo197243225tT_a_m > c,H: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( comp_M750374444_m_m_c @ ( comp_c997395372tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ F @ ( comp_M1062614966_m_c_c @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_35_comp__assoc,axiom,
% 0.30/0.46 ! [F: m > m,G2: m > m,H: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( comp_m263856566tT_a_m @ ( comp_m_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ F @ ( comp_m263856566tT_a_m @ G2 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_36_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,V: c] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_37_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: m > m,D: c > m,V: c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_m_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_38_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: c > m,D: c > c,V: c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_39_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: c > m,B: c > c,C: m > m,D: c > m,V: c] :
% 0.30/0.46 ( ( ( comp_c_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_m_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_40_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: c > m,B: c > c,C: c > m,D: c > c,V: c] :
% 0.30/0.46 ( ( ( comp_c_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_41_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: m > m,D: c > m,V: c] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_m_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_42_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c > c,V: c] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_43_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: m > m,B: monomo197243225tT_a_m > m,C: m > m,D: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_m263856566tT_a_m @ A2 @ B )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_44_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,V: c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_45_comp__eq__dest,axiom,
% 0.30/0.46 ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,D: c > c,V: c] :
% 0.30/0.46 ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ C @ D ) )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ ( D @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_46_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_47_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: m > m,D: c > m] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_m_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_48_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: c > m,D: c > c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_49_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: c > m,B: c > c,C: m > m,D: c > m] :
% 0.30/0.46 ( ( ( comp_c_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_m_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_50_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: c > m,B: c > c,C: c > m,D: c > c] :
% 0.30/0.46 ( ( ( comp_c_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_51_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: m > m,D: c > m] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_m_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_52_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c > c] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_53_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: m > m,B: monomo197243225tT_a_m > m,C: m > m,D: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_m263856566tT_a_m @ A2 @ B )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ C @ D ) )
% 0.30/0.46 => ! [V2: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_54_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_55_comp__eq__elim,axiom,
% 0.30/0.46 ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,D: c > c] :
% 0.30/0.46 ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ C @ D ) )
% 0.30/0.46 => ! [V2: c] :
% 0.30/0.46 ( ( A2 @ ( B @ V2 ) )
% 0.30/0.46 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_56_comp__cong,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: monomo197243225tT_a_m > m,G3: c > monomo197243225tT_a_m,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_57_comp__cong,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,X: c,F3: m > m,G3: c > m,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_58_comp__cong,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,X: c,F3: c > m,G3: c > c,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_59_comp__cong,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,X: c,F3: m > m,G3: c > m,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_60_comp__cong,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,X: c,F3: c > m,G3: c > c,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_61_comp__cong,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: m > m,G3: c > m,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_62_comp__cong,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: c > m,G3: c > c,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_63_comp__cong,axiom,
% 0.30/0.46 ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,F3: m > m,G3: c > m,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_64_comp__cong,axiom,
% 0.30/0.46 ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,F3: c > m,G3: c > c,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_65_comp__cong,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,X: c,F3: monomo197243225tT_a_m > m,G3: c > monomo197243225tT_a_m,X3: c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( F3 @ ( G3 @ X3 ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_cong
% 0.30/0.46 thf(fact_66_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_M1944986301tT_a_m @ A2 @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_67_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [A2: m > m,B: monomo197243225tT_a_m > m,C: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_m263856566tT_a_m @ A2 @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_68_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [A2: m > m,B: c > m,C: c > m,V: c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ A2 @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_69_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,V: c] :
% 0.30/0.46 ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_70_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [A2: c > m,B: c > c,C: c > m,V: c] :
% 0.30/0.46 ( ( ( comp_c_m_c @ A2 @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_71_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,V: c] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ( A2 @ ( B @ V ) )
% 0.30/0.46 = ( C @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_72_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: monomo197243225tT_a_m > m,K: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_73_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,X: c,H: m > m,K: c > m] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_74_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,X: c,H: c > m,K: c > c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_75_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,X: c,H: m > m,K: c > m] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_76_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,X: c,H: c > m,K: c > c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_77_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: m > m,K: c > m] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_78_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: c > m,K: c > c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_79_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,H: m > m,K: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_80_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,X: c,H: monomo197243225tT_a_m > m,K: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_81_comp__apply__eq,axiom,
% 0.30/0.46 ! [F: c > monomo197243225tT_a_m,G2: c > c,X: c,H: c > monomo197243225tT_a_m,K: c > c] :
% 0.30/0.46 ( ( ( F @ ( G2 @ X ) )
% 0.30/0.46 = ( H @ ( K @ X ) ) )
% 0.30/0.46 => ( ( comp_c1772230468_a_m_c @ F @ G2 @ X )
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ H @ K @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply_eq
% 0.30/0.46 thf(fact_82_nondetT_Oinject,axiom,
% 0.30/0.46 ! [X: m,Ya: m] :
% 0.30/0.46 ( ( ( monomo412532791tT_m_a @ X )
% 0.30/0.46 = ( monomo412532791tT_m_a @ Ya ) )
% 0.30/0.46 = ( X = Ya ) ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.inject
% 0.30/0.46 thf(fact_83_nondetT_Ocollapse,axiom,
% 0.30/0.46 ! [NondetT: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ NondetT ) )
% 0.30/0.46 = NondetT ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.collapse
% 0.30/0.46 thf(fact_84_nondetT_Oexhaust,axiom,
% 0.30/0.46 ! [Y: monomo197243225tT_a_m] :
% 0.30/0.46 ~ ! [X4: m] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( monomo412532791tT_m_a @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.exhaust
% 0.30/0.46 thf(fact_85_nondetT_Oinduct,axiom,
% 0.30/0.46 ! [P: monomo197243225tT_a_m > $o,NondetT: monomo197243225tT_a_m] :
% 0.30/0.46 ( ! [Xa: m] : ( P @ ( monomo412532791tT_m_a @ Xa ) )
% 0.30/0.46 => ( P @ NondetT ) ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.induct
% 0.30/0.46 thf(fact_86_nondetT_Oexhaust__sel,axiom,
% 0.30/0.46 ! [NondetT: monomo197243225tT_a_m] :
% 0.30/0.46 ( NondetT
% 0.30/0.46 = ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ NondetT ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.exhaust_sel
% 0.30/0.46 thf(fact_87_nondetT_Osel,axiom,
% 0.30/0.46 ! [X: m] :
% 0.30/0.46 ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ X ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % nondetT.sel
% 0.30/0.46 thf(fact_88_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: c > monomo197243225tT_a_m,H: c > c,R1: monomo197243225tT_a_m > monomo197243225tT_a_m,R2: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m,L: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_c1772230468_a_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_M864375327_a_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_M1944986301tT_a_m @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_89_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R1: c > monomo197243225tT_a_m,R2: c > c,F: monomo197243225tT_a_m > m,L: c > m] :
% 0.30/0.46 ( ( ( comp_M864375327_a_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_M750374444_m_m_c @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_90_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R1: monomo197243225tT_a_m > m,R2: c > monomo197243225tT_a_m,F: m > m,L: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_m263856566tT_a_m @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_91_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: c > c,H: c > c,R1: m > c,R2: c > m,F: c > m,L: m > m] :
% 0.30/0.46 ( ( ( comp_c_c_c @ G2 @ H )
% 0.30/0.46 = ( comp_m_c_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_c_m_m @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_92_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: m > c,H: c > m,R1: c > c,R2: c > c,F: c > m,L: c > m] :
% 0.30/0.46 ( ( ( comp_m_c_c @ G2 @ H )
% 0.30/0.46 = ( comp_c_c_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_c_m_c @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_93_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: c > c,H: c > c,R1: c > c,R2: c > c,F: c > m,L: c > m] :
% 0.30/0.46 ( ( ( comp_c_c_c @ G2 @ H )
% 0.30/0.46 = ( comp_c_c_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_c_m_c @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_94_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: m > m,H: c > m,R1: m > m,R2: c > m,F: m > m,L: m > m] :
% 0.30/0.46 ( ( ( comp_m_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_m_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_m_m_m @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_95_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: m > m,H: c > m,R1: c > m,R2: c > c,F: m > m,L: c > m] :
% 0.30/0.46 ( ( ( comp_m_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_c_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_m_m_c @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_96_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: c > m,H: c > c,R1: m > m,R2: c > m,F: m > m,L: m > m] :
% 0.30/0.46 ( ( ( comp_c_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_m_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_m_m_m @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_97_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [G2: c > m,H: c > c,R1: c > m,R2: c > c,F: m > m,L: c > m] :
% 0.30/0.46 ( ( ( comp_c_m_c @ G2 @ H )
% 0.30/0.46 = ( comp_c_m_c @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp_m_m_c @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_98_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: m > m,G2: monomo197243225tT_a_m > m,L1: monomo197243225tT_a_m > m,L2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_m263856566tT_a_m @ F @ G2 )
% 0.30/0.46 = ( comp_M1944986301tT_a_m @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_M864375327_a_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_99_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,L1: m > m,L2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R: c > m] :
% 0.30/0.46 ( ( ( comp_M1944986301tT_a_m @ F @ G2 )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_M750374444_m_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_100_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,L1: monomo197243225tT_a_m > m,L2: c > monomo197243225tT_a_m,H: c > c,R: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ F @ G2 )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_c1772230468_a_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_101_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: m > m,G2: m > m,L1: c > m,L2: m > c,H: c > m,R: c > c] :
% 0.30/0.46 ( ( ( comp_m_m_m @ F @ G2 )
% 0.30/0.46 = ( comp_c_m_m @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_m_c_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_102_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: m > m,G2: m > m,L1: m > m,L2: m > m,H: c > m,R: c > m] :
% 0.30/0.46 ( ( ( comp_m_m_m @ F @ G2 )
% 0.30/0.46 = ( comp_m_m_m @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_m_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_103_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: c > m,G2: m > c,L1: m > m,L2: m > m,H: c > m,R: c > m] :
% 0.30/0.46 ( ( ( comp_c_m_m @ F @ G2 )
% 0.30/0.46 = ( comp_m_m_m @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_m_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_104_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,L1: m > m,L2: c > m,H: c > c,R: c > m] :
% 0.30/0.46 ( ( ( comp_m_m_c @ F @ G2 )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_c_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_105_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,L1: c > m,L2: c > c,H: c > c,R: c > c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ F @ G2 )
% 0.30/0.46 = ( comp_c_m_c @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_c_c_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_106_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,L1: m > m,L2: c > m,H: c > c,R: c > m] :
% 0.30/0.46 ( ( ( comp_c_m_c @ F @ G2 )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_c_m_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_107_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,L1: c > m,L2: c > c,H: c > c,R: c > c] :
% 0.30/0.46 ( ( ( comp_c_m_c @ F @ G2 )
% 0.30/0.46 = ( comp_c_m_c @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp_c_c_c @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c_m_c @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_108_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: c > monomo197243225tT_a_m,H: c > c,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_c1772230468_a_m_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_109_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R: c > m,F: m > m] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_110_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_M864375327_a_m_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_111_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: m > c,H: c > m,R: c > c,F: c > m] :
% 0.30/0.46 ( ( ( comp_m_c_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_112_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: c > c,H: c > c,R: c > c,F: c > m] :
% 0.30/0.46 ( ( ( comp_c_c_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_113_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: m > m,H: c > m,R: c > m,F: m > m] :
% 0.30/0.46 ( ( ( comp_m_m_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_114_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: c > m,H: c > c,R: c > m,F: m > m] :
% 0.30/0.46 ( ( ( comp_c_m_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_115_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: c > m,H: monomo197243225tT_a_m > c,R: monomo197243225tT_a_m > m,F: m > m] :
% 0.30/0.46 ( ( ( comp_c997395372tT_a_m @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_116_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > c,H: c > monomo197243225tT_a_m,R: c > c,F: c > m] :
% 0.30/0.46 ( ( ( comp_M1062614966_m_c_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ ( comp_c997395372tT_a_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_c_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_117_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [G2: m > monomo197243225tT_a_m,H: c > m,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_m1038691662_a_m_c @ G2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_M750374454_m_m_m @ F @ G2 ) @ H )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_118_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: m > m,G2: monomo197243225tT_a_m > m,L: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_m263856566tT_a_m @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_119_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,L: c > m,H: c > c] :
% 0.30/0.46 ( ( ( comp_M750374444_m_m_c @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_120_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,L: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( comp_M1944986301tT_a_m @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_121_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: m > m,G2: m > m,L: m > m,H: c > m] :
% 0.30/0.46 ( ( ( comp_m_m_m @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_122_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: c > m,G2: m > c,L: m > m,H: c > m] :
% 0.30/0.46 ( ( ( comp_c_m_m @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_123_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: m > m,G2: c > m,L: c > m,H: c > c] :
% 0.30/0.46 ( ( ( comp_m_m_c @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_124_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: c > m,G2: c > c,L: c > m,H: c > c] :
% 0.30/0.46 ( ( ( comp_c_m_c @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_125_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: m > monomo197243225tT_a_m,G2: c > m,L: c > monomo197243225tT_a_m,H: c > c] :
% 0.30/0.46 ( ( ( comp_m1038691662_a_m_c @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m1038691662_a_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_126_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: monomo197243225tT_a_m > m,G2: m > monomo197243225tT_a_m,L: m > m,H: c > m] :
% 0.30/0.46 ( ( ( comp_M750374454_m_m_m @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ F @ ( comp_m1038691662_a_m_c @ G2 @ H ) )
% 0.30/0.46 = ( comp_m_m_c @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_127_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [F: m > m,G2: m > m,L: m > m,H: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( comp_m_m_m @ F @ G2 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp_m263856566tT_a_m @ F @ ( comp_m263856566tT_a_m @ G2 @ H ) )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_128_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > monomo197243225tT_a_m,G2: c > c,X: c,N: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_129_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: monomo197243225tT_a_m > monomo197243225tT_a_m,G2: c > monomo197243225tT_a_m,X: c,N: c > monomo197243225tT_a_m,H: c > c,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_130_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: m > m,G2: c > m,X: c,N: c > m,H: c > c,F: m > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_m_m_c @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_131_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: m > c,G2: c > m,X: c,N: c > c,H: c > c,F: c > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_c_m_c @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_132_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > m,G2: c > c,X: c,N: m > m,H: c > m,F: m > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ ( comp_m_m_m @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_133_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > m,G2: c > c,X: c,N: c > m,H: c > c,F: m > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_m_m_c @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_134_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > c,G2: c > c,X: c,N: m > c,H: c > m,F: c > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_m_m_c @ ( comp_c_m_m @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_135_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > c,G2: c > c,X: c,N: c > c,H: c > c,F: c > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_c_m_c @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_136_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > m,G2: monomo197243225tT_a_m > c,X: monomo197243225tT_a_m,N: m > m,H: monomo197243225tT_a_m > m,F: m > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ ( comp_m_m_m @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_137_type__copy__map__cong0,axiom,
