TSTP Solution File: ITP112^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP112^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 : Thu Aug 31 03:18:20 EDT 2023
% Result : Timeout 299.79s 300.14s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : ITP112^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.20 % Command : do_cvc5 %s %d
% 0.19/0.41 % Computer : n031.cluster.edu
% 0.19/0.41 % Model : x86_64 x86_64
% 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.41 % Memory : 8042.1875MB
% 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Sun Aug 27 11:23:24 EDT 2023
% 0.19/0.41 % CPUTime :
% 0.25/0.60 %----Proving TH0
% 0.25/0.61 %------------------------------------------------------------------------------
% 0.25/0.61 % File : ITP112^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.61 % Domain : Interactive Theorem Proving
% 0.25/0.61 % Problem : Sledgehammer Lower_Semicontinuous problem prob_385__6250846_1
% 0.25/0.61 % Version : Especial.
% 0.25/0.61 % English :
% 0.25/0.61
% 0.25/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.61 % Source : [Des21]
% 0.25/0.61 % Names : Lower_Semicontinuous/prob_385__6250846_1 [Des21]
% 0.25/0.61
% 0.25/0.61 % Status : Theorem
% 0.25/0.61 % Rating : 0.69 v8.1.0, 0.73 v7.5.0
% 0.25/0.61 % Syntax : Number of formulae : 451 ( 130 unt; 95 typ; 0 def)
% 0.25/0.61 % Number of atoms : 1312 ( 382 equ; 0 cnn)
% 0.25/0.61 % Maximal formula atoms : 81 ( 3 avg)
% 0.25/0.61 % Number of connectives : 4092 ( 116 ~; 34 |; 57 &;3135 @)
% 0.25/0.61 % ( 0 <=>; 750 =>; 0 <=; 0 <~>)
% 0.25/0.61 % Maximal formula depth : 34 ( 8 avg)
% 0.25/0.61 % Number of types : 13 ( 12 usr)
% 0.25/0.61 % Number of type conns : 500 ( 500 >; 0 *; 0 +; 0 <<)
% 0.25/0.61 % Number of symbols : 84 ( 83 usr; 6 con; 0-3 aty)
% 0.25/0.61 % Number of variables : 1297 ( 136 ^;1117 !; 44 ?;1297 :)
% 0.25/0.61 % SPC : TH0_THM_EQU_NAR
% 0.25/0.61
% 0.25/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:41:16.220
% 0.25/0.61 %------------------------------------------------------------------------------
% 0.25/0.61 % Could-be-implicit typings (12)
% 0.25/0.61 thf(ty_n_t__Filter__Ofilter_It__Extended____Real__Oereal_J,type,
% 0.25/0.61 filter2049122004_ereal: $tType ).
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% 0.25/0.61
% 0.25/0.61 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 0.25/0.61
% 0.25/0.61 thf(ty_n_t__Filter__Ofilter_It__Int__Oint_J,type,
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% 0.25/0.61
% 0.25/0.61 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
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% 0.25/0.61
% 0.25/0.61 thf(ty_n_t__Filter__Ofilter_Itf__a_J,type,
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% 0.25/0.61 thf(ty_n_t__Int__Oint,type,
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% 0.25/0.61
% 0.25/0.61 thf(ty_n_tf__a,type,
% 0.25/0.61 a: $tType ).
% 0.25/0.61
% 0.25/0.61 % Explicit typings (83)
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% 0.25/0.61 extend1289208545_ereal: extended_ereal ).
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% 0.25/0.61
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% 0.25/0.61 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Int__Oint,type,
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% 0.25/0.61 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.25/0.61 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
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% 0.25/0.61 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.25/0.61 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001tf__a,type,
% 0.25/0.61 filterlim_nat_a: ( nat > a ) > filter_a > filter_nat > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Extended____Real__Oereal_001t__Extended____Real__Oereal_001t__Nat__Onat,type,
% 0.25/0.61 comp_E1308517939al_nat: ( extended_ereal > extended_ereal ) > ( nat > extended_ereal ) > nat > extended_ereal ).
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Extended____Real__Oereal_001t__Int__Oint_001t__Nat__Onat,type,
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Extended____Real__Oereal_001t__Nat__Onat,type,
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001tf__a_001t__Nat__Onat,type,
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Extended____Real__Oereal_001t__Nat__Onat,type,
% 0.25/0.61 comp_r1410008527al_nat: ( real > extended_ereal ) > ( nat > real ) > nat > extended_ereal ).
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Int__Oint_001t__Nat__Onat,type,
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% 0.25/0.61 thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Extended____Real__Oereal,type,
% 0.25/0.61 topolo1069469409_ereal: ( nat > extended_ereal ) > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 0.25/0.61 topolo411883481eq_int: ( nat > int ) > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 0.25/0.61 topolo1922093437eq_nat: ( nat > nat ) > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 0.25/0.61 topolo144289241q_real: ( nat > real ) > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Extended____Real__Oereal,type,
% 0.25/0.61 topolo2140997059_ereal: extended_ereal > filter2049122004_ereal ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Int__Oint,type,
% 0.25/0.61 topolo54776183ds_int: int > filter_int ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Nat__Onat,type,
% 0.25/0.61 topolo1564986139ds_nat: nat > filter_nat ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 0.25/0.61 topolo1664202871s_real: real > filter_real ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001tf__a,type,
% 0.25/0.61 topolo705128563nhds_a: a > filter_a ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_member_001t__Extended____Real__Oereal,type,
% 0.25/0.61 member1900190071_ereal: extended_ereal > set_Extended_ereal > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_c_member_001t__Real__Oreal,type,
% 0.25/0.61 member_real: real > set_real > $o ).
% 0.25/0.61
% 0.25/0.61 thf(sy_v_A____,type,
% 0.25/0.61 a2: extended_ereal ).
% 0.25/0.61
% 0.25/0.61 thf(sy_v_f,type,
% 0.25/0.61 f: a > extended_ereal ).
% 0.25/0.61
% 0.25/0.61 thf(sy_v_x0,type,
% 0.25/0.61 x0: a ).
% 0.25/0.61
% 0.25/0.61 thf(sy_v_x____,type,
% 0.25/0.61 x: nat > a ).
% 0.25/0.61
% 0.25/0.61 % Relevant facts (355)
% 0.25/0.61 thf(fact_0_x__def_I1_J,axiom,
% 0.25/0.61 filterlim_nat_a @ x @ ( topolo705128563nhds_a @ x0 ) @ at_top_nat ).
% 0.25/0.61
% 0.25/0.61 % x_def(1)
% 0.25/0.61 thf(fact_1_x__def_I2_J,axiom,
% 0.25/0.61 filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat ).
% 0.25/0.61
% 0.25/0.61 % x_def(2)
% 0.25/0.61 thf(fact_2__092_060open_062_092_060And_062F_O_A_I_If_A_092_060circ_062_Ax_J_A_092_060longlongrightarrow_062_AA_J_AF_A_092_060Longrightarrow_062_A_I_I_092_060lambda_062xa_O_A_N_A_If_A_092_060circ_062_Ax_J_Axa_J_A_092_060longlongrightarrow_062_A_N_AA_J_AF_092_060close_062,axiom,
% 0.25/0.61 ! [F: filter_nat] :
% 0.25/0.61 ( ( filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ F )
% 0.25/0.61 => ( filter1531173832_ereal
% 0.25/0.61 @ ^ [X: nat] : ( uminus1208298309_ereal @ ( comp_a1112243075al_nat @ f @ x @ X ) )
% 0.25/0.61 @ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
% 0.25/0.61 @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % \<open>\<And>F. ((f \<circ> x) \<longlongrightarrow> A) F \<Longrightarrow> ((\<lambda>xa. - (f \<circ> x) xa) \<longlongrightarrow> - A) F\<close>
% 0.25/0.61 thf(fact_3_lsc,axiom,
% 0.25/0.61 ( lower_191460856_ereal @ x0
% 0.25/0.61 @ ^ [X: a] : ( uminus1208298309_ereal @ ( f @ X ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc
% 0.25/0.61 thf(fact_4_tendsto__uminus__ereal,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,X2: extended_ereal,F: filter_nat] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ X2 ) @ F )
% 0.25/0.61 => ( filter1531173832_ereal
% 0.25/0.61 @ ^ [X: nat] : ( uminus1208298309_ereal @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X2 ) )
% 0.25/0.61 @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_uminus_ereal
% 0.25/0.61 thf(fact_5_tendsto__const,axiom,
% 0.25/0.61 ! [K: real,F: filter_real] :
% 0.25/0.61 ( filterlim_real_real
% 0.25/0.61 @ ^ [X: real] : K
% 0.25/0.61 @ ( topolo1664202871s_real @ K )
% 0.25/0.61 @ F ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_const
% 0.25/0.61 thf(fact_6_tendsto__const,axiom,
% 0.25/0.61 ! [K: real,F: filter_nat] :
% 0.25/0.61 ( filterlim_nat_real
% 0.25/0.61 @ ^ [X: nat] : K
% 0.25/0.61 @ ( topolo1664202871s_real @ K )
% 0.25/0.61 @ F ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_const
% 0.25/0.61 thf(fact_7_tendsto__const,axiom,
% 0.25/0.61 ! [K: extended_ereal,F: filter_nat] :
% 0.25/0.61 ( filter1531173832_ereal
% 0.25/0.61 @ ^ [X: nat] : K
% 0.25/0.61 @ ( topolo2140997059_ereal @ K )
% 0.25/0.61 @ F ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_const
% 0.25/0.61 thf(fact_8_tendsto__const,axiom,
% 0.25/0.61 ! [K: a,F: filter_nat] :
% 0.25/0.61 ( filterlim_nat_a
% 0.25/0.61 @ ^ [X: nat] : K
% 0.25/0.61 @ ( topolo705128563nhds_a @ K )
% 0.25/0.61 @ F ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_const
% 0.25/0.61 thf(fact_9_ereal__Lim__uminus,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,F0: extended_ereal,Net: filter_nat] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ F0 ) @ Net )
% 0.25/0.61 = ( filter1531173832_ereal
% 0.25/0.61 @ ^ [X: nat] : ( uminus1208298309_ereal @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ F0 ) )
% 0.25/0.61 @ Net ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_Lim_uminus
% 0.25/0.61 thf(fact_10_LIMSEQ__const__iff,axiom,
% 0.25/0.61 ! [K: real,L: real] :
% 0.25/0.61 ( ( filterlim_nat_real
% 0.25/0.61 @ ^ [N: nat] : K
% 0.25/0.61 @ ( topolo1664202871s_real @ L )
% 0.25/0.61 @ at_top_nat )
% 0.25/0.61 = ( K = L ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_const_iff
% 0.25/0.61 thf(fact_11_LIMSEQ__const__iff,axiom,
% 0.25/0.61 ! [K: extended_ereal,L: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal
% 0.25/0.61 @ ^ [N: nat] : K
% 0.25/0.61 @ ( topolo2140997059_ereal @ L )
% 0.25/0.61 @ at_top_nat )
% 0.25/0.61 = ( K = L ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_const_iff
% 0.25/0.61 thf(fact_12_LIMSEQ__const__iff,axiom,
% 0.25/0.61 ! [K: a,L: a] :
% 0.25/0.61 ( ( filterlim_nat_a
% 0.25/0.61 @ ^ [N: nat] : K
% 0.25/0.61 @ ( topolo705128563nhds_a @ L )
% 0.25/0.61 @ at_top_nat )
% 0.25/0.61 = ( K = L ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_const_iff
% 0.25/0.61 thf(fact_13_tendsto__minus__cancel,axiom,
% 0.25/0.61 ! [F2: real > real,A: real,F: filter_real] :
% 0.25/0.61 ( ( filterlim_real_real
% 0.25/0.61 @ ^ [X: real] : ( uminus_uminus_real @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo1664202871s_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.61 @ F )
% 0.25/0.61 => ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ A ) @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_minus_cancel
% 0.25/0.61 thf(fact_14_tendsto__minus__cancel,axiom,
% 0.25/0.61 ! [F2: nat > real,A: real,F: filter_nat] :
% 0.25/0.61 ( ( filterlim_nat_real
% 0.25/0.61 @ ^ [X: nat] : ( uminus_uminus_real @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo1664202871s_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.61 @ F )
% 0.25/0.61 => ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ A ) @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_minus_cancel
% 0.25/0.61 thf(fact_15_tendsto__minus__cancel__left,axiom,
% 0.25/0.61 ! [F2: real > real,Y: real,F: filter_real] :
% 0.25/0.61 ( ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ ( uminus_uminus_real @ Y ) ) @ F )
% 0.25/0.61 = ( filterlim_real_real
% 0.25/0.61 @ ^ [X: real] : ( uminus_uminus_real @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo1664202871s_real @ Y )
% 0.25/0.61 @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_minus_cancel_left
% 0.25/0.61 thf(fact_16_tendsto__minus__cancel__left,axiom,
% 0.25/0.61 ! [F2: nat > real,Y: real,F: filter_nat] :
% 0.25/0.61 ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ ( uminus_uminus_real @ Y ) ) @ F )
% 0.25/0.61 = ( filterlim_nat_real
% 0.25/0.61 @ ^ [X: nat] : ( uminus_uminus_real @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo1664202871s_real @ Y )
% 0.25/0.61 @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_minus_cancel_left
% 0.25/0.61 thf(fact_17_tendsto__minus,axiom,
% 0.25/0.61 ! [F2: real > real,A: real,F: filter_real] :
% 0.25/0.61 ( ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ A ) @ F )
% 0.25/0.61 => ( filterlim_real_real
% 0.25/0.61 @ ^ [X: real] : ( uminus_uminus_real @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo1664202871s_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.61 @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_minus
% 0.25/0.61 thf(fact_18_tendsto__minus,axiom,
% 0.25/0.61 ! [F2: nat > real,A: real,F: filter_nat] :
% 0.25/0.61 ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ A ) @ F )
% 0.25/0.61 => ( filterlim_nat_real
% 0.25/0.61 @ ^ [X: nat] : ( uminus_uminus_real @ ( F2 @ X ) )
% 0.25/0.61 @ ( topolo1664202871s_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.61 @ F ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_minus
% 0.25/0.61 thf(fact_19_LIMSEQ__unique,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal,A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ A ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ B ) @ at_top_nat )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_unique
% 0.25/0.61 thf(fact_20_LIMSEQ__unique,axiom,
% 0.25/0.61 ! [X3: nat > a,A: a,B: a] :
% 0.25/0.61 ( ( filterlim_nat_a @ X3 @ ( topolo705128563nhds_a @ A ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_a @ X3 @ ( topolo705128563nhds_a @ B ) @ at_top_nat )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_unique
% 0.25/0.61 thf(fact_21_LIMSEQ__unique,axiom,
% 0.25/0.61 ! [X3: nat > real,A: real,B: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ A ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ B ) @ at_top_nat )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_unique
% 0.25/0.61 thf(fact_22_tendsto__uminus__nhds,axiom,
% 0.25/0.61 ! [A: real] : ( filterlim_real_real @ uminus_uminus_real @ ( topolo1664202871s_real @ ( uminus_uminus_real @ A ) ) @ ( topolo1664202871s_real @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_uminus_nhds
% 0.25/0.61 thf(fact_23_ereal__uminus__eq__iff,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ( uminus1208298309_ereal @ A )
% 0.25/0.61 = ( uminus1208298309_ereal @ B ) )
% 0.25/0.61 = ( A = B ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_uminus_eq_iff
% 0.25/0.61 thf(fact_24_ereal__uminus__uminus,axiom,
% 0.25/0.61 ! [A: extended_ereal] :
% 0.25/0.61 ( ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ A ) )
% 0.25/0.61 = A ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_uminus_uminus
% 0.25/0.61 thf(fact_25_verit__minus__simplify_I4_J,axiom,
% 0.25/0.61 ! [B: real] :
% 0.25/0.61 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 0.25/0.61 = B ) ).
% 0.25/0.61
% 0.25/0.61 % verit_minus_simplify(4)
% 0.25/0.61 thf(fact_26_verit__negate__coefficient_I3_J,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 => ( ( uminus_uminus_real @ A )
% 0.25/0.61 = ( uminus_uminus_real @ B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % verit_negate_coefficient(3)
% 0.25/0.61 thf(fact_27_ereal__uminus__eq__reorder,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ( uminus1208298309_ereal @ A )
% 0.25/0.61 = B )
% 0.25/0.61 = ( A
% 0.25/0.61 = ( uminus1208298309_ereal @ B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_uminus_eq_reorder
% 0.25/0.61 thf(fact_28_tendsto__eq__rhs,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,X2: extended_ereal,F: filter_nat,Y: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ X2 ) @ F )
% 0.25/0.61 => ( ( X2 = Y )
% 0.25/0.61 => ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ Y ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_eq_rhs
% 0.25/0.61 thf(fact_29_tendsto__eq__rhs,axiom,
% 0.25/0.61 ! [F2: nat > a,X2: a,F: filter_nat,Y: a] :
% 0.25/0.61 ( ( filterlim_nat_a @ F2 @ ( topolo705128563nhds_a @ X2 ) @ F )
% 0.25/0.61 => ( ( X2 = Y )
% 0.25/0.61 => ( filterlim_nat_a @ F2 @ ( topolo705128563nhds_a @ Y ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_eq_rhs
% 0.25/0.61 thf(fact_30_tendsto__eq__rhs,axiom,
% 0.25/0.61 ! [F2: real > real,X2: real,F: filter_real,Y: real] :
% 0.25/0.61 ( ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ X2 ) @ F )
% 0.25/0.61 => ( ( X2 = Y )
% 0.25/0.61 => ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ Y ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_eq_rhs
% 0.25/0.61 thf(fact_31_tendsto__eq__rhs,axiom,
% 0.25/0.61 ! [F2: nat > real,X2: real,F: filter_nat,Y: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ X2 ) @ F )
% 0.25/0.61 => ( ( X2 = Y )
% 0.25/0.61 => ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ Y ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_eq_rhs
% 0.25/0.61 thf(fact_32_tendsto__cong__limit,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,L: extended_ereal,F: filter_nat,K: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ F )
% 0.25/0.61 => ( ( K = L )
% 0.25/0.61 => ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ K ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_cong_limit
% 0.25/0.61 thf(fact_33_tendsto__cong__limit,axiom,
% 0.25/0.61 ! [F2: nat > a,L: a,F: filter_nat,K: a] :
% 0.25/0.61 ( ( filterlim_nat_a @ F2 @ ( topolo705128563nhds_a @ L ) @ F )
% 0.25/0.61 => ( ( K = L )
% 0.25/0.61 => ( filterlim_nat_a @ F2 @ ( topolo705128563nhds_a @ K ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_cong_limit
% 0.25/0.61 thf(fact_34_tendsto__cong__limit,axiom,
% 0.25/0.61 ! [F2: real > real,L: real,F: filter_real,K: real] :
% 0.25/0.61 ( ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ L ) @ F )
% 0.25/0.61 => ( ( K = L )
% 0.25/0.61 => ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ K ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_cong_limit
% 0.25/0.61 thf(fact_35_tendsto__cong__limit,axiom,
% 0.25/0.61 ! [F2: nat > real,L: real,F: filter_nat,K: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ L ) @ F )
% 0.25/0.61 => ( ( K = L )
% 0.25/0.61 => ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ K ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_cong_limit
% 0.25/0.61 thf(fact_36_comp__apply,axiom,
% 0.25/0.61 ( comp_a1112243075al_nat
% 0.25/0.61 = ( ^ [F3: a > extended_ereal,G: nat > a,X: nat] : ( F3 @ ( G @ X ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_apply
% 0.25/0.61 thf(fact_37_neg__equal__iff__equal,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( ( uminus_uminus_real @ A )
% 0.25/0.61 = ( uminus_uminus_real @ B ) )
% 0.25/0.61 = ( A = B ) ) ).
% 0.25/0.61
% 0.25/0.61 % neg_equal_iff_equal
% 0.25/0.61 thf(fact_38_add_Oinverse__inverse,axiom,
% 0.25/0.61 ! [A: real] :
% 0.25/0.61 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.61 = A ) ).