% 0.30/0.46 ! [M: c > c,G2: monomo197243225tT_a_m > c,X: monomo197243225tT_a_m,N: m > c,H: monomo197243225tT_a_m > m,F: c > m] :
% 0.30/0.46 ( ( ( M @ ( G2 @ X ) )
% 0.30/0.46 = ( N @ ( H @ X ) ) )
% 0.30/0.46 => ( ( comp_c997395372tT_a_m @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
% 0.30/0.46 = ( comp_m263856566tT_a_m @ ( comp_c_m_m @ F @ N ) @ H @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % type_copy_map_cong0
% 0.30/0.46 thf(fact_138_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: m > m,F: monomo197243225tT_a_m > m,V: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( comp_m_m_c @ G2 @ ( comp_M750374444_m_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_139_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,F: c > monomo197243225tT_a_m,V: c > c] :
% 0.30/0.46 ( ( comp_M750374444_m_m_c @ G2 @ ( comp_c1772230468_a_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_M750374444_m_m_c @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_140_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > monomo197243225tT_a_m,V: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( comp_M750374444_m_m_c @ G2 @ ( comp_M864375327_a_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_141_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: m > m,F: m > m,V: c > m] :
% 0.30/0.46 ( ( comp_m_m_c @ G2 @ ( comp_m_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_m_m_c @ ( comp_m_m_m @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_142_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: m > m,F: c > m,V: c > c] :
% 0.30/0.46 ( ( comp_m_m_c @ G2 @ ( comp_c_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_m_m_c @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_143_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: c > m,F: m > c,V: c > m] :
% 0.30/0.46 ( ( comp_c_m_c @ G2 @ ( comp_m_c_c @ F @ V ) )
% 0.30/0.46 = ( comp_m_m_c @ ( comp_c_m_m @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_144_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: c > m,F: c > c,V: c > c] :
% 0.30/0.46 ( ( comp_c_m_c @ G2 @ ( comp_c_c_c @ F @ V ) )
% 0.30/0.46 = ( comp_c_m_c @ ( comp_c_m_c @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_145_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: m > monomo197243225tT_a_m,F: c > m,V: c > c] :
% 0.30/0.46 ( ( comp_m1038691662_a_m_c @ G2 @ ( comp_c_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ ( comp_m1038691662_a_m_c @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_146_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,F: m > monomo197243225tT_a_m,V: c > m] :
% 0.30/0.46 ( ( comp_M750374444_m_m_c @ G2 @ ( comp_m1038691662_a_m_c @ F @ V ) )
% 0.30/0.46 = ( comp_m_m_c @ ( comp_M750374454_m_m_m @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_147_fun_Omap__comp,axiom,
% 0.30/0.46 ! [G2: m > m,F: c > m,V: monomo197243225tT_a_m > c] :
% 0.30/0.46 ( ( comp_m263856566tT_a_m @ G2 @ ( comp_c997395372tT_a_m @ F @ V ) )
% 0.30/0.46 = ( comp_c997395372tT_a_m @ ( comp_m_m_c @ G2 @ F ) @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % fun.map_comp
% 0.30/0.46 thf(fact_148_function__factors__left,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ! [X2: monomo197243225tT_a_m,Y2: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( G2 @ X2 )
% 0.30/0.46 = ( G2 @ Y2 ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( F @ Y2 ) ) ) )
% 0.30/0.46 = ( ? [H2: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_M1944986301tT_a_m @ H2 @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_left
% 0.30/0.46 thf(fact_149_function__factors__left,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ! [X2: monomo197243225tT_a_m,Y2: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ( G2 @ X2 )
% 0.30/0.46 = ( G2 @ Y2 ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( F @ Y2 ) ) ) )
% 0.30/0.46 = ( ? [H2: m > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_m263856566tT_a_m @ H2 @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_left
% 0.30/0.46 thf(fact_150_function__factors__left,axiom,
% 0.30/0.46 ! [G2: c > m,F: c > m] :
% 0.30/0.46 ( ( ! [X2: c,Y2: c] :
% 0.30/0.46 ( ( ( G2 @ X2 )
% 0.30/0.46 = ( G2 @ Y2 ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( F @ Y2 ) ) ) )
% 0.30/0.46 = ( ? [H2: m > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_m_m_c @ H2 @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_left
% 0.30/0.46 thf(fact_151_function__factors__left,axiom,
% 0.30/0.46 ! [G2: c > c,F: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ! [X2: c,Y2: c] :
% 0.30/0.46 ( ( ( G2 @ X2 )
% 0.30/0.46 = ( G2 @ Y2 ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( F @ Y2 ) ) ) )
% 0.30/0.46 = ( ? [H2: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ H2 @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_left
% 0.30/0.46 thf(fact_152_function__factors__left,axiom,
% 0.30/0.46 ! [G2: c > c,F: c > m] :
% 0.30/0.46 ( ( ! [X2: c,Y2: c] :
% 0.30/0.46 ( ( ( G2 @ X2 )
% 0.30/0.46 = ( G2 @ Y2 ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( F @ Y2 ) ) ) )
% 0.30/0.46 = ( ? [H2: c > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_c_m_c @ H2 @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_left
% 0.30/0.46 thf(fact_153_function__factors__left,axiom,
% 0.30/0.46 ! [G2: c > monomo197243225tT_a_m,F: c > m] :
% 0.30/0.46 ( ( ! [X2: c,Y2: c] :
% 0.30/0.46 ( ( ( G2 @ X2 )
% 0.30/0.46 = ( G2 @ Y2 ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( F @ Y2 ) ) ) )
% 0.30/0.46 = ( ? [H2: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_M750374444_m_m_c @ H2 @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_left
% 0.30/0.46 thf(fact_154_function__factors__right,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ! [X2: monomo197243225tT_a_m] :
% 0.30/0.46 ? [Y2: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( G2 @ Y2 )
% 0.30/0.46 = ( F @ X2 ) ) )
% 0.30/0.46 = ( ? [H2: monomo197243225tT_a_m > monomo197243225tT_a_m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_M1944986301tT_a_m @ G2 @ H2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_right
% 0.30/0.46 thf(fact_155_function__factors__right,axiom,
% 0.30/0.46 ! [G2: m > m,F: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( ( ! [X2: monomo197243225tT_a_m] :
% 0.30/0.46 ? [Y2: m] :
% 0.30/0.46 ( ( G2 @ Y2 )
% 0.30/0.46 = ( F @ X2 ) ) )
% 0.30/0.46 = ( ? [H2: monomo197243225tT_a_m > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_m263856566tT_a_m @ G2 @ H2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_right
% 0.30/0.46 thf(fact_156_function__factors__right,axiom,
% 0.30/0.46 ! [G2: m > m,F: c > m] :
% 0.30/0.46 ( ( ! [X2: c] :
% 0.30/0.46 ? [Y2: m] :
% 0.30/0.46 ( ( G2 @ Y2 )
% 0.30/0.46 = ( F @ X2 ) ) )
% 0.30/0.46 = ( ? [H2: c > m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_m_m_c @ G2 @ H2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_right
% 0.30/0.46 thf(fact_157_function__factors__right,axiom,
% 0.30/0.46 ! [G2: c > monomo197243225tT_a_m,F: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( ( ! [X2: c] :
% 0.30/0.46 ? [Y2: c] :
% 0.30/0.46 ( ( G2 @ Y2 )
% 0.30/0.46 = ( F @ X2 ) ) )
% 0.30/0.46 = ( ? [H2: c > c] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_c1772230468_a_m_c @ G2 @ H2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_right
% 0.30/0.46 thf(fact_158_function__factors__right,axiom,
% 0.30/0.46 ! [G2: c > m,F: c > m] :
% 0.30/0.46 ( ( ! [X2: c] :
% 0.30/0.46 ? [Y2: c] :
% 0.30/0.46 ( ( G2 @ Y2 )
% 0.30/0.46 = ( F @ X2 ) ) )
% 0.30/0.46 = ( ? [H2: c > c] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_c_m_c @ G2 @ H2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_right
% 0.30/0.46 thf(fact_159_function__factors__right,axiom,
% 0.30/0.46 ! [G2: monomo197243225tT_a_m > m,F: c > m] :
% 0.30/0.46 ( ( ! [X2: c] :
% 0.30/0.46 ? [Y2: monomo197243225tT_a_m] :
% 0.30/0.46 ( ( G2 @ Y2 )
% 0.30/0.46 = ( F @ X2 ) ) )
% 0.30/0.46 = ( ? [H2: c > monomo197243225tT_a_m] :
% 0.30/0.46 ( F
% 0.30/0.46 = ( comp_M750374444_m_m_c @ G2 @ H2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % function_factors_right
% 0.30/0.46 thf(fact_160_cinsert__cDiff__single,axiom,
% 0.30/0.46 ! [A2: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( counta472291938sert_c @ A2 @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) )
% 0.30/0.46 = ( counta472291938sert_c @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_cDiff_single
% 0.30/0.46 thf(fact_161_cDiff__idemp,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ B2 )
% 0.30/0.46 = ( minus_1646763425cset_c @ A @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_idemp
% 0.30/0.46 thf(fact_162_cDiff__cancel,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ( minus_1646763425cset_c @ A @ A )
% 0.30/0.46 = bot_bo1320844070cset_c ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_cancel
% 0.30/0.46 thf(fact_163_cDiff__cempty,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_cempty
% 0.30/0.46 thf(fact_164_cempty__cDiff,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
% 0.30/0.46 = bot_bo1320844070cset_c ) ).
% 0.30/0.46
% 0.30/0.46 % cempty_cDiff
% 0.30/0.46 thf(fact_165_cDiff__cinsert,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,A2: c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ B2 ) )
% 0.30/0.46 = ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_cinsert
% 0.30/0.46 thf(fact_166_cDiff__cinsert2,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,A2: c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ B2 ) )
% 0.30/0.46 = ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_cinsert2
% 0.30/0.46 thf(fact_167_cDiff__single__cinsert,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_single_cinsert
% 0.30/0.46 thf(fact_168_cinsert__cDiff,axiom,
% 0.30/0.46 ! [A2: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ A )
% 0.30/0.46 => ( ( counta472291938sert_c @ A2 @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_cDiff
% 0.30/0.46 thf(fact_169_order__refl,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c] : ( ord_le15364698cset_c @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_170_csubset__antisym,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B2 @ A )
% 0.30/0.46 => ( A = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_antisym
% 0.30/0.46 thf(fact_171_all__not__cin__conv,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ( ! [X2: c] :
% 0.30/0.46 ~ ( countable_Set_cin_c @ X2 @ A ) )
% 0.30/0.46 = ( A = bot_bo1320844070cset_c ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_cin_conv
% 0.30/0.46 thf(fact_172_cempty__iff,axiom,
% 0.30/0.46 ! [C: c] :
% 0.30/0.46 ~ ( countable_Set_cin_c @ C @ bot_bo1320844070cset_c ) ).
% 0.30/0.46
% 0.30/0.46 % cempty_iff
% 0.30/0.46 thf(fact_173_cinsert__iff,axiom,
% 0.30/0.46 ! [A2: c,B: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ A ) )
% 0.30/0.46 = ( ( A2 = B )
% 0.30/0.46 | ( countable_Set_cin_c @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_iff
% 0.30/0.46 thf(fact_174_cinsertCI,axiom,
% 0.30/0.46 ! [A2: c,B2: countable_Set_cset_c,B: c] :
% 0.30/0.46 ( ( ~ ( countable_Set_cin_c @ A2 @ B2 )
% 0.30/0.46 => ( A2 = B ) )
% 0.30/0.46 => ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsertCI
% 0.30/0.46 thf(fact_175_csubsetI,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ! [X4: c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ X4 @ A )
% 0.30/0.46 => ( countable_Set_cin_c @ X4 @ B2 ) )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubsetI
% 0.30/0.46 thf(fact_176_cempty__fsubsetI,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ X ) ).
% 0.30/0.46
% 0.30/0.46 % cempty_fsubsetI
% 0.30/0.46 thf(fact_177_csubset__cempty,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
% 0.30/0.46 = ( A = bot_bo1320844070cset_c ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_cempty
% 0.30/0.46 thf(fact_178_cDiff__iff,axiom,
% 0.30/0.46 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 0.30/0.46 = ( ( countable_Set_cin_c @ C @ A )
% 0.30/0.46 & ~ ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_iff
% 0.30/0.46 thf(fact_179_cDiffI,axiom,
% 0.30/0.46 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ C @ A )
% 0.30/0.46 => ( ~ ( countable_Set_cin_c @ C @ B2 )
% 0.30/0.46 => ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiffI
% 0.30/0.46 thf(fact_180_cinsert__csubset,axiom,
% 0.30/0.46 ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 0.30/0.46 = ( ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 & ( ord_le15364698cset_c @ A @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_csubset
% 0.30/0.46 thf(fact_181_cinsert__cDiff1,axiom,
% 0.30/0.46 ! [X: c,B2: countable_Set_cset_c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 0.30/0.46 = ( minus_1646763425cset_c @ A @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_cDiff1
% 0.30/0.46 thf(fact_182_csubset__cinsert,axiom,
% 0.30/0.46 ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ~ ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
% 0.30/0.46 = ( ord_le15364698cset_c @ A @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_cinsert
% 0.30/0.46 thf(fact_183_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ B @ A2 )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( A2 = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_184_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ B3 @ A4 )
% 0.30/0.46 & ( ord_le15364698cset_c @ A4 @ B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_185_dual__order_Otrans,axiom,
% 0.30/0.46 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ B @ A2 )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ C @ B )
% 0.30/0.46 => ( ord_le15364698cset_c @ C @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_186_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c] : ( ord_le15364698cset_c @ A2 @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_187_order__trans,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ Y @ Z2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_188_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B @ A2 )
% 0.30/0.46 => ( A2 = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_189_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( B = C )
% 0.30/0.46 => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_190_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( A2 = B )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B @ C )
% 0.30/0.46 => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_191_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A4 @ B3 )
% 0.30/0.46 & ( ord_le15364698cset_c @ B3 @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_192_antisym__conv,axiom,
% 0.30/0.46 ! [Y: countable_Set_cset_c,X: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ Y @ X )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_193_eqcelem__imp__iff,axiom,
% 0.30/0.46 ! [X: c,Y: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 = ( countable_Set_cin_c @ Y @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eqcelem_imp_iff
% 0.30/0.46 thf(fact_194_cset__eq__csubset,axiom,
% 0.30/0.46 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A3 @ B4 )
% 0.30/0.46 & ( ord_le15364698cset_c @ B4 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cset_eq_csubset
% 0.30/0.46 thf(fact_195_order_Otrans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B @ C )
% 0.30/0.46 => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_196_eqcset__imp__iff,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,X: c] :
% 0.30/0.46 ( ( A = B2 )
% 0.30/0.46 => ( ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 = ( countable_Set_cin_c @ X @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eqcset_imp_iff
% 0.30/0.46 thf(fact_197_eq__refl,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ord_le15364698cset_c @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_198_if__split__cin2,axiom,
% 0.30/0.46 ! [A2: c,Q: $o,X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ ( if_Cou1542198912cset_c @ Q @ X @ Y ) )
% 0.30/0.46 = ( ( Q
% 0.30/0.46 => ( countable_Set_cin_c @ A2 @ X ) )
% 0.30/0.46 & ( ~ Q
% 0.30/0.46 => ( countable_Set_cin_c @ A2 @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % if_split_cin2
% 0.30/0.46 thf(fact_199_if__split__cin1,axiom,
% 0.30/0.46 ! [Q: $o,X: c,Y: c,B: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ ( if_c @ Q @ X @ Y ) @ B )
% 0.30/0.46 = ( ( Q
% 0.30/0.46 => ( countable_Set_cin_c @ X @ B ) )
% 0.30/0.46 & ( ~ Q
% 0.30/0.46 => ( countable_Set_cin_c @ Y @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % if_split_cin1
% 0.30/0.46 thf(fact_200_eq__cmem__trans,axiom,
% 0.30/0.46 ! [A2: c,B: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( A2 = B )
% 0.30/0.46 => ( ( countable_Set_cin_c @ B @ A )
% 0.30/0.46 => ( countable_Set_cin_c @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_cmem_trans
% 0.30/0.46 thf(fact_201_csubset__trans,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B2 @ C2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_trans
% 0.30/0.46 thf(fact_202_csubset__refl,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_refl
% 0.30/0.46 thf(fact_203_cequalityD2,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( A = B2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ B2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cequalityD2
% 0.30/0.46 thf(fact_204_cequalityD1,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( A = B2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cequalityD1
% 0.30/0.46 thf(fact_205_cequalityCE,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
% 0.30/0.46 ( ( A = B2 )
% 0.30/0.46 => ( ( ( countable_Set_cin_c @ C @ A )
% 0.30/0.46 => ~ ( countable_Set_cin_c @ C @ B2 ) )
% 0.30/0.46 => ~ ( ~ ( countable_Set_cin_c @ C @ A )
% 0.30/0.46 => ( countable_Set_cin_c @ C @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cequalityCE
% 0.30/0.46 thf(fact_206_antisym,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_207_cequalityE,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( A = B2 )
% 0.30/0.46 => ~ ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ~ ( ord_le15364698cset_c @ B2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cequalityE
% 0.30/0.46 thf(fact_208_eq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X2 @ Y2 )
% 0.30/0.46 & ( ord_le15364698cset_c @ Y2 @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_209_csubsetD,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ( ( countable_Set_cin_c @ C @ A )
% 0.30/0.46 => ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubsetD
% 0.30/0.46 thf(fact_210_cset__eqI,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ! [X4: c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ X4 @ A )
% 0.30/0.46 = ( countable_Set_cin_c @ X4 @ B2 ) )
% 0.30/0.46 => ( A = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cset_eqI
% 0.30/0.46 thf(fact_211_cin__mono,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,X: c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ( ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( countable_Set_cin_c @ X @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cin_mono
% 0.30/0.46 thf(fact_212_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ( F @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_213_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F @ B ) )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le15364698cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_214_order__subst2,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_215_order__subst1,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le15364698cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_216_equals__cemptyI,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ! [Y4: c] :
% 0.30/0.46 ~ ( countable_Set_cin_c @ Y4 @ A )
% 0.30/0.46 => ( A = bot_bo1320844070cset_c ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals_cemptyI
% 0.30/0.46 thf(fact_217_equals__cemptyD,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,A2: c] :
% 0.30/0.46 ( ( A = bot_bo1320844070cset_c )
% 0.30/0.46 => ~ ( countable_Set_cin_c @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals_cemptyD
% 0.30/0.46 thf(fact_218_ex__cin__conv,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c] :
% 0.30/0.46 ( ( ? [X2: c] : ( countable_Set_cin_c @ X2 @ A ) )
% 0.30/0.46 = ( A != bot_bo1320844070cset_c ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_cin_conv
% 0.30/0.46 thf(fact_219_cemptyE,axiom,
% 0.30/0.46 ! [A2: c] :
% 0.30/0.46 ~ ( countable_Set_cin_c @ A2 @ bot_bo1320844070cset_c ) ).