% 0.25/0.61
% 0.25/0.61 % add.inverse_inverse
% 0.25/0.61 thf(fact_39_lsc__sequentially__mem,axiom,
% 0.25/0.61 ! [X0: real,F2: real > extended_ereal,X2: nat > real,C: nat > extended_ereal,C0: extended_ereal] :
% 0.25/0.61 ( ( lower_551915512_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ C @ ( topolo2140997059_ereal @ C0 ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] : ( ord_le824540014_ereal @ ( F2 @ ( X2 @ N2 ) ) @ ( C @ N2 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X0 ) @ C0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_sequentially_mem
% 0.25/0.61 thf(fact_40_lsc__sequentially__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > extended_ereal,X2: nat > a,C: nat > extended_ereal,C0: extended_ereal] :
% 0.25/0.61 ( ( lower_191460856_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ C @ ( topolo2140997059_ereal @ C0 ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] : ( ord_le824540014_ereal @ ( F2 @ ( X2 @ N2 ) ) @ ( C @ N2 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X0 ) @ C0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_sequentially_mem
% 0.25/0.61 thf(fact_41_lsc__sequentially__gen,axiom,
% 0.25/0.61 ( lower_551915512_ereal
% 0.25/0.61 = ( ^ [X02: real,F3: real > extended_ereal] :
% 0.25/0.61 ! [X: nat > real,C2: nat > extended_ereal,C02: extended_ereal] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filter1531173832_ereal @ C2 @ ( topolo2140997059_ereal @ C02 ) @ at_top_nat )
% 0.25/0.61 & ! [N: nat] : ( ord_le824540014_ereal @ ( F3 @ ( X @ N ) ) @ ( C2 @ N ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ C02 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_sequentially_gen
% 0.25/0.61 thf(fact_42_lsc__sequentially__gen,axiom,
% 0.25/0.61 ( lower_191460856_ereal
% 0.25/0.61 = ( ^ [X02: a,F3: a > extended_ereal] :
% 0.25/0.61 ! [X: nat > a,C2: nat > extended_ereal,C02: extended_ereal] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filter1531173832_ereal @ C2 @ ( topolo2140997059_ereal @ C02 ) @ at_top_nat )
% 0.25/0.61 & ! [N: nat] : ( ord_le824540014_ereal @ ( F3 @ ( X @ N ) ) @ ( C2 @ N ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ C02 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_sequentially_gen
% 0.25/0.61 thf(fact_43_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > nat,X2: nat > extended_ereal,A2: nat] :
% 0.25/0.61 ( ( lower_1558406774al_nat @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ ( comp_E1523169101at_nat @ F2 @ X2 ) @ ( topolo1564986139ds_nat @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_44_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > int,X2: nat > extended_ereal,A2: int] :
% 0.25/0.61 ( ( lower_48196818al_int @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ ( comp_E1436437929nt_nat @ F2 @ X2 ) @ ( topolo54776183ds_int @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_45_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > extended_ereal,X2: nat > extended_ereal,A2: extended_ereal] :
% 0.25/0.61 ( ( lower_1087098792_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ ( comp_E1308517939al_nat @ F2 @ X2 ) @ ( topolo2140997059_ereal @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_46_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > real,X2: nat > extended_ereal,A2: real] :
% 0.25/0.61 ( ( lower_1165973074l_real @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ ( comp_E1477338153al_nat @ F2 @ X2 ) @ ( topolo1664202871s_real @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_47_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > nat,X2: nat > a,A2: nat] :
% 0.25/0.61 ( ( lower_319689766_a_nat @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ ( comp_a_nat_nat @ F2 @ X2 ) @ ( topolo1564986139ds_nat @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_48_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > int,X2: nat > a,A2: int] :
% 0.25/0.61 ( ( lower_956963458_a_int @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ ( comp_a_int_nat @ F2 @ X2 ) @ ( topolo54776183ds_int @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_49_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > real,X2: nat > a,A2: real] :
% 0.25/0.61 ( ( lower_231615490a_real @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ ( comp_a_real_nat @ F2 @ X2 ) @ ( topolo1664202871s_real @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_50_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: real,F2: real > nat,X2: nat > real,A2: nat] :
% 0.25/0.61 ( ( lower_1664121382al_nat @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ ( comp_real_nat_nat @ F2 @ X2 ) @ ( topolo1564986139ds_nat @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_51_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: real,F2: real > int,X2: nat > real,A2: int] :
% 0.25/0.61 ( ( lower_153911426al_int @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ ( comp_real_int_nat @ F2 @ X2 ) @ ( topolo54776183ds_int @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_52_lsc__at__mem,axiom,
% 0.25/0.61 ! [X0: real,F2: real > extended_ereal,X2: nat > real,A2: extended_ereal] :
% 0.25/0.61 ( ( lower_551915512_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ ( comp_r1410008527al_nat @ F2 @ X2 ) @ ( topolo2140997059_ereal @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X0 ) @ A2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_mem
% 0.25/0.61 thf(fact_53_lsc__at__def,axiom,
% 0.25/0.61 ( lower_1558406774al_nat
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > nat] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: nat] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_nat @ ( comp_E1523169101at_nat @ F3 @ X4 ) @ ( topolo1564986139ds_nat @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_54_lsc__at__def,axiom,
% 0.25/0.61 ( lower_48196818al_int
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > int] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: int] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_int @ ( comp_E1436437929nt_nat @ F3 @ X4 ) @ ( topolo54776183ds_int @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_55_lsc__at__def,axiom,
% 0.25/0.61 ( lower_1087098792_ereal
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > extended_ereal] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: extended_ereal] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filter1531173832_ereal @ ( comp_E1308517939al_nat @ F3 @ X4 ) @ ( topolo2140997059_ereal @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_56_lsc__at__def,axiom,
% 0.25/0.61 ( lower_1165973074l_real
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > real] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: real] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_real @ ( comp_E1477338153al_nat @ F3 @ X4 ) @ ( topolo1664202871s_real @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_real @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_57_lsc__at__def,axiom,
% 0.25/0.61 ( lower_319689766_a_nat
% 0.25/0.61 = ( ^ [X02: a,F3: a > nat] :
% 0.25/0.61 ! [X4: nat > a,L2: nat] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_nat @ ( comp_a_nat_nat @ F3 @ X4 ) @ ( topolo1564986139ds_nat @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_58_lsc__at__def,axiom,
% 0.25/0.61 ( lower_956963458_a_int
% 0.25/0.61 = ( ^ [X02: a,F3: a > int] :
% 0.25/0.61 ! [X4: nat > a,L2: int] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_int @ ( comp_a_int_nat @ F3 @ X4 ) @ ( topolo54776183ds_int @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_59_lsc__at__def,axiom,
% 0.25/0.61 ( lower_231615490a_real
% 0.25/0.61 = ( ^ [X02: a,F3: a > real] :
% 0.25/0.61 ! [X4: nat > a,L2: real] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_real @ ( comp_a_real_nat @ F3 @ X4 ) @ ( topolo1664202871s_real @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_real @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_60_lsc__at__def,axiom,
% 0.25/0.61 ( lower_1664121382al_nat
% 0.25/0.61 = ( ^ [X02: real,F3: real > nat] :
% 0.25/0.61 ! [X4: nat > real,L2: nat] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X4 @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_nat @ ( comp_real_nat_nat @ F3 @ X4 ) @ ( topolo1564986139ds_nat @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_61_lsc__at__def,axiom,
% 0.25/0.61 ( lower_153911426al_int
% 0.25/0.61 = ( ^ [X02: real,F3: real > int] :
% 0.25/0.61 ! [X4: nat > real,L2: int] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X4 @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_int @ ( comp_real_int_nat @ F3 @ X4 ) @ ( topolo54776183ds_int @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_62_lsc__at__def,axiom,
% 0.25/0.61 ( lower_551915512_ereal
% 0.25/0.61 = ( ^ [X02: real,F3: real > extended_ereal] :
% 0.25/0.61 ! [X4: nat > real,L2: extended_ereal] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X4 @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filter1531173832_ereal @ ( comp_r1410008527al_nat @ F3 @ X4 ) @ ( topolo2140997059_ereal @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ L2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_at_def
% 0.25/0.61 thf(fact_63_neg__le__iff__le,axiom,
% 0.25/0.61 ! [B: real,A: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.25/0.61 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.25/0.61
% 0.25/0.61 % neg_le_iff_le
% 0.25/0.61 thf(fact_64_neg__le__iff__le,axiom,
% 0.25/0.61 ! [B: int,A: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.25/0.61 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.25/0.61
% 0.25/0.61 % neg_le_iff_le
% 0.25/0.61 thf(fact_65_ereal__minus__le__minus,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ ( uminus1208298309_ereal @ A ) @ ( uminus1208298309_ereal @ B ) )
% 0.25/0.61 = ( ord_le824540014_ereal @ B @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_minus_le_minus
% 0.25/0.61 thf(fact_66_verit__la__disequality,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 | ~ ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 | ~ ( ord_le824540014_ereal @ B @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % verit_la_disequality
% 0.25/0.61 thf(fact_67_verit__la__disequality,axiom,
% 0.25/0.61 ! [A: nat,B: nat] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 | ~ ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % verit_la_disequality
% 0.25/0.61 thf(fact_68_verit__la__disequality,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 | ~ ( ord_less_eq_real @ A @ B )
% 0.25/0.61 | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % verit_la_disequality
% 0.25/0.61 thf(fact_69_verit__la__disequality,axiom,
% 0.25/0.61 ! [A: int,B: int] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 | ~ ( ord_less_eq_int @ A @ B )
% 0.25/0.61 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % verit_la_disequality
% 0.25/0.61 thf(fact_70_ereal__complete__Inf,axiom,
% 0.25/0.61 ! [S: set_Extended_ereal] :
% 0.25/0.61 ? [X5: extended_ereal] :
% 0.25/0.61 ( ! [Xa: extended_ereal] :
% 0.25/0.61 ( ( member1900190071_ereal @ Xa @ S )
% 0.25/0.61 => ( ord_le824540014_ereal @ X5 @ Xa ) )
% 0.25/0.61 & ! [Z: extended_ereal] :
% 0.25/0.61 ( ! [Xa2: extended_ereal] :
% 0.25/0.61 ( ( member1900190071_ereal @ Xa2 @ S )
% 0.25/0.61 => ( ord_le824540014_ereal @ Z @ Xa2 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ Z @ X5 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_complete_Inf
% 0.25/0.61 thf(fact_71_ereal__complete__Sup,axiom,
% 0.25/0.61 ! [S: set_Extended_ereal] :
% 0.25/0.61 ? [X5: extended_ereal] :
% 0.25/0.61 ( ! [Xa: extended_ereal] :
% 0.25/0.61 ( ( member1900190071_ereal @ Xa @ S )
% 0.25/0.61 => ( ord_le824540014_ereal @ Xa @ X5 ) )
% 0.25/0.61 & ! [Z: extended_ereal] :
% 0.25/0.61 ( ! [Xa2: extended_ereal] :
% 0.25/0.61 ( ( member1900190071_ereal @ Xa2 @ S )
% 0.25/0.61 => ( ord_le824540014_ereal @ Xa2 @ Z ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ X5 @ Z ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_complete_Sup
% 0.25/0.61 thf(fact_72_le__minus__iff,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.25/0.61 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_minus_iff
% 0.25/0.61 thf(fact_73_le__minus__iff,axiom,
% 0.25/0.61 ! [A: int,B: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.25/0.61 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_minus_iff
% 0.25/0.61 thf(fact_74_minus__le__iff,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.61 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % minus_le_iff
% 0.25/0.61 thf(fact_75_minus__le__iff,axiom,
% 0.25/0.61 ! [A: int,B: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.61 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % minus_le_iff
% 0.25/0.61 thf(fact_76_le__imp__neg__le,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_imp_neg_le
% 0.25/0.61 thf(fact_77_le__imp__neg__le,axiom,
% 0.25/0.61 ! [A: int,B: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.61 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_imp_neg_le
% 0.25/0.61 thf(fact_78_ereal__uminus__le__reorder,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ ( uminus1208298309_ereal @ A ) @ B )
% 0.25/0.61 = ( ord_le824540014_ereal @ ( uminus1208298309_ereal @ B ) @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_uminus_le_reorder
% 0.25/0.61 thf(fact_79_lim__mono,axiom,
% 0.25/0.61 ! [N3: nat,X3: nat > nat,Y2: nat > nat,X2: nat,Y: nat] :
% 0.25/0.61 ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ( filterlim_nat_nat @ X3 @ ( topolo1564986139ds_nat @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ Y2 @ ( topolo1564986139ds_nat @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lim_mono
% 0.25/0.61 thf(fact_80_lim__mono,axiom,
% 0.25/0.61 ! [N3: nat,X3: nat > int,Y2: nat > int,X2: int,Y: int] :
% 0.25/0.61 ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ( filterlim_nat_int @ X3 @ ( topolo54776183ds_int @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ Y2 @ ( topolo54776183ds_int @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lim_mono
% 0.25/0.61 thf(fact_81_lim__mono,axiom,
% 0.25/0.61 ! [N3: nat,X3: nat > extended_ereal,Y2: nat > extended_ereal,X2: extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ Y2 @ ( topolo2140997059_ereal @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lim_mono
% 0.25/0.61 thf(fact_82_lim__mono,axiom,
% 0.25/0.61 ! [N3: nat,X3: nat > real,Y2: nat > real,X2: real,Y: real] :
% 0.25/0.61 ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ Y2 @ ( topolo1664202871s_real @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_real @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lim_mono
% 0.25/0.61 thf(fact_83_LIMSEQ__le,axiom,
% 0.25/0.61 ! [X3: nat > nat,X2: nat,Y2: nat > nat,Y: nat] :
% 0.25/0.61 ( ( filterlim_nat_nat @ X3 @ ( topolo1564986139ds_nat @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ Y2 @ ( topolo1564986139ds_nat @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le
% 0.25/0.61 thf(fact_84_LIMSEQ__le,axiom,
% 0.25/0.61 ! [X3: nat > int,X2: int,Y2: nat > int,Y: int] :
% 0.25/0.61 ( ( filterlim_nat_int @ X3 @ ( topolo54776183ds_int @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ Y2 @ ( topolo54776183ds_int @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le
% 0.25/0.61 thf(fact_85_LIMSEQ__le,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal,X2: extended_ereal,Y2: nat > extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ Y2 @ ( topolo2140997059_ereal @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le
% 0.25/0.61 thf(fact_86_LIMSEQ__le,axiom,
% 0.25/0.61 ! [X3: nat > real,X2: real,Y2: nat > real,Y: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ Y2 @ ( topolo1664202871s_real @ Y ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ ( X3 @ N2 ) @ ( Y2 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ X2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le
% 0.25/0.61 thf(fact_87_mem__Collect__eq,axiom,
% 0.25/0.61 ! [A: real,P: real > $o] :
% 0.25/0.61 ( ( member_real @ A @ ( collect_real @ P ) )
% 0.25/0.61 = ( P @ A ) ) ).
% 0.25/0.61
% 0.25/0.61 % mem_Collect_eq
% 0.25/0.61 thf(fact_88_Collect__mem__eq,axiom,
% 0.25/0.61 ! [A2: set_real] :
% 0.25/0.61 ( ( collect_real
% 0.25/0.61 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 0.25/0.61 = A2 ) ).
% 0.25/0.61
% 0.25/0.61 % Collect_mem_eq
% 0.25/0.61 thf(fact_89_Collect__cong,axiom,
% 0.25/0.61 ! [P: real > $o,Q: real > $o] :
% 0.25/0.61 ( ! [X5: real] :
% 0.25/0.61 ( ( P @ X5 )
% 0.25/0.61 = ( Q @ X5 ) )
% 0.25/0.61 => ( ( collect_real @ P )
% 0.25/0.61 = ( collect_real @ Q ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Collect_cong
% 0.25/0.61 thf(fact_90_Lim__bounded,axiom,
% 0.25/0.61 ! [F2: nat > nat,L: nat,M: nat,C3: nat] :
% 0.25/0.61 ( ( filterlim_nat_nat @ F2 @ ( topolo1564986139ds_nat @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ N2 ) @ C3 ) )
% 0.25/0.61 => ( ord_less_eq_nat @ L @ C3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded
% 0.25/0.61 thf(fact_91_Lim__bounded,axiom,
% 0.25/0.61 ! [F2: nat > int,L: int,M: nat,C3: int] :
% 0.25/0.61 ( ( filterlim_nat_int @ F2 @ ( topolo54776183ds_int @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ N2 ) @ C3 ) )
% 0.25/0.61 => ( ord_less_eq_int @ L @ C3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded
% 0.25/0.61 thf(fact_92_Lim__bounded,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,L: extended_ereal,M: nat,C3: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ N2 ) @ C3 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ L @ C3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded
% 0.25/0.61 thf(fact_93_Lim__bounded,axiom,
% 0.25/0.61 ! [F2: nat > real,L: real,M: nat,C3: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ N2 ) @ C3 ) )
% 0.25/0.61 => ( ord_less_eq_real @ L @ C3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded
% 0.25/0.61 thf(fact_94_Lim__bounded2,axiom,
% 0.25/0.61 ! [F2: nat > nat,L: nat,N3: nat,C3: nat] :
% 0.25/0.61 ( ( filterlim_nat_nat @ F2 @ ( topolo1564986139ds_nat @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ C3 @ ( F2 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ C3 @ L ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded2
% 0.25/0.61 thf(fact_95_Lim__bounded2,axiom,
% 0.25/0.61 ! [F2: nat > int,L: int,N3: nat,C3: int] :
% 0.25/0.61 ( ( filterlim_nat_int @ F2 @ ( topolo54776183ds_int @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ C3 @ ( F2 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ C3 @ L ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded2
% 0.25/0.61 thf(fact_96_Lim__bounded2,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,L: extended_ereal,N3: nat,C3: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ C3 @ ( F2 @ N2 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ C3 @ L ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded2
% 0.25/0.61 thf(fact_97_Lim__bounded2,axiom,
% 0.25/0.61 ! [F2: nat > real,L: real,N3: nat,C3: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ C3 @ ( F2 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ C3 @ L ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded2
% 0.25/0.61 thf(fact_98_LIMSEQ__le__const,axiom,
% 0.25/0.61 ! [X3: nat > nat,X2: nat,A: nat] :
% 0.25/0.61 ( ( filterlim_nat_nat @ X3 @ ( topolo1564986139ds_nat @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ X2 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const
% 0.25/0.61 thf(fact_99_LIMSEQ__le__const,axiom,
% 0.25/0.61 ! [X3: nat > int,X2: int,A: int] :
% 0.25/0.61 ( ( filterlim_nat_int @ X3 @ ( topolo54776183ds_int @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ A @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ A @ X2 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const
% 0.25/0.61 thf(fact_100_LIMSEQ__le__const,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal,X2: extended_ereal,A: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ X2 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const
% 0.25/0.61 thf(fact_101_LIMSEQ__le__const,axiom,
% 0.25/0.61 ! [X3: nat > real,X2: real,A: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ A @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ A @ X2 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const
% 0.25/0.61 thf(fact_102_LIMSEQ__le__const2,axiom,
% 0.25/0.61 ! [X3: nat > nat,X2: nat,A: nat] :
% 0.25/0.61 ( ( filterlim_nat_nat @ X3 @ ( topolo1564986139ds_nat @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X3 @ N2 ) @ A ) )
% 0.25/0.61 => ( ord_less_eq_nat @ X2 @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const2
% 0.25/0.61 thf(fact_103_LIMSEQ__le__const2,axiom,
% 0.25/0.61 ! [X3: nat > int,X2: int,A: int] :
% 0.25/0.61 ( ( filterlim_nat_int @ X3 @ ( topolo54776183ds_int @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ ( X3 @ N2 ) @ A ) )
% 0.25/0.61 => ( ord_less_eq_int @ X2 @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const2
% 0.25/0.61 thf(fact_104_LIMSEQ__le__const2,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal,X2: extended_ereal,A: extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X3 @ N2 ) @ A ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ X2 @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const2
% 0.25/0.61 thf(fact_105_LIMSEQ__le__const2,axiom,
% 0.25/0.61 ! [X3: nat > real,X2: real,A: real] :
% 0.25/0.61 ( ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ? [N4: nat] :
% 0.25/0.61 ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N4 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ ( X3 @ N2 ) @ A ) )
% 0.25/0.61 => ( ord_less_eq_real @ X2 @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_le_const2
% 0.25/0.61 thf(fact_106_tendsto__mono,axiom,
% 0.25/0.61 ! [F: filter_nat,F4: filter_nat,F2: nat > extended_ereal,L: extended_ereal] :
% 0.25/0.61 ( ( ord_le1745708096er_nat @ F @ F4 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ F4 )
% 0.25/0.61 => ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_mono
% 0.25/0.61 thf(fact_107_tendsto__mono,axiom,
% 0.25/0.61 ! [F: filter_nat,F4: filter_nat,F2: nat > a,L: a] :
% 0.25/0.61 ( ( ord_le1745708096er_nat @ F @ F4 )
% 0.25/0.61 => ( ( filterlim_nat_a @ F2 @ ( topolo705128563nhds_a @ L ) @ F4 )
% 0.25/0.61 => ( filterlim_nat_a @ F2 @ ( topolo705128563nhds_a @ L ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_mono
% 0.25/0.61 thf(fact_108_tendsto__mono,axiom,
% 0.25/0.61 ! [F: filter_real,F4: filter_real,F2: real > real,L: real] :
% 0.25/0.61 ( ( ord_le132810396r_real @ F @ F4 )
% 0.25/0.61 => ( ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ L ) @ F4 )
% 0.25/0.61 => ( filterlim_real_real @ F2 @ ( topolo1664202871s_real @ L ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_mono
% 0.25/0.61 thf(fact_109_tendsto__mono,axiom,
% 0.25/0.61 ! [F: filter_nat,F4: filter_nat,F2: nat > real,L: real] :
% 0.25/0.61 ( ( ord_le1745708096er_nat @ F @ F4 )
% 0.25/0.61 => ( ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ L ) @ F4 )
% 0.25/0.61 => ( filterlim_nat_real @ F2 @ ( topolo1664202871s_real @ L ) @ F ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % tendsto_mono
% 0.25/0.61 thf(fact_110_equation__minus__iff,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( uminus_uminus_real @ B ) )
% 0.25/0.61 = ( B
% 0.25/0.61 = ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % equation_minus_iff
% 0.25/0.61 thf(fact_111_minus__equation__iff,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( ( uminus_uminus_real @ A )
% 0.25/0.61 = B )
% 0.25/0.61 = ( ( uminus_uminus_real @ B )
% 0.25/0.61 = A ) ) ).
% 0.25/0.61
% 0.25/0.61 % minus_equation_iff
% 0.25/0.61 thf(fact_112_comp__eq__dest__lhs,axiom,
% 0.25/0.61 ! [A: a > extended_ereal,B: nat > a,C: nat > extended_ereal,V: nat] :
% 0.25/0.61 ( ( ( comp_a1112243075al_nat @ A @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ( A @ ( B @ V ) )
% 0.25/0.61 = ( C @ V ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_eq_dest_lhs
% 0.25/0.61 thf(fact_113_comp__eq__elim,axiom,
% 0.25/0.61 ! [A: a > extended_ereal,B: nat > a,C: a > extended_ereal,D: nat > a] :
% 0.25/0.61 ( ( ( comp_a1112243075al_nat @ A @ B )
% 0.25/0.61 = ( comp_a1112243075al_nat @ C @ D ) )
% 0.25/0.61 => ! [V2: nat] :
% 0.25/0.61 ( ( A @ ( B @ V2 ) )
% 0.25/0.61 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_eq_elim
% 0.25/0.61 thf(fact_114_comp__eq__dest,axiom,
% 0.25/0.61 ! [A: a > extended_ereal,B: nat > a,C: a > extended_ereal,D: nat > a,V: nat] :
% 0.25/0.61 ( ( ( comp_a1112243075al_nat @ A @ B )
% 0.25/0.61 = ( comp_a1112243075al_nat @ C @ D ) )
% 0.25/0.61 => ( ( A @ ( B @ V ) )
% 0.25/0.61 = ( C @ ( D @ V ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_eq_dest
% 0.25/0.61 thf(fact_115_comp__assoc,axiom,
% 0.25/0.61 ! [F2: a > extended_ereal,G2: nat > a,H: nat > nat] :
% 0.25/0.61 ( ( comp_n1096781355al_nat @ ( comp_a1112243075al_nat @ F2 @ G2 ) @ H )
% 0.25/0.61 = ( comp_a1112243075al_nat @ F2 @ ( comp_nat_a_nat @ G2 @ H ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_assoc
% 0.25/0.61 thf(fact_116_comp__assoc,axiom,
% 0.25/0.61 ! [F2: extended_ereal > extended_ereal,G2: a > extended_ereal,H: nat > a] :
% 0.25/0.61 ( ( comp_a1112243075al_nat @ ( comp_E489644891real_a @ F2 @ G2 ) @ H )
% 0.25/0.61 = ( comp_E1308517939al_nat @ F2 @ ( comp_a1112243075al_nat @ G2 @ H ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_assoc
% 0.25/0.61 thf(fact_117_comp__assoc,axiom,
% 0.25/0.61 ! [F2: a > extended_ereal,G2: a > a,H: nat > a] :
% 0.25/0.61 ( ( comp_a1112243075al_nat @ ( comp_a780206603real_a @ F2 @ G2 ) @ H )
% 0.25/0.61 = ( comp_a1112243075al_nat @ F2 @ ( comp_a_a_nat @ G2 @ H ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_assoc
% 0.25/0.61 thf(fact_118_comp__def,axiom,
% 0.25/0.61 ( comp_a1112243075al_nat
% 0.25/0.61 = ( ^ [F3: a > extended_ereal,G: nat > a,X: nat] : ( F3 @ ( G @ X ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % comp_def
% 0.25/0.61 thf(fact_119_lsc__sequentially,axiom,
% 0.25/0.61 ( lower_551915512_ereal
% 0.25/0.61 = ( ^ [X02: real,F3: real > extended_ereal] :
% 0.25/0.61 ! [X: nat > real,C2: extended_ereal] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ! [N: nat] : ( ord_le824540014_ereal @ ( F3 @ ( X @ N ) ) @ C2 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ C2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_sequentially
% 0.25/0.61 thf(fact_120_lsc__sequentially,axiom,
% 0.25/0.61 ( lower_191460856_ereal
% 0.25/0.61 = ( ^ [X02: a,F3: a > extended_ereal] :
% 0.25/0.61 ! [X: nat > a,C2: extended_ereal] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ! [N: nat] : ( ord_le824540014_ereal @ ( F3 @ ( X @ N ) ) @ C2 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ C2 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_sequentially
% 0.25/0.61 thf(fact_121_usc__at__def,axiom,
% 0.25/0.61 ( lower_114093al_nat
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > nat] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: nat] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_nat @ ( comp_E1523169101at_nat @ F3 @ X4 ) @ ( topolo1564986139ds_nat @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_nat @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_122_usc__at__def,axiom,
% 0.25/0.61 ( lower_637387785al_int
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > int] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: int] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_int @ ( comp_E1436437929nt_nat @ F3 @ X4 ) @ ( topolo54776183ds_int @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_int @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_123_usc__at__def,axiom,
% 0.25/0.61 ( lower_1071158961_ereal
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > extended_ereal] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: extended_ereal] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filter1531173832_ereal @ ( comp_E1308517939al_nat @ F3 @ X4 ) @ ( topolo2140997059_ereal @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_124_usc__at__def,axiom,
% 0.25/0.61 ( lower_737640969l_real
% 0.25/0.61 = ( ^ [X02: extended_ereal,F3: extended_ereal > real] :
% 0.25/0.61 ! [X4: nat > extended_ereal,L2: real] :
% 0.25/0.61 ( ( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_real @ ( comp_E1477338153al_nat @ F3 @ X4 ) @ ( topolo1664202871s_real @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_real @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_125_usc__at__def,axiom,
% 0.25/0.61 ( lower_1035717085_a_nat
% 0.25/0.61 = ( ^ [X02: a,F3: a > nat] :
% 0.25/0.61 ! [X4: nat > a,L2: nat] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_nat @ ( comp_a_nat_nat @ F3 @ X4 ) @ ( topolo1564986139ds_nat @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_nat @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_126_usc__at__def,axiom,
% 0.25/0.61 ( lower_1672990777_a_int
% 0.25/0.61 = ( ^ [X02: a,F3: a > int] :
% 0.25/0.61 ! [X4: nat > a,L2: int] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_int @ ( comp_a_int_nat @ F3 @ X4 ) @ ( topolo54776183ds_int @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_int @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_127_usc__at__def,axiom,
% 0.25/0.61 ( lower_534855297_ereal
% 0.25/0.61 = ( ^ [X02: a,F3: a > extended_ereal] :
% 0.25/0.61 ! [X4: nat > a,L2: extended_ereal] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filter1531173832_ereal @ ( comp_a1112243075al_nat @ F3 @ X4 ) @ ( topolo2140997059_ereal @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_128_usc__at__def,axiom,
% 0.25/0.61 ( lower_755922489a_real
% 0.25/0.61 = ( ^ [X02: a,F3: a > real] :
% 0.25/0.61 ! [X4: nat > a,L2: real] :
% 0.25/0.61 ( ( ( filterlim_nat_a @ X4 @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_real @ ( comp_a_real_nat @ F3 @ X4 ) @ ( topolo1664202871s_real @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_real @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_129_usc__at__def,axiom,
% 0.25/0.61 ( lower_438231087al_nat
% 0.25/0.61 = ( ^ [X02: real,F3: real > nat] :
% 0.25/0.61 ! [X4: nat > real,L2: nat] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X4 @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_nat @ ( comp_real_nat_nat @ F3 @ X4 ) @ ( topolo1564986139ds_nat @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_nat @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_130_usc__at__def,axiom,
% 0.25/0.61 ( lower_1075504779al_int
% 0.25/0.61 = ( ^ [X02: real,F3: real > int] :
% 0.25/0.61 ! [X4: nat > real,L2: int] :
% 0.25/0.61 ( ( ( filterlim_nat_real @ X4 @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 & ( filterlim_nat_int @ ( comp_real_int_nat @ F3 @ X4 ) @ ( topolo54776183ds_int @ L2 ) @ at_top_nat ) )
% 0.25/0.61 => ( ord_less_eq_int @ L2 @ ( F3 @ X02 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_def
% 0.25/0.61 thf(fact_131_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > nat,X2: nat > extended_ereal,A2: nat] :
% 0.25/0.61 ( ( lower_114093al_nat @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ ( comp_E1523169101at_nat @ F2 @ X2 ) @ ( topolo1564986139ds_nat @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_132_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > int,X2: nat > extended_ereal,A2: int] :
% 0.25/0.61 ( ( lower_637387785al_int @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ ( comp_E1436437929nt_nat @ F2 @ X2 ) @ ( topolo54776183ds_int @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_133_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > extended_ereal,X2: nat > extended_ereal,A2: extended_ereal] :
% 0.25/0.61 ( ( lower_1071158961_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ ( comp_E1308517939al_nat @ F2 @ X2 ) @ ( topolo2140997059_ereal @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_134_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: extended_ereal,F2: extended_ereal > real,X2: nat > extended_ereal,A2: real] :
% 0.25/0.61 ( ( lower_737640969l_real @ X0 @ F2 )
% 0.25/0.61 => ( ( filter1531173832_ereal @ X2 @ ( topolo2140997059_ereal @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ ( comp_E1477338153al_nat @ F2 @ X2 ) @ ( topolo1664202871s_real @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_real @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_135_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > nat,X2: nat > a,A2: nat] :
% 0.25/0.61 ( ( lower_1035717085_a_nat @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ ( comp_a_nat_nat @ F2 @ X2 ) @ ( topolo1564986139ds_nat @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_136_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > int,X2: nat > a,A2: int] :
% 0.25/0.61 ( ( lower_1672990777_a_int @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ ( comp_a_int_nat @ F2 @ X2 ) @ ( topolo54776183ds_int @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_137_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > extended_ereal,X2: nat > a,A2: extended_ereal] :
% 0.25/0.61 ( ( lower_534855297_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filter1531173832_ereal @ ( comp_a1112243075al_nat @ F2 @ X2 ) @ ( topolo2140997059_ereal @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_138_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: a,F2: a > real,X2: nat > a,A2: real] :
% 0.25/0.61 ( ( lower_755922489a_real @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_real @ ( comp_a_real_nat @ F2 @ X2 ) @ ( topolo1664202871s_real @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_real @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_139_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: real,F2: real > nat,X2: nat > real,A2: nat] :
% 0.25/0.61 ( ( lower_438231087al_nat @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_nat @ ( comp_real_nat_nat @ F2 @ X2 ) @ ( topolo1564986139ds_nat @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_nat @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_140_usc__at__mem,axiom,
% 0.25/0.61 ! [X0: real,F2: real > int,X2: nat > real,A2: int] :
% 0.25/0.61 ( ( lower_1075504779al_int @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ( filterlim_nat_int @ ( comp_real_int_nat @ F2 @ X2 ) @ ( topolo54776183ds_int @ A2 ) @ at_top_nat )
% 0.25/0.61 => ( ord_less_eq_int @ A2 @ ( F2 @ X0 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % usc_at_mem
% 0.25/0.61 thf(fact_141_lim__decreasing__cl,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal] :
% 0.25/0.61 ( ! [N2: nat,M2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ N2 ) @ ( F2 @ M2 ) ) )
% 0.25/0.61 => ~ ! [L3: extended_ereal] :
% 0.25/0.61 ~ ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L3 ) @ at_top_nat ) ) ).
% 0.25/0.61
% 0.25/0.61 % lim_decreasing_cl
% 0.25/0.61 thf(fact_142_lim__increasing__cl,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal] :
% 0.25/0.61 ( ! [N2: nat,M2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ M2 ) @ ( F2 @ N2 ) ) )
% 0.25/0.61 => ~ ! [L3: extended_ereal] :
% 0.25/0.61 ~ ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L3 ) @ at_top_nat ) ) ).
% 0.25/0.61
% 0.25/0.61 % lim_increasing_cl
% 0.25/0.61 thf(fact_143_order__refl,axiom,
% 0.25/0.61 ! [X2: extended_ereal] : ( ord_le824540014_ereal @ X2 @ X2 ) ).
% 0.25/0.61
% 0.25/0.61 % order_refl
% 0.25/0.61 thf(fact_144_order__refl,axiom,
% 0.25/0.61 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.25/0.61
% 0.25/0.61 % order_refl
% 0.25/0.61 thf(fact_145_order__refl,axiom,
% 0.25/0.61 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 0.25/0.61
% 0.25/0.61 % order_refl
% 0.25/0.61 thf(fact_146_order__refl,axiom,
% 0.25/0.61 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 0.25/0.61
% 0.25/0.61 % order_refl
% 0.25/0.61 thf(fact_147_monoseq__le,axiom,
% 0.25/0.61 ! [A: nat > nat,X2: nat] :
% 0.25/0.61 ( ( topolo1922093437eq_nat @ A )
% 0.25/0.61 => ( ( filterlim_nat_nat @ A @ ( topolo1564986139ds_nat @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( ! [N5: nat] : ( ord_less_eq_nat @ ( A @ N5 ) @ X2 )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( A @ M3 ) @ ( A @ N5 ) ) ) )
% 0.25/0.61 | ( ! [N5: nat] : ( ord_less_eq_nat @ X2 @ ( A @ N5 ) )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( A @ N5 ) @ ( A @ M3 ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_le
% 0.25/0.61 thf(fact_148_monoseq__le,axiom,
% 0.25/0.61 ! [A: nat > int,X2: int] :
% 0.25/0.61 ( ( topolo411883481eq_int @ A )
% 0.25/0.61 => ( ( filterlim_nat_int @ A @ ( topolo54776183ds_int @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( ! [N5: nat] : ( ord_less_eq_int @ ( A @ N5 ) @ X2 )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_less_eq_int @ ( A @ M3 ) @ ( A @ N5 ) ) ) )
% 0.25/0.61 | ( ! [N5: nat] : ( ord_less_eq_int @ X2 @ ( A @ N5 ) )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_less_eq_int @ ( A @ N5 ) @ ( A @ M3 ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_le
% 0.25/0.61 thf(fact_149_monoseq__le,axiom,
% 0.25/0.61 ! [A: nat > extended_ereal,X2: extended_ereal] :
% 0.25/0.61 ( ( topolo1069469409_ereal @ A )
% 0.25/0.61 => ( ( filter1531173832_ereal @ A @ ( topolo2140997059_ereal @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( ! [N5: nat] : ( ord_le824540014_ereal @ ( A @ N5 ) @ X2 )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( A @ M3 ) @ ( A @ N5 ) ) ) )
% 0.25/0.61 | ( ! [N5: nat] : ( ord_le824540014_ereal @ X2 @ ( A @ N5 ) )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( A @ N5 ) @ ( A @ M3 ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_le
% 0.25/0.61 thf(fact_150_monoseq__le,axiom,
% 0.25/0.61 ! [A: nat > real,X2: real] :
% 0.25/0.61 ( ( topolo144289241q_real @ A )
% 0.25/0.61 => ( ( filterlim_nat_real @ A @ ( topolo1664202871s_real @ X2 ) @ at_top_nat )
% 0.25/0.61 => ( ( ! [N5: nat] : ( ord_less_eq_real @ ( A @ N5 ) @ X2 )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_less_eq_real @ ( A @ M3 ) @ ( A @ N5 ) ) ) )
% 0.25/0.61 | ( ! [N5: nat] : ( ord_less_eq_real @ X2 @ ( A @ N5 ) )
% 0.25/0.61 & ! [M3: nat,N5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M3 @ N5 )
% 0.25/0.61 => ( ord_less_eq_real @ ( A @ N5 ) @ ( A @ M3 ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_le
% 0.25/0.61 thf(fact_151_lsc__liminf,axiom,
% 0.25/0.61 ( lower_551915512_ereal
% 0.25/0.61 = ( ^ [X02: real,F3: real > extended_ereal] :
% 0.25/0.61 ! [X: nat > real] :
% 0.25/0.61 ( ( filterlim_nat_real @ X @ ( topolo1664202871s_real @ X02 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ ( liminf1045857232_ereal @ at_top_nat @ ( comp_r1410008527al_nat @ F3 @ X ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_liminf
% 0.25/0.61 thf(fact_152_lsc__liminf,axiom,
% 0.25/0.61 ( lower_191460856_ereal
% 0.25/0.61 = ( ^ [X02: a,F3: a > extended_ereal] :
% 0.25/0.61 ! [X: nat > a] :
% 0.25/0.61 ( ( filterlim_nat_a @ X @ ( topolo705128563nhds_a @ X02 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F3 @ X02 ) @ ( liminf1045857232_ereal @ at_top_nat @ ( comp_a1112243075al_nat @ F3 @ X ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_liminf
% 0.25/0.61 thf(fact_153_lsc__imp__liminf,axiom,
% 0.25/0.61 ! [X0: real,F2: real > extended_ereal,X2: nat > real] :
% 0.25/0.61 ( ( lower_551915512_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_real @ X2 @ ( topolo1664202871s_real @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X0 ) @ ( liminf1045857232_ereal @ at_top_nat @ ( comp_r1410008527al_nat @ F2 @ X2 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_imp_liminf
% 0.25/0.61 thf(fact_154_lsc__imp__liminf,axiom,
% 0.25/0.61 ! [X0: a,F2: a > extended_ereal,X2: nat > a] :
% 0.25/0.61 ( ( lower_191460856_ereal @ X0 @ F2 )
% 0.25/0.61 => ( ( filterlim_nat_a @ X2 @ ( topolo705128563nhds_a @ X0 ) @ at_top_nat )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X0 ) @ ( liminf1045857232_ereal @ at_top_nat @ ( comp_a1112243075al_nat @ F2 @ X2 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % lsc_imp_liminf
% 0.25/0.61 thf(fact_155_LIMSEQ__Uniq,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal] :
% 0.25/0.61 ( uniq_Extended_ereal
% 0.25/0.61 @ ^ [L2: extended_ereal] : ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ L2 ) @ at_top_nat ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_Uniq
% 0.25/0.61 thf(fact_156_LIMSEQ__Uniq,axiom,
% 0.25/0.61 ! [X3: nat > a] :
% 0.25/0.61 ( uniq_a
% 0.25/0.61 @ ^ [L2: a] : ( filterlim_nat_a @ X3 @ ( topolo705128563nhds_a @ L2 ) @ at_top_nat ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_Uniq
% 0.25/0.61 thf(fact_157_LIMSEQ__Uniq,axiom,
% 0.25/0.61 ! [X3: nat > real] :
% 0.25/0.61 ( uniq_real
% 0.25/0.61 @ ^ [L2: real] : ( filterlim_nat_real @ X3 @ ( topolo1664202871s_real @ L2 ) @ at_top_nat ) ) ).
% 0.25/0.61
% 0.25/0.61 % LIMSEQ_Uniq
% 0.25/0.61 thf(fact_158_monoseq__def,axiom,
% 0.25/0.61 ( topolo1069469409_ereal
% 0.25/0.61 = ( ^ [X4: nat > extended_ereal] :
% 0.25/0.61 ( ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X4 @ M4 ) @ ( X4 @ N ) ) )
% 0.25/0.61 | ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X4 @ N ) @ ( X4 @ M4 ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_def
% 0.25/0.61 thf(fact_159_monoseq__def,axiom,
% 0.25/0.61 ( topolo1922093437eq_nat
% 0.25/0.61 = ( ^ [X4: nat > nat] :
% 0.25/0.61 ( ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X4 @ M4 ) @ ( X4 @ N ) ) )
% 0.25/0.61 | ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X4 @ N ) @ ( X4 @ M4 ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_def
% 0.25/0.61 thf(fact_160_monoseq__def,axiom,
% 0.25/0.61 ( topolo144289241q_real
% 0.25/0.61 = ( ^ [X4: nat > real] :
% 0.25/0.61 ( ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_less_eq_real @ ( X4 @ M4 ) @ ( X4 @ N ) ) )
% 0.25/0.61 | ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_less_eq_real @ ( X4 @ N ) @ ( X4 @ M4 ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_def
% 0.25/0.61 thf(fact_161_monoseq__def,axiom,
% 0.25/0.61 ( topolo411883481eq_int
% 0.25/0.61 = ( ^ [X4: nat > int] :
% 0.25/0.61 ( ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_less_eq_int @ ( X4 @ M4 ) @ ( X4 @ N ) ) )
% 0.25/0.61 | ! [M4: nat,N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M4 @ N )
% 0.25/0.61 => ( ord_less_eq_int @ ( X4 @ N ) @ ( X4 @ M4 ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_def
% 0.25/0.61 thf(fact_162_monoI2,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X3 @ N2 ) @ ( X3 @ M2 ) ) )
% 0.25/0.61 => ( topolo1069469409_ereal @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI2
% 0.25/0.61 thf(fact_163_monoI2,axiom,
% 0.25/0.61 ! [X3: nat > nat] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X3 @ N2 ) @ ( X3 @ M2 ) ) )
% 0.25/0.61 => ( topolo1922093437eq_nat @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI2
% 0.25/0.61 thf(fact_164_monoI2,axiom,
% 0.25/0.61 ! [X3: nat > real] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ ( X3 @ N2 ) @ ( X3 @ M2 ) ) )
% 0.25/0.61 => ( topolo144289241q_real @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI2
% 0.25/0.61 thf(fact_165_monoI2,axiom,
% 0.25/0.61 ! [X3: nat > int] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ ( X3 @ N2 ) @ ( X3 @ M2 ) ) )
% 0.25/0.61 => ( topolo411883481eq_int @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI2
% 0.25/0.61 thf(fact_166_monoI1,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( X3 @ M2 ) @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( topolo1069469409_ereal @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI1
% 0.25/0.61 thf(fact_167_monoI1,axiom,
% 0.25/0.61 ! [X3: nat > nat] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( X3 @ M2 ) @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( topolo1922093437eq_nat @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI1
% 0.25/0.61 thf(fact_168_monoI1,axiom,
% 0.25/0.61 ! [X3: nat > real] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_less_eq_real @ ( X3 @ M2 ) @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( topolo144289241q_real @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI1
% 0.25/0.61 thf(fact_169_monoI1,axiom,
% 0.25/0.61 ! [X3: nat > int] :
% 0.25/0.61 ( ! [M2: nat,N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.25/0.61 => ( ord_less_eq_int @ ( X3 @ M2 ) @ ( X3 @ N2 ) ) )
% 0.25/0.61 => ( topolo411883481eq_int @ X3 ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoI1
% 0.25/0.61 thf(fact_170_monoseq__minus,axiom,
% 0.25/0.61 ! [A: nat > real] :
% 0.25/0.61 ( ( topolo144289241q_real @ A )
% 0.25/0.61 => ( topolo144289241q_real
% 0.25/0.61 @ ^ [N: nat] : ( uminus_uminus_real @ ( A @ N ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % monoseq_minus
% 0.25/0.61 thf(fact_171_order__subst1,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: extended_ereal > extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_172_order__subst1,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: nat > extended_ereal,B: nat,C: nat] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_173_order__subst1,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: real > extended_ereal,B: real,C: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_174_order__subst1,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: int > extended_ereal,B: int,C: int] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_int @ B @ C )
% 0.25/0.61 => ( ! [X5: int,Y3: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_175_order__subst1,axiom,
% 0.25/0.61 ! [A: nat,F2: extended_ereal > nat,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_176_order__subst1,axiom,
% 0.25/0.61 ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_177_order__subst1,axiom,
% 0.25/0.61 ! [A: nat,F2: real > nat,B: real,C: real] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_178_order__subst1,axiom,
% 0.25/0.61 ! [A: nat,F2: int > nat,B: int,C: int] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_int @ B @ C )
% 0.25/0.61 => ( ! [X5: int,Y3: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_179_order__subst1,axiom,
% 0.25/0.61 ! [A: real,F2: extended_ereal > real,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_180_order__subst1,axiom,
% 0.25/0.61 ! [A: real,F2: nat > real,B: nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst1
% 0.25/0.61 thf(fact_181_order__subst2,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_182_order__subst2,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > nat,C: nat] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_183_order__subst2,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > real,C: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_184_order__subst2,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > int,C: int] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_185_order__subst2,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_186_order__subst2,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_187_order__subst2,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > real,C: real] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_188_order__subst2,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > int,C: int] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_189_order__subst2,axiom,
% 0.25/0.61 ! [A: real,B: real,F2: real > extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_190_order__subst2,axiom,
% 0.25/0.61 ! [A: real,B: real,F2: real > nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_subst2