% 0.30/0.46
% 0.30/0.46 % cemptyE
% 0.30/0.46 thf(fact_220_mk__disjoint__cinsert,axiom,
% 0.30/0.46 ! [A2: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ A )
% 0.30/0.46 => ? [B5: countable_Set_cset_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( counta472291938sert_c @ A2 @ B5 ) )
% 0.30/0.46 & ~ ( countable_Set_cin_c @ A2 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_cinsert
% 0.30/0.46 thf(fact_221_cinsert__absorb,axiom,
% 0.30/0.46 ! [A2: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ A )
% 0.30/0.46 => ( ( counta472291938sert_c @ A2 @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_absorb
% 0.30/0.46 thf(fact_222_cinsert__ident,axiom,
% 0.30/0.46 ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ~ ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ~ ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 => ( ( ( counta472291938sert_c @ X @ A )
% 0.30/0.46 = ( counta472291938sert_c @ X @ B2 ) )
% 0.30/0.46 = ( A = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_ident
% 0.30/0.46 thf(fact_223_set__cinsert,axiom,
% 0.30/0.46 ! [X: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ~ ! [B5: countable_Set_cset_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( counta472291938sert_c @ X @ B5 ) )
% 0.30/0.46 => ( countable_Set_cin_c @ X @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_cinsert
% 0.30/0.46 thf(fact_224_cinsertI2,axiom,
% 0.30/0.46 ! [A2: c,B2: countable_Set_cset_c,B: c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ B2 )
% 0.30/0.46 => ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsertI2
% 0.30/0.46 thf(fact_225_cinsertI1,axiom,
% 0.30/0.46 ! [A2: c,B2: countable_Set_cset_c] : ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsertI1
% 0.30/0.46 thf(fact_226_cinsertE,axiom,
% 0.30/0.46 ! [A2: c,B: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ A ) )
% 0.30/0.46 => ( ( A2 != B )
% 0.30/0.46 => ( countable_Set_cin_c @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsertE
% 0.30/0.46 thf(fact_227_bot_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ bot_bo1320844070cset_c )
% 0.30/0.46 => ( A2 = bot_bo1320844070cset_c ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_uniqueI
% 0.30/0.46 thf(fact_228_bot_Oextremum__unique,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ bot_bo1320844070cset_c )
% 0.30/0.46 = ( A2 = bot_bo1320844070cset_c ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_unique
% 0.30/0.46 thf(fact_229_bot_Oextremum,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum
% 0.30/0.46 thf(fact_230_cDiffD2,axiom,
% 0.30/0.46 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 0.30/0.46 => ~ ( countable_Set_cin_c @ C @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiffD2
% 0.30/0.46 thf(fact_231_cDiffD1,axiom,
% 0.30/0.46 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 0.30/0.46 => ( countable_Set_cin_c @ C @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiffD1
% 0.30/0.46 thf(fact_232_cDiffE,axiom,
% 0.30/0.46 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 0.30/0.46 => ~ ( ( countable_Set_cin_c @ C @ A )
% 0.30/0.46 => ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiffE
% 0.30/0.46 thf(fact_233_csubset__cinsertI2,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,B: c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_cinsertI2
% 0.30/0.46 thf(fact_234_csubset__cinsertI,axiom,
% 0.30/0.46 ! [B2: countable_Set_cset_c,A2: c] : ( ord_le15364698cset_c @ B2 @ ( counta472291938sert_c @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_cinsertI
% 0.30/0.46 thf(fact_235_cinsert__mono,axiom,
% 0.30/0.46 ! [C2: countable_Set_cset_c,D2: countable_Set_cset_c,A2: c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ C2 @ D2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( counta472291938sert_c @ A2 @ C2 ) @ ( counta472291938sert_c @ A2 @ D2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_mono
% 0.30/0.46 thf(fact_236_cDiff__csubset,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ A ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_csubset
% 0.30/0.46 thf(fact_237_double__cDiff,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B2 @ C2 )
% 0.30/0.46 => ( ( minus_1646763425cset_c @ B2 @ ( minus_1646763425cset_c @ C2 @ A ) )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % double_cDiff
% 0.30/0.46 thf(fact_238_cminus__mono,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,C2: countable_Set_cset_c,D2: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ C2 )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ D2 @ B2 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ ( minus_1646763425cset_c @ C2 @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cminus_mono
% 0.30/0.46 thf(fact_239_csubset__cinsert__iff,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
% 0.30/0.46 = ( ( ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 ) )
% 0.30/0.46 & ( ~ ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_cinsert_iff
% 0.30/0.46 thf(fact_240_csingleton__iff,axiom,
% 0.30/0.46 ! [B: c,A2: c] :
% 0.30/0.46 ( ( countable_Set_cin_c @ B @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) )
% 0.30/0.46 = ( B = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % csingleton_iff
% 0.30/0.46 thf(fact_241_cinsert__cDiff__if,axiom,
% 0.30/0.46 ! [X: c,B2: countable_Set_cset_c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ( ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 0.30/0.46 = ( minus_1646763425cset_c @ A @ B2 ) ) )
% 0.30/0.46 & ( ~ ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 0.30/0.46 = ( counta472291938sert_c @ X @ ( minus_1646763425cset_c @ A @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cinsert_cDiff_if
% 0.30/0.46 thf(fact_242_csubset__csingletonD,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,X: c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) )
% 0.30/0.46 => ( ( A = bot_bo1320844070cset_c )
% 0.30/0.46 | ( A
% 0.30/0.46 = ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % csubset_csingletonD
% 0.30/0.46 thf(fact_243_cDiff__cinsert__absorb,axiom,
% 0.30/0.46 ! [X: c,A: countable_Set_cset_c] :
% 0.30/0.46 ( ~ ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % cDiff_cinsert_absorb
% 0.30/0.46 thf(fact_244_cpsubset__finsert__iff,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
% 0.30/0.46 = ( ( ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A @ B2 ) )
% 0.30/0.46 & ( ~ ( countable_Set_cin_c @ X @ B2 )
% 0.30/0.46 => ( ( ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 ) )
% 0.30/0.46 & ( ~ ( countable_Set_cin_c @ X @ A )
% 0.30/0.46 => ( ord_le15364698cset_c @ A @ B2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cpsubset_finsert_iff
% 0.30/0.46 thf(fact_245_Greatest__equality,axiom,
% 0.30/0.46 ! [P: countable_Set_cset_c > $o,X: countable_Set_cset_c] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ Y4 @ X ) )
% 0.30/0.46 => ( ( order_1683649299cset_c @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Greatest_equality
% 0.30/0.46 thf(fact_246_GreatestI2__order,axiom,
% 0.30/0.46 ! [P: countable_Set_cset_c > $o,X: countable_Set_cset_c,Q: countable_Set_cset_c > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ Y4 @ X ) )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ! [Y5: countable_Set_cset_c] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( ord_le15364698cset_c @ Y5 @ X4 ) )
% 0.30/0.46 => ( Q @ X4 ) ) )
% 0.30/0.46 => ( Q @ ( order_1683649299cset_c @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % GreatestI2_order
% 0.30/0.46 thf(fact_247_le__rel__bool__arg__iff,axiom,
% 0.30/0.46 ( ord_le1376176871cset_c
% 0.30/0.46 = ( ^ [X5: $o > countable_Set_cset_c,Y6: $o > countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.30/0.46 & ( ord_le15364698cset_c @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_rel_bool_arg_iff
% 0.30/0.46 thf(fact_248_ord__eq__less__subst,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F @ B ) )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ B @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_less_subst
% 0.30/0.46 thf(fact_249_ord__less__eq__subst,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ( F @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_less_eq_subst
% 0.30/0.46 thf(fact_250_order__less__subst1,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ B @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_subst1
% 0.30/0.46 thf(fact_251_order__less__subst2,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_subst2
% 0.30/0.46 thf(fact_252_order_Oasym,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ B @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.asym
% 0.30/0.46 thf(fact_253_cpsubset__trans,axiom,
% 0.30/0.46 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A @ B2 )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ B2 @ C2 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cpsubset_trans
% 0.30/0.46 thf(fact_254_less__imp__neq,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( X != Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_neq
% 0.30/0.46 thf(fact_255_less__asym,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_asym
% 0.30/0.46 thf(fact_256_less__asym_H,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ B @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_asym'
% 0.30/0.46 thf(fact_257_less__trans,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ Y @ Z2 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_trans
% 0.30/0.46 thf(fact_258_less__irrefl,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c] :
% 0.30/0.46 ~ ( ord_le1587667814cset_c @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % less_irrefl
% 0.30/0.46 thf(fact_259_ord__eq__less__trans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( A2 = B )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ B @ C )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_less_trans
% 0.30/0.46 thf(fact_260_ord__less__eq__trans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ( ( B = C )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_less_eq_trans
% 0.30/0.46 thf(fact_261_dual__order_Oasym,axiom,
% 0.30/0.46 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ B @ A2 )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.asym
% 0.30/0.46 thf(fact_262_less__imp__not__eq,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( X != Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_not_eq
% 0.30/0.46 thf(fact_263_less__not__sym,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_sym
% 0.30/0.46 thf(fact_264_less__imp__not__eq2,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( Y != X ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_not_eq2
% 0.30/0.46 thf(fact_265_less__imp__triv,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,P: $o] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ Y @ X )
% 0.30/0.46 => P ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_triv
% 0.30/0.46 thf(fact_266_dual__order_Oirrefl,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c] :
% 0.30/0.46 ~ ( ord_le1587667814cset_c @ A2 @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.irrefl
% 0.30/0.46 thf(fact_267_order_Ostrict__trans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ B @ C )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_trans
% 0.30/0.46 thf(fact_268_less__imp__not__less,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_not_less
% 0.30/0.46 thf(fact_269_dual__order_Ostrict__trans,axiom,
% 0.30/0.46 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ B @ A2 )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ C @ B )
% 0.30/0.46 => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_trans
% 0.30/0.46 thf(fact_270_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ( A2 != B ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_implies_not_eq
% 0.30/0.46 thf(fact_271_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.46 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ B @ A2 )
% 0.30/0.46 => ( A2 != B ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_implies_not_eq
% 0.30/0.46 thf(fact_272_leD,axiom,
% 0.30/0.46 ! [Y: countable_Set_cset_c,X: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ Y @ X )
% 0.30/0.46 => ~ ( ord_le1587667814cset_c @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % leD
% 0.30/0.46 thf(fact_273_le__less,axiom,
% 0.30/0.46 ( ord_le15364698cset_c
% 0.30/0.46 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X2 @ Y2 )
% 0.30/0.46 | ( X2 = Y2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less
% 0.30/0.46 thf(fact_274_less__le,axiom,
% 0.30/0.46 ( ord_le1587667814cset_c
% 0.30/0.46 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X2 @ Y2 )
% 0.30/0.46 & ( X2 != Y2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_le
% 0.30/0.46 thf(fact_275_order__le__less__subst1,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ B @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_le_less_subst1
% 0.30/0.46 thf(fact_276_order__le__less__subst2,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_le_less_subst2
% 0.30/0.46 thf(fact_277_order__less__le__subst1,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ B @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_le_subst1
% 0.30/0.46 thf(fact_278_order__less__le__subst2,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_le_subst2
% 0.30/0.46 thf(fact_279_le__neq__trans,axiom,
% 0.30/0.46 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.46 => ( ( A2 != B )
% 0.30/0.46 => ( ord_le1587667814cset_c @ A2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_neq_trans
% 0.30/0.46 thf(fact_280_antisym__conv1,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ~ ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv1
% 0.30/0.46 thf(fact_281_antisym__conv2,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 => ( ( ~ ( ord_le1587667814cset_c @ X @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv2
% 0.30/0.46 thf(fact_282_less__imp__le,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( ord_le15364698cset_c @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_le
% 0.30/0.46 thf(fact_283_le__less__trans,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ Y @ Z2 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less_trans
% 0.30/0.46 thf(fact_284_less__le__trans,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le15364698cset_c @ Y @ Z2 )
% 0.30/0.46 => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_le_trans
% 0.30/0.46 thf(fact_285_le__imp__less__or__eq,axiom,
% 0.30/0.46 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.46 ( ( ord_le15364698cset_c @ X @ Y )
% 0.30/0.46 => ( ( ord_le1587667814cset_c @ X @ Y )
% 0.30/0.46 | ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_imp_less_or_eq
% 0.30/0.46 thf(fact_286_less__le__not__le,axiom,
% 0.30/0.46 ( ord_le1587667814cset_c
% 0.30/0.46 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ X2 @ Y2 )
% 0.30/0.47 & ~ ( ord_le15364698cset_c @ Y2 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le_not_le
% 0.30/0.47 thf(fact_287_order_Ostrict__trans1,axiom,
% 0.30/0.47 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.47 => ( ( ord_le1587667814cset_c @ B @ C )
% 0.30/0.47 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans1
% 0.30/0.47 thf(fact_288_order_Ostrict__trans2,axiom,
% 0.30/0.47 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.47 => ( ( ord_le15364698cset_c @ B @ C )
% 0.30/0.47 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans2
% 0.30/0.47 thf(fact_289_order_Oorder__iff__strict,axiom,
% 0.30/0.47 ( ord_le15364698cset_c
% 0.30/0.47 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A4 @ B3 )
% 0.30/0.47 | ( A4 = B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.order_iff_strict
% 0.30/0.47 thf(fact_290_order_Ostrict__iff__order,axiom,
% 0.30/0.47 ( ord_le1587667814cset_c
% 0.30/0.47 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ A4 @ B3 )
% 0.30/0.47 & ( A4 != B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_iff_order
% 0.30/0.47 thf(fact_291_dual__order_Ostrict__trans1,axiom,
% 0.30/0.47 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ B @ A2 )
% 0.30/0.47 => ( ( ord_le1587667814cset_c @ C @ B )
% 0.30/0.47 => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans1
% 0.30/0.47 thf(fact_292_dual__order_Ostrict__trans2,axiom,
% 0.30/0.47 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ B @ A2 )
% 0.30/0.47 => ( ( ord_le15364698cset_c @ C @ B )
% 0.30/0.47 => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans2
% 0.30/0.47 thf(fact_293_order_Ostrict__implies__order,axiom,
% 0.30/0.47 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A2 @ B )
% 0.30/0.47 => ( ord_le15364698cset_c @ A2 @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_order
% 0.30/0.47 thf(fact_294_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.47 ( ord_le15364698cset_c
% 0.30/0.47 = ( ^ [B3: countable_Set_cset_c,A4: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ B3 @ A4 )
% 0.30/0.47 | ( A4 = B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.order_iff_strict
% 0.30/0.47 thf(fact_295_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.47 ( ord_le1587667814cset_c
% 0.30/0.47 = ( ^ [B3: countable_Set_cset_c,A4: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ B3 @ A4 )
% 0.30/0.47 & ( A4 != B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_iff_order
% 0.30/0.47 thf(fact_296_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.47 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ B @ A2 )
% 0.30/0.47 => ( ord_le15364698cset_c @ B @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_order
% 0.30/0.47 thf(fact_297_order_Onot__eq__order__implies__strict,axiom,
% 0.30/0.47 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 0.30/0.47 ( ( A2 != B )
% 0.30/0.47 => ( ( ord_le15364698cset_c @ A2 @ B )
% 0.30/0.47 => ( ord_le1587667814cset_c @ A2 @ B ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.not_eq_order_implies_strict
% 0.30/0.47 thf(fact_298_bot_Oextremum__strict,axiom,
% 0.30/0.47 ! [A2: countable_Set_cset_c] :
% 0.30/0.47 ~ ( ord_le1587667814cset_c @ A2 @ bot_bo1320844070cset_c ) ).
% 0.30/0.47
% 0.30/0.47 % bot.extremum_strict
% 0.30/0.47 thf(fact_299_bot_Onot__eq__extremum,axiom,
% 0.30/0.47 ! [A2: countable_Set_cset_c] :
% 0.30/0.47 ( ( A2 != bot_bo1320844070cset_c )
% 0.30/0.47 = ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot.not_eq_extremum
% 0.30/0.47 thf(fact_300_cpsubsetD,axiom,
% 0.30/0.47 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A @ B2 )
% 0.30/0.47 => ( ( countable_Set_cin_c @ C @ A )
% 0.30/0.47 => ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % cpsubsetD
% 0.30/0.47 thf(fact_301_not__cpsubset__cempty,axiom,
% 0.30/0.47 ! [A: countable_Set_cset_c] :
% 0.30/0.47 ~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ) ).