% 0.25/0.61 thf(fact_191_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: extended_ereal > extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_192_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: nat,F2: extended_ereal > nat,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_193_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: real,F2: extended_ereal > real,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_194_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: int,F2: extended_ereal > int,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_195_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: nat > extended_ereal,B: nat,C: nat] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_196_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_197_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: real,F2: nat > real,B: nat,C: nat] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_198_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: int,F2: nat > int,B: nat,C: nat] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_199_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,F2: real > extended_ereal,B: real,C: real] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_200_ord__eq__le__subst,axiom,
% 0.25/0.61 ! [A: nat,F2: real > nat,B: real,C: real] :
% 0.25/0.61 ( ( A
% 0.25/0.61 = ( F2 @ B ) )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_subst
% 0.25/0.61 thf(fact_201_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_202_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > nat,C: nat] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_203_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > real,C: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_204_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,F2: extended_ereal > int,C: int] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: extended_ereal,Y3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_205_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_206_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_207_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > real,C: real] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_208_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: nat,B: nat,F2: nat > int,C: int] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: nat,Y3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_209_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: real,B: real,F2: real > extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_210_ord__le__eq__subst,axiom,
% 0.25/0.61 ! [A: real,B: real,F2: real > nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( ( F2 @ B )
% 0.25/0.61 = C )
% 0.25/0.61 => ( ! [X5: real,Y3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X5 @ Y3 )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y3 ) ) )
% 0.25/0.61 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_subst
% 0.25/0.61 thf(fact_211_eq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: extended_ereal,Z2: extended_ereal] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [X: extended_ereal,Y5: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X @ Y5 )
% 0.25/0.61 & ( ord_le824540014_ereal @ Y5 @ X ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_iff
% 0.25/0.61 thf(fact_212_eq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [X: nat,Y5: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X @ Y5 )
% 0.25/0.61 & ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_iff
% 0.25/0.61 thf(fact_213_eq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [X: real,Y5: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X @ Y5 )
% 0.25/0.61 & ( ord_less_eq_real @ Y5 @ X ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_iff
% 0.25/0.61 thf(fact_214_eq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [X: int,Y5: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ X @ Y5 )
% 0.25/0.61 & ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_iff
% 0.25/0.61 thf(fact_215_antisym,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ Y @ X2 )
% 0.25/0.61 => ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym
% 0.25/0.61 thf(fact_216_antisym,axiom,
% 0.25/0.61 ! [X2: nat,Y: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.25/0.61 => ( ( ord_less_eq_nat @ Y @ X2 )
% 0.25/0.61 => ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym
% 0.25/0.61 thf(fact_217_antisym,axiom,
% 0.25/0.61 ! [X2: real,Y: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 => ( ( ord_less_eq_real @ Y @ X2 )
% 0.25/0.61 => ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym
% 0.25/0.61 thf(fact_218_antisym,axiom,
% 0.25/0.61 ! [X2: int,Y: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ X2 @ Y )
% 0.25/0.61 => ( ( ord_less_eq_int @ Y @ X2 )
% 0.25/0.61 => ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym
% 0.25/0.61 thf(fact_219_linear,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 | ( ord_le824540014_ereal @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % linear
% 0.25/0.61 thf(fact_220_linear,axiom,
% 0.25/0.61 ! [X2: nat,Y: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.25/0.61 | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % linear
% 0.25/0.61 thf(fact_221_linear,axiom,
% 0.25/0.61 ! [X2: real,Y: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 | ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % linear
% 0.25/0.61 thf(fact_222_linear,axiom,
% 0.25/0.61 ! [X2: int,Y: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ X2 @ Y )
% 0.25/0.61 | ( ord_less_eq_int @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % linear
% 0.25/0.61 thf(fact_223_eq__refl,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ( X2 = Y )
% 0.25/0.61 => ( ord_le824540014_ereal @ X2 @ Y ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_refl
% 0.25/0.61 thf(fact_224_eq__refl,axiom,
% 0.25/0.61 ! [X2: nat,Y: nat] :
% 0.25/0.61 ( ( X2 = Y )
% 0.25/0.61 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_refl
% 0.25/0.61 thf(fact_225_eq__refl,axiom,
% 0.25/0.61 ! [X2: real,Y: real] :
% 0.25/0.61 ( ( X2 = Y )
% 0.25/0.61 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_refl
% 0.25/0.61 thf(fact_226_eq__refl,axiom,
% 0.25/0.61 ! [X2: int,Y: int] :
% 0.25/0.61 ( ( X2 = Y )
% 0.25/0.61 => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 0.25/0.61
% 0.25/0.61 % eq_refl
% 0.25/0.61 thf(fact_227_le__cases,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ~ ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 => ( ord_le824540014_ereal @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases
% 0.25/0.61 thf(fact_228_le__cases,axiom,
% 0.25/0.61 ! [X2: nat,Y: nat] :
% 0.25/0.61 ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 0.25/0.61 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases
% 0.25/0.61 thf(fact_229_le__cases,axiom,
% 0.25/0.61 ! [X2: real,Y: real] :
% 0.25/0.61 ( ~ ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases
% 0.25/0.61 thf(fact_230_le__cases,axiom,
% 0.25/0.61 ! [X2: int,Y: int] :
% 0.25/0.61 ( ~ ( ord_less_eq_int @ X2 @ Y )
% 0.25/0.61 => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases
% 0.25/0.61 thf(fact_231_order_Otrans,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order.trans
% 0.25/0.61 thf(fact_232_order_Otrans,axiom,
% 0.25/0.61 ! [A: nat,B: nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order.trans
% 0.25/0.61 thf(fact_233_order_Otrans,axiom,
% 0.25/0.61 ! [A: real,B: real,C: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ C )
% 0.25/0.61 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order.trans
% 0.25/0.61 thf(fact_234_order_Otrans,axiom,
% 0.25/0.61 ! [A: int,B: int,C: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_int @ B @ C )
% 0.25/0.61 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order.trans
% 0.25/0.61 thf(fact_235_le__cases3,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.25/0.61 ( ( ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 => ~ ( ord_le824540014_ereal @ Y @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_le824540014_ereal @ Y @ X2 )
% 0.25/0.61 => ~ ( ord_le824540014_ereal @ X2 @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_le824540014_ereal @ X2 @ Z3 )
% 0.25/0.61 => ~ ( ord_le824540014_ereal @ Z3 @ Y ) )
% 0.25/0.61 => ( ( ( ord_le824540014_ereal @ Z3 @ Y )
% 0.25/0.61 => ~ ( ord_le824540014_ereal @ Y @ X2 ) )
% 0.25/0.61 => ( ( ( ord_le824540014_ereal @ Y @ Z3 )
% 0.25/0.61 => ~ ( ord_le824540014_ereal @ Z3 @ X2 ) )
% 0.25/0.61 => ~ ( ( ord_le824540014_ereal @ Z3 @ X2 )
% 0.25/0.61 => ~ ( ord_le824540014_ereal @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases3
% 0.25/0.61 thf(fact_236_le__cases3,axiom,
% 0.25/0.61 ! [X2: nat,Y: nat,Z3: nat] :
% 0.25/0.61 ( ( ( ord_less_eq_nat @ X2 @ Y )
% 0.25/0.61 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 0.25/0.61 => ~ ( ord_less_eq_nat @ X2 @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_nat @ X2 @ Z3 )
% 0.25/0.61 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 0.25/0.61 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 0.25/0.61 => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.25/0.61 => ~ ( ord_less_eq_nat @ Z3 @ X2 ) )
% 0.25/0.61 => ~ ( ( ord_less_eq_nat @ Z3 @ X2 )
% 0.25/0.61 => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases3
% 0.25/0.61 thf(fact_237_le__cases3,axiom,
% 0.25/0.61 ! [X2: real,Y: real,Z3: real] :
% 0.25/0.61 ( ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 => ~ ( ord_less_eq_real @ Y @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_real @ Y @ X2 )
% 0.25/0.61 => ~ ( ord_less_eq_real @ X2 @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_real @ X2 @ Z3 )
% 0.25/0.61 => ~ ( ord_less_eq_real @ Z3 @ Y ) )
% 0.25/0.61 => ( ( ( ord_less_eq_real @ Z3 @ Y )
% 0.25/0.61 => ~ ( ord_less_eq_real @ Y @ X2 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_real @ Y @ Z3 )
% 0.25/0.61 => ~ ( ord_less_eq_real @ Z3 @ X2 ) )
% 0.25/0.61 => ~ ( ( ord_less_eq_real @ Z3 @ X2 )
% 0.25/0.61 => ~ ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases3
% 0.25/0.61 thf(fact_238_le__cases3,axiom,
% 0.25/0.61 ! [X2: int,Y: int,Z3: int] :
% 0.25/0.61 ( ( ( ord_less_eq_int @ X2 @ Y )
% 0.25/0.61 => ~ ( ord_less_eq_int @ Y @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_int @ Y @ X2 )
% 0.25/0.61 => ~ ( ord_less_eq_int @ X2 @ Z3 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_int @ X2 @ Z3 )
% 0.25/0.61 => ~ ( ord_less_eq_int @ Z3 @ Y ) )
% 0.25/0.61 => ( ( ( ord_less_eq_int @ Z3 @ Y )
% 0.25/0.61 => ~ ( ord_less_eq_int @ Y @ X2 ) )
% 0.25/0.61 => ( ( ( ord_less_eq_int @ Y @ Z3 )
% 0.25/0.61 => ~ ( ord_less_eq_int @ Z3 @ X2 ) )
% 0.25/0.61 => ~ ( ( ord_less_eq_int @ Z3 @ X2 )
% 0.25/0.61 => ~ ( ord_less_eq_int @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_cases3
% 0.25/0.61 thf(fact_239_antisym__conv,axiom,
% 0.25/0.61 ! [Y: extended_ereal,X2: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ Y @ X2 )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 = ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym_conv
% 0.25/0.61 thf(fact_240_antisym__conv,axiom,
% 0.25/0.61 ! [Y: nat,X2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ Y @ X2 )
% 0.25/0.61 => ( ( ord_less_eq_nat @ X2 @ Y )
% 0.25/0.61 = ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym_conv
% 0.25/0.61 thf(fact_241_antisym__conv,axiom,
% 0.25/0.61 ! [Y: real,X2: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ Y @ X2 )
% 0.25/0.61 => ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 = ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym_conv
% 0.25/0.61 thf(fact_242_antisym__conv,axiom,
% 0.25/0.61 ! [Y: int,X2: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ Y @ X2 )
% 0.25/0.61 => ( ( ord_less_eq_int @ X2 @ Y )
% 0.25/0.61 = ( X2 = Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % antisym_conv
% 0.25/0.61 thf(fact_243_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: extended_ereal,Z2: extended_ereal] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [A3: extended_ereal,B2: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A3 @ B2 )
% 0.25/0.61 & ( ord_le824540014_ereal @ B2 @ A3 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.eq_iff
% 0.25/0.61 thf(fact_244_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [A3: nat,B2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.25/0.61 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.eq_iff
% 0.25/0.61 thf(fact_245_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [A3: real,B2: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A3 @ B2 )
% 0.25/0.61 & ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.eq_iff
% 0.25/0.61 thf(fact_246_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.61 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.25/0.61 = ( ^ [A3: int,B2: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A3 @ B2 )
% 0.25/0.61 & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.eq_iff
% 0.25/0.61 thf(fact_247_ord__eq__le__trans,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ C )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_trans
% 0.25/0.61 thf(fact_248_ord__eq__le__trans,axiom,
% 0.25/0.61 ! [A: nat,B: nat,C: nat] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_trans
% 0.25/0.61 thf(fact_249_ord__eq__le__trans,axiom,
% 0.25/0.61 ! [A: real,B: real,C: real] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ C )
% 0.25/0.61 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_trans
% 0.25/0.61 thf(fact_250_ord__eq__le__trans,axiom,
% 0.25/0.61 ! [A: int,B: int,C: int] :
% 0.25/0.61 ( ( A = B )
% 0.25/0.61 => ( ( ord_less_eq_int @ B @ C )
% 0.25/0.61 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_eq_le_trans
% 0.25/0.61 thf(fact_251_ord__le__eq__trans,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( B = C )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_trans
% 0.25/0.61 thf(fact_252_ord__le__eq__trans,axiom,
% 0.25/0.61 ! [A: nat,B: nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( B = C )
% 0.25/0.61 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_trans
% 0.25/0.61 thf(fact_253_ord__le__eq__trans,axiom,
% 0.25/0.61 ! [A: real,B: real,C: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( B = C )
% 0.25/0.61 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_trans
% 0.25/0.61 thf(fact_254_ord__le__eq__trans,axiom,
% 0.25/0.61 ! [A: int,B: int,C: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.61 => ( ( B = C )
% 0.25/0.61 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ord_le_eq_trans
% 0.25/0.61 thf(fact_255_order__class_Oorder_Oantisym,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ B @ A )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.antisym
% 0.25/0.61 thf(fact_256_order__class_Oorder_Oantisym,axiom,
% 0.25/0.61 ! [A: nat,B: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.antisym
% 0.25/0.61 thf(fact_257_order__class_Oorder_Oantisym,axiom,
% 0.25/0.61 ! [A: real,B: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_real @ B @ A )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.antisym
% 0.25/0.61 thf(fact_258_order__class_Oorder_Oantisym,axiom,
% 0.25/0.61 ! [A: int,B: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.61 => ( ( ord_less_eq_int @ B @ A )
% 0.25/0.61 => ( A = B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_class.order.antisym
% 0.25/0.61 thf(fact_259_order__trans,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ Y @ Z3 )
% 0.25/0.61 => ( ord_le824540014_ereal @ X2 @ Z3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_trans
% 0.25/0.61 thf(fact_260_order__trans,axiom,
% 0.25/0.61 ! [X2: nat,Y: nat,Z3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.25/0.61 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.25/0.61 => ( ord_less_eq_nat @ X2 @ Z3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_trans
% 0.25/0.61 thf(fact_261_order__trans,axiom,
% 0.25/0.61 ! [X2: real,Y: real,Z3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 => ( ( ord_less_eq_real @ Y @ Z3 )
% 0.25/0.61 => ( ord_less_eq_real @ X2 @ Z3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_trans
% 0.25/0.61 thf(fact_262_order__trans,axiom,
% 0.25/0.61 ! [X2: int,Y: int,Z3: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ X2 @ Y )
% 0.25/0.61 => ( ( ord_less_eq_int @ Y @ Z3 )
% 0.25/0.61 => ( ord_less_eq_int @ X2 @ Z3 ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % order_trans
% 0.25/0.61 thf(fact_263_dual__order_Orefl,axiom,
% 0.25/0.61 ! [A: extended_ereal] : ( ord_le824540014_ereal @ A @ A ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.refl
% 0.25/0.61 thf(fact_264_dual__order_Orefl,axiom,
% 0.25/0.61 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.refl
% 0.25/0.61 thf(fact_265_dual__order_Orefl,axiom,
% 0.25/0.61 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.refl
% 0.25/0.61 thf(fact_266_dual__order_Orefl,axiom,
% 0.25/0.61 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.refl
% 0.25/0.61 thf(fact_267_linorder__wlog,axiom,
% 0.25/0.61 ! [P: extended_ereal > extended_ereal > $o,A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ! [A4: extended_ereal,B3: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A4 @ B3 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( ! [A4: extended_ereal,B3: extended_ereal] :
% 0.25/0.61 ( ( P @ B3 @ A4 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( P @ A @ B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % linorder_wlog
% 0.25/0.61 thf(fact_268_linorder__wlog,axiom,
% 0.25/0.61 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.25/0.61 ( ! [A4: nat,B3: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( ! [A4: nat,B3: nat] :
% 0.25/0.61 ( ( P @ B3 @ A4 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( P @ A @ B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % linorder_wlog
% 0.25/0.61 thf(fact_269_linorder__wlog,axiom,
% 0.25/0.61 ! [P: real > real > $o,A: real,B: real] :
% 0.25/0.61 ( ! [A4: real,B3: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ A4 @ B3 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( ! [A4: real,B3: real] :
% 0.25/0.61 ( ( P @ B3 @ A4 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( P @ A @ B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % linorder_wlog
% 0.25/0.61 thf(fact_270_linorder__wlog,axiom,
% 0.25/0.61 ! [P: int > int > $o,A: int,B: int] :
% 0.25/0.61 ( ! [A4: int,B3: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ A4 @ B3 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( ! [A4: int,B3: int] :
% 0.25/0.61 ( ( P @ B3 @ A4 )
% 0.25/0.61 => ( P @ A4 @ B3 ) )
% 0.25/0.61 => ( P @ A @ B ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % linorder_wlog
% 0.25/0.61 thf(fact_271_dual__order_Otrans,axiom,
% 0.25/0.61 ! [B: nat,A: nat,C: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.61 => ( ( ord_less_eq_nat @ C @ B )
% 0.25/0.61 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.trans
% 0.25/0.61 thf(fact_272_dual__order_Otrans,axiom,
% 0.25/0.61 ! [B: real,A: real,C: real] :
% 0.25/0.61 ( ( ord_less_eq_real @ B @ A )
% 0.25/0.61 => ( ( ord_less_eq_real @ C @ B )
% 0.25/0.61 => ( ord_less_eq_real @ C @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.trans
% 0.25/0.61 thf(fact_273_dual__order_Otrans,axiom,
% 0.25/0.61 ! [B: int,A: int,C: int] :
% 0.25/0.61 ( ( ord_less_eq_int @ B @ A )
% 0.25/0.61 => ( ( ord_less_eq_int @ C @ B )
% 0.25/0.61 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % dual_order.trans
% 0.25/0.61 thf(fact_274_liminf__PInfty,axiom,
% 0.25/0.61 ! [X3: nat > extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ X3 @ ( topolo2140997059_ereal @ extend1289208545_ereal ) @ at_top_nat )
% 0.25/0.61 = ( ( liminf1045857232_ereal @ at_top_nat @ X3 )
% 0.25/0.61 = extend1289208545_ereal ) ) ).
% 0.25/0.61
% 0.25/0.61 % liminf_PInfty
% 0.25/0.61 thf(fact_275_ereal__infty__less__eq_I1_J,axiom,
% 0.25/0.61 ! [X2: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ extend1289208545_ereal @ X2 )
% 0.25/0.61 = ( X2 = extend1289208545_ereal ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_infty_less_eq(1)
% 0.25/0.61 thf(fact_276_ereal__infty__less__eq_I2_J,axiom,
% 0.25/0.61 ! [X2: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X2 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 = ( X2
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_infty_less_eq(2)
% 0.25/0.61 thf(fact_277_MInfty__neq__PInfty_I1_J,axiom,
% 0.25/0.61 ( extend1289208545_ereal
% 0.25/0.61 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.25/0.61
% 0.25/0.61 % MInfty_neq_PInfty(1)
% 0.25/0.61 thf(fact_278_ereal__less__eq_I1_J,axiom,
% 0.25/0.61 ! [X2: extended_ereal] : ( ord_le824540014_ereal @ X2 @ extend1289208545_ereal ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_less_eq(1)
% 0.25/0.61 thf(fact_279_ereal__infty__less__eq2_I1_J,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( A = extend1289208545_ereal )
% 0.25/0.61 => ( B = extend1289208545_ereal ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_infty_less_eq2(1)
% 0.25/0.61 thf(fact_280_neq__PInf__trans,axiom,
% 0.25/0.61 ! [Y: extended_ereal,X2: extended_ereal] :
% 0.25/0.61 ( ( Y != extend1289208545_ereal )
% 0.25/0.61 => ( ( ord_le824540014_ereal @ X2 @ Y )
% 0.25/0.61 => ( X2 != extend1289208545_ereal ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % neq_PInf_trans
% 0.25/0.61 thf(fact_281_ereal__infty__less__eq2_I2_J,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.61 => ( ( B
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( A
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_infty_less_eq2(2)
% 0.25/0.61 thf(fact_282_ereal__less__eq_I2_J,axiom,
% 0.25/0.61 ! [X2: extended_ereal] : ( ord_le824540014_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ X2 ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_less_eq(2)
% 0.25/0.61 thf(fact_283_Lim__MInfty,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) @ at_top_nat )
% 0.25/0.61 = ( ! [B4: real] :
% 0.25/0.61 ? [N6: nat] :
% 0.25/0.61 ! [N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N6 @ N )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ N ) @ ( extended_ereal2 @ B4 ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_MInfty
% 0.25/0.61 thf(fact_284_Lim__bounded__MInfty,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,L: extended_ereal,B5: real] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] : ( ord_le824540014_ereal @ ( extended_ereal2 @ B5 ) @ ( F2 @ N2 ) )
% 0.25/0.61 => ( L
% 0.25/0.61 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded_MInfty
% 0.25/0.61 thf(fact_285_Lim__PInfty,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ extend1289208545_ereal ) @ at_top_nat )
% 0.25/0.61 = ( ! [B4: real] :
% 0.25/0.61 ? [N6: nat] :
% 0.25/0.61 ! [N: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N6 @ N )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( extended_ereal2 @ B4 ) @ ( F2 @ N ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_PInfty
% 0.25/0.61 thf(fact_286_Lim__bounded__PInfty2,axiom,
% 0.25/0.61 ! [F2: nat > extended_ereal,L: extended_ereal,N3: nat,B5: real] :
% 0.25/0.61 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ at_top_nat )
% 0.25/0.61 => ( ! [N2: nat] :
% 0.25/0.61 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( F2 @ N2 ) @ ( extended_ereal2 @ B5 ) ) )
% 0.25/0.61 => ( L != extend1289208545_ereal ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % Lim_bounded_PInfty2
% 0.25/0.61 thf(fact_287_ereal_Oinject,axiom,
% 0.25/0.61 ! [X1: real,Y1: real] :
% 0.25/0.61 ( ( ( extended_ereal2 @ X1 )
% 0.25/0.61 = ( extended_ereal2 @ Y1 ) )
% 0.25/0.61 = ( X1 = Y1 ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal.inject
% 0.25/0.61 thf(fact_288_ereal__cong,axiom,
% 0.25/0.61 ! [X2: real,Y: real] :
% 0.25/0.61 ( ( X2 = Y )
% 0.25/0.61 => ( ( extended_ereal2 @ X2 )
% 0.25/0.61 = ( extended_ereal2 @ Y ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_cong
% 0.25/0.61 thf(fact_289_ereal__less__eq_I3_J,axiom,
% 0.25/0.61 ! [R: real,P2: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ ( extended_ereal2 @ R ) @ ( extended_ereal2 @ P2 ) )
% 0.25/0.61 = ( ord_less_eq_real @ R @ P2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_less_eq(3)
% 0.25/0.61 thf(fact_290_PInfty__neq__ereal_I1_J,axiom,
% 0.25/0.61 ! [R: real] :
% 0.25/0.61 ( ( extended_ereal2 @ R )
% 0.25/0.61 != extend1289208545_ereal ) ).