% 0.30/0.47
% 0.30/0.47 % not_cpsubset_cempty
% 0.30/0.47 thf(fact_302_cpsubset__eq,axiom,
% 0.30/0.47 ( ord_le1587667814cset_c
% 0.30/0.47 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ A3 @ B4 )
% 0.30/0.47 & ( A3 != B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % cpsubset_eq
% 0.30/0.47 thf(fact_303_less__cset__def,axiom,
% 0.30/0.47 ( ord_le1587667814cset_c
% 0.30/0.47 = ( ^ [Xs: countable_Set_cset_c,Ys: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ Xs @ Ys )
% 0.30/0.47 & ( Xs != Ys ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_cset_def
% 0.30/0.47 thf(fact_304_cpsubset__imp__fsubset,axiom,
% 0.30/0.47 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A @ B2 )
% 0.30/0.47 => ( ord_le15364698cset_c @ A @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % cpsubset_imp_fsubset
% 0.30/0.47 thf(fact_305_cpsubset__csubset__trans,axiom,
% 0.30/0.47 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A @ B2 )
% 0.30/0.47 => ( ( ord_le15364698cset_c @ B2 @ C2 )
% 0.30/0.47 => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % cpsubset_csubset_trans
% 0.30/0.47 thf(fact_306_csubset__cpsubset__trans,axiom,
% 0.30/0.47 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ A @ B2 )
% 0.30/0.47 => ( ( ord_le1587667814cset_c @ B2 @ C2 )
% 0.30/0.47 => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % csubset_cpsubset_trans
% 0.30/0.47 thf(fact_307_csubset__not__fsubset__eq,axiom,
% 0.30/0.47 ( ord_le1587667814cset_c
% 0.30/0.47 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le15364698cset_c @ A3 @ B4 )
% 0.30/0.47 & ~ ( ord_le15364698cset_c @ B4 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % csubset_not_fsubset_eq
% 0.30/0.47 thf(fact_308_csubset__iff__pfsubset__eq,axiom,
% 0.30/0.47 ( ord_le15364698cset_c
% 0.30/0.47 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A3 @ B4 )
% 0.30/0.47 | ( A3 = B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % csubset_iff_pfsubset_eq
% 0.30/0.47 thf(fact_309_cpsubset__imp__ex__fmem,axiom,
% 0.30/0.47 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 0.30/0.47 ( ( ord_le1587667814cset_c @ A @ B2 )
% 0.30/0.47 => ? [B6: c] : ( countable_Set_cin_c @ B6 @ ( minus_1646763425cset_c @ B2 @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % cpsubset_imp_ex_fmem
% 0.30/0.47
% 0.30/0.47 % Helper facts (5)
% 0.30/0.47 thf(help_If_2_1_If_001tf__c_T,axiom,
% 0.30/0.47 ! [X: c,Y: c] :
% 0.30/0.47 ( ( if_c @ $false @ X @ Y )
% 0.30/0.47 = Y ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_If_001tf__c_T,axiom,
% 0.30/0.47 ! [X: c,Y: c] :
% 0.30/0.47 ( ( if_c @ $true @ X @ Y )
% 0.30/0.47 = X ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_3_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
% 0.30/0.47 ! [P: $o] :
% 0.30/0.47 ( ( P = $true )
% 0.30/0.47 | ( P = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
% 0.30/0.47 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.47 ( ( if_Cou1542198912cset_c @ $false @ X @ Y )
% 0.30/0.47 = Y ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
% 0.30/0.47 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 0.30/0.47 ( ( if_Cou1542198912cset_c @ $true @ X @ Y )
% 0.30/0.47 = X ) ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
% 0.30/0.47 = ( f @ x ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.69/1.51 ---- Embedded in THF ---
% 2.69/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.69/1.51 %%% Generated on Tue Feb 24 08:27:28 EST 2026
% 2.69/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.69/1.51 %%% Logic specification used:
% 2.69/1.51 %%% thf(spec, logic, $$dhol).
% 2.69/1.51
% 2.69/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2DTF15252.p
% See solution above
% 2.69/1.51 ------------------------
% 2.69/1.55 ---- Cleaned THF ---
% 2.69/1.55 thf(ty_n_t__Countable____Set____Type__Ocset_It__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_J,type,
% 2.69/1.55 counta191869203tT_a_m: $tType ).
% 2.69/1.55
% 2.69/1.55 thf(ty_n_t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 2.69/1.55 monomo197243225tT_a_m: $tType ).
% 2.69/1.55
% 2.69/1.55 thf(ty_n_t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 countable_Set_cset_c: $tType ).
% 2.69/1.55
% 2.69/1.55 thf(ty_n_tf__m,type,
% 2.69/1.55 m: $tType ).
% 2.69/1.55
% 2.69/1.55 thf(ty_n_tf__c,type,
% 2.69/1.55 c: $tType ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Countable__Set__Type_Ocin_001tf__c,type,
% 2.69/1.55 countable_Set_cin_c: c > countable_Set_cset_c > $o ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Countable__Set__Type_Ocinsert_001tf__c,type,
% 2.69/1.55 counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
% 2.69/1.55 comp_M864375327_a_m_c: ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c_001tf__c,type,
% 2.69/1.55 comp_M1062614966_m_c_c: ( monomo197243225tT_a_m > c ) > ( c > monomo197243225tT_a_m ) > c > c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 2.69/1.55 comp_M1944986301tT_a_m: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__c,type,
% 2.69/1.55 comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__m,type,
% 2.69/1.55 comp_M750374454_m_m_m: ( monomo197243225tT_a_m > m ) > ( m > monomo197243225tT_a_m ) > m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__c_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
% 2.69/1.55 comp_c1772230468_a_m_c: ( c > monomo197243225tT_a_m ) > ( c > c ) > c > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__c_001tf__c_001tf__c,type,
% 2.69/1.55 comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 2.69/1.55 comp_c997395372tT_a_m: ( c > m ) > ( monomo197243225tT_a_m > c ) > monomo197243225tT_a_m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001tf__c,type,
% 2.69/1.55 comp_c_m_c: ( c > m ) > ( c > c ) > c > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001tf__m,type,
% 2.69/1.55 comp_c_m_m: ( c > m ) > ( m > c ) > m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
% 2.69/1.55 comp_m1038691662_a_m_c: ( m > monomo197243225tT_a_m ) > ( c > m ) > c > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__m_001tf__c_001tf__c,type,
% 2.69/1.55 comp_m_c_c: ( m > c ) > ( c > m ) > c > c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
% 2.69/1.55 comp_m263856566tT_a_m: ( m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001tf__c,type,
% 2.69/1.55 comp_m_m_c: ( m > m ) > ( c > m ) > c > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001tf__m,type,
% 2.69/1.55 comp_m_m_m: ( m > m ) > ( m > m ) > m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Groups_Ominus__class_Ominus_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_If_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_If_001tf__c,type,
% 2.69/1.55 if_c: $o > c > c > c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_Ocset__nondetM__base_Oaltc__nondet_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__a,type,
% 2.69/1.55 monomo2081011572_m_m_a: ( counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m ) > counta191869203tT_a_m > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_Ocset__nondetM__base_Oaltc__nondet_001tf__c_001tf__m_001tf__a,type,
% 2.69/1.55 monomo463139869_c_m_a: ( countable_Set_cset_c > ( c > m ) > m ) > countable_Set_cset_c > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_OnondetT_ONondetT_001tf__m_001tf__a,type,
% 2.69/1.55 monomo412532791tT_m_a: m > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_OnondetT_Orun__nondet_001tf__a_001tf__m,type,
% 2.69/1.55 monomo624345106et_a_m: monomo197243225tT_a_m > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 bot_bo1320844070cset_c: countable_Set_cset_c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Countable____Set____Type__Ocset_Itf__c_J_J,type,
% 2.69/1.55 ord_le1376176871cset_c: ( $o > countable_Set_cset_c ) > ( $o > countable_Set_cset_c ) > $o ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
% 2.69/1.55
% 2.69/1.55 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
% 2.69/1.55 order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
% 2.69/1.55
% 2.69/1.55 thf(sy_v_f____,type,
% 2.69/1.55 f: c > monomo197243225tT_a_m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_v_mergec,type,
% 2.69/1.55 mergec: countable_Set_cset_c > ( c > m ) > m ).
% 2.69/1.55
% 2.69/1.55 thf(sy_v_x____,type,
% 2.69/1.55 x: c ).
% 2.69/1.55
% 2.69/1.55 thf(fact_0_mergec__single,axiom,
% 2.69/1.55 ! [X: c,F: c > m] :
% 2.69/1.55 ( ( mergec @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) @ F )
% 2.69/1.55 = ( F @ X ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_1_cset__nondetM__base_Oaltc__nondet_Ocong,axiom,
% 2.69/1.55 monomo463139869_c_m_a = monomo463139869_c_m_a ).
% 2.69/1.55
% 2.69/1.55 thf(fact_2_cinsert__absorb2,axiom,
% 2.69/1.55 ! [X: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( counta472291938sert_c @ X @ ( counta472291938sert_c @ X @ A ) )
% 2.69/1.55 = ( counta472291938sert_c @ X @ A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_3_cdoubleton__eq__iff,axiom,
% 2.69/1.55 ! [A2: c,B: c,C: c,D: c] :
% 2.69/1.55 ( ( ( counta472291938sert_c @ A2 @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
% 2.69/1.55 = ( counta472291938sert_c @ C @ ( counta472291938sert_c @ D @ bot_bo1320844070cset_c ) ) )
% 2.69/1.55 = ( ( ( A2 = C )
% 2.69/1.55 & ( B = D ) )
% 2.69/1.55 | ( ( A2 = D )
% 2.69/1.55 & ( B = C ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_4_csingleton__inject,axiom,
% 2.69/1.55 ! [A2: c,B: c] :
% 2.69/1.55 ( ( ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c )
% 2.69/1.55 = ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
% 2.69/1.55 => ( A2 = B ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_5_cinsert__not__cempty,axiom,
% 2.69/1.55 ! [A2: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( counta472291938sert_c @ A2 @ A )
% 2.69/1.55 != bot_bo1320844070cset_c ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_6_cinsert__commute,axiom,
% 2.69/1.55 ! [X: c,Y: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( counta472291938sert_c @ X @ ( counta472291938sert_c @ Y @ A ) )
% 2.69/1.55 = ( counta472291938sert_c @ Y @ ( counta472291938sert_c @ X @ A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_7_run__altc__nondet,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ mergec @ A @ F ) )
% 2.69/1.55 = ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_8_nondetT_Oexpand,axiom,
% 2.69/1.55 ! [NondetT: monomo197243225tT_a_m,NondetT2: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( monomo624345106et_a_m @ NondetT )
% 2.69/1.55 = ( monomo624345106et_a_m @ NondetT2 ) )
% 2.69/1.55 => ( NondetT = NondetT2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_9_cset__nondetM__base_Orun__altc__nondet,axiom,
% 2.69/1.55 ! [Mergec: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,A: counta191869203tT_a_m,F: monomo197243225tT_a_m > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ Mergec @ A @ F ) )
% 2.69/1.55 = ( Mergec @ A @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ F ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_10_cset__nondetM__base_Orun__altc__nondet,axiom,
% 2.69/1.55 ! [Mergec: countable_Set_cset_c > ( c > m ) > m,A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ Mergec @ A @ F ) )
% 2.69/1.55 = ( Mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_11_altc__nondet__def,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( monomo463139869_c_m_a @ mergec @ A @ F )
% 2.69/1.55 = ( monomo412532791tT_m_a @ ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_12_comp__apply,axiom,
% 2.69/1.55 ( comp_M1944986301tT_a_m
% 2.69/1.55 = ( ^ [F2: monomo197243225tT_a_m > m,G: monomo197243225tT_a_m > monomo197243225tT_a_m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_13_comp__apply,axiom,
% 2.69/1.55 ( comp_m263856566tT_a_m
% 2.69/1.55 = ( ^ [F2: m > m,G: monomo197243225tT_a_m > m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_14_comp__apply,axiom,
% 2.69/1.55 ( comp_m_m_c
% 2.69/1.55 = ( ^ [F2: m > m,G: c > m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_15_comp__apply,axiom,
% 2.69/1.55 ( comp_c1772230468_a_m_c
% 2.69/1.55 = ( ^ [F2: c > monomo197243225tT_a_m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_16_comp__apply,axiom,
% 2.69/1.55 ( comp_c_m_c
% 2.69/1.55 = ( ^ [F2: c > m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_17_comp__apply,axiom,
% 2.69/1.55 ( comp_M750374444_m_m_c
% 2.69/1.55 = ( ^ [F2: monomo197243225tT_a_m > m,G: c > monomo197243225tT_a_m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_18_cset__nondetM__base_Oaltc__nondet__def,axiom,
% 2.69/1.55 ( monomo2081011572_m_m_a
% 2.69/1.55 = ( ^ [Mergec2: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,A3: counta191869203tT_a_m,F2: monomo197243225tT_a_m > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Mergec2 @ A3 @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ F2 ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_19_cset__nondetM__base_Oaltc__nondet__def,axiom,
% 2.69/1.55 ( monomo463139869_c_m_a
% 2.69/1.55 = ( ^ [Mergec2: countable_Set_cset_c > ( c > m ) > m,A3: countable_Set_cset_c,F2: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Mergec2 @ A3 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F2 ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_20_comp__def,axiom,
% 2.69/1.55 ( comp_M1944986301tT_a_m
% 2.69/1.55 = ( ^ [F2: monomo197243225tT_a_m > m,G: monomo197243225tT_a_m > monomo197243225tT_a_m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_21_comp__def,axiom,
% 2.69/1.55 ( comp_m263856566tT_a_m
% 2.69/1.55 = ( ^ [F2: m > m,G: monomo197243225tT_a_m > m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_22_comp__def,axiom,
% 2.69/1.55 ( comp_m_m_c
% 2.69/1.55 = ( ^ [F2: m > m,G: c > m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_23_comp__def,axiom,
% 2.69/1.55 ( comp_c1772230468_a_m_c
% 2.69/1.55 = ( ^ [F2: c > monomo197243225tT_a_m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_24_comp__def,axiom,
% 2.69/1.55 ( comp_c_m_c
% 2.69/1.55 = ( ^ [F2: c > m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_25_comp__def,axiom,
% 2.69/1.55 ( comp_M750374444_m_m_c
% 2.69/1.55 = ( ^ [F2: monomo197243225tT_a_m > m,G: c > monomo197243225tT_a_m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_26_comp__assoc,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,H: c > c] :
% 2.69/1.55 ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_27_comp__assoc,axiom,
% 2.69/1.55 ! [F: m > m,G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_28_comp__assoc,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_29_comp__assoc,axiom,
% 2.69/1.55 ! [F: m > m,G2: m > m,H: c > m] :
% 2.69/1.55 ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_30_comp__assoc,axiom,
% 2.69/1.55 ! [F: c > m,G2: m > c,H: c > m] :
% 2.69/1.55 ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_31_comp__assoc,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,H: c > c] :
% 2.69/1.55 ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_32_comp__assoc,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,H: c > c] :
% 2.69/1.55 ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_33_comp__assoc,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,H: monomo197243225tT_a_m > c] :
% 2.69/1.55 ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ F @ ( comp_c997395372tT_a_m @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_34_comp__assoc,axiom,
% 2.69/1.55 ! [F: c > m,G2: monomo197243225tT_a_m > c,H: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( comp_M750374444_m_m_c @ ( comp_c997395372tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ F @ ( comp_M1062614966_m_c_c @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_35_comp__assoc,axiom,
% 2.69/1.55 ! [F: m > m,G2: m > m,H: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( comp_m263856566tT_a_m @ ( comp_m_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ F @ ( comp_m263856566tT_a_m @ G2 @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_36_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,V: c] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_37_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: m > m,D: c > m,V: c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_m_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_38_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: c > m,D: c > c,V: c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_39_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: c > m,B: c > c,C: m > m,D: c > m,V: c] :
% 2.69/1.55 ( ( ( comp_c_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_m_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_40_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: c > m,B: c > c,C: c > m,D: c > c,V: c] :
% 2.69/1.55 ( ( ( comp_c_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_41_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: m > m,D: c > m,V: c] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_m_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_42_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c > c,V: c] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_43_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: m > m,B: monomo197243225tT_a_m > m,C: m > m,D: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_m263856566tT_a_m @ A2 @ B )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_44_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,V: c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_45_comp__eq__dest,axiom,
% 2.69/1.55 ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,D: c > c,V: c] :
% 2.69/1.55 ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ C @ D ) )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ ( D @ V ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_46_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_47_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: m > m,D: c > m] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_m_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_48_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: c > m,D: c > c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_49_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: c > m,B: c > c,C: m > m,D: c > m] :
% 2.69/1.55 ( ( ( comp_c_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_m_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_50_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: c > m,B: c > c,C: c > m,D: c > c] :
% 2.69/1.55 ( ( ( comp_c_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_51_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: m > m,D: c > m] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_m_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_52_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c > c] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_53_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: m > m,B: monomo197243225tT_a_m > m,C: m > m,D: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_m263856566tT_a_m @ A2 @ B )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ C @ D ) )
% 2.69/1.55 => ! [V2: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_54_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_55_comp__eq__elim,axiom,
% 2.69/1.55 ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,D: c > c] :
% 2.69/1.55 ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ C @ D ) )
% 2.69/1.55 => ! [V2: c] :
% 2.69/1.55 ( ( A2 @ ( B @ V2 ) )
% 2.69/1.55 = ( C @ ( D @ V2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_56_comp__cong,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: monomo197243225tT_a_m > m,G3: c > monomo197243225tT_a_m,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_57_comp__cong,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,X: c,F3: m > m,G3: c > m,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_58_comp__cong,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,X: c,F3: c > m,G3: c > c,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_59_comp__cong,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,X: c,F3: m > m,G3: c > m,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_60_comp__cong,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,X: c,F3: c > m,G3: c > c,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_61_comp__cong,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: m > m,G3: c > m,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_62_comp__cong,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: c > m,G3: c > c,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_63_comp__cong,axiom,
% 2.69/1.55 ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,F3: m > m,G3: c > m,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_64_comp__cong,axiom,
% 2.69/1.55 ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,F3: c > m,G3: c > c,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_65_comp__cong,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,X: c,F3: monomo197243225tT_a_m > m,G3: c > monomo197243225tT_a_m,X3: c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( F3 @ ( G3 @ X3 ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F3 @ G3 @ X3 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_66_comp__eq__dest__lhs,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_M1944986301tT_a_m @ A2 @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ V ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_67_comp__eq__dest__lhs,axiom,
% 2.69/1.55 ! [A2: m > m,B: monomo197243225tT_a_m > m,C: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_m263856566tT_a_m @ A2 @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ V ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_68_comp__eq__dest__lhs,axiom,
% 2.69/1.55 ! [A2: m > m,B: c > m,C: c > m,V: c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ A2 @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ V ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_69_comp__eq__dest__lhs,axiom,
% 2.69/1.55 ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,V: c] :
% 2.69/1.55 ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ V ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_70_comp__eq__dest__lhs,axiom,
% 2.69/1.55 ! [A2: c > m,B: c > c,C: c > m,V: c] :
% 2.69/1.55 ( ( ( comp_c_m_c @ A2 @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ V ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_71_comp__eq__dest__lhs,axiom,
% 2.69/1.55 ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,V: c] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ A2 @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ( A2 @ ( B @ V ) )
% 2.69/1.55 = ( C @ V ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_72_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: monomo197243225tT_a_m > m,K: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_73_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,X: c,H: m > m,K: c > m] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_74_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,X: c,H: c > m,K: c > c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_75_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,X: c,H: m > m,K: c > m] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_76_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,X: c,H: c > m,K: c > c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_77_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: m > m,K: c > m] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_78_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: c > m,K: c > c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_79_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,H: m > m,K: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_80_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,X: c,H: monomo197243225tT_a_m > m,K: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_81_comp__apply__eq,axiom,