% 0.25/0.61
% 0.25/0.61 % PInfty_neq_ereal(1)
% 0.25/0.61 thf(fact_291_uminus__ereal_Osimps_I1_J,axiom,
% 0.25/0.61 ! [R: real] :
% 0.25/0.61 ( ( uminus1208298309_ereal @ ( extended_ereal2 @ R ) )
% 0.25/0.61 = ( extended_ereal2 @ ( uminus_uminus_real @ R ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % uminus_ereal.simps(1)
% 0.25/0.61 thf(fact_292_ereal__le__le,axiom,
% 0.25/0.61 ! [Y: real,A: extended_ereal,X2: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ ( extended_ereal2 @ Y ) @ A )
% 0.25/0.61 => ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 => ( ord_le824540014_ereal @ ( extended_ereal2 @ X2 ) @ A ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_le_le
% 0.25/0.61 thf(fact_293_le__ereal__le,axiom,
% 0.25/0.61 ! [A: extended_ereal,X2: real,Y: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ A @ ( extended_ereal2 @ X2 ) )
% 0.25/0.61 => ( ( ord_less_eq_real @ X2 @ Y )
% 0.25/0.61 => ( ord_le824540014_ereal @ A @ ( extended_ereal2 @ Y ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % le_ereal_le
% 0.25/0.61 thf(fact_294_ereal__le__real,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.25/0.61 ( ! [Z4: real] :
% 0.25/0.61 ( ( ord_le824540014_ereal @ X2 @ ( extended_ereal2 @ Z4 ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ Y @ ( extended_ereal2 @ Z4 ) ) )
% 0.25/0.61 => ( ord_le824540014_ereal @ Y @ X2 ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_le_real
% 0.25/0.61 thf(fact_295_ereal__semiline__unique,axiom,
% 0.25/0.61 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.61 ( ( ( collect_real
% 0.25/0.61 @ ^ [Y5: real] : ( ord_le824540014_ereal @ A @ ( extended_ereal2 @ Y5 ) ) )
% 0.25/0.61 = ( collect_real
% 0.25/0.61 @ ^ [Y5: real] : ( ord_le824540014_ereal @ B @ ( extended_ereal2 @ Y5 ) ) ) )
% 0.25/0.61 = ( A = B ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_semiline_unique
% 0.25/0.61 thf(fact_296_real__of__ereal_Oinduct,axiom,
% 0.25/0.61 ! [P: extended_ereal > $o,A0: extended_ereal] :
% 0.25/0.61 ( ! [R2: real] : ( P @ ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( P @ extend1289208545_ereal )
% 0.25/0.61 => ( ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( P @ A0 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % real_of_ereal.induct
% 0.25/0.61 thf(fact_297_real__of__ereal_Ocases,axiom,
% 0.25/0.61 ! [X2: extended_ereal] :
% 0.25/0.61 ( ! [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 != ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( X2 != extend1289208545_ereal )
% 0.25/0.61 => ( X2
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % real_of_ereal.cases
% 0.25/0.61 thf(fact_298_times__ereal_Oinduct,axiom,
% 0.25/0.61 ! [P: extended_ereal > extended_ereal > $o,A0: extended_ereal,A1: extended_ereal] :
% 0.25/0.61 ( ! [R2: real,P3: real] : ( P @ ( extended_ereal2 @ R2 ) @ ( extended_ereal2 @ P3 ) )
% 0.25/0.61 => ( ! [R2: real] : ( P @ ( extended_ereal2 @ R2 ) @ extend1289208545_ereal )
% 0.25/0.61 => ( ! [R2: real] : ( P @ extend1289208545_ereal @ ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ! [R2: real] : ( P @ ( extended_ereal2 @ R2 ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( ! [R2: real] : ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( P @ extend1289208545_ereal @ extend1289208545_ereal )
% 0.25/0.61 => ( ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ extend1289208545_ereal )
% 0.25/0.61 => ( ( P @ extend1289208545_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % times_ereal.induct
% 0.25/0.61 thf(fact_299_plus__ereal_Oinduct,axiom,
% 0.25/0.61 ! [P: extended_ereal > extended_ereal > $o,A0: extended_ereal,A1: extended_ereal] :
% 0.25/0.61 ( ! [R2: real,P3: real] : ( P @ ( extended_ereal2 @ R2 ) @ ( extended_ereal2 @ P3 ) )
% 0.25/0.61 => ( ! [X_1: extended_ereal] : ( P @ extend1289208545_ereal @ X_1 )
% 0.25/0.61 => ( ! [A4: extended_ereal] : ( P @ A4 @ extend1289208545_ereal )
% 0.25/0.61 => ( ! [R2: real] : ( P @ ( extended_ereal2 @ R2 ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( ! [P3: real] : ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( extended_ereal2 @ P3 ) )
% 0.25/0.61 => ( ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % plus_ereal.induct
% 0.25/0.61 thf(fact_300_less__ereal_Oinduct,axiom,
% 0.25/0.61 ! [P: extended_ereal > extended_ereal > $o,A0: extended_ereal,A1: extended_ereal] :
% 0.25/0.61 ( ! [X5: real,Y3: real] : ( P @ ( extended_ereal2 @ X5 ) @ ( extended_ereal2 @ Y3 ) )
% 0.25/0.61 => ( ! [X_1: extended_ereal] : ( P @ extend1289208545_ereal @ X_1 )
% 0.25/0.61 => ( ! [A4: extended_ereal] : ( P @ A4 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( ! [X5: real] : ( P @ ( extended_ereal2 @ X5 ) @ extend1289208545_ereal )
% 0.25/0.61 => ( ! [R2: real] : ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ extend1289208545_ereal )
% 0.25/0.61 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % less_ereal.induct
% 0.25/0.61 thf(fact_301_abs__ereal_Oinduct,axiom,
% 0.25/0.61 ! [P: extended_ereal > $o,A0: extended_ereal] :
% 0.25/0.61 ( ! [R2: real] : ( P @ ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( P @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( ( P @ extend1289208545_ereal )
% 0.25/0.61 => ( P @ A0 ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % abs_ereal.induct
% 0.25/0.61 thf(fact_302_ereal__all__split,axiom,
% 0.25/0.61 ( ( ^ [P4: extended_ereal > $o] :
% 0.25/0.61 ! [X6: extended_ereal] : ( P4 @ X6 ) )
% 0.25/0.61 = ( ^ [P5: extended_ereal > $o] :
% 0.25/0.61 ( ( P5 @ extend1289208545_ereal )
% 0.25/0.61 & ! [X: real] : ( P5 @ ( extended_ereal2 @ X ) )
% 0.25/0.61 & ( P5 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_all_split
% 0.25/0.61 thf(fact_303_abs__ereal_Ocases,axiom,
% 0.25/0.61 ! [X2: extended_ereal] :
% 0.25/0.61 ( ! [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 != ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( X2
% 0.25/0.61 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( X2 = extend1289208545_ereal ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % abs_ereal.cases
% 0.25/0.61 thf(fact_304_ereal__ex__split,axiom,
% 0.25/0.61 ( ( ^ [P4: extended_ereal > $o] :
% 0.25/0.61 ? [X6: extended_ereal] : ( P4 @ X6 ) )
% 0.25/0.61 = ( ^ [P5: extended_ereal > $o] :
% 0.25/0.61 ( ( P5 @ extend1289208545_ereal )
% 0.25/0.61 | ? [X: real] : ( P5 @ ( extended_ereal2 @ X ) )
% 0.25/0.61 | ( P5 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ).
% 0.25/0.61
% 0.25/0.61 % ereal_ex_split
% 0.25/0.61 thf(fact_305_ereal3__cases,axiom,
% 0.25/0.61 ! [X2: extended_ereal,Xa3: extended_ereal,Xb: extended_ereal] :
% 0.25/0.61 ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ? [Ra: real] :
% 0.25/0.61 ( Xa3
% 0.25/0.61 = ( extended_ereal2 @ Ra ) )
% 0.25/0.61 => ! [Rb: real] :
% 0.25/0.61 ( Xb
% 0.25/0.61 != ( extended_ereal2 @ Rb ) ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ? [Ra: real] :
% 0.25/0.61 ( Xa3
% 0.25/0.61 = ( extended_ereal2 @ Ra ) )
% 0.25/0.61 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ? [Ra: real] :
% 0.25/0.61 ( Xa3
% 0.25/0.61 = ( extended_ereal2 @ Ra ) )
% 0.25/0.61 => ( Xb
% 0.25/0.61 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.61 => ! [Ra: real] :
% 0.25/0.61 ( Xb
% 0.25/0.61 != ( extended_ereal2 @ Ra ) ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.61 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.61 => ( Xb
% 0.25/0.61 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( Xa3
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ! [Ra: real] :
% 0.25/0.61 ( Xb
% 0.25/0.61 != ( extended_ereal2 @ Ra ) ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( Xa3
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.61 => ( ( ? [R2: real] :
% 0.25/0.61 ( X2
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ( ( Xa3
% 0.25/0.61 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.61 => ( Xb
% 0.25/0.61 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.61 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.61 => ( ? [R2: real] :
% 0.25/0.61 ( Xa3
% 0.25/0.61 = ( extended_ereal2 @ R2 ) )
% 0.25/0.61 => ! [Ra: real] :
% 0.25/0.62 ( Xb
% 0.25/0.62 != ( extended_ereal2 @ Ra ) ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ? [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ? [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( Xb
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ! [R2: real] :
% 0.25/0.62 ( Xb
% 0.25/0.62 != ( extended_ereal2 @ R2 ) ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ( Xb
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ! [R2: real] :
% 0.25/0.62 ( Xb
% 0.25/0.62 != ( extended_ereal2 @ R2 ) ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Xb
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ? [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ! [Ra: real] :
% 0.25/0.62 ( Xb
% 0.25/0.62 != ( extended_ereal2 @ Ra ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ? [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ? [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( Xb
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ! [R2: real] :
% 0.25/0.62 ( Xb
% 0.25/0.62 != ( extended_ereal2 @ R2 ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ( Xb
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ! [R2: real] :
% 0.25/0.62 ( Xb
% 0.25/0.62 != ( extended_ereal2 @ R2 ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Xb != extend1289208545_ereal ) ) )
% 0.25/0.62 => ~ ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Xb
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal3_cases
% 0.25/0.62 thf(fact_306_ereal2__cases,axiom,
% 0.25/0.62 ! [X2: extended_ereal,Xa3: extended_ereal] :
% 0.25/0.62 ( ( ? [R2: real] :
% 0.25/0.62 ( X2
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ! [Ra: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 != ( extended_ereal2 @ Ra ) ) )
% 0.25/0.62 => ( ( ? [R2: real] :
% 0.25/0.62 ( X2
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( Xa3 != extend1289208545_ereal ) )
% 0.25/0.62 => ( ( ? [R2: real] :
% 0.25/0.62 ( X2
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( Xa3
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ! [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 != ( extended_ereal2 @ R2 ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( Xa3 != extend1289208545_ereal ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( Xa3
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ! [R2: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 != ( extended_ereal2 @ R2 ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Xa3 != extend1289208545_ereal ) )
% 0.25/0.62 => ~ ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Xa3
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal2_cases
% 0.25/0.62 thf(fact_307_ereal__cases,axiom,
% 0.25/0.62 ! [X2: extended_ereal] :
% 0.25/0.62 ( ! [R2: real] :
% 0.25/0.62 ( X2
% 0.25/0.62 != ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( ( X2 != extend1289208545_ereal )
% 0.25/0.62 => ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_cases
% 0.25/0.62 thf(fact_308_MInfty__neq__ereal_I1_J,axiom,
% 0.25/0.62 ! [R: real] :
% 0.25/0.62 ( ( extended_ereal2 @ R )
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.25/0.62
% 0.25/0.62 % MInfty_neq_ereal(1)
% 0.25/0.62 thf(fact_309_ereal__top,axiom,
% 0.25/0.62 ! [X2: extended_ereal] :
% 0.25/0.62 ( ! [B6: real] : ( ord_le824540014_ereal @ ( extended_ereal2 @ B6 ) @ X2 )
% 0.25/0.62 => ( X2 = extend1289208545_ereal ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_top
% 0.25/0.62 thf(fact_310_ereal__bot,axiom,
% 0.25/0.62 ! [X2: extended_ereal] :
% 0.25/0.62 ( ! [B6: real] : ( ord_le824540014_ereal @ X2 @ ( extended_ereal2 @ B6 ) )
% 0.25/0.62 => ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_bot
% 0.25/0.62 thf(fact_311_Lim__bounded__PInfty,axiom,
% 0.25/0.62 ! [F2: nat > extended_ereal,L: extended_ereal,B5: real] :
% 0.25/0.62 ( ( filter1531173832_ereal @ F2 @ ( topolo2140997059_ereal @ L ) @ at_top_nat )
% 0.25/0.62 => ( ! [N2: nat] : ( ord_le824540014_ereal @ ( F2 @ N2 ) @ ( extended_ereal2 @ B5 ) )
% 0.25/0.62 => ( L != extend1289208545_ereal ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % Lim_bounded_PInfty
% 0.25/0.62 thf(fact_312_ereal__minus__real__tendsto__MInf,axiom,
% 0.25/0.62 ( filter1531173832_ereal
% 0.25/0.62 @ ^ [X: nat] : ( extended_ereal2 @ ( uminus_uminus_real @ ( semiri2110766477t_real @ X ) ) )
% 0.25/0.62 @ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 @ at_top_nat ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_minus_real_tendsto_MInf
% 0.25/0.62 thf(fact_313_ereal__PInfty__eq__plus,axiom,
% 0.25/0.62 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.62 ( ( extend1289208545_ereal
% 0.25/0.62 = ( plus_p2118002693_ereal @ A @ B ) )
% 0.25/0.62 = ( ( A = extend1289208545_ereal )
% 0.25/0.62 | ( B = extend1289208545_ereal ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_PInfty_eq_plus
% 0.25/0.62 thf(fact_314_ereal__plus__eq__PInfty,axiom,
% 0.25/0.62 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.62 ( ( ( plus_p2118002693_ereal @ A @ B )
% 0.25/0.62 = extend1289208545_ereal )
% 0.25/0.62 = ( ( A = extend1289208545_ereal )
% 0.25/0.62 | ( B = extend1289208545_ereal ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_plus_eq_PInfty
% 0.25/0.62 thf(fact_315_ereal__MInfty__eq__plus,axiom,
% 0.25/0.62 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.62 ( ( ( uminus1208298309_ereal @ extend1289208545_ereal )
% 0.25/0.62 = ( plus_p2118002693_ereal @ A @ B ) )
% 0.25/0.62 = ( ( ( A
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 & ( B != extend1289208545_ereal ) )
% 0.25/0.62 | ( ( B
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 & ( A != extend1289208545_ereal ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_MInfty_eq_plus
% 0.25/0.62 thf(fact_316_ereal__plus__eq__MInfty,axiom,
% 0.25/0.62 ! [A: extended_ereal,B: extended_ereal] :
% 0.25/0.62 ( ( ( plus_p2118002693_ereal @ A @ B )
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 = ( ( ( A
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 | ( B
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) )
% 0.25/0.62 & ( A != extend1289208545_ereal )
% 0.25/0.62 & ( B != extend1289208545_ereal ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_plus_eq_MInfty
% 0.25/0.62 thf(fact_317_plus__ereal_Osimps_I2_J,axiom,
% 0.25/0.62 ! [A: extended_ereal] :
% 0.25/0.62 ( ( plus_p2118002693_ereal @ extend1289208545_ereal @ A )
% 0.25/0.62 = extend1289208545_ereal ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.simps(2)
% 0.25/0.62 thf(fact_318_plus__ereal_Osimps_I3_J,axiom,
% 0.25/0.62 ! [A: extended_ereal] :
% 0.25/0.62 ( ( plus_p2118002693_ereal @ A @ extend1289208545_ereal )
% 0.25/0.62 = extend1289208545_ereal ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.simps(3)
% 0.25/0.62 thf(fact_319_plus__ereal_Osimps_I6_J,axiom,
% 0.25/0.62 ( ( plus_p2118002693_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.simps(6)
% 0.25/0.62 thf(fact_320_ereal__add__cancel__left,axiom,
% 0.25/0.62 ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.62 ( ( A
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( ( plus_p2118002693_ereal @ A @ B )
% 0.25/0.62 = ( plus_p2118002693_ereal @ A @ C ) )
% 0.25/0.62 = ( ( A = extend1289208545_ereal )
% 0.25/0.62 | ( B = C ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_add_cancel_left
% 0.25/0.62 thf(fact_321_ereal__add__cancel__right,axiom,
% 0.25/0.62 ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
% 0.25/0.62 ( ( A
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( ( plus_p2118002693_ereal @ B @ A )
% 0.25/0.62 = ( plus_p2118002693_ereal @ C @ A ) )
% 0.25/0.62 = ( ( A = extend1289208545_ereal )
% 0.25/0.62 | ( B = C ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_add_cancel_right
% 0.25/0.62 thf(fact_322_plus__ereal_Osimps_I5_J,axiom,
% 0.25/0.62 ! [P2: real] :
% 0.25/0.62 ( ( plus_p2118002693_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( extended_ereal2 @ P2 ) )
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.simps(5)
% 0.25/0.62 thf(fact_323_plus__ereal_Osimps_I4_J,axiom,
% 0.25/0.62 ! [R: real] :
% 0.25/0.62 ( ( plus_p2118002693_ereal @ ( extended_ereal2 @ R ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.simps(4)
% 0.25/0.62 thf(fact_324_ereal__add__le__add__iff,axiom,
% 0.25/0.62 ! [C: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 0.25/0.62 ( ( ord_le824540014_ereal @ ( plus_p2118002693_ereal @ C @ A ) @ ( plus_p2118002693_ereal @ C @ B ) )
% 0.25/0.62 = ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.62 | ( C = extend1289208545_ereal )
% 0.25/0.62 | ( ( C
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 & ( A != extend1289208545_ereal )
% 0.25/0.62 & ( B != extend1289208545_ereal ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_add_le_add_iff
% 0.25/0.62 thf(fact_325_ereal__add__le__add__iff2,axiom,
% 0.25/0.62 ! [A: extended_ereal,C: extended_ereal,B: extended_ereal] :
% 0.25/0.62 ( ( ord_le824540014_ereal @ ( plus_p2118002693_ereal @ A @ C ) @ ( plus_p2118002693_ereal @ B @ C ) )
% 0.25/0.62 = ( ( ord_le824540014_ereal @ A @ B )
% 0.25/0.62 | ( C = extend1289208545_ereal )
% 0.25/0.62 | ( ( C
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 & ( A != extend1289208545_ereal )
% 0.25/0.62 & ( B != extend1289208545_ereal ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_add_le_add_iff2
% 0.25/0.62 thf(fact_326_id__nat__ereal__tendsto__PInf,axiom,
% 0.25/0.62 ( filter1531173832_ereal
% 0.25/0.62 @ ^ [X: nat] : ( extended_ereal2 @ ( semiri2110766477t_real @ X ) )
% 0.25/0.62 @ ( topolo2140997059_ereal @ extend1289208545_ereal )
% 0.25/0.62 @ at_top_nat ) ).
% 0.25/0.62
% 0.25/0.62 % id_nat_ereal_tendsto_PInf
% 0.25/0.62 thf(fact_327_ereal__liminf__add__mono,axiom,
% 0.25/0.62 ! [U: nat > extended_ereal,V: nat > extended_ereal] :
% 0.25/0.62 ( ~ ( ( ( ( liminf1045857232_ereal @ at_top_nat @ U )
% 0.25/0.62 = extend1289208545_ereal )
% 0.25/0.62 & ( ( liminf1045857232_ereal @ at_top_nat @ V )
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) )
% 0.25/0.62 | ( ( ( liminf1045857232_ereal @ at_top_nat @ U )
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 & ( ( liminf1045857232_ereal @ at_top_nat @ V )
% 0.25/0.62 = extend1289208545_ereal ) ) )
% 0.25/0.62 => ( ord_le824540014_ereal @ ( plus_p2118002693_ereal @ ( liminf1045857232_ereal @ at_top_nat @ U ) @ ( liminf1045857232_ereal @ at_top_nat @ V ) )
% 0.25/0.62 @ ( liminf1045857232_ereal @ at_top_nat
% 0.25/0.62 @ ^ [N: nat] : ( plus_p2118002693_ereal @ ( U @ N ) @ ( V @ N ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % ereal_liminf_add_mono
% 0.25/0.62 thf(fact_328_nat__add__left__cancel__le,axiom,
% 0.25/0.62 ! [K: nat,M5: nat,N7: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M5 ) @ ( plus_plus_nat @ K @ N7 ) )
% 0.25/0.62 = ( ord_less_eq_nat @ M5 @ N7 ) ) ).
% 0.25/0.62
% 0.25/0.62 % nat_add_left_cancel_le
% 0.25/0.62 thf(fact_329_nat__int__comparison_I3_J,axiom,
% 0.25/0.62 ( ord_less_eq_nat
% 0.25/0.62 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri2019852685at_int @ A3 ) @ ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % nat_int_comparison(3)
% 0.25/0.62 thf(fact_330_add__leE,axiom,
% 0.25/0.62 ! [M5: nat,K: nat,N7: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M5 @ K ) @ N7 )
% 0.25/0.62 => ~ ( ( ord_less_eq_nat @ M5 @ N7 )
% 0.25/0.62 => ~ ( ord_less_eq_nat @ K @ N7 ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % add_leE
% 0.25/0.62 thf(fact_331_le__add1,axiom,
% 0.25/0.62 ! [N7: nat,M5: nat] : ( ord_less_eq_nat @ N7 @ ( plus_plus_nat @ N7 @ M5 ) ) ).
% 0.25/0.62
% 0.25/0.62 % le_add1
% 0.25/0.62 thf(fact_332_le__add2,axiom,
% 0.25/0.62 ! [N7: nat,M5: nat] : ( ord_less_eq_nat @ N7 @ ( plus_plus_nat @ M5 @ N7 ) ) ).
% 0.25/0.62
% 0.25/0.62 % le_add2
% 0.25/0.62 thf(fact_333_add__leD1,axiom,
% 0.25/0.62 ! [M5: nat,K: nat,N7: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M5 @ K ) @ N7 )
% 0.25/0.62 => ( ord_less_eq_nat @ M5 @ N7 ) ) ).
% 0.25/0.62
% 0.25/0.62 % add_leD1
% 0.25/0.62 thf(fact_334_add__leD2,axiom,
% 0.25/0.62 ! [M5: nat,K: nat,N7: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M5 @ K ) @ N7 )
% 0.25/0.62 => ( ord_less_eq_nat @ K @ N7 ) ) ).
% 0.25/0.62
% 0.25/0.62 % add_leD2
% 0.25/0.62 thf(fact_335_le__Suc__ex,axiom,
% 0.25/0.62 ! [K: nat,L: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ K @ L )
% 0.25/0.62 => ? [N2: nat] :
% 0.25/0.62 ( L
% 0.25/0.62 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % le_Suc_ex
% 0.25/0.62 thf(fact_336_add__le__mono,axiom,
% 0.25/0.62 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.62 => ( ( ord_less_eq_nat @ K @ L )
% 0.25/0.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % add_le_mono
% 0.25/0.62 thf(fact_337_add__le__mono1,axiom,
% 0.25/0.62 ! [I: nat,J: nat,K: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % add_le_mono1
% 0.25/0.62 thf(fact_338_trans__le__add1,axiom,
% 0.25/0.62 ! [I: nat,J: nat,M5: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.62 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M5 ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % trans_le_add1
% 0.25/0.62 thf(fact_339_trans__le__add2,axiom,
% 0.25/0.62 ! [I: nat,J: nat,M5: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.62 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M5 @ J ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % trans_le_add2
% 0.25/0.62 thf(fact_340_nat__le__iff__add,axiom,
% 0.25/0.62 ( ord_less_eq_nat
% 0.25/0.62 = ( ^ [M4: nat,N: nat] :
% 0.25/0.62 ? [K2: nat] :
% 0.25/0.62 ( N
% 0.25/0.62 = ( plus_plus_nat @ M4 @ K2 ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % nat_le_iff_add
% 0.25/0.62 thf(fact_341_nat__leq__as__int,axiom,
% 0.25/0.62 ( ord_less_eq_nat
% 0.25/0.62 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri2019852685at_int @ A3 ) @ ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % nat_leq_as_int
% 0.25/0.62 thf(fact_342_plus__ereal_Osimps_I1_J,axiom,
% 0.25/0.62 ! [R: real,P2: real] :
% 0.25/0.62 ( ( plus_p2118002693_ereal @ ( extended_ereal2 @ R ) @ ( extended_ereal2 @ P2 ) )
% 0.25/0.62 = ( extended_ereal2 @ ( plus_plus_real @ R @ P2 ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.simps(1)
% 0.25/0.62 thf(fact_343_filterlim__uminus__at__bot__at__top,axiom,
% 0.25/0.62 filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real ).
% 0.25/0.62
% 0.25/0.62 % filterlim_uminus_at_bot_at_top
% 0.25/0.62 thf(fact_344_filterlim__uminus__at__top__at__bot,axiom,
% 0.25/0.62 filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real ).
% 0.25/0.62
% 0.25/0.62 % filterlim_uminus_at_top_at_bot
% 0.25/0.62 thf(fact_345_Nat_Oex__has__greatest__nat,axiom,
% 0.25/0.62 ! [P: nat > $o,K: nat,B: nat] :
% 0.25/0.62 ( ( P @ K )
% 0.25/0.62 => ( ! [Y3: nat] :
% 0.25/0.62 ( ( P @ Y3 )
% 0.25/0.62 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.25/0.62 => ? [X5: nat] :
% 0.25/0.62 ( ( P @ X5 )
% 0.25/0.62 & ! [Y6: nat] :
% 0.25/0.62 ( ( P @ Y6 )
% 0.25/0.62 => ( ord_less_eq_nat @ Y6 @ X5 ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % Nat.ex_has_greatest_nat
% 0.25/0.62 thf(fact_346_nat__le__linear,axiom,
% 0.25/0.62 ! [M5: nat,N7: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ M5 @ N7 )
% 0.25/0.62 | ( ord_less_eq_nat @ N7 @ M5 ) ) ).
% 0.25/0.62
% 0.25/0.62 % nat_le_linear
% 0.25/0.62 thf(fact_347_le__antisym,axiom,
% 0.25/0.62 ! [M5: nat,N7: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ M5 @ N7 )
% 0.25/0.62 => ( ( ord_less_eq_nat @ N7 @ M5 )
% 0.25/0.62 => ( M5 = N7 ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % le_antisym
% 0.25/0.62 thf(fact_348_eq__imp__le,axiom,
% 0.25/0.62 ! [M5: nat,N7: nat] :
% 0.25/0.62 ( ( M5 = N7 )
% 0.25/0.62 => ( ord_less_eq_nat @ M5 @ N7 ) ) ).
% 0.25/0.62
% 0.25/0.62 % eq_imp_le
% 0.25/0.62 thf(fact_349_le__trans,axiom,
% 0.25/0.62 ! [I: nat,J: nat,K: nat] :
% 0.25/0.62 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.62 => ( ( ord_less_eq_nat @ J @ K )
% 0.25/0.62 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % le_trans
% 0.25/0.62 thf(fact_350_le__refl,axiom,
% 0.25/0.62 ! [N7: nat] : ( ord_less_eq_nat @ N7 @ N7 ) ).
% 0.25/0.62
% 0.25/0.62 % le_refl
% 0.25/0.62 thf(fact_351_plus__ereal_Oelims,axiom,
% 0.25/0.62 ! [X2: extended_ereal,Xa3: extended_ereal,Y: extended_ereal] :
% 0.25/0.62 ( ( ( plus_p2118002693_ereal @ X2 @ Xa3 )
% 0.25/0.62 = Y )
% 0.25/0.62 => ( ! [R2: real] :
% 0.25/0.62 ( ( X2
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ! [P3: real] :
% 0.25/0.62 ( ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ P3 ) )
% 0.25/0.62 => ( Y
% 0.25/0.62 != ( extended_ereal2 @ ( plus_plus_real @ R2 @ P3 ) ) ) ) )
% 0.25/0.62 => ( ( ( X2 = extend1289208545_ereal )
% 0.25/0.62 => ( Y != extend1289208545_ereal ) )
% 0.25/0.62 => ( ( ( Xa3 = extend1289208545_ereal )
% 0.25/0.62 => ( Y != extend1289208545_ereal ) )
% 0.25/0.62 => ( ( ? [R2: real] :
% 0.25/0.62 ( X2
% 0.25/0.62 = ( extended_ereal2 @ R2 ) )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Y
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ( ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ? [P3: real] :
% 0.25/0.62 ( Xa3
% 0.25/0.62 = ( extended_ereal2 @ P3 ) )
% 0.25/0.62 => ( Y
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) )
% 0.25/0.62 => ~ ( ( X2
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( ( Xa3
% 0.25/0.62 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.25/0.62 => ( Y
% 0.25/0.62 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % plus_ereal.elims
% 0.25/0.62 thf(fact_352_filterlim__real__sequentially,axiom,
% 0.25/0.62 filterlim_nat_real @ semiri2110766477t_real @ at_top_real @ at_top_nat ).
% 0.25/0.62
% 0.25/0.62 % filterlim_real_sequentially
% 0.25/0.62 thf(fact_353_int__ops_I5_J,axiom,
% 0.25/0.62 ! [A: nat,B: nat] :
% 0.25/0.62 ( ( semiri2019852685at_int @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.62 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % int_ops(5)
% 0.25/0.62 thf(fact_354_nat__int__comparison_I1_J,axiom,
% 0.25/0.70 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.25/0.70 = ( ^ [A3: nat,B2: nat] :
% 0.25/0.70 ( ( semiri2019852685at_int @ A3 )
% 0.25/0.70 = ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 0.25/0.70
% 0.25/0.70 % nat_int_comparison(1)
% 0.25/0.70
% 0.25/0.70 % Conjectures (1)
% 0.25/0.70 thf(conj_0,conjecture,
% 0.25/0.70 ( filter1531173832_ereal
% 0.25/0.70 @ ^ [I2: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ I2 ) ) )
% 0.25/0.70 @ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
% 0.25/0.70 @ at_top_nat ) ).
% 0.25/0.70
% 0.25/0.70 %------------------------------------------------------------------------------
% 0.25/0.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ibymKLH1aL/cvc5---1.0.5_25831.p...
% 0.25/0.70 (declare-sort $$unsorted 0)
% 0.25/0.70 (declare-sort tptp.filter2049122004_ereal 0)
% 0.25/0.70 (declare-sort tptp.set_Extended_ereal 0)
% 0.25/0.70 (declare-sort tptp.filter_real 0)
% 0.25/0.70 (declare-sort tptp.filter_nat 0)
% 0.25/0.70 (declare-sort tptp.filter_int 0)
% 0.25/0.70 (declare-sort tptp.set_real 0)
% 0.25/0.70 (declare-sort tptp.filter_a 0)
% 0.25/0.70 (declare-sort tptp.extended_ereal 0)
% 0.25/0.70 (declare-sort tptp.real 0)
% 0.25/0.70 (declare-sort tptp.nat 0)
% 0.25/0.70 (declare-sort tptp.int 0)
% 0.25/0.70 (declare-sort tptp.a 0)
% 0.25/0.70 (declare-fun tptp.extend1289208545_ereal () tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.extended_ereal2 (tptp.real) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 0.25/0.70 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 0.25/0.70 (declare-fun tptp.at_top_real () tptp.filter_real)
% 0.25/0.70 (declare-fun tptp.filter1531173832_ereal ((-> tptp.nat tptp.extended_ereal) tptp.filter2049122004_ereal tptp.filter_nat) Bool)
% 0.25/0.70 (declare-fun tptp.filterlim_nat_int ((-> tptp.nat tptp.int) tptp.filter_int tptp.filter_nat) Bool)
% 0.25/0.70 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 0.25/0.70 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 0.25/0.70 (declare-fun tptp.filterlim_nat_a ((-> tptp.nat tptp.a) tptp.filter_a tptp.filter_nat) Bool)
% 0.25/0.70 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 0.25/0.70 (declare-fun tptp.comp_E1308517939al_nat ((-> tptp.extended_ereal tptp.extended_ereal) (-> tptp.nat tptp.extended_ereal) tptp.nat) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.comp_E489644891real_a ((-> tptp.extended_ereal tptp.extended_ereal) (-> tptp.a tptp.extended_ereal) tptp.a) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.comp_E1436437929nt_nat ((-> tptp.extended_ereal tptp.int) (-> tptp.nat tptp.extended_ereal) tptp.nat) tptp.int)
% 0.25/0.70 (declare-fun tptp.comp_E1523169101at_nat ((-> tptp.extended_ereal tptp.nat) (-> tptp.nat tptp.extended_ereal) tptp.nat) tptp.nat)
% 0.25/0.70 (declare-fun tptp.comp_E1477338153al_nat ((-> tptp.extended_ereal tptp.real) (-> tptp.nat tptp.extended_ereal) tptp.nat) tptp.real)
% 0.25/0.70 (declare-fun tptp.comp_n1096781355al_nat ((-> tptp.nat tptp.extended_ereal) (-> tptp.nat tptp.nat) tptp.nat) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.comp_nat_a_nat ((-> tptp.nat tptp.a) (-> tptp.nat tptp.nat) tptp.nat) tptp.a)
% 0.25/0.70 (declare-fun tptp.comp_r1410008527al_nat ((-> tptp.real tptp.extended_ereal) (-> tptp.nat tptp.real) tptp.nat) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.comp_real_int_nat ((-> tptp.real tptp.int) (-> tptp.nat tptp.real) tptp.nat) tptp.int)
% 0.25/0.70 (declare-fun tptp.comp_real_nat_nat ((-> tptp.real tptp.nat) (-> tptp.nat tptp.real) tptp.nat) tptp.nat)
% 0.25/0.70 (declare-fun tptp.comp_a1112243075al_nat ((-> tptp.a tptp.extended_ereal) (-> tptp.nat tptp.a) tptp.nat) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.comp_a780206603real_a ((-> tptp.a tptp.extended_ereal) (-> tptp.a tptp.a) tptp.a) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.comp_a_int_nat ((-> tptp.a tptp.int) (-> tptp.nat tptp.a) tptp.nat) tptp.int)
% 0.25/0.70 (declare-fun tptp.comp_a_nat_nat ((-> tptp.a tptp.nat) (-> tptp.nat tptp.a) tptp.nat) tptp.nat)
% 0.25/0.70 (declare-fun tptp.comp_a_real_nat ((-> tptp.a tptp.real) (-> tptp.nat tptp.a) tptp.nat) tptp.real)
% 0.25/0.70 (declare-fun tptp.comp_a_a_nat ((-> tptp.a tptp.a) (-> tptp.nat tptp.a) tptp.nat) tptp.a)
% 0.25/0.70 (declare-fun tptp.plus_p2118002693_ereal (tptp.extended_ereal tptp.extended_ereal) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.25/0.70 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.25/0.70 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 0.25/0.70 (declare-fun tptp.uminus1208298309_ereal (tptp.extended_ereal) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 0.25/0.70 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 0.25/0.70 (declare-fun tptp.uniq_Extended_ereal ((-> tptp.extended_ereal Bool)) Bool)
% 0.25/0.70 (declare-fun tptp.uniq_real ((-> tptp.real Bool)) Bool)
% 0.25/0.70 (declare-fun tptp.uniq_a ((-> tptp.a Bool)) Bool)
% 0.25/0.70 (declare-fun tptp.liminf1045857232_ereal (tptp.filter_nat (-> tptp.nat tptp.extended_ereal)) tptp.extended_ereal)
% 0.25/0.70 (declare-fun tptp.lower_1087098792_ereal (tptp.extended_ereal (-> tptp.extended_ereal tptp.extended_ereal)) Bool)
% 0.25/0.70 (declare-fun tptp.lower_48196818al_int (tptp.extended_ereal (-> tptp.extended_ereal tptp.int)) Bool)
% 0.25/0.70 (declare-fun tptp.lower_1558406774al_nat (tptp.extended_ereal (-> tptp.extended_ereal tptp.nat)) Bool)
% 0.25/0.70 (declare-fun tptp.lower_1165973074l_real (tptp.extended_ereal (-> tptp.extended_ereal tptp.real)) Bool)
% 0.25/0.70 (declare-fun tptp.lower_551915512_ereal (tptp.real (-> tptp.real tptp.extended_ereal)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_153911426al_int (tptp.real (-> tptp.real tptp.int)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_1664121382al_nat (tptp.real (-> tptp.real tptp.nat)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_191460856_ereal (tptp.a (-> tptp.a tptp.extended_ereal)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_956963458_a_int (tptp.a (-> tptp.a tptp.int)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_319689766_a_nat (tptp.a (-> tptp.a tptp.nat)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_231615490a_real (tptp.a (-> tptp.a tptp.real)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_1071158961_ereal (tptp.extended_ereal (-> tptp.extended_ereal tptp.extended_ereal)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_637387785al_int (tptp.extended_ereal (-> tptp.extended_ereal tptp.int)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_114093al_nat (tptp.extended_ereal (-> tptp.extended_ereal tptp.nat)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_737640969l_real (tptp.extended_ereal (-> tptp.extended_ereal tptp.real)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_1075504779al_int (tptp.real (-> tptp.real tptp.int)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_438231087al_nat (tptp.real (-> tptp.real tptp.nat)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_534855297_ereal (tptp.a (-> tptp.a tptp.extended_ereal)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_1672990777_a_int (tptp.a (-> tptp.a tptp.int)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_1035717085_a_nat (tptp.a (-> tptp.a tptp.nat)) Bool)
% 0.25/0.71 (declare-fun tptp.lower_755922489a_real (tptp.a (-> tptp.a tptp.real)) Bool)
% 0.25/0.71 (declare-fun tptp.semiri2019852685at_int (tptp.nat) tptp.int)
% 0.25/0.71 (declare-fun tptp.semiri2110766477t_real (tptp.nat) tptp.real)
% 0.25/0.71 (declare-fun tptp.ord_le824540014_ereal (tptp.extended_ereal tptp.extended_ereal) Bool)
% 0.25/0.71 (declare-fun tptp.ord_le1745708096er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 0.25/0.71 (declare-fun tptp.ord_le132810396r_real (tptp.filter_real tptp.filter_real) Bool)
% 0.25/0.71 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.25/0.71 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.71 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.25/0.71 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 0.25/0.71 (declare-fun tptp.topolo1069469409_ereal ((-> tptp.nat tptp.extended_ereal)) Bool)
% 0.25/0.71 (declare-fun tptp.topolo411883481eq_int ((-> tptp.nat tptp.int)) Bool)
% 0.25/0.71 (declare-fun tptp.topolo1922093437eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 0.25/0.71 (declare-fun tptp.topolo144289241q_real ((-> tptp.nat tptp.real)) Bool)
% 0.25/0.71 (declare-fun tptp.topolo2140997059_ereal (tptp.extended_ereal) tptp.filter2049122004_ereal)
% 0.25/0.71 (declare-fun tptp.topolo54776183ds_int (tptp.int) tptp.filter_int)
% 0.25/0.71 (declare-fun tptp.topolo1564986139ds_nat (tptp.nat) tptp.filter_nat)
% 0.25/0.71 (declare-fun tptp.topolo1664202871s_real (tptp.real) tptp.filter_real)
% 0.25/0.71 (declare-fun tptp.topolo705128563nhds_a (tptp.a) tptp.filter_a)
% 0.25/0.71 (declare-fun tptp.member1900190071_ereal (tptp.extended_ereal tptp.set_Extended_ereal) Bool)
% 0.25/0.71 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 0.25/0.71 (declare-fun tptp.a2 () tptp.extended_ereal)
% 0.25/0.71 (declare-fun tptp.f (tptp.a) tptp.extended_ereal)
% 0.25/0.71 (declare-fun tptp.x0 () tptp.a)
% 0.25/0.71 (declare-fun tptp.x (tptp.nat) tptp.a)
% 0.25/0.71 (assert (@ (@ (@ tptp.filterlim_nat_a tptp.x) (@ tptp.topolo705128563nhds_a tptp.x0)) tptp.at_top_nat))
% 0.25/0.71 (assert (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_a1112243075al_nat tptp.f) tptp.x)) (@ tptp.topolo2140997059_ereal tptp.a2)) tptp.at_top_nat))
% 0.25/0.71 (assert (forall ((F tptp.filter_nat)) (=> (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_a1112243075al_nat tptp.f) tptp.x)) (@ tptp.topolo2140997059_ereal tptp.a2)) F) (@ (@ (@ tptp.filter1531173832_ereal (lambda ((X tptp.nat)) (@ tptp.uminus1208298309_ereal (@ (@ (@ tptp.comp_a1112243075al_nat tptp.f) tptp.x) X)))) (@ tptp.topolo2140997059_ereal (@ tptp.uminus1208298309_ereal tptp.a2))) F))))
% 0.25/0.71 (assert (@ (@ tptp.lower_191460856_ereal tptp.x0) (lambda ((X tptp.a)) (@ tptp.uminus1208298309_ereal (@ tptp.f X)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal) (F tptp.filter_nat)) (=> (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal X2)) F) (@ (@ (@ tptp.filter1531173832_ereal (lambda ((X tptp.nat)) (@ tptp.uminus1208298309_ereal (@ F2 X)))) (@ tptp.topolo2140997059_ereal (@ tptp.uminus1208298309_ereal X2))) F))))
% 0.25/0.71 (assert (forall ((K tptp.real) (F tptp.filter_real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) K)) (@ tptp.topolo1664202871s_real K)) F)))
% 0.25/0.71 (assert (forall ((K tptp.real) (F tptp.filter_nat)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((X tptp.nat)) K)) (@ tptp.topolo1664202871s_real K)) F)))
% 0.25/0.71 (assert (forall ((K tptp.extended_ereal) (F tptp.filter_nat)) (@ (@ (@ tptp.filter1531173832_ereal (lambda ((X tptp.nat)) K)) (@ tptp.topolo2140997059_ereal K)) F)))
% 0.25/0.71 (assert (forall ((K tptp.a) (F tptp.filter_nat)) (@ (@ (@ tptp.filterlim_nat_a (lambda ((X tptp.nat)) K)) (@ tptp.topolo705128563nhds_a K)) F)))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (F0 tptp.extended_ereal) (Net tptp.filter_nat)) (= (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal F0)) Net) (@ (@ (@ tptp.filter1531173832_ereal (lambda ((X tptp.nat)) (@ tptp.uminus1208298309_ereal (@ F2 X)))) (@ tptp.topolo2140997059_ereal (@ tptp.uminus1208298309_ereal F0))) Net))))
% 0.25/0.71 (assert (forall ((K tptp.real) (L tptp.real)) (= (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) K)) (@ tptp.topolo1664202871s_real L)) tptp.at_top_nat) (= K L))))
% 0.25/0.71 (assert (forall ((K tptp.extended_ereal) (L tptp.extended_ereal)) (= (@ (@ (@ tptp.filter1531173832_ereal (lambda ((N tptp.nat)) K)) (@ tptp.topolo2140997059_ereal L)) tptp.at_top_nat) (= K L))))
% 0.25/0.71 (assert (forall ((K tptp.a) (L tptp.a)) (= (@ (@ (@ tptp.filterlim_nat_a (lambda ((N tptp.nat)) K)) (@ tptp.topolo705128563nhds_a L)) tptp.at_top_nat) (= K L))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.real tptp.real)) (A tptp.real) (F tptp.filter_real)) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ tptp.uminus_uminus_real (@ F2 X)))) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real A))) F) (@ (@ (@ tptp.filterlim_real_real F2) (@ tptp.topolo1664202871s_real A)) F))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.real) (F tptp.filter_nat)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((X tptp.nat)) (@ tptp.uminus_uminus_real (@ F2 X)))) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real A))) F) (@ (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo1664202871s_real A)) F))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.real tptp.real)) (Y tptp.real) (F tptp.filter_real)) (= (@ (@ (@ tptp.filterlim_real_real F2) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real Y))) F) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ tptp.uminus_uminus_real (@ F2 X)))) (@ tptp.topolo1664202871s_real Y)) F))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (Y tptp.real) (F tptp.filter_nat)) (= (@ (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real Y))) F) (@ (@ (@ tptp.filterlim_nat_real (lambda ((X tptp.nat)) (@ tptp.uminus_uminus_real (@ F2 X)))) (@ tptp.topolo1664202871s_real Y)) F))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.real tptp.real)) (A tptp.real) (F tptp.filter_real)) (=> (@ (@ (@ tptp.filterlim_real_real F2) (@ tptp.topolo1664202871s_real A)) F) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ tptp.uminus_uminus_real (@ F2 X)))) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real A))) F))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.real) (F tptp.filter_nat)) (=> (@ (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo1664202871s_real A)) F) (@ (@ (@ tptp.filterlim_nat_real (lambda ((X tptp.nat)) (@ tptp.uminus_uminus_real (@ F2 X)))) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real A))) F))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal)) (A tptp.extended_ereal) (B tptp.extended_ereal)) (let ((_let_1 (@ tptp.filter1531173832_ereal X3))) (=> (@ (@ _let_1 (@ tptp.topolo2140997059_ereal A)) tptp.at_top_nat) (=> (@ (@ _let_1 (@ tptp.topolo2140997059_ereal B)) tptp.at_top_nat) (= A B))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.filterlim_nat_a X3))) (=> (@ (@ _let_1 (@ tptp.topolo705128563nhds_a A)) tptp.at_top_nat) (=> (@ (@ _let_1 (@ tptp.topolo705128563nhds_a B)) tptp.at_top_nat) (= A B))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.filterlim_nat_real X3))) (=> (@ (@ _let_1 (@ tptp.topolo1664202871s_real A)) tptp.at_top_nat) (=> (@ (@ _let_1 (@ tptp.topolo1664202871s_real B)) tptp.at_top_nat) (= A B))))))
% 0.25/0.71 (assert (forall ((A tptp.real)) (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) (@ tptp.topolo1664202871s_real (@ tptp.uminus_uminus_real A))) (@ tptp.topolo1664202871s_real A))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (= (@ tptp.uminus1208298309_ereal A) (@ tptp.uminus1208298309_ereal B)) (= A B))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal)) (= (@ tptp.uminus1208298309_ereal (@ tptp.uminus1208298309_ereal A)) A)))
% 0.25/0.71 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (= (@ tptp.uminus1208298309_ereal A) B) (= A (@ tptp.uminus1208298309_ereal B)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal) (F tptp.filter_nat) (Y tptp.extended_ereal)) (let ((_let_1 (@ tptp.filter1531173832_ereal F2))) (=> (@ (@ _let_1 (@ tptp.topolo2140997059_ereal X2)) F) (=> (= X2 Y) (@ (@ _let_1 (@ tptp.topolo2140997059_ereal Y)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.a)) (X2 tptp.a) (F tptp.filter_nat) (Y tptp.a)) (let ((_let_1 (@ tptp.filterlim_nat_a F2))) (=> (@ (@ _let_1 (@ tptp.topolo705128563nhds_a X2)) F) (=> (= X2 Y) (@ (@ _let_1 (@ tptp.topolo705128563nhds_a Y)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.real tptp.real)) (X2 tptp.real) (F tptp.filter_real) (Y tptp.real)) (let ((_let_1 (@ tptp.filterlim_real_real F2))) (=> (@ (@ _let_1 (@ tptp.topolo1664202871s_real X2)) F) (=> (= X2 Y) (@ (@ _let_1 (@ tptp.topolo1664202871s_real Y)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (X2 tptp.real) (F tptp.filter_nat) (Y tptp.real)) (let ((_let_1 (@ tptp.filterlim_nat_real F2))) (=> (@ (@ _let_1 (@ tptp.topolo1664202871s_real X2)) F) (=> (= X2 Y) (@ (@ _let_1 (@ tptp.topolo1664202871s_real Y)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal) (F tptp.filter_nat) (K tptp.extended_ereal)) (let ((_let_1 (@ tptp.filter1531173832_ereal F2))) (=> (@ (@ _let_1 (@ tptp.topolo2140997059_ereal L)) F) (=> (= K L) (@ (@ _let_1 (@ tptp.topolo2140997059_ereal K)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.a)) (L tptp.a) (F tptp.filter_nat) (K tptp.a)) (let ((_let_1 (@ tptp.filterlim_nat_a F2))) (=> (@ (@ _let_1 (@ tptp.topolo705128563nhds_a L)) F) (=> (= K L) (@ (@ _let_1 (@ tptp.topolo705128563nhds_a K)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.real tptp.real)) (L tptp.real) (F tptp.filter_real) (K tptp.real)) (let ((_let_1 (@ tptp.filterlim_real_real F2))) (=> (@ (@ _let_1 (@ tptp.topolo1664202871s_real L)) F) (=> (= K L) (@ (@ _let_1 (@ tptp.topolo1664202871s_real K)) F))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (L tptp.real) (F tptp.filter_nat) (K tptp.real)) (let ((_let_1 (@ tptp.filterlim_nat_real F2))) (=> (@ (@ _let_1 (@ tptp.topolo1664202871s_real L)) F) (=> (= K L) (@ (@ _let_1 (@ tptp.topolo1664202871s_real K)) F))))))
% 0.25/0.71 (assert (= tptp.comp_a1112243075al_nat (lambda ((F3 (-> tptp.a tptp.extended_ereal)) (G (-> tptp.nat tptp.a)) (X tptp.nat)) (@ F3 (@ G X)))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 0.25/0.71 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.extended_ereal)) (X2 (-> tptp.nat tptp.real)) (C (-> tptp.nat tptp.extended_ereal)) (C0 tptp.extended_ereal)) (=> (@ (@ tptp.lower_551915512_ereal X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal C) (@ tptp.topolo2140997059_ereal C0)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F2 (@ X2 N2))) (@ C N2))) (@ (@ tptp.ord_le824540014_ereal (@ F2 X0)) C0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.extended_ereal)) (X2 (-> tptp.nat tptp.a)) (C (-> tptp.nat tptp.extended_ereal)) (C0 tptp.extended_ereal)) (=> (@ (@ tptp.lower_191460856_ereal X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal C) (@ tptp.topolo2140997059_ereal C0)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F2 (@ X2 N2))) (@ C N2))) (@ (@ tptp.ord_le824540014_ereal (@ F2 X0)) C0)))))))
% 0.25/0.71 (assert (= tptp.lower_551915512_ereal (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.extended_ereal))) (forall ((X (-> tptp.nat tptp.real)) (C2 (-> tptp.nat tptp.extended_ereal)) (C02 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ (@ tptp.filter1531173832_ereal C2) (@ tptp.topolo2140997059_ereal C02)) tptp.at_top_nat) (forall ((N tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F3 (@ X N))) (@ C2 N)))) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) C02))))))