% 2.69/1.55 ! [F: c > monomo197243225tT_a_m,G2: c > c,X: c,H: c > monomo197243225tT_a_m,K: c > c] :
% 2.69/1.55 ( ( ( F @ ( G2 @ X ) )
% 2.69/1.55 = ( H @ ( K @ X ) ) )
% 2.69/1.55 => ( ( comp_c1772230468_a_m_c @ F @ G2 @ X )
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ H @ K @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_82_nondetT_Oinject,axiom,
% 2.69/1.55 ! [X: m,Ya: m] :
% 2.69/1.55 ( ( ( monomo412532791tT_m_a @ X )
% 2.69/1.55 = ( monomo412532791tT_m_a @ Ya ) )
% 2.69/1.55 = ( X = Ya ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_83_nondetT_Ocollapse,axiom,
% 2.69/1.55 ! [NondetT: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ NondetT ) )
% 2.69/1.55 = NondetT ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_84_nondetT_Oexhaust,axiom,
% 2.69/1.55 ! [Y: monomo197243225tT_a_m] :
% 2.69/1.55 ~ ! [X4: m] :
% 2.69/1.55 ( Y
% 2.69/1.55 != ( monomo412532791tT_m_a @ X4 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_85_nondetT_Oinduct,axiom,
% 2.69/1.55 ! [P: monomo197243225tT_a_m > $o,NondetT: monomo197243225tT_a_m] :
% 2.69/1.55 ( ! [Xa: m] : ( P @ ( monomo412532791tT_m_a @ Xa ) )
% 2.69/1.55 => ( P @ NondetT ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_86_nondetT_Oexhaust__sel,axiom,
% 2.69/1.55 ! [NondetT: monomo197243225tT_a_m] :
% 2.69/1.55 ( NondetT
% 2.69/1.55 = ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ NondetT ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_87_nondetT_Osel,axiom,
% 2.69/1.55 ! [X: m] :
% 2.69/1.55 ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ X ) )
% 2.69/1.55 = X ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_88_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: c > monomo197243225tT_a_m,H: c > c,R1: monomo197243225tT_a_m > monomo197243225tT_a_m,R2: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m,L: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_c1772230468_a_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_M864375327_a_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_M1944986301tT_a_m @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_89_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R1: c > monomo197243225tT_a_m,R2: c > c,F: monomo197243225tT_a_m > m,L: c > m] :
% 2.69/1.55 ( ( ( comp_M864375327_a_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_M750374444_m_m_c @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_90_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R1: monomo197243225tT_a_m > m,R2: c > monomo197243225tT_a_m,F: m > m,L: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_m263856566tT_a_m @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_91_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: c > c,H: c > c,R1: m > c,R2: c > m,F: c > m,L: m > m] :
% 2.69/1.55 ( ( ( comp_c_c_c @ G2 @ H )
% 2.69/1.55 = ( comp_m_c_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_c_m_m @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_92_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: m > c,H: c > m,R1: c > c,R2: c > c,F: c > m,L: c > m] :
% 2.69/1.55 ( ( ( comp_m_c_c @ G2 @ H )
% 2.69/1.55 = ( comp_c_c_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_c_m_c @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_93_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: c > c,H: c > c,R1: c > c,R2: c > c,F: c > m,L: c > m] :
% 2.69/1.55 ( ( ( comp_c_c_c @ G2 @ H )
% 2.69/1.55 = ( comp_c_c_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_c_m_c @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_94_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: m > m,H: c > m,R1: m > m,R2: c > m,F: m > m,L: m > m] :
% 2.69/1.55 ( ( ( comp_m_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_m_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_m_m_m @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_95_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: m > m,H: c > m,R1: c > m,R2: c > c,F: m > m,L: c > m] :
% 2.69/1.55 ( ( ( comp_m_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_c_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_m_m_c @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_96_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: c > m,H: c > c,R1: m > m,R2: c > m,F: m > m,L: m > m] :
% 2.69/1.55 ( ( ( comp_c_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_m_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_m_m_m @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_97_rewriteR__comp__comp2,axiom,
% 2.69/1.55 ! [G2: c > m,H: c > c,R1: c > m,R2: c > c,F: m > m,L: c > m] :
% 2.69/1.55 ( ( ( comp_c_m_c @ G2 @ H )
% 2.69/1.55 = ( comp_c_m_c @ R1 @ R2 ) )
% 2.69/1.55 => ( ( ( comp_m_m_c @ F @ R1 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ L @ R2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_98_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: m > m,G2: monomo197243225tT_a_m > m,L1: monomo197243225tT_a_m > m,L2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_m263856566tT_a_m @ F @ G2 )
% 2.69/1.55 = ( comp_M1944986301tT_a_m @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_M864375327_a_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_99_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,L1: m > m,L2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R: c > m] :
% 2.69/1.55 ( ( ( comp_M1944986301tT_a_m @ F @ G2 )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_M750374444_m_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_100_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,L1: monomo197243225tT_a_m > m,L2: c > monomo197243225tT_a_m,H: c > c,R: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ F @ G2 )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_c1772230468_a_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_101_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: m > m,G2: m > m,L1: c > m,L2: m > c,H: c > m,R: c > c] :
% 2.69/1.55 ( ( ( comp_m_m_m @ F @ G2 )
% 2.69/1.55 = ( comp_c_m_m @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_m_c_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_102_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: m > m,G2: m > m,L1: m > m,L2: m > m,H: c > m,R: c > m] :
% 2.69/1.55 ( ( ( comp_m_m_m @ F @ G2 )
% 2.69/1.55 = ( comp_m_m_m @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_m_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_103_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: c > m,G2: m > c,L1: m > m,L2: m > m,H: c > m,R: c > m] :
% 2.69/1.55 ( ( ( comp_c_m_m @ F @ G2 )
% 2.69/1.55 = ( comp_m_m_m @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_m_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_104_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,L1: m > m,L2: c > m,H: c > c,R: c > m] :
% 2.69/1.55 ( ( ( comp_m_m_c @ F @ G2 )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_c_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_105_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,L1: c > m,L2: c > c,H: c > c,R: c > c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ F @ G2 )
% 2.69/1.55 = ( comp_c_m_c @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_c_c_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_106_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,L1: m > m,L2: c > m,H: c > c,R: c > m] :
% 2.69/1.55 ( ( ( comp_c_m_c @ F @ G2 )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_c_m_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_107_rewriteL__comp__comp2,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,L1: c > m,L2: c > c,H: c > c,R: c > c] :
% 2.69/1.55 ( ( ( comp_c_m_c @ F @ G2 )
% 2.69/1.55 = ( comp_c_m_c @ L1 @ L2 ) )
% 2.69/1.55 => ( ( ( comp_c_c_c @ L2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c_m_c @ L1 @ R ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_108_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: c > monomo197243225tT_a_m,H: c > c,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_c1772230468_a_m_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_109_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R: c > m,F: m > m] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_110_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_M864375327_a_m_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_111_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: m > c,H: c > m,R: c > c,F: c > m] :
% 2.69/1.55 ( ( ( comp_m_c_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_112_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: c > c,H: c > c,R: c > c,F: c > m] :
% 2.69/1.55 ( ( ( comp_c_c_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_113_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: m > m,H: c > m,R: c > m,F: m > m] :
% 2.69/1.55 ( ( ( comp_m_m_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_114_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: c > m,H: c > c,R: c > m,F: m > m] :
% 2.69/1.55 ( ( ( comp_c_m_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_115_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: c > m,H: monomo197243225tT_a_m > c,R: monomo197243225tT_a_m > m,F: m > m] :
% 2.69/1.55 ( ( ( comp_c997395372tT_a_m @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_116_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > c,H: c > monomo197243225tT_a_m,R: c > c,F: c > m] :
% 2.69/1.55 ( ( ( comp_M1062614966_m_c_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ ( comp_c997395372tT_a_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_c_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_117_rewriteR__comp__comp,axiom,
% 2.69/1.55 ! [G2: m > monomo197243225tT_a_m,H: c > m,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_m1038691662_a_m_c @ G2 @ H )
% 2.69/1.55 = R )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_M750374454_m_m_m @ F @ G2 ) @ H )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_118_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: m > m,G2: monomo197243225tT_a_m > m,L: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_m263856566tT_a_m @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_119_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,L: c > m,H: c > c] :
% 2.69/1.55 ( ( ( comp_M750374444_m_m_c @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_120_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,L: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( comp_M1944986301tT_a_m @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_121_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: m > m,G2: m > m,L: m > m,H: c > m] :
% 2.69/1.55 ( ( ( comp_m_m_m @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_122_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: c > m,G2: m > c,L: m > m,H: c > m] :
% 2.69/1.55 ( ( ( comp_c_m_m @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_123_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: m > m,G2: c > m,L: c > m,H: c > c] :
% 2.69/1.55 ( ( ( comp_m_m_c @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_124_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: c > m,G2: c > c,L: c > m,H: c > c] :
% 2.69/1.55 ( ( ( comp_c_m_c @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_125_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: m > monomo197243225tT_a_m,G2: c > m,L: c > monomo197243225tT_a_m,H: c > c] :
% 2.69/1.55 ( ( ( comp_m1038691662_a_m_c @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m1038691662_a_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_126_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: monomo197243225tT_a_m > m,G2: m > monomo197243225tT_a_m,L: m > m,H: c > m] :
% 2.69/1.55 ( ( ( comp_M750374454_m_m_m @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ F @ ( comp_m1038691662_a_m_c @ G2 @ H ) )
% 2.69/1.55 = ( comp_m_m_c @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_127_rewriteL__comp__comp,axiom,
% 2.69/1.55 ! [F: m > m,G2: m > m,L: m > m,H: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( comp_m_m_m @ F @ G2 )
% 2.69/1.55 = L )
% 2.69/1.55 => ( ( comp_m263856566tT_a_m @ F @ ( comp_m263856566tT_a_m @ G2 @ H ) )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ L @ H ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_128_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > monomo197243225tT_a_m,G2: c > c,X: c,N: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_129_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: monomo197243225tT_a_m > monomo197243225tT_a_m,G2: c > monomo197243225tT_a_m,X: c,N: c > monomo197243225tT_a_m,H: c > c,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_130_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: m > m,G2: c > m,X: c,N: c > m,H: c > c,F: m > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_m_m_c @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_131_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: m > c,G2: c > m,X: c,N: c > c,H: c > c,F: c > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_c_m_c @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_132_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > m,G2: c > c,X: c,N: m > m,H: c > m,F: m > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ ( comp_m_m_m @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_133_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > m,G2: c > c,X: c,N: c > m,H: c > c,F: m > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_m_m_c @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_134_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > c,G2: c > c,X: c,N: m > c,H: c > m,F: c > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_m_m_c @ ( comp_c_m_m @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_135_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > c,G2: c > c,X: c,N: c > c,H: c > c,F: c > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_c_m_c @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_136_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > m,G2: monomo197243225tT_a_m > c,X: monomo197243225tT_a_m,N: m > m,H: monomo197243225tT_a_m > m,F: m > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ ( comp_m_m_m @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_137_type__copy__map__cong0,axiom,
% 2.69/1.55 ! [M: c > c,G2: monomo197243225tT_a_m > c,X: monomo197243225tT_a_m,N: m > c,H: monomo197243225tT_a_m > m,F: c > m] :
% 2.69/1.55 ( ( ( M @ ( G2 @ X ) )
% 2.69/1.55 = ( N @ ( H @ X ) ) )
% 2.69/1.55 => ( ( comp_c997395372tT_a_m @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
% 2.69/1.55 = ( comp_m263856566tT_a_m @ ( comp_c_m_m @ F @ N ) @ H @ X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_138_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: m > m,F: monomo197243225tT_a_m > m,V: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( comp_m_m_c @ G2 @ ( comp_M750374444_m_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_139_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,F: c > monomo197243225tT_a_m,V: c > c] :
% 2.69/1.55 ( ( comp_M750374444_m_m_c @ G2 @ ( comp_c1772230468_a_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_M750374444_m_m_c @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_140_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > monomo197243225tT_a_m,V: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( comp_M750374444_m_m_c @ G2 @ ( comp_M864375327_a_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_141_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: m > m,F: m > m,V: c > m] :
% 2.69/1.55 ( ( comp_m_m_c @ G2 @ ( comp_m_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_m_m_c @ ( comp_m_m_m @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_142_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: m > m,F: c > m,V: c > c] :
% 2.69/1.55 ( ( comp_m_m_c @ G2 @ ( comp_c_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_m_m_c @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_143_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: c > m,F: m > c,V: c > m] :
% 2.69/1.55 ( ( comp_c_m_c @ G2 @ ( comp_m_c_c @ F @ V ) )
% 2.69/1.55 = ( comp_m_m_c @ ( comp_c_m_m @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_144_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: c > m,F: c > c,V: c > c] :
% 2.69/1.55 ( ( comp_c_m_c @ G2 @ ( comp_c_c_c @ F @ V ) )
% 2.69/1.55 = ( comp_c_m_c @ ( comp_c_m_c @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_145_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: m > monomo197243225tT_a_m,F: c > m,V: c > c] :
% 2.69/1.55 ( ( comp_m1038691662_a_m_c @ G2 @ ( comp_c_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ ( comp_m1038691662_a_m_c @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_146_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,F: m > monomo197243225tT_a_m,V: c > m] :
% 2.69/1.55 ( ( comp_M750374444_m_m_c @ G2 @ ( comp_m1038691662_a_m_c @ F @ V ) )
% 2.69/1.55 = ( comp_m_m_c @ ( comp_M750374454_m_m_m @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_147_fun_Omap__comp,axiom,
% 2.69/1.55 ! [G2: m > m,F: c > m,V: monomo197243225tT_a_m > c] :
% 2.69/1.55 ( ( comp_m263856566tT_a_m @ G2 @ ( comp_c997395372tT_a_m @ F @ V ) )
% 2.69/1.55 = ( comp_c997395372tT_a_m @ ( comp_m_m_c @ G2 @ F ) @ V ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_148_function__factors__left,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ! [X2: monomo197243225tT_a_m,Y2: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( G2 @ X2 )
% 2.69/1.55 = ( G2 @ Y2 ) )
% 2.69/1.55 => ( ( F @ X2 )
% 2.69/1.55 = ( F @ Y2 ) ) ) )
% 2.69/1.55 = ( ? [H2: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_M1944986301tT_a_m @ H2 @ G2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_149_function__factors__left,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ! [X2: monomo197243225tT_a_m,Y2: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ( G2 @ X2 )
% 2.69/1.55 = ( G2 @ Y2 ) )
% 2.69/1.55 => ( ( F @ X2 )
% 2.69/1.55 = ( F @ Y2 ) ) ) )
% 2.69/1.55 = ( ? [H2: m > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_m263856566tT_a_m @ H2 @ G2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_150_function__factors__left,axiom,
% 2.69/1.55 ! [G2: c > m,F: c > m] :
% 2.69/1.55 ( ( ! [X2: c,Y2: c] :
% 2.69/1.55 ( ( ( G2 @ X2 )
% 2.69/1.55 = ( G2 @ Y2 ) )
% 2.69/1.55 => ( ( F @ X2 )
% 2.69/1.55 = ( F @ Y2 ) ) ) )
% 2.69/1.55 = ( ? [H2: m > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_m_m_c @ H2 @ G2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_151_function__factors__left,axiom,
% 2.69/1.55 ! [G2: c > c,F: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ! [X2: c,Y2: c] :
% 2.69/1.55 ( ( ( G2 @ X2 )
% 2.69/1.55 = ( G2 @ Y2 ) )
% 2.69/1.55 => ( ( F @ X2 )
% 2.69/1.55 = ( F @ Y2 ) ) ) )
% 2.69/1.55 = ( ? [H2: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ H2 @ G2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_152_function__factors__left,axiom,
% 2.69/1.55 ! [G2: c > c,F: c > m] :
% 2.69/1.55 ( ( ! [X2: c,Y2: c] :
% 2.69/1.55 ( ( ( G2 @ X2 )
% 2.69/1.55 = ( G2 @ Y2 ) )
% 2.69/1.55 => ( ( F @ X2 )
% 2.69/1.55 = ( F @ Y2 ) ) ) )
% 2.69/1.55 = ( ? [H2: c > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_c_m_c @ H2 @ G2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_153_function__factors__left,axiom,
% 2.69/1.55 ! [G2: c > monomo197243225tT_a_m,F: c > m] :
% 2.69/1.55 ( ( ! [X2: c,Y2: c] :
% 2.69/1.55 ( ( ( G2 @ X2 )
% 2.69/1.55 = ( G2 @ Y2 ) )
% 2.69/1.55 => ( ( F @ X2 )
% 2.69/1.55 = ( F @ Y2 ) ) ) )
% 2.69/1.55 = ( ? [H2: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_M750374444_m_m_c @ H2 @ G2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_154_function__factors__right,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ! [X2: monomo197243225tT_a_m] :
% 2.69/1.55 ? [Y2: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( G2 @ Y2 )
% 2.69/1.55 = ( F @ X2 ) ) )
% 2.69/1.55 = ( ? [H2: monomo197243225tT_a_m > monomo197243225tT_a_m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_M1944986301tT_a_m @ G2 @ H2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_155_function__factors__right,axiom,
% 2.69/1.55 ! [G2: m > m,F: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( ( ! [X2: monomo197243225tT_a_m] :
% 2.69/1.55 ? [Y2: m] :
% 2.69/1.55 ( ( G2 @ Y2 )
% 2.69/1.55 = ( F @ X2 ) ) )
% 2.69/1.55 = ( ? [H2: monomo197243225tT_a_m > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_m263856566tT_a_m @ G2 @ H2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_156_function__factors__right,axiom,
% 2.69/1.55 ! [G2: m > m,F: c > m] :
% 2.69/1.55 ( ( ! [X2: c] :
% 2.69/1.55 ? [Y2: m] :
% 2.69/1.55 ( ( G2 @ Y2 )
% 2.69/1.55 = ( F @ X2 ) ) )
% 2.69/1.55 = ( ? [H2: c > m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_m_m_c @ G2 @ H2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_157_function__factors__right,axiom,
% 2.69/1.55 ! [G2: c > monomo197243225tT_a_m,F: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( ( ! [X2: c] :
% 2.69/1.55 ? [Y2: c] :
% 2.69/1.55 ( ( G2 @ Y2 )
% 2.69/1.55 = ( F @ X2 ) ) )
% 2.69/1.55 = ( ? [H2: c > c] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_c1772230468_a_m_c @ G2 @ H2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_158_function__factors__right,axiom,
% 2.69/1.55 ! [G2: c > m,F: c > m] :
% 2.69/1.55 ( ( ! [X2: c] :
% 2.69/1.55 ? [Y2: c] :
% 2.69/1.55 ( ( G2 @ Y2 )
% 2.69/1.55 = ( F @ X2 ) ) )
% 2.69/1.55 = ( ? [H2: c > c] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_c_m_c @ G2 @ H2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_159_function__factors__right,axiom,
% 2.69/1.55 ! [G2: monomo197243225tT_a_m > m,F: c > m] :
% 2.69/1.55 ( ( ! [X2: c] :
% 2.69/1.55 ? [Y2: monomo197243225tT_a_m] :
% 2.69/1.55 ( ( G2 @ Y2 )
% 2.69/1.55 = ( F @ X2 ) ) )
% 2.69/1.55 = ( ? [H2: c > monomo197243225tT_a_m] :
% 2.69/1.55 ( F
% 2.69/1.55 = ( comp_M750374444_m_m_c @ G2 @ H2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_160_cinsert__cDiff__single,axiom,
% 2.69/1.55 ! [A2: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( counta472291938sert_c @ A2 @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) )
% 2.69/1.55 = ( counta472291938sert_c @ A2 @ A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_161_cDiff__idemp,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ B2 )
% 2.69/1.55 = ( minus_1646763425cset_c @ A @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_162_cDiff__cancel,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ( minus_1646763425cset_c @ A @ A )
% 2.69/1.55 = bot_bo1320844070cset_c ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_163_cDiff__cempty,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
% 2.69/1.55 = A ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_164_cempty__cDiff,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