% 0.25/0.71 (assert (= tptp.lower_191460856_ereal (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.extended_ereal))) (forall ((X (-> tptp.nat tptp.a)) (C2 (-> tptp.nat tptp.extended_ereal)) (C02 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filter1531173832_ereal C2) (@ tptp.topolo2140997059_ereal C02)) tptp.at_top_nat) (forall ((N tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F3 (@ X N))) (@ C2 N)))) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) C02))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.nat)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.nat)) (=> (@ (@ tptp.lower_1558406774al_nat X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_E1523169101at_nat F2) X2)) (@ tptp.topolo1564986139ds_nat A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.int)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.int)) (=> (@ (@ tptp.lower_48196818al_int X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_E1436437929nt_nat F2) X2)) (@ tptp.topolo54776183ds_int A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.extended_ereal)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.extended_ereal)) (=> (@ (@ tptp.lower_1087098792_ereal X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_E1308517939al_nat F2) X2)) (@ tptp.topolo2140997059_ereal A2)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.real)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.real)) (=> (@ (@ tptp.lower_1165973074l_real X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_E1477338153al_nat F2) X2)) (@ tptp.topolo1664202871s_real A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_real (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.nat)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.nat)) (=> (@ (@ tptp.lower_319689766_a_nat X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_a_nat_nat F2) X2)) (@ tptp.topolo1564986139ds_nat A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.int)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.int)) (=> (@ (@ tptp.lower_956963458_a_int X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_a_int_nat F2) X2)) (@ tptp.topolo54776183ds_int A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.real)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.real)) (=> (@ (@ tptp.lower_231615490a_real X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_a_real_nat F2) X2)) (@ tptp.topolo1664202871s_real A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_real (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.nat)) (X2 (-> tptp.nat tptp.real)) (A2 tptp.nat)) (=> (@ (@ tptp.lower_1664121382al_nat X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_real_nat_nat F2) X2)) (@ tptp.topolo1564986139ds_nat A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.int)) (X2 (-> tptp.nat tptp.real)) (A2 tptp.int)) (=> (@ (@ tptp.lower_153911426al_int X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_real_int_nat F2) X2)) (@ tptp.topolo54776183ds_int A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.extended_ereal)) (X2 (-> tptp.nat tptp.real)) (A2 tptp.extended_ereal)) (=> (@ (@ tptp.lower_551915512_ereal X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_r1410008527al_nat F2) X2)) (@ tptp.topolo2140997059_ereal A2)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal (@ F2 X0)) A2))))))
% 0.25/0.71 (assert (= tptp.lower_1558406774al_nat (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.nat))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.nat)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_E1523169101at_nat F3) X4)) (@ tptp.topolo1564986139ds_nat L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_nat (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_48196818al_int (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.int))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.int)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_E1436437929nt_nat F3) X4)) (@ tptp.topolo54776183ds_int L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_int (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_1087098792_ereal (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.extended_ereal))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_E1308517939al_nat F3) X4)) (@ tptp.topolo2140997059_ereal L2)) tptp.at_top_nat)) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_1165973074l_real (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.real))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.real)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_E1477338153al_nat F3) X4)) (@ tptp.topolo1664202871s_real L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_real (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_319689766_a_nat (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.nat))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.nat)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_a_nat_nat F3) X4)) (@ tptp.topolo1564986139ds_nat L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_nat (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_956963458_a_int (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.int))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.int)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_a_int_nat F3) X4)) (@ tptp.topolo54776183ds_int L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_int (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_231615490a_real (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.real))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.real)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_a_real_nat F3) X4)) (@ tptp.topolo1664202871s_real L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_real (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_1664121382al_nat (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.nat))) (forall ((X4 (-> tptp.nat tptp.real)) (L2 tptp.nat)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X4) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_real_nat_nat F3) X4)) (@ tptp.topolo1564986139ds_nat L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_nat (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_153911426al_int (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.int))) (forall ((X4 (-> tptp.nat tptp.real)) (L2 tptp.int)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X4) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_real_int_nat F3) X4)) (@ tptp.topolo54776183ds_int L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_int (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (= tptp.lower_551915512_ereal (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.extended_ereal))) (forall ((X4 (-> tptp.nat tptp.real)) (L2 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X4) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_r1410008527al_nat F3) X4)) (@ tptp.topolo2140997059_ereal L2)) tptp.at_top_nat)) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) L2))))))
% 0.25/0.71 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 0.25/0.71 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (@ (@ tptp.ord_le824540014_ereal (@ tptp.uminus1208298309_ereal A)) (@ tptp.uminus1208298309_ereal B)) (@ (@ tptp.ord_le824540014_ereal B) A))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (or (= A B) (not (@ (@ tptp.ord_le824540014_ereal A) B)) (not (@ (@ tptp.ord_le824540014_ereal B) A)))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (or (= A B) (not (@ (@ tptp.ord_less_eq_real A) B)) (not (@ (@ tptp.ord_less_eq_real B) A)))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 0.25/0.71 (assert (forall ((S tptp.set_Extended_ereal)) (exists ((X5 tptp.extended_ereal)) (and (forall ((Xa tptp.extended_ereal)) (=> (@ (@ tptp.member1900190071_ereal Xa) S) (@ (@ tptp.ord_le824540014_ereal X5) Xa))) (forall ((Z tptp.extended_ereal)) (=> (forall ((Xa2 tptp.extended_ereal)) (=> (@ (@ tptp.member1900190071_ereal Xa2) S) (@ (@ tptp.ord_le824540014_ereal Z) Xa2))) (@ (@ tptp.ord_le824540014_ereal Z) X5)))))))
% 0.25/0.71 (assert (forall ((S tptp.set_Extended_ereal)) (exists ((X5 tptp.extended_ereal)) (and (forall ((Xa tptp.extended_ereal)) (=> (@ (@ tptp.member1900190071_ereal Xa) S) (@ (@ tptp.ord_le824540014_ereal Xa) X5))) (forall ((Z tptp.extended_ereal)) (=> (forall ((Xa2 tptp.extended_ereal)) (=> (@ (@ tptp.member1900190071_ereal Xa2) S) (@ (@ tptp.ord_le824540014_ereal Xa2) Z))) (@ (@ tptp.ord_le824540014_ereal X5) Z)))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (@ (@ tptp.ord_le824540014_ereal (@ tptp.uminus1208298309_ereal A)) B) (@ (@ tptp.ord_le824540014_ereal (@ tptp.uminus1208298309_ereal B)) A))))
% 0.25/0.71 (assert (forall ((N3 tptp.nat) (X3 (-> tptp.nat tptp.nat)) (Y2 (-> tptp.nat tptp.nat)) (X2 tptp.nat) (Y tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_less_eq_nat (@ X3 N2)) (@ Y2 N2)))) (=> (@ (@ (@ tptp.filterlim_nat_nat X3) (@ tptp.topolo1564986139ds_nat X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat Y2) (@ tptp.topolo1564986139ds_nat Y)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 0.25/0.71 (assert (forall ((N3 tptp.nat) (X3 (-> tptp.nat tptp.int)) (Y2 (-> tptp.nat tptp.int)) (X2 tptp.int) (Y tptp.int)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_less_eq_int (@ X3 N2)) (@ Y2 N2)))) (=> (@ (@ (@ tptp.filterlim_nat_int X3) (@ tptp.topolo54776183ds_int X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int Y2) (@ tptp.topolo54776183ds_int Y)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int X2) Y))))))
% 0.25/0.71 (assert (forall ((N3 tptp.nat) (X3 (-> tptp.nat tptp.extended_ereal)) (Y2 (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal) (Y tptp.extended_ereal)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_le824540014_ereal (@ X3 N2)) (@ Y2 N2)))) (=> (@ (@ (@ tptp.filter1531173832_ereal X3) (@ tptp.topolo2140997059_ereal X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal Y2) (@ tptp.topolo2140997059_ereal Y)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal X2) Y))))))
% 0.25/0.71 (assert (forall ((N3 tptp.nat) (X3 (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real)) (X2 tptp.real) (Y tptp.real)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_less_eq_real (@ X3 N2)) (@ Y2 N2)))) (=> (@ (@ (@ tptp.filterlim_nat_real X3) (@ tptp.topolo1664202871s_real X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_real Y2) (@ tptp.topolo1664202871s_real Y)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.nat)) (X2 tptp.nat) (Y2 (-> tptp.nat tptp.nat)) (Y tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_nat X3) (@ tptp.topolo1564986139ds_nat X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat Y2) (@ tptp.topolo1564986139ds_nat Y)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_nat (@ X3 N2)) (@ Y2 N2))))) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.int)) (X2 tptp.int) (Y2 (-> tptp.nat tptp.int)) (Y tptp.int)) (=> (@ (@ (@ tptp.filterlim_nat_int X3) (@ tptp.topolo54776183ds_int X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int Y2) (@ tptp.topolo54776183ds_int Y)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_int (@ X3 N2)) (@ Y2 N2))))) (@ (@ tptp.ord_less_eq_int X2) Y))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal) (Y2 (-> tptp.nat tptp.extended_ereal)) (Y tptp.extended_ereal)) (=> (@ (@ (@ tptp.filter1531173832_ereal X3) (@ tptp.topolo2140997059_ereal X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal Y2) (@ tptp.topolo2140997059_ereal Y)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_le824540014_ereal (@ X3 N2)) (@ Y2 N2))))) (@ (@ tptp.ord_le824540014_ereal X2) Y))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real)) (X2 tptp.real) (Y2 (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X3) (@ tptp.topolo1664202871s_real X2)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_real Y2) (@ tptp.topolo1664202871s_real Y)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real (@ X3 N2)) (@ Y2 N2))))) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 0.25/0.71 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)))
% 0.25/0.71 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (L tptp.nat) (M tptp.nat) (C3 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_nat F2) (@ tptp.topolo1564986139ds_nat L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ F2 N2)) C3))) (@ (@ tptp.ord_less_eq_nat L) C3)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.int)) (L tptp.int) (M tptp.nat) (C3 tptp.int)) (=> (@ (@ (@ tptp.filterlim_nat_int F2) (@ tptp.topolo54776183ds_int L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ F2 N2)) C3))) (@ (@ tptp.ord_less_eq_int L) C3)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal) (M tptp.nat) (C3 tptp.extended_ereal)) (=> (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_le824540014_ereal (@ F2 N2)) C3))) (@ (@ tptp.ord_le824540014_ereal L) C3)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (L tptp.real) (M tptp.nat) (C3 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo1664202871s_real L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ F2 N2)) C3))) (@ (@ tptp.ord_less_eq_real L) C3)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (L tptp.nat) (N3 tptp.nat) (C3 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_nat F2) (@ tptp.topolo1564986139ds_nat L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_less_eq_nat C3) (@ F2 N2)))) (@ (@ tptp.ord_less_eq_nat C3) L)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.int)) (L tptp.int) (N3 tptp.nat) (C3 tptp.int)) (=> (@ (@ (@ tptp.filterlim_nat_int F2) (@ tptp.topolo54776183ds_int L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_less_eq_int C3) (@ F2 N2)))) (@ (@ tptp.ord_less_eq_int C3) L)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal) (N3 tptp.nat) (C3 tptp.extended_ereal)) (=> (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_le824540014_ereal C3) (@ F2 N2)))) (@ (@ tptp.ord_le824540014_ereal C3) L)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.real)) (L tptp.real) (N3 tptp.nat) (C3 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo1664202871s_real L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_less_eq_real C3) (@ F2 N2)))) (@ (@ tptp.ord_less_eq_real C3) L)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.nat)) (X2 tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_nat X3) (@ tptp.topolo1564986139ds_nat X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_nat A) (@ X3 N2))))) (@ (@ tptp.ord_less_eq_nat A) X2)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.int)) (X2 tptp.int) (A tptp.int)) (=> (@ (@ (@ tptp.filterlim_nat_int X3) (@ tptp.topolo54776183ds_int X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_int A) (@ X3 N2))))) (@ (@ tptp.ord_less_eq_int A) X2)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal) (A tptp.extended_ereal)) (=> (@ (@ (@ tptp.filter1531173832_ereal X3) (@ tptp.topolo2140997059_ereal X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_le824540014_ereal A) (@ X3 N2))))) (@ (@ tptp.ord_le824540014_ereal A) X2)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real)) (X2 tptp.real) (A tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X3) (@ tptp.topolo1664202871s_real X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real A) (@ X3 N2))))) (@ (@ tptp.ord_less_eq_real A) X2)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.nat)) (X2 tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_nat X3) (@ tptp.topolo1564986139ds_nat X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_nat (@ X3 N2)) A)))) (@ (@ tptp.ord_less_eq_nat X2) A)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.int)) (X2 tptp.int) (A tptp.int)) (=> (@ (@ (@ tptp.filterlim_nat_int X3) (@ tptp.topolo54776183ds_int X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_int (@ X3 N2)) A)))) (@ (@ tptp.ord_less_eq_int X2) A)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal) (A tptp.extended_ereal)) (=> (@ (@ (@ tptp.filter1531173832_ereal X3) (@ tptp.topolo2140997059_ereal X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_le824540014_ereal (@ X3 N2)) A)))) (@ (@ tptp.ord_le824540014_ereal X2) A)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real)) (X2 tptp.real) (A tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X3) (@ tptp.topolo1664202871s_real X2)) tptp.at_top_nat) (=> (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ (@ tptp.ord_less_eq_real (@ X3 N2)) A)))) (@ (@ tptp.ord_less_eq_real X2) A)))))
% 0.25/0.71 (assert (forall ((F tptp.filter_nat) (F4 tptp.filter_nat) (F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal)) (let ((_let_1 (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L)))) (=> (@ (@ tptp.ord_le1745708096er_nat F) F4) (=> (@ _let_1 F4) (@ _let_1 F))))))
% 0.25/0.71 (assert (forall ((F tptp.filter_nat) (F4 tptp.filter_nat) (F2 (-> tptp.nat tptp.a)) (L tptp.a)) (let ((_let_1 (@ (@ tptp.filterlim_nat_a F2) (@ tptp.topolo705128563nhds_a L)))) (=> (@ (@ tptp.ord_le1745708096er_nat F) F4) (=> (@ _let_1 F4) (@ _let_1 F))))))
% 0.25/0.71 (assert (forall ((F tptp.filter_real) (F4 tptp.filter_real) (F2 (-> tptp.real tptp.real)) (L tptp.real)) (let ((_let_1 (@ (@ tptp.filterlim_real_real F2) (@ tptp.topolo1664202871s_real L)))) (=> (@ (@ tptp.ord_le132810396r_real F) F4) (=> (@ _let_1 F4) (@ _let_1 F))))))
% 0.25/0.71 (assert (forall ((F tptp.filter_nat) (F4 tptp.filter_nat) (F2 (-> tptp.nat tptp.real)) (L tptp.real)) (let ((_let_1 (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo1664202871s_real L)))) (=> (@ (@ tptp.ord_le1745708096er_nat F) F4) (=> (@ _let_1 F4) (@ _let_1 F))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 0.25/0.71 (assert (forall ((A (-> tptp.a tptp.extended_ereal)) (B (-> tptp.nat tptp.a)) (C (-> tptp.nat tptp.extended_ereal)) (V tptp.nat)) (=> (= (@ (@ tptp.comp_a1112243075al_nat A) B) C) (= (@ A (@ B V)) (@ C V)))))
% 0.25/0.71 (assert (forall ((A (-> tptp.a tptp.extended_ereal)) (B (-> tptp.nat tptp.a)) (C (-> tptp.a tptp.extended_ereal)) (D (-> tptp.nat tptp.a))) (=> (= (@ (@ tptp.comp_a1112243075al_nat A) B) (@ (@ tptp.comp_a1112243075al_nat C) D)) (forall ((V2 tptp.nat)) (= (@ A (@ B V2)) (@ C (@ D V2)))))))
% 0.25/0.71 (assert (forall ((A (-> tptp.a tptp.extended_ereal)) (B (-> tptp.nat tptp.a)) (C (-> tptp.a tptp.extended_ereal)) (D (-> tptp.nat tptp.a)) (V tptp.nat)) (=> (= (@ (@ tptp.comp_a1112243075al_nat A) B) (@ (@ tptp.comp_a1112243075al_nat C) D)) (= (@ A (@ B V)) (@ C (@ D V))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.a tptp.extended_ereal)) (G2 (-> tptp.nat tptp.a)) (H (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.comp_a1112243075al_nat F2))) (= (@ (@ tptp.comp_n1096781355al_nat (@ _let_1 G2)) H) (@ _let_1 (@ (@ tptp.comp_nat_a_nat G2) H))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.extended_ereal tptp.extended_ereal)) (G2 (-> tptp.a tptp.extended_ereal)) (H (-> tptp.nat tptp.a))) (= (@ (@ tptp.comp_a1112243075al_nat (@ (@ tptp.comp_E489644891real_a F2) G2)) H) (@ (@ tptp.comp_E1308517939al_nat F2) (@ (@ tptp.comp_a1112243075al_nat G2) H)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.a tptp.extended_ereal)) (G2 (-> tptp.a tptp.a)) (H (-> tptp.nat tptp.a))) (= (@ (@ tptp.comp_a1112243075al_nat (@ (@ tptp.comp_a780206603real_a F2) G2)) H) (@ (@ tptp.comp_a1112243075al_nat F2) (@ (@ tptp.comp_a_a_nat G2) H)))))
% 0.25/0.71 (assert (= tptp.comp_a1112243075al_nat (lambda ((F3 (-> tptp.a tptp.extended_ereal)) (G (-> tptp.nat tptp.a)) (X tptp.nat)) (@ F3 (@ G X)))))
% 0.25/0.71 (assert (= tptp.lower_551915512_ereal (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.extended_ereal))) (forall ((X (-> tptp.nat tptp.real)) (C2 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (forall ((N tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F3 (@ X N))) C2))) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) C2))))))
% 0.25/0.71 (assert (= tptp.lower_191460856_ereal (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.extended_ereal))) (forall ((X (-> tptp.nat tptp.a)) (C2 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (forall ((N tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F3 (@ X N))) C2))) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) C2))))))
% 0.25/0.71 (assert (= tptp.lower_114093al_nat (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.nat))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.nat)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_E1523169101at_nat F3) X4)) (@ tptp.topolo1564986139ds_nat L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_nat L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_637387785al_int (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.int))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.int)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_E1436437929nt_nat F3) X4)) (@ tptp.topolo54776183ds_int L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_int L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_1071158961_ereal (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.extended_ereal))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_E1308517939al_nat F3) X4)) (@ tptp.topolo2140997059_ereal L2)) tptp.at_top_nat)) (@ (@ tptp.ord_le824540014_ereal L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_737640969l_real (lambda ((X02 tptp.extended_ereal) (F3 (-> tptp.extended_ereal tptp.real))) (forall ((X4 (-> tptp.nat tptp.extended_ereal)) (L2 tptp.real)) (=> (and (@ (@ (@ tptp.filter1531173832_ereal X4) (@ tptp.topolo2140997059_ereal X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_E1477338153al_nat F3) X4)) (@ tptp.topolo1664202871s_real L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_real L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_1035717085_a_nat (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.nat))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.nat)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_a_nat_nat F3) X4)) (@ tptp.topolo1564986139ds_nat L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_nat L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_1672990777_a_int (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.int))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.int)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_a_int_nat F3) X4)) (@ tptp.topolo54776183ds_int L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_int L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_534855297_ereal (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.extended_ereal))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.extended_ereal)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_a1112243075al_nat F3) X4)) (@ tptp.topolo2140997059_ereal L2)) tptp.at_top_nat)) (@ (@ tptp.ord_le824540014_ereal L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_755922489a_real (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.real))) (forall ((X4 (-> tptp.nat tptp.a)) (L2 tptp.real)) (=> (and (@ (@ (@ tptp.filterlim_nat_a X4) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_a_real_nat F3) X4)) (@ tptp.topolo1664202871s_real L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_real L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_438231087al_nat (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.nat))) (forall ((X4 (-> tptp.nat tptp.real)) (L2 tptp.nat)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X4) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_real_nat_nat F3) X4)) (@ tptp.topolo1564986139ds_nat L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_nat L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (= tptp.lower_1075504779al_int (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.int))) (forall ((X4 (-> tptp.nat tptp.real)) (L2 tptp.int)) (=> (and (@ (@ (@ tptp.filterlim_nat_real X4) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_real_int_nat F3) X4)) (@ tptp.topolo54776183ds_int L2)) tptp.at_top_nat)) (@ (@ tptp.ord_less_eq_int L2) (@ F3 X02)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.nat)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.nat)) (=> (@ (@ tptp.lower_114093al_nat X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_E1523169101at_nat F2) X2)) (@ tptp.topolo1564986139ds_nat A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.int)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.int)) (=> (@ (@ tptp.lower_637387785al_int X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_E1436437929nt_nat F2) X2)) (@ tptp.topolo54776183ds_int A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.extended_ereal)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.extended_ereal)) (=> (@ (@ tptp.lower_1071158961_ereal X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_E1308517939al_nat F2) X2)) (@ tptp.topolo2140997059_ereal A2)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.real)) (X2 (-> tptp.nat tptp.extended_ereal)) (A2 tptp.real)) (=> (@ (@ tptp.lower_737640969l_real X0) F2) (=> (@ (@ (@ tptp.filter1531173832_ereal X2) (@ tptp.topolo2140997059_ereal X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_E1477338153al_nat F2) X2)) (@ tptp.topolo1664202871s_real A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_real A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.nat)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.nat)) (=> (@ (@ tptp.lower_1035717085_a_nat X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_a_nat_nat F2) X2)) (@ tptp.topolo1564986139ds_nat A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.int)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.int)) (=> (@ (@ tptp.lower_1672990777_a_int X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_a_int_nat F2) X2)) (@ tptp.topolo54776183ds_int A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.extended_ereal)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.extended_ereal)) (=> (@ (@ tptp.lower_534855297_ereal X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filter1531173832_ereal (@ (@ tptp.comp_a1112243075al_nat F2) X2)) (@ tptp.topolo2140997059_ereal A2)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.real)) (X2 (-> tptp.nat tptp.a)) (A2 tptp.real)) (=> (@ (@ tptp.lower_755922489a_real X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_real (@ (@ tptp.comp_a_real_nat F2) X2)) (@ tptp.topolo1664202871s_real A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_real A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.nat)) (X2 (-> tptp.nat tptp.real)) (A2 tptp.nat)) (=> (@ (@ tptp.lower_438231087al_nat X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_nat (@ (@ tptp.comp_real_nat_nat F2) X2)) (@ tptp.topolo1564986139ds_nat A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_nat A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.int)) (X2 (-> tptp.nat tptp.real)) (A2 tptp.int)) (=> (@ (@ tptp.lower_1075504779al_int X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (=> (@ (@ (@ tptp.filterlim_nat_int (@ (@ tptp.comp_real_int_nat F2) X2)) (@ tptp.topolo54776183ds_int A2)) tptp.at_top_nat) (@ (@ tptp.ord_less_eq_int A2) (@ F2 X0)))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal))) (=> (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_le824540014_ereal (@ F2 N2)) (@ F2 M2)))) (not (forall ((L3 tptp.extended_ereal)) (not (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L3)) tptp.at_top_nat)))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal))) (=> (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_le824540014_ereal (@ F2 M2)) (@ F2 N2)))) (not (forall ((L3 tptp.extended_ereal)) (not (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L3)) tptp.at_top_nat)))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (@ (@ tptp.ord_le824540014_ereal X2) X2)))