% 2.69/1.55 = bot_bo1320844070cset_c ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_165_cDiff__cinsert,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,A2: c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ B2 ) )
% 2.69/1.55 = ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_166_cDiff__cinsert2,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,A2: c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ B2 ) )
% 2.69/1.55 = ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_167_cDiff__single__cinsert,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_168_cinsert__cDiff,axiom,
% 2.69/1.55 ! [A2: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ A )
% 2.69/1.55 => ( ( counta472291938sert_c @ A2 @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) )
% 2.69/1.55 = A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_169_order__refl,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c] : ( ord_le15364698cset_c @ X @ X ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_170_csubset__antisym,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B2 @ A )
% 2.69/1.55 => ( A = B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_171_all__not__cin__conv,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ( ! [X2: c] :
% 2.69/1.55 ~ ( countable_Set_cin_c @ X2 @ A ) )
% 2.69/1.55 = ( A = bot_bo1320844070cset_c ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_172_cempty__iff,axiom,
% 2.69/1.55 ! [C: c] :
% 2.69/1.55 ~ ( countable_Set_cin_c @ C @ bot_bo1320844070cset_c ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_173_cinsert__iff,axiom,
% 2.69/1.55 ! [A2: c,B: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ A ) )
% 2.69/1.55 = ( ( A2 = B )
% 2.69/1.55 | ( countable_Set_cin_c @ A2 @ A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_174_cinsertCI,axiom,
% 2.69/1.55 ! [A2: c,B2: countable_Set_cset_c,B: c] :
% 2.69/1.55 ( ( ~ ( countable_Set_cin_c @ A2 @ B2 )
% 2.69/1.55 => ( A2 = B ) )
% 2.69/1.55 => ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_175_csubsetI,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ! [X4: c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ X4 @ A )
% 2.69/1.55 => ( countable_Set_cin_c @ X4 @ B2 ) )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_176_cempty__fsubsetI,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ X ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_177_csubset__cempty,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
% 2.69/1.55 = ( A = bot_bo1320844070cset_c ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_178_cDiff__iff,axiom,
% 2.69/1.55 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 2.69/1.55 = ( ( countable_Set_cin_c @ C @ A )
% 2.69/1.55 & ~ ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_179_cDiffI,axiom,
% 2.69/1.55 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ C @ A )
% 2.69/1.55 => ( ~ ( countable_Set_cin_c @ C @ B2 )
% 2.69/1.55 => ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_180_cinsert__csubset,axiom,
% 2.69/1.55 ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 2.69/1.55 = ( ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 & ( ord_le15364698cset_c @ A @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_181_cinsert__cDiff1,axiom,
% 2.69/1.55 ! [X: c,B2: countable_Set_cset_c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 2.69/1.55 = ( minus_1646763425cset_c @ A @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_182_csubset__cinsert,axiom,
% 2.69/1.55 ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ~ ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
% 2.69/1.55 = ( ord_le15364698cset_c @ A @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_183_dual__order_Oantisym,axiom,
% 2.69/1.55 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ B @ A2 )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.55 => ( A2 = B ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_184_dual__order_Oeq__iff,axiom,
% 2.69/1.55 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 2.69/1.55 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ B3 @ A4 )
% 2.69/1.55 & ( ord_le15364698cset_c @ A4 @ B3 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_185_dual__order_Otrans,axiom,
% 2.69/1.55 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ B @ A2 )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ C @ B )
% 2.69/1.55 => ( ord_le15364698cset_c @ C @ A2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_186_dual__order_Orefl,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c] : ( ord_le15364698cset_c @ A2 @ A2 ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_187_order__trans,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ Y @ Z2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ X @ Z2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_188_order__class_Oorder_Oantisym,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B @ A2 )
% 2.69/1.55 => ( A2 = B ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_189_ord__le__eq__trans,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.55 => ( ( B = C )
% 2.69/1.55 => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_190_ord__eq__le__trans,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( A2 = B )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B @ C )
% 2.69/1.55 => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_191_order__class_Oorder_Oeq__iff,axiom,
% 2.69/1.55 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 2.69/1.55 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A4 @ B3 )
% 2.69/1.55 & ( ord_le15364698cset_c @ B3 @ A4 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_192_antisym__conv,axiom,
% 2.69/1.55 ! [Y: countable_Set_cset_c,X: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ Y @ X )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.55 = ( X = Y ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_193_eqcelem__imp__iff,axiom,
% 2.69/1.55 ! [X: c,Y: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( X = Y )
% 2.69/1.55 => ( ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 = ( countable_Set_cin_c @ Y @ A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_194_cset__eq__csubset,axiom,
% 2.69/1.55 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 2.69/1.55 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A3 @ B4 )
% 2.69/1.55 & ( ord_le15364698cset_c @ B4 @ A3 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_195_order_Otrans,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B @ C )
% 2.69/1.55 => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_196_eqcset__imp__iff,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,X: c] :
% 2.69/1.55 ( ( A = B2 )
% 2.69/1.55 => ( ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 = ( countable_Set_cin_c @ X @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_197_eq__refl,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( X = Y )
% 2.69/1.55 => ( ord_le15364698cset_c @ X @ Y ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_198_if__split__cin2,axiom,
% 2.69/1.55 ! [A2: c,Q: $o,X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ ( if_Cou1542198912cset_c @ Q @ X @ Y ) )
% 2.69/1.55 = ( ( Q
% 2.69/1.55 => ( countable_Set_cin_c @ A2 @ X ) )
% 2.69/1.55 & ( ~ Q
% 2.69/1.55 => ( countable_Set_cin_c @ A2 @ Y ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_199_if__split__cin1,axiom,
% 2.69/1.55 ! [Q: $o,X: c,Y: c,B: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ ( if_c @ Q @ X @ Y ) @ B )
% 2.69/1.55 = ( ( Q
% 2.69/1.55 => ( countable_Set_cin_c @ X @ B ) )
% 2.69/1.55 & ( ~ Q
% 2.69/1.55 => ( countable_Set_cin_c @ Y @ B ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_200_eq__cmem__trans,axiom,
% 2.69/1.55 ! [A2: c,B: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( A2 = B )
% 2.69/1.55 => ( ( countable_Set_cin_c @ B @ A )
% 2.69/1.55 => ( countable_Set_cin_c @ A2 @ A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_201_csubset__trans,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B2 @ C2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ C2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_202_csubset__refl,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_203_cequalityD2,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( A = B2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ B2 @ A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_204_cequalityD1,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( A = B2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_205_cequalityCE,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
% 2.69/1.55 ( ( A = B2 )
% 2.69/1.55 => ( ( ( countable_Set_cin_c @ C @ A )
% 2.69/1.55 => ~ ( countable_Set_cin_c @ C @ B2 ) )
% 2.69/1.55 => ~ ( ~ ( countable_Set_cin_c @ C @ A )
% 2.69/1.55 => ( countable_Set_cin_c @ C @ B2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_206_antisym,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ Y @ X )
% 2.69/1.55 => ( X = Y ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_207_cequalityE,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( A = B2 )
% 2.69/1.55 => ~ ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ~ ( ord_le15364698cset_c @ B2 @ A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_208_eq__iff,axiom,
% 2.69/1.55 ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : ( Y3 = Z ) )
% 2.69/1.55 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X2 @ Y2 )
% 2.69/1.55 & ( ord_le15364698cset_c @ Y2 @ X2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_209_csubsetD,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ( ( countable_Set_cin_c @ C @ A )
% 2.69/1.55 => ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_210_cset__eqI,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ! [X4: c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ X4 @ A )
% 2.69/1.55 = ( countable_Set_cin_c @ X4 @ B2 ) )
% 2.69/1.55 => ( A = B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_211_cin__mono,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,X: c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ( ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( countable_Set_cin_c @ X @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_212_ord__le__eq__subst,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ( F @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_213_ord__eq__le__subst,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( A2
% 2.69/1.55 = ( F @ B ) )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B @ C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le15364698cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_214_order__subst2,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ ( F @ B ) @ C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_215_order__subst1,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ ( F @ B ) )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B @ C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le15364698cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_216_equals__cemptyI,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ! [Y4: c] :
% 2.69/1.55 ~ ( countable_Set_cin_c @ Y4 @ A )
% 2.69/1.55 => ( A = bot_bo1320844070cset_c ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_217_equals__cemptyD,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,A2: c] :
% 2.69/1.55 ( ( A = bot_bo1320844070cset_c )
% 2.69/1.55 => ~ ( countable_Set_cin_c @ A2 @ A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_218_ex__cin__conv,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c] :
% 2.69/1.55 ( ( ? [X2: c] : ( countable_Set_cin_c @ X2 @ A ) )
% 2.69/1.55 = ( A != bot_bo1320844070cset_c ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_219_cemptyE,axiom,
% 2.69/1.55 ! [A2: c] :
% 2.69/1.55 ~ ( countable_Set_cin_c @ A2 @ bot_bo1320844070cset_c ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_220_mk__disjoint__cinsert,axiom,
% 2.69/1.55 ! [A2: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ A )
% 2.69/1.55 => ? [B5: countable_Set_cset_c] :
% 2.69/1.55 ( ( A
% 2.69/1.55 = ( counta472291938sert_c @ A2 @ B5 ) )
% 2.69/1.55 & ~ ( countable_Set_cin_c @ A2 @ B5 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_221_cinsert__absorb,axiom,
% 2.69/1.55 ! [A2: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ A )
% 2.69/1.55 => ( ( counta472291938sert_c @ A2 @ A )
% 2.69/1.55 = A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_222_cinsert__ident,axiom,
% 2.69/1.55 ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ~ ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ~ ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 => ( ( ( counta472291938sert_c @ X @ A )
% 2.69/1.55 = ( counta472291938sert_c @ X @ B2 ) )
% 2.69/1.55 = ( A = B2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_223_set__cinsert,axiom,
% 2.69/1.55 ! [X: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ~ ! [B5: countable_Set_cset_c] :
% 2.69/1.55 ( ( A
% 2.69/1.55 = ( counta472291938sert_c @ X @ B5 ) )
% 2.69/1.55 => ( countable_Set_cin_c @ X @ B5 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_224_cinsertI2,axiom,
% 2.69/1.55 ! [A2: c,B2: countable_Set_cset_c,B: c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ B2 )
% 2.69/1.55 => ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_225_cinsertI1,axiom,
% 2.69/1.55 ! [A2: c,B2: countable_Set_cset_c] : ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ A2 @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_226_cinsertE,axiom,
% 2.69/1.55 ! [A2: c,B: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ A ) )
% 2.69/1.55 => ( ( A2 != B )
% 2.69/1.55 => ( countable_Set_cin_c @ A2 @ A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_227_bot_Oextremum__uniqueI,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ bot_bo1320844070cset_c )
% 2.69/1.55 => ( A2 = bot_bo1320844070cset_c ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_228_bot_Oextremum__unique,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A2 @ bot_bo1320844070cset_c )
% 2.69/1.55 = ( A2 = bot_bo1320844070cset_c ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_229_bot_Oextremum,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A2 ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_230_cDiffD2,axiom,
% 2.69/1.55 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 2.69/1.55 => ~ ( countable_Set_cin_c @ C @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_231_cDiffD1,axiom,
% 2.69/1.55 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 2.69/1.55 => ( countable_Set_cin_c @ C @ A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_232_cDiffE,axiom,
% 2.69/1.55 ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
% 2.69/1.55 => ~ ( ( countable_Set_cin_c @ C @ A )
% 2.69/1.55 => ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_233_csubset__cinsertI2,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,B: c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ B2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_234_csubset__cinsertI,axiom,
% 2.69/1.55 ! [B2: countable_Set_cset_c,A2: c] : ( ord_le15364698cset_c @ B2 @ ( counta472291938sert_c @ A2 @ B2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_235_cinsert__mono,axiom,
% 2.69/1.55 ! [C2: countable_Set_cset_c,D2: countable_Set_cset_c,A2: c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ C2 @ D2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( counta472291938sert_c @ A2 @ C2 ) @ ( counta472291938sert_c @ A2 @ D2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_236_cDiff__csubset,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ A ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_237_double__cDiff,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ B2 @ C2 )
% 2.69/1.55 => ( ( minus_1646763425cset_c @ B2 @ ( minus_1646763425cset_c @ C2 @ A ) )
% 2.69/1.55 = A ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_238_cminus__mono,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,C2: countable_Set_cset_c,D2: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ C2 )
% 2.69/1.55 => ( ( ord_le15364698cset_c @ D2 @ B2 )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ ( minus_1646763425cset_c @ C2 @ D2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_239_csubset__cinsert__iff,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
% 2.69/1.55 = ( ( ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 ) )
% 2.69/1.55 & ( ~ ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ B2 ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_240_csingleton__iff,axiom,
% 2.69/1.55 ! [B: c,A2: c] :
% 2.69/1.55 ( ( countable_Set_cin_c @ B @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) )
% 2.69/1.55 = ( B = A2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_241_cinsert__cDiff__if,axiom,
% 2.69/1.55 ! [X: c,B2: countable_Set_cset_c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ( ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 2.69/1.55 = ( minus_1646763425cset_c @ A @ B2 ) ) )
% 2.69/1.55 & ( ~ ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
% 2.69/1.55 = ( counta472291938sert_c @ X @ ( minus_1646763425cset_c @ A @ B2 ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_242_csubset__csingletonD,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,X: c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) )
% 2.69/1.55 => ( ( A = bot_bo1320844070cset_c )
% 2.69/1.55 | ( A
% 2.69/1.55 = ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_243_cDiff__cinsert__absorb,axiom,
% 2.69/1.55 ! [X: c,A: countable_Set_cset_c] :
% 2.69/1.55 ( ~ ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) )
% 2.69/1.55 = A ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_244_cpsubset__finsert__iff,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
% 2.69/1.55 = ( ( ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A @ B2 ) )
% 2.69/1.55 & ( ~ ( countable_Set_cin_c @ X @ B2 )
% 2.69/1.55 => ( ( ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 ) )
% 2.69/1.55 & ( ~ ( countable_Set_cin_c @ X @ A )
% 2.69/1.55 => ( ord_le15364698cset_c @ A @ B2 ) ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_245_Greatest__equality,axiom,
% 2.69/1.55 ! [P: countable_Set_cset_c > $o,X: countable_Set_cset_c] :
% 2.69/1.55 ( ( P @ X )
% 2.69/1.55 => ( ! [Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( P @ Y4 )
% 2.69/1.55 => ( ord_le15364698cset_c @ Y4 @ X ) )
% 2.69/1.55 => ( ( order_1683649299cset_c @ P )
% 2.69/1.55 = X ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_246_GreatestI2__order,axiom,
% 2.69/1.55 ! [P: countable_Set_cset_c > $o,X: countable_Set_cset_c,Q: countable_Set_cset_c > $o] :
% 2.69/1.55 ( ( P @ X )
% 2.69/1.55 => ( ! [Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( P @ Y4 )
% 2.69/1.55 => ( ord_le15364698cset_c @ Y4 @ X ) )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c] :
% 2.69/1.55 ( ( P @ X4 )
% 2.69/1.55 => ( ! [Y5: countable_Set_cset_c] :
% 2.69/1.55 ( ( P @ Y5 )
% 2.69/1.55 => ( ord_le15364698cset_c @ Y5 @ X4 ) )
% 2.69/1.55 => ( Q @ X4 ) ) )
% 2.69/1.55 => ( Q @ ( order_1683649299cset_c @ P ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_247_le__rel__bool__arg__iff,axiom,
% 2.69/1.55 ( ord_le1376176871cset_c
% 2.69/1.55 = ( ^ [X5: $o > countable_Set_cset_c,Y6: $o > countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le15364698cset_c @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 2.69/1.55 & ( ord_le15364698cset_c @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_248_ord__eq__less__subst,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( A2
% 2.69/1.55 = ( F @ B ) )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ B @ C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_249_ord__less__eq__subst,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ( F @ B )
% 2.69/1.55 = C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_250_order__less__subst1,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ ( F @ B ) )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ B @ C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_251_order__less__subst2,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ ( F @ B ) @ C )
% 2.69/1.55 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.55 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_252_order_Oasym,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.55 => ~ ( ord_le1587667814cset_c @ B @ A2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_253_cpsubset__trans,axiom,
% 2.69/1.55 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A @ B2 )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ B2 @ C2 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_254_less__imp__neq,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ( X != Y ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_255_less__asym,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_256_less__asym_H,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.55 => ~ ( ord_le1587667814cset_c @ B @ A2 ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_257_less__trans,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ Y @ Z2 )
% 2.69/1.55 => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_258_less__irrefl,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c] :
% 2.69/1.55 ~ ( ord_le1587667814cset_c @ X @ X ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_259_ord__eq__less__trans,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( A2 = B )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ B @ C )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_260_ord__less__eq__trans,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.55 => ( ( B = C )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_261_dual__order_Oasym,axiom,
% 2.69/1.55 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ B @ A2 )
% 2.69/1.55 => ~ ( ord_le1587667814cset_c @ A2 @ B ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_262_less__imp__not__eq,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ( X != Y ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_263_less__not__sym,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_264_less__imp__not__eq2,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ( Y != X ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_265_less__imp__triv,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,P: $o] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ Y @ X )
% 2.69/1.55 => P ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_266_dual__order_Oirrefl,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c] :
% 2.69/1.55 ~ ( ord_le1587667814cset_c @ A2 @ A2 ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_267_order_Ostrict__trans,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ B @ C )
% 2.69/1.55 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_268_less__imp__not__less,axiom,
% 2.69/1.55 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.55 => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_269_dual__order_Ostrict__trans,axiom,
% 2.69/1.55 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.55 ( ( ord_le1587667814cset_c @ B @ A2 )
% 2.69/1.55 => ( ( ord_le1587667814cset_c @ C @ B )
% 2.69/1.55 => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).