% 0.25/0.71 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 0.25/0.71 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) X2)))
% 0.25/0.71 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 0.25/0.71 (assert (forall ((A (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (@ tptp.topolo1922093437eq_nat A) (=> (@ (@ (@ tptp.filterlim_nat_nat A) (@ tptp.topolo1564986139ds_nat X2)) tptp.at_top_nat) (or (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ A N5)) X2)) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_less_eq_nat (@ A M3)) (@ A N5))))) (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) (@ A N5))) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_less_eq_nat (@ A N5)) (@ A M3))))))))))
% 0.25/0.71 (assert (forall ((A (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (@ tptp.topolo411883481eq_int A) (=> (@ (@ (@ tptp.filterlim_nat_int A) (@ tptp.topolo54776183ds_int X2)) tptp.at_top_nat) (or (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ A N5)) X2)) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_less_eq_int (@ A M3)) (@ A N5))))) (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_int X2) (@ A N5))) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_less_eq_int (@ A N5)) (@ A M3))))))))))
% 0.25/0.71 (assert (forall ((A (-> tptp.nat tptp.extended_ereal)) (X2 tptp.extended_ereal)) (=> (@ tptp.topolo1069469409_ereal A) (=> (@ (@ (@ tptp.filter1531173832_ereal A) (@ tptp.topolo2140997059_ereal X2)) tptp.at_top_nat) (or (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ A N5)) X2)) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_le824540014_ereal (@ A M3)) (@ A N5))))) (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_le824540014_ereal X2) (@ A N5))) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_le824540014_ereal (@ A N5)) (@ A M3))))))))))
% 0.25/0.71 (assert (forall ((A (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.topolo144289241q_real A) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo1664202871s_real X2)) tptp.at_top_nat) (or (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A N5)) X2)) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_less_eq_real (@ A M3)) (@ A N5))))) (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ A N5))) (forall ((M3 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N5) (@ (@ tptp.ord_less_eq_real (@ A N5)) (@ A M3))))))))))
% 0.25/0.71 (assert (= tptp.lower_551915512_ereal (lambda ((X02 tptp.real) (F3 (-> tptp.real tptp.extended_ereal))) (forall ((X (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real X) (@ tptp.topolo1664202871s_real X02)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) (@ (@ tptp.liminf1045857232_ereal tptp.at_top_nat) (@ (@ tptp.comp_r1410008527al_nat F3) X))))))))
% 0.25/0.71 (assert (= tptp.lower_191460856_ereal (lambda ((X02 tptp.a) (F3 (-> tptp.a tptp.extended_ereal))) (forall ((X (-> tptp.nat tptp.a))) (=> (@ (@ (@ tptp.filterlim_nat_a X) (@ tptp.topolo705128563nhds_a X02)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal (@ F3 X02)) (@ (@ tptp.liminf1045857232_ereal tptp.at_top_nat) (@ (@ tptp.comp_a1112243075al_nat F3) X))))))))
% 0.25/0.71 (assert (forall ((X0 tptp.real) (F2 (-> tptp.real tptp.extended_ereal)) (X2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.lower_551915512_ereal X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_real X2) (@ tptp.topolo1664202871s_real X0)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal (@ F2 X0)) (@ (@ tptp.liminf1045857232_ereal tptp.at_top_nat) (@ (@ tptp.comp_r1410008527al_nat F2) X2)))))))
% 0.25/0.71 (assert (forall ((X0 tptp.a) (F2 (-> tptp.a tptp.extended_ereal)) (X2 (-> tptp.nat tptp.a))) (=> (@ (@ tptp.lower_191460856_ereal X0) F2) (=> (@ (@ (@ tptp.filterlim_nat_a X2) (@ tptp.topolo705128563nhds_a X0)) tptp.at_top_nat) (@ (@ tptp.ord_le824540014_ereal (@ F2 X0)) (@ (@ tptp.liminf1045857232_ereal tptp.at_top_nat) (@ (@ tptp.comp_a1112243075al_nat F2) X2)))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal))) (@ tptp.uniq_Extended_ereal (lambda ((L2 tptp.extended_ereal)) (@ (@ (@ tptp.filter1531173832_ereal X3) (@ tptp.topolo2140997059_ereal L2)) tptp.at_top_nat)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.a))) (@ tptp.uniq_a (lambda ((L2 tptp.a)) (@ (@ (@ tptp.filterlim_nat_a X3) (@ tptp.topolo705128563nhds_a L2)) tptp.at_top_nat)))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real))) (@ tptp.uniq_real (lambda ((L2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real X3) (@ tptp.topolo1664202871s_real L2)) tptp.at_top_nat)))))
% 0.25/0.71 (assert (= tptp.topolo1069469409_ereal (lambda ((X4 (-> tptp.nat tptp.extended_ereal))) (or (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_le824540014_ereal (@ X4 M4)) (@ X4 N)))) (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_le824540014_ereal (@ X4 N)) (@ X4 M4))))))))
% 0.25/0.71 (assert (= tptp.topolo1922093437eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_less_eq_nat (@ X4 M4)) (@ X4 N)))) (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 M4))))))))
% 0.25/0.71 (assert (= tptp.topolo144289241q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ X4 M4)) (@ X4 N)))) (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 M4))))))))
% 0.25/0.71 (assert (= tptp.topolo411883481eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_less_eq_int (@ X4 M4)) (@ X4 N)))) (forall ((M4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 M4))))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_le824540014_ereal (@ X3 N2)) (@ X3 M2)))) (@ tptp.topolo1069469409_ereal X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.nat))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X3 N2)) (@ X3 M2)))) (@ tptp.topolo1922093437eq_nat X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X3 N2)) (@ X3 M2)))) (@ tptp.topolo144289241q_real X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.int))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X3 N2)) (@ X3 M2)))) (@ tptp.topolo411883481eq_int X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_le824540014_ereal (@ X3 M2)) (@ X3 N2)))) (@ tptp.topolo1069469409_ereal X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.nat))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X3 M2)) (@ X3 N2)))) (@ tptp.topolo1922093437eq_nat X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.real))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X3 M2)) (@ X3 N2)))) (@ tptp.topolo144289241q_real X3))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.int))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X3 M2)) (@ X3 N2)))) (@ tptp.topolo411883481eq_int X3))))
% 0.25/0.71 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ tptp.topolo144289241q_real A) (@ tptp.topolo144289241q_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ A N)))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.extended_ereal)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.nat tptp.extended_ereal)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.real tptp.extended_ereal)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.int tptp.extended_ereal)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.extended_ereal tptp.nat)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (F2 (-> tptp.extended_ereal tptp.real)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (F2 (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ _let_1 (@ F2 C))))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.extended_ereal)) (C tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (@ (@ tptp.ord_le824540014_ereal (@ F2 B)) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_real (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F2 B)) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.extended_ereal)) (C tptp.extended_ereal)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le824540014_ereal (@ F2 B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_real (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F2 B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.extended_ereal)) (C tptp.extended_ereal)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_le824540014_ereal (@ F2 B)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.extended_ereal)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.extended_ereal tptp.nat)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (F2 (-> tptp.extended_ereal tptp.real)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.int) (F2 (-> tptp.extended_ereal tptp.int)) (B tptp.extended_ereal) (C tptp.extended_ereal)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.nat tptp.extended_ereal)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (F2 (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.int) (F2 (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (F2 (-> tptp.real tptp.extended_ereal)) (B tptp.real) (C tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (F2 (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F2 C)))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.extended_ereal)) (C tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_real (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (F2 (-> tptp.extended_ereal tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.extended_ereal) (Y3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.extended_ereal)) (C tptp.extended_ereal)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_real (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.extended_ereal)) (C tptp.extended_ereal)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le824540014_ereal (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_le824540014_ereal (@ F2 A)) C))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F2 B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X5)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C))))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.extended_ereal) (Z2 tptp.extended_ereal)) (= Y4 Z2)) (lambda ((X tptp.extended_ereal) (Y5 tptp.extended_ereal)) (and (@ (@ tptp.ord_le824540014_ereal X) Y5) (@ (@ tptp.ord_le824540014_ereal Y5) X)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((X tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y5) (@ (@ tptp.ord_less_eq_real Y5) X)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y5) (@ (@ tptp.ord_less_eq_int Y5) X)))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X2) Y) (=> (@ (@ tptp.ord_le824540014_ereal Y) X2) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal)) (or (@ (@ tptp.ord_le824540014_ereal X2) Y) (@ (@ tptp.ord_le824540014_ereal Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal)) (=> (= X2 Y) (@ (@ tptp.ord_le824540014_ereal X2) Y))))
% 0.25/0.71 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 0.25/0.71 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal)) (=> (not (@ (@ tptp.ord_le824540014_ereal X2) Y)) (@ (@ tptp.ord_le824540014_ereal Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 0.25/0.71 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (C tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal) (Z3 tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_le824540014_ereal X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_le824540014_ereal Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_le824540014_ereal Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.71 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_real Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_real Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.71 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.71 (assert (forall ((Y tptp.extended_ereal) (X2 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal Y) X2) (= (@ (@ tptp.ord_le824540014_ereal X2) Y) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (= (@ (@ tptp.ord_less_eq_real X2) Y) (= X2 Y)))))
% 0.25/0.71 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y) (= X2 Y)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.extended_ereal) (Z2 tptp.extended_ereal)) (= Y4 Z2)) (lambda ((A3 tptp.extended_ereal) (B2 tptp.extended_ereal)) (and (@ (@ tptp.ord_le824540014_ereal A3) B2) (@ (@ tptp.ord_le824540014_ereal B2) A3)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (@ (@ tptp.ord_less_eq_real B2) A3)))))
% 0.25/0.71 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ tptp.ord_less_eq_int B2) A3)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (C tptp.extended_ereal)) (=> (= A B) (=> (@ (@ tptp.ord_le824540014_ereal B) C) (@ (@ tptp.ord_le824540014_ereal A) C)))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_eq_real A) C)))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (C tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (@ (@ tptp.ord_le824540014_ereal B) A) (= A B)))))
% 0.25/0.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 0.25/0.71 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A B)))))
% 0.25/0.71 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal) (Z3 tptp.extended_ereal)) (let ((_let_1 (@ tptp.ord_le824540014_ereal X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le824540014_ereal Y) Z3) (@ _let_1 Z3))))))
% 0.25/0.71 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z3) (@ _let_1 Z3))))))
% 0.25/0.71 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal)) (@ (@ tptp.ord_le824540014_ereal A) A)))
% 0.25/0.71 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 0.25/0.71 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 0.25/0.71 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 0.25/0.71 (assert (forall ((P (-> tptp.extended_ereal tptp.extended_ereal Bool)) (A tptp.extended_ereal) (B tptp.extended_ereal)) (=> (forall ((A4 tptp.extended_ereal) (B3 tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.extended_ereal) (B3 tptp.extended_ereal)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 0.25/0.71 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 0.25/0.71 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 0.25/0.71 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 0.25/0.71 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.71 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.71 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.71 (assert (forall ((X3 (-> tptp.nat tptp.extended_ereal))) (= (@ (@ (@ tptp.filter1531173832_ereal X3) (@ tptp.topolo2140997059_ereal tptp.extend1289208545_ereal)) tptp.at_top_nat) (= (@ (@ tptp.liminf1045857232_ereal tptp.at_top_nat) X3) tptp.extend1289208545_ereal))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (= (@ (@ tptp.ord_le824540014_ereal tptp.extend1289208545_ereal) X2) (= X2 tptp.extend1289208545_ereal))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (@ (@ tptp.ord_le824540014_ereal X2) _let_1) (= X2 _let_1)))))
% 0.25/0.71 (assert (not (= tptp.extend1289208545_ereal (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (@ (@ tptp.ord_le824540014_ereal X2) tptp.extend1289208545_ereal)))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (= A tptp.extend1289208545_ereal) (= B tptp.extend1289208545_ereal)))))
% 0.25/0.71 (assert (forall ((Y tptp.extended_ereal) (X2 tptp.extended_ereal)) (=> (not (= Y tptp.extend1289208545_ereal)) (=> (@ (@ tptp.ord_le824540014_ereal X2) Y) (not (= X2 tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (=> (@ (@ tptp.ord_le824540014_ereal A) B) (=> (= B _let_1) (= A _let_1))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (@ (@ tptp.ord_le824540014_ereal (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) X2)))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal))) (= (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) tptp.at_top_nat) (forall ((B4 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_le824540014_ereal (@ F2 N)) (@ tptp.extended_ereal2 B4)))))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal) (B5 tptp.real)) (=> (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ tptp.extended_ereal2 B5)) (@ F2 N2))) (not (= L (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal))) (= (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal tptp.extend1289208545_ereal)) tptp.at_top_nat) (forall ((B4 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_le824540014_ereal (@ tptp.extended_ereal2 B4)) (@ F2 N)))))))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal) (N3 tptp.nat) (B5 tptp.real)) (=> (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N2) (@ (@ tptp.ord_le824540014_ereal (@ F2 N2)) (@ tptp.extended_ereal2 B5)))) (not (= L tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (forall ((X1 tptp.real) (Y1 tptp.real)) (= (= (@ tptp.extended_ereal2 X1) (@ tptp.extended_ereal2 Y1)) (= X1 Y1))))
% 0.25/0.71 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (= X2 Y) (= (@ tptp.extended_ereal2 X2) (@ tptp.extended_ereal2 Y)))))
% 0.25/0.71 (assert (forall ((R tptp.real) (P2 tptp.real)) (= (@ (@ tptp.ord_le824540014_ereal (@ tptp.extended_ereal2 R)) (@ tptp.extended_ereal2 P2)) (@ (@ tptp.ord_less_eq_real R) P2))))
% 0.25/0.71 (assert (forall ((R tptp.real)) (not (= (@ tptp.extended_ereal2 R) tptp.extend1289208545_ereal))))
% 0.25/0.71 (assert (forall ((R tptp.real)) (= (@ tptp.uminus1208298309_ereal (@ tptp.extended_ereal2 R)) (@ tptp.extended_ereal2 (@ tptp.uminus_uminus_real R)))))
% 0.25/0.71 (assert (forall ((Y tptp.real) (A tptp.extended_ereal) (X2 tptp.real)) (=> (@ (@ tptp.ord_le824540014_ereal (@ tptp.extended_ereal2 Y)) A) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_le824540014_ereal (@ tptp.extended_ereal2 X2)) A)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_le824540014_ereal A))) (=> (@ _let_1 (@ tptp.extended_ereal2 X2)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ _let_1 (@ tptp.extended_ereal2 Y)))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Y tptp.extended_ereal)) (=> (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.extended_ereal2 Z4))) (=> (@ (@ tptp.ord_le824540014_ereal X2) _let_1) (@ (@ tptp.ord_le824540014_ereal Y) _let_1)))) (@ (@ tptp.ord_le824540014_ereal Y) X2))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (= (@ tptp.collect_real (lambda ((Y5 tptp.real)) (@ (@ tptp.ord_le824540014_ereal A) (@ tptp.extended_ereal2 Y5)))) (@ tptp.collect_real (lambda ((Y5 tptp.real)) (@ (@ tptp.ord_le824540014_ereal B) (@ tptp.extended_ereal2 Y5))))) (= A B))))
% 0.25/0.71 (assert (forall ((P (-> tptp.extended_ereal Bool)) (A0 tptp.extended_ereal)) (=> (forall ((R2 tptp.real)) (@ P (@ tptp.extended_ereal2 R2))) (=> (@ P tptp.extend1289208545_ereal) (=> (@ P (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (@ P A0))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (=> (forall ((R2 tptp.real)) (not (= X2 (@ tptp.extended_ereal2 R2)))) (=> (not (= X2 tptp.extend1289208545_ereal)) (= X2 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (forall ((P (-> tptp.extended_ereal tptp.extended_ereal Bool)) (A0 tptp.extended_ereal) (A1 tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (let ((_let_2 (@ P _let_1))) (let ((_let_3 (@ P tptp.extend1289208545_ereal))) (=> (forall ((R2 tptp.real) (P3 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 R2)) (@ tptp.extended_ereal2 P3))) (=> (forall ((R2 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 R2)) tptp.extend1289208545_ereal)) (=> (forall ((R2 tptp.real)) (@ (@ P tptp.extend1289208545_ereal) (@ tptp.extended_ereal2 R2))) (=> (forall ((R2 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 R2)) (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (=> (forall ((R2 tptp.real)) (@ (@ P (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (@ tptp.extended_ereal2 R2))) (=> (@ _let_3 tptp.extend1289208545_ereal) (=> (@ _let_2 tptp.extend1289208545_ereal) (=> (@ _let_3 _let_1) (=> (@ _let_2 _let_1) (@ (@ P A0) A1)))))))))))))))
% 0.25/0.71 (assert (forall ((P (-> tptp.extended_ereal tptp.extended_ereal Bool)) (A0 tptp.extended_ereal) (A1 tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (=> (forall ((R2 tptp.real) (P3 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 R2)) (@ tptp.extended_ereal2 P3))) (=> (forall ((X_1 tptp.extended_ereal)) (@ (@ P tptp.extend1289208545_ereal) X_1)) (=> (forall ((A4 tptp.extended_ereal)) (@ (@ P A4) tptp.extend1289208545_ereal)) (=> (forall ((R2 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 R2)) (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (=> (forall ((P3 tptp.real)) (@ (@ P (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (@ tptp.extended_ereal2 P3))) (=> (@ (@ P _let_1) _let_1) (@ (@ P A0) A1))))))))))
% 0.25/0.71 (assert (forall ((P (-> tptp.extended_ereal tptp.extended_ereal Bool)) (A0 tptp.extended_ereal