% 2.69/1.55
% 2.69/1.55 thf(fact_270_order_Ostrict__implies__not__eq,axiom,
% 2.69/1.55 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.56 => ( A2 != B ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_271_dual__order_Ostrict__implies__not__eq,axiom,
% 2.69/1.56 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ B @ A2 )
% 2.69/1.56 => ( A2 != B ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_272_leD,axiom,
% 2.69/1.56 ! [Y: countable_Set_cset_c,X: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ Y @ X )
% 2.69/1.56 => ~ ( ord_le1587667814cset_c @ X @ Y ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_273_le__less,axiom,
% 2.69/1.56 ( ord_le15364698cset_c
% 2.69/1.56 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ X2 @ Y2 )
% 2.69/1.56 | ( X2 = Y2 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_274_less__le,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X2 @ Y2 )
% 2.69/1.56 & ( X2 != Y2 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_275_order__le__less__subst1,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A2 @ ( F @ B ) )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ B @ C )
% 2.69/1.56 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 2.69/1.56 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_276_order__le__less__subst2,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ ( F @ B ) @ C )
% 2.69/1.56 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 2.69/1.56 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.56 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_277_order__less__le__subst1,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A2 @ ( F @ B ) )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ B @ C )
% 2.69/1.56 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X4 @ Y4 )
% 2.69/1.56 => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_278_order__less__le__subst2,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ ( F @ B ) @ C )
% 2.69/1.56 => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ X4 @ Y4 )
% 2.69/1.56 => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.69/1.56 => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_279_le__neq__trans,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.56 => ( ( A2 != B )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A2 @ B ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_280_antisym__conv1,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.56 ( ~ ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.56 = ( X = Y ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_281_antisym__conv2,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.56 => ( ( ~ ( ord_le1587667814cset_c @ X @ Y ) )
% 2.69/1.56 = ( X = Y ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_282_less__imp__le,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.56 => ( ord_le15364698cset_c @ X @ Y ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_283_le__less__trans,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ Y @ Z2 )
% 2.69/1.56 => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_284_less__le__trans,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ Y @ Z2 )
% 2.69/1.56 => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_285_le__imp__less__or__eq,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X @ Y )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ X @ Y )
% 2.69/1.56 | ( X = Y ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_286_less__le__not__le,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ X2 @ Y2 )
% 2.69/1.56 & ~ ( ord_le15364698cset_c @ Y2 @ X2 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_287_order_Ostrict__trans1,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ B @ C )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_288_order_Ostrict__trans2,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ B @ C )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_289_order_Oorder__iff__strict,axiom,
% 2.69/1.56 ( ord_le15364698cset_c
% 2.69/1.56 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A4 @ B3 )
% 2.69/1.56 | ( A4 = B3 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_290_order_Ostrict__iff__order,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A4 @ B3 )
% 2.69/1.56 & ( A4 != B3 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_291_dual__order_Ostrict__trans1,axiom,
% 2.69/1.56 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ B @ A2 )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ C @ B )
% 2.69/1.56 => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_292_dual__order_Ostrict__trans2,axiom,
% 2.69/1.56 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ B @ A2 )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ C @ B )
% 2.69/1.56 => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_293_order_Ostrict__implies__order,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A2 @ B )
% 2.69/1.56 => ( ord_le15364698cset_c @ A2 @ B ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_294_dual__order_Oorder__iff__strict,axiom,
% 2.69/1.56 ( ord_le15364698cset_c
% 2.69/1.56 = ( ^ [B3: countable_Set_cset_c,A4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ B3 @ A4 )
% 2.69/1.56 | ( A4 = B3 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_295_dual__order_Ostrict__iff__order,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [B3: countable_Set_cset_c,A4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ B3 @ A4 )
% 2.69/1.56 & ( A4 != B3 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_296_dual__order_Ostrict__implies__order,axiom,
% 2.69/1.56 ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ B @ A2 )
% 2.69/1.56 => ( ord_le15364698cset_c @ B @ A2 ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_297_order_Onot__eq__order__implies__strict,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
% 2.69/1.56 ( ( A2 != B )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ A2 @ B )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A2 @ B ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_298_bot_Oextremum__strict,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c] :
% 2.69/1.56 ~ ( ord_le1587667814cset_c @ A2 @ bot_bo1320844070cset_c ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_299_bot_Onot__eq__extremum,axiom,
% 2.69/1.56 ! [A2: countable_Set_cset_c] :
% 2.69/1.56 ( ( A2 != bot_bo1320844070cset_c )
% 2.69/1.56 = ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A2 ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_300_cpsubsetD,axiom,
% 2.69/1.56 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A @ B2 )
% 2.69/1.56 => ( ( countable_Set_cin_c @ C @ A )
% 2.69/1.56 => ( countable_Set_cin_c @ C @ B2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_301_not__cpsubset__cempty,axiom,
% 2.69/1.56 ! [A: countable_Set_cset_c] :
% 2.69/1.56 ~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_302_cpsubset__eq,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A3 @ B4 )
% 2.69/1.56 & ( A3 != B4 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_303_less__cset__def,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [Xs: countable_Set_cset_c,Ys: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ Xs @ Ys )
% 2.69/1.56 & ( Xs != Ys ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_304_cpsubset__imp__fsubset,axiom,
% 2.69/1.56 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A @ B2 )
% 2.69/1.56 => ( ord_le15364698cset_c @ A @ B2 ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_305_cpsubset__csubset__trans,axiom,
% 2.69/1.56 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A @ B2 )
% 2.69/1.56 => ( ( ord_le15364698cset_c @ B2 @ C2 )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_306_csubset__cpsubset__trans,axiom,
% 2.69/1.56 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A @ B2 )
% 2.69/1.56 => ( ( ord_le1587667814cset_c @ B2 @ C2 )
% 2.69/1.56 => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_307_csubset__not__fsubset__eq,axiom,
% 2.69/1.56 ( ord_le1587667814cset_c
% 2.69/1.56 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le15364698cset_c @ A3 @ B4 )
% 2.69/1.56 & ~ ( ord_le15364698cset_c @ B4 @ A3 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_308_csubset__iff__pfsubset__eq,axiom,
% 2.69/1.56 ( ord_le15364698cset_c
% 2.69/1.56 = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A3 @ B4 )
% 2.69/1.56 | ( A3 = B4 ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(fact_309_cpsubset__imp__ex__fmem,axiom,
% 2.69/1.56 ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
% 2.69/1.56 ( ( ord_le1587667814cset_c @ A @ B2 )
% 2.69/1.56 => ? [B6: c] : ( countable_Set_cin_c @ B6 @ ( minus_1646763425cset_c @ B2 @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(help_If_2_1_If_001tf__c_T,axiom,
% 2.69/1.56 ! [X: c,Y: c] :
% 2.69/1.56 ( ( if_c @ $false @ X @ Y )
% 2.69/1.56 = Y ) ).
% 2.69/1.56
% 2.69/1.56 thf(help_If_1_1_If_001tf__c_T,axiom,
% 2.69/1.56 ! [X: c,Y: c] :
% 2.69/1.56 ( ( if_c @ $true @ X @ Y )
% 2.69/1.56 = X ) ).
% 2.69/1.56
% 2.69/1.56 thf(help_If_3_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
% 2.69/1.56 ! [P: $o] :
% 2.69/1.56 ( ( P = $true )
% 2.69/1.56 | ( P = $false ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(help_If_2_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.56 ( ( if_Cou1542198912cset_c @ $false @ X @ Y )
% 2.69/1.56 = Y ) ).
% 2.69/1.56
% 2.69/1.56 thf(help_If_1_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
% 2.69/1.56 ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
% 2.69/1.56 ( ( if_Cou1542198912cset_c @ $true @ X @ Y )
% 2.69/1.56 = X ) ).
% 2.69/1.56
% 2.69/1.56 thf(conj_0,conjecture,
% 2.69/1.56 ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
% 2.69/1.56 = ( f @ x ) ) ).
% 2.69/1.56 ------------------------
% 2.69/1.59 % (15542)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/2Mi)
% 2.69/1.59 % (15540)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/4Mi)
% 2.69/1.59 % (15544)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/275Mi)
% 2.69/1.59 % (15542)Instruction limit reached!
% 2.69/1.59 % (15542)------------------------------
% 2.69/1.59 % (15542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (15542)Termination reason: Unknown
% 2.69/1.59 % (15542)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (15542)Memory used [KB]: 1407
% 2.69/1.59 % (15542)Time elapsed: 0.003 s
% 2.69/1.59 % (15542)Instructions burned: 3 (million)
% 2.69/1.59 % (15542)------------------------------
% 2.69/1.59 % (15542)------------------------------
% 2.69/1.59 % (15540)Instruction limit reached!
% 2.69/1.59 % (15540)------------------------------
% 2.69/1.59 % (15540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (15540)Termination reason: Unknown
% 2.69/1.59 % (15540)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (15540)Memory used [KB]: 1407
% 2.69/1.59 % (15540)Time elapsed: 0.003 s
% 2.69/1.59 % (15540)Instructions burned: 5 (million)
% 2.69/1.59 % (15540)------------------------------
% 2.69/1.59 % (15540)------------------------------
% 2.69/1.60 % (15539)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/183Mi)
% 2.69/1.60 % (15541)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/27Mi)
% 2.69/1.60 % (15543)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/2Mi)
% 2.69/1.60 % (15545)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/18Mi)
% 2.76/1.60 % (15543)Instruction limit reached!
% 2.76/1.60 % (15543)------------------------------
% 2.76/1.60 % (15543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.60 % (15543)Termination reason: Unknown
% 2.76/1.60 % (15543)Termination phase: shuffling
% 2.76/1.60
% 2.76/1.60 % (15543)Memory used [KB]: 1407
% 2.76/1.60 % (15543)Time elapsed: 0.004 s
% 2.76/1.60 % (15543)Instructions burned: 3 (million)
% 2.76/1.60 % (15543)------------------------------
% 2.76/1.60 % (15543)------------------------------
% 2.76/1.60 % (15546)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/3Mi)
% 2.76/1.60 % (15547)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/37Mi)
% 2.76/1.60 % (15546)Instruction limit reached!
% 2.76/1.60 % (15546)------------------------------
% 2.76/1.60 % (15546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.60 % (15546)Termination reason: Unknown
% 2.76/1.60 % (15546)Termination phase: shuffling
% 2.76/1.60
% 2.76/1.60 % (15546)Memory used [KB]: 1407
% 2.76/1.60 % (15546)Time elapsed: 0.003 s
% 2.76/1.60 % (15546)Instructions burned: 5 (million)
% 2.76/1.60 % (15546)------------------------------
% 2.76/1.60 % (15546)------------------------------
% 2.76/1.61 % (15545)Instruction limit reached!
% 2.76/1.61 % (15545)------------------------------
% 2.76/1.61 % (15545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.61 % (15545)Termination reason: Unknown
% 2.76/1.61 % (15545)Termination phase: Property scanning
% 2.76/1.61
% 2.76/1.61 % (15545)Memory used [KB]: 1535
% 2.76/1.61 % (15545)Time elapsed: 0.013 s
% 2.76/1.61 % (15545)Instructions burned: 18 (million)
% 2.76/1.61 % (15545)------------------------------
% 2.76/1.61 % (15545)------------------------------
% 2.76/1.61 % (15544)First to succeed.
% 2.76/1.61 % (15541)Instruction limit reached!
% 2.76/1.61 % (15541)------------------------------
% 2.76/1.61 % (15541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.61 % (15541)Termination reason: Unknown
% 2.76/1.61 % (15549)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15252 for (2999ds/3Mi)
% 2.76/1.61 % (15541)Termination phase: Property scanning
% 2.76/1.61
% 2.76/1.61 % (15541)Memory used [KB]: 1535
% 2.76/1.61 % (15541)Time elapsed: 0.017 s
% 2.76/1.61 % (15541)Instructions burned: 27 (million)
% 2.76/1.61 % (15541)------------------------------
% 2.76/1.61 % (15541)------------------------------
% 2.76/1.61 % (15549)Instruction limit reached!
% 2.76/1.61 % (15549)------------------------------
% 2.76/1.61 % (15549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.61 % (15549)Termination reason: Unknown
% 2.76/1.61 % (15549)Termination phase: shuffling
% 2.76/1.61
% 2.76/1.61 % (15549)Memory used [KB]: 1407
% 2.76/1.61 % (15549)Time elapsed: 0.002 s
% 2.76/1.61 % (15549)Instructions burned: 3 (million)
% 2.76/1.61 % (15549)------------------------------
% 2.76/1.61 % (15549)------------------------------
% 2.76/1.61 % (15544)Refutation found. Thanks to Tanya!
% 2.76/1.61 % SZS status Theorem for DTF2THF_15252
% 2.76/1.61 % SZS output start Proof for DTF2THF_15252
% 2.76/1.61 thf(type_def_5, type, c: $tType).
% 2.76/1.61 thf(type_def_6, type, countable_Set_cset_c: $tType).
% 2.76/1.61 thf(type_def_8, type, monomo197243225tT_a_m: $tType).
% 2.76/1.61 thf(type_def_9, type, m: $tType).
% 2.76/1.61 thf(type_def_10, type, counta191869203tT_a_m: $tType).
% 2.76/1.61 thf(func_def_0, type, counta191869203tT_a_m: $tType).
% 2.76/1.61 thf(func_def_1, type, monomo197243225tT_a_m: $tType).
% 2.76/1.61 thf(func_def_2, type, countable_Set_cset_c: $tType).
% 2.76/1.61 thf(func_def_3, type, m: $tType).
% 2.76/1.61 thf(func_def_4, type, c: $tType).
% 2.76/1.61 thf(func_def_5, type, countable_Set_cin_c: c > countable_Set_cset_c > $o).
% 2.76/1.61 thf(func_def_6, type, counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_7, type, comp_M864375327_a_m_c: (monomo197243225tT_a_m > monomo197243225tT_a_m) > (c > monomo197243225tT_a_m) > c > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_8, type, comp_M1062614966_m_c_c: (monomo197243225tT_a_m > c) > (c > monomo197243225tT_a_m) > c > c).
% 2.76/1.61 thf(func_def_9, type, comp_M1944986301tT_a_m: (monomo197243225tT_a_m > m) > (monomo197243225tT_a_m > monomo197243225tT_a_m) > monomo197243225tT_a_m > m).
% 2.76/1.61 thf(func_def_10, type, comp_M750374444_m_m_c: (monomo197243225tT_a_m > m) > (c > monomo197243225tT_a_m) > c > m).
% 2.76/1.61 thf(func_def_11, type, comp_M750374454_m_m_m: (monomo197243225tT_a_m > m) > (m > monomo197243225tT_a_m) > m > m).
% 2.76/1.61 thf(func_def_12, type, comp_c1772230468_a_m_c: (c > monomo197243225tT_a_m) > (c > c) > c > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_13, type, comp_c_c_c: (c > c) > (c > c) > c > c).
% 2.76/1.61 thf(func_def_14, type, comp_c997395372tT_a_m: (c > m) > (monomo197243225tT_a_m > c) > monomo197243225tT_a_m > m).
% 2.76/1.61 thf(func_def_15, type, comp_c_m_c: (c > m) > (c > c) > c > m).
% 2.76/1.61 thf(func_def_16, type, comp_c_m_m: (c > m) > (m > c) > m > m).
% 2.76/1.61 thf(func_def_17, type, comp_m1038691662_a_m_c: (m > monomo197243225tT_a_m) > (c > m) > c > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_18, type, comp_m_c_c: (m > c) > (c > m) > c > c).
% 2.76/1.61 thf(func_def_19, type, comp_m263856566tT_a_m: (m > m) > (monomo197243225tT_a_m > m) > monomo197243225tT_a_m > m).
% 2.76/1.61 thf(func_def_20, type, comp_m_m_c: (m > m) > (c > m) > c > m).
% 2.76/1.61 thf(func_def_21, type, comp_m_m_m: (m > m) > (m > m) > m > m).
% 2.76/1.61 thf(func_def_22, type, minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_23, type, if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_24, type, if_c: $o > c > c > c).
% 2.76/1.61 thf(func_def_25, type, monomo2081011572_m_m_a: (counta191869203tT_a_m > (monomo197243225tT_a_m > m) > m) > counta191869203tT_a_m > (monomo197243225tT_a_m > monomo197243225tT_a_m) > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_26, type, monomo463139869_c_m_a: (countable_Set_cset_c > (c > m) > m) > countable_Set_cset_c > (c > monomo197243225tT_a_m) > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_27, type, monomo412532791tT_m_a: m > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_28, type, monomo624345106et_a_m: monomo197243225tT_a_m > m).
% 2.76/1.61 thf(func_def_29, type, bot_bo1320844070cset_c: countable_Set_cset_c).
% 2.76/1.61 thf(func_def_30, type, ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o).
% 2.76/1.61 thf(func_def_31, type, ord_le1376176871cset_c: ($o > countable_Set_cset_c) > ($o > countable_Set_cset_c) > $o).
% 2.76/1.61 thf(func_def_32, type, ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o).
% 2.76/1.61 thf(func_def_33, type, order_1683649299cset_c: (countable_Set_cset_c > $o) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_34, type, f: c > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_35, type, mergec: countable_Set_cset_c > (c > m) > m).
% 2.76/1.61 thf(func_def_36, type, x: c).
% 2.76/1.61 thf(func_def_48, type, sK0: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_49, type, sK1: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_50, type, sK2: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_51, type, sK3: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_52, type, sK4: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_53, type, sK5: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_54, type, sK6: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_55, type, sK7: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_56, type, sK8: countable_Set_cset_c > c).
% 2.76/1.61 thf(func_def_57, type, sK9: (c > m) > (c > monomo197243225tT_a_m) > monomo197243225tT_a_m > m).
% 2.76/1.61 thf(func_def_58, type, sK10: (c > m) > (c > monomo197243225tT_a_m) > c).
% 2.76/1.61 thf(func_def_59, type, sK11: (c > m) > (c > monomo197243225tT_a_m) > c).
% 2.76/1.61 thf(func_def_60, type, sK12: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_61, type, sK13: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_62, type, sK14: c > (monomo197243225tT_a_m > m) > (c > m) > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_63, type, sK15: (monomo197243225tT_a_m > m) > (c > m) > c > monomo197243225tT_a_m).
% 2.76/1.61 thf(func_def_64, type, sK16: (monomo197243225tT_a_m > m) > (c > m) > c).
% 2.76/1.61 thf(func_def_65, type, sK17: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_66, type, sK18: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_67, type, sK19: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_68, type, sK20: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_69, type, sK21: monomo197243225tT_a_m > m).
% 2.76/1.61 thf(func_def_70, type, sK22: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_71, type, sK23: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_72, type, sK24: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_73, type, sK25: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_74, type, sK26: countable_Set_cset_c > c).
% 2.76/1.61 thf(func_def_75, type, sK27: (monomo197243225tT_a_m > $o) > m).
% 2.76/1.61 thf(func_def_76, type, sK28: countable_Set_cset_c > c).
% 2.76/1.61 thf(func_def_77, type, sK29: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_78, type, sK30: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_79, type, sK31: countable_Set_cset_c > countable_Set_cset_c > c).
% 2.76/1.61 thf(func_def_80, type, sK32: c > countable_Set_cset_c > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_81, type, sK33: countable_Set_cset_c > c > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_82, type, sK34: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_83, type, sK35: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_84, type, sK36: countable_Set_cset_c > countable_Set_cset_c > c).
% 2.76/1.61 thf(func_def_85, type, sK37: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_86, type, sK38: (countable_Set_cset_c > countable_Set_cset_c) > countable_Set_cset_c).
% 2.76/1.61 thf(func_def_88, type, ph40: !>[X0: $tType]:(X0)).
% 2.76/1.61 thf(f1268,plain,(
% 2.76/1.61 $false),
% 2.76/1.61 inference(subsumption_resolution,[status(thm)],[f1267,f999])).
% 2.76/1.61 thf(f999,plain,(
% 2.76/1.61 ( ! [X0 : monomo197243225tT_a_m] : (((monomo412532791tT_m_a @ (monomo624345106et_a_m @ X0)) = X0)) )),
% 2.76/1.61 inference(cnf_transformation,[status(thm)],[f711])).
% 2.76/1.61 thf(f711,plain,(
% 2.76/1.61 ! [X0 : monomo197243225tT_a_m] : ((monomo412532791tT_m_a @ (monomo624345106et_a_m @ X0)) = X0)),
% 2.76/1.61 inference(rectify,[status(thm)],[f87])).
% 2.76/1.61 thf(f87,axiom,(
% 2.76/1.61 ! [X8 : monomo197243225tT_a_m] : ((monomo412532791tT_m_a @ (monomo624345106et_a_m @ X8)) = X8)),
% 2.76/1.61 file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_86_nondetT_Oexhaust__sel)).
% 2.76/1.61 thf(f1267,plain,(
% 2.76/1.61 ((f @ x) != (monomo412532791tT_m_a @ (monomo624345106et_a_m @ (f @ x))))),
% 2.76/1.61 inference(beta_eta_normalization,[status(thm)],[f1266])).
% 2.76/1.61 thf(f1266,plain,(
% 2.76/1.61 ((f @ x) != (monomo412532791tT_m_a @ ((^[Y0 : c]: (monomo624345106et_a_m @ (f @ Y0))) @ x)))),
% 2.76/1.61 inference(forward_demodulation,[status(thm)],[f1265,f1057])).
% 2.76/1.61 thf(f1057,plain,(
% 2.76/1.61 ( ! [X0 : c,X1 : c > m] : (((mergec @ (counta472291938sert_c @ X0 @ bot_bo1320844070cset_c) @ X1) = (X1 @ X0))) )),
% 2.76/1.61 inference(cnf_transformation,[status(thm)],[f1])).
% 2.76/1.61 thf(f1,axiom,(
% 2.76/1.61 ! [X0 : c,X1 : c > m] : ((mergec @ (counta472291938sert_c @ X0 @ bot_bo1320844070cset_c) @ X1) = (X1 @ X0))),
% 2.76/1.61 file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_0_mergec__single)).
% 2.76/1.61 thf(f1265,plain,(
% 2.76/1.61 ((f @ x) != (monomo412532791tT_m_a @ (mergec @ (counta472291938sert_c @ x @ bot_bo1320844070cset_c) @ (^[Y0 : c]: (monomo624345106et_a_m @ (f @ Y0))))))),
% 2.76/1.61 inference(beta_eta_normalization,[status(thm)],[f1180])).
% 2.76/1.61 thf(f1180,plain,(
% 2.76/1.61 ((f @ x) != ((^[Y0 : countable_Set_cset_c > (c > m) > m]: ((^[Y1 : countable_Set_cset_c]: ((^[Y2 : c > monomo197243225tT_a_m]: (monomo412532791tT_m_a @ (Y0 @ Y1 @ ((^[Y3 : monomo197243225tT_a_m > m]: ((^[Y4 : c > monomo197243225tT_a_m]: ((^[Y5 : c]: (Y3 @ (Y4 @ Y5))))))) @ monomo624345106et_a_m @ Y2)))))))) @ mergec @ (counta472291938sert_c @ x @ bot_bo1320844070cset_c) @ f))),
% 2.76/1.61 inference(definition_unfolding,[status(thm)],[f1095,f1154])).
% 2.76/1.61 thf(f1154,plain,(
% 2.76/1.61 (monomo463139869_c_m_a = (^[Y0 : countable_Set_cset_c > (c > m) > m]: ((^[Y1 : countable_Set_cset_c]: ((^[Y2 : c > monomo197243225tT_a_m]: (monomo412532791tT_m_a @ (Y0 @ Y1 @ ((^[Y3 : monomo197243225tT_a_m > m]: ((^[Y4 : c > monomo197243225tT_a_m]: ((^[Y5 : c]: (Y3 @ (Y4 @ Y5))))))) @ monomo624345106et_a_m @ Y2)))))))))),
% 2.76/1.61 inference(definition_unfolding,[status(thm)],[f1009,f1012])).
% 2.76/1.61 thf(f1012,plain,(
% 2.76/1.61 (comp_M750374444_m_m_c = (^[Y0 : monomo197243225tT_a_m > m]: ((^[Y1 : c > monomo197243225tT_a_m]: ((^[Y2 : c]: (Y0 @ (Y1 @ Y2))))))))),
% 2.76/1.61 inference(cnf_transformation,[status(thm)],[f602])).
% 2.76/1.61 thf(f602,plain,(
% 2.76/1.61 (comp_M750374444_m_m_c = (^[Y0 : monomo197243225tT_a_m > m]: ((^[Y1 : c > monomo197243225tT_a_m]: ((^[Y2 : c]: (Y0 @ (Y1 @ Y2))))))))),
% 2.76/1.61 inference(fool_elimination,[status(thm)],[f601])).
% 2.76/1.61 thf(f601,plain,(
% 2.76/1.61 (comp_M750374444_m_m_c = (^[X0 : monomo197243225tT_a_m > m, X1 : c > monomo197243225tT_a_m, X2 : c] : (X0 @ (X1 @ X2))))),
% 2.76/1.61 inference(rectify,[status(thm)],[f18])).
% 2.76/1.61 thf(f18,axiom,(
% 2.76/1.61 (comp_M750374444_m_m_c = (^[X11 : monomo197243225tT_a_m > m, X12 : c > monomo197243225tT_a_m, X13 : c] : (X11 @ (X12 @ X13))))),
% 2.76/1.61 file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_17_comp__apply)).
% 2.76/1.61 thf(f1009,plain,(
% 2.76/1.61 (monomo463139869_c_m_a = (^[Y0 : countable_Set_cset_c > (c > m) > m]: ((^[Y1 : countable_Set_cset_c]: ((^[Y2 : c > monomo197243225tT_a_m]: (monomo412532791tT_m_a @ (Y0 @ Y1 @ (comp_M750374444_m_m_c @ monomo624345106et_a_m @ Y2)))))))))),
% 2.76/1.61 inference(cnf_transformation,[status(thm)],[f334])).
% 2.76/1.61 thf(f334,plain,(
% 2.76/1.61 (monomo463139869_c_m_a = (^[Y0 : countable_Set_cset_c > (c > m) > m]: ((^[Y1 : countable_Set_cset_c]: ((^[Y2 : c > monomo197243225tT_a_m]: (monomo412532791tT_m_a @ (Y0 @ Y1 @ (comp_M750374444_m_m_c @ monomo624345106et_a_m @ Y2)))))))))),
% 2.76/1.61 inference(fool_elimination,[status(thm)],[f333])).
% 2.76/1.61 thf(f333,plain,(
% 2.76/1.61 (monomo463139869_c_m_a = (^[X0 : countable_Set_cset_c > (c > m) > m, X1 : countable_Set_cset_c, X2 : c > monomo197243225tT_a_m] : (monomo412532791tT_m_a @ (X0 @ X1 @ (comp_M750374444_m_m_c @ monomo624345106et_a_m @ X2)))))),
% 2.76/1.61 inference(rectify,[status(thm)],[f20])).
% 2.76/1.61 thf(f20,axiom,(
% 2.76/1.61 (monomo463139869_c_m_a = (^[X14 : countable_Set_cset_c > (c > m) > m, X15 : countable_Set_cset_c, X11 : c > monomo197243225tT_a_m] : (monomo412532791tT_m_a @ (X14 @ X15 @ (comp_M750374444_m_m_c @ monomo624345106et_a_m @ X11)))))),
% 2.76/1.61 file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',fact_19_cset__nondetM__base_Oaltc__nondet__def)).
% 2.76/1.61 thf(f1095,plain,(
% 2.76/1.61 ((monomo463139869_c_m_a @ mergec @ (counta472291938sert_c @ x @ bot_bo1320844070cset_c) @ f) != (f @ x))),
% 2.76/1.61 inference(cnf_transformation,[status(thm)],[f667])).
% 2.76/1.61 thf(f667,plain,(
% 2.76/1.61 ((monomo463139869_c_m_a @ mergec @ (counta472291938sert_c @ x @ bot_bo1320844070cset_c) @ f) != (f @ x))),
% 2.76/1.61 inference(flattening,[status(thm)],[f317])).
% 2.76/1.61 thf(f317,negated_conjecture,(
% 2.76/1.61 ~((monomo463139869_c_m_a @ mergec @ (counta472291938sert_c @ x @ bot_bo1320844070cset_c) @ f) = (f @ x))),
% 2.76/1.61 inference(negated_conjecture,[status(cth)],[f316])).
% 2.76/1.61 thf(f316,conjecture,(
% 2.76/1.61 ((monomo463139869_c_m_a @ mergec @ (counta472291938sert_c @ x @ bot_bo1320844070cset_c) @ f) = (f @ x))),
% 2.76/1.61 file('/export/starexec/sandbox/tmp/tmp.5dat82mrWO/DTF2THF_15252.p',conj_0)).
% 2.76/1.61 % SZS output end Proof for DTF2THF_15252
% 2.76/1.61 % (15544)------------------------------
% 2.76/1.61 % (15544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.61 % (15544)Termination reason: Refutation
% 2.76/1.61
% 2.76/1.61 % (15544)Memory used [KB]: 6524
% 2.76/1.61 % (15544)Time elapsed: 0.023 s
% 2.76/1.61 % (15544)Instructions burned: 65 (million)
% 2.76/1.61 % (15544)------------------------------
% 2.76/1.61 % (15544)------------------------------
% 2.76/1.61 % (15538)Success in time 0.051 s
%------------------------------------------------------------------------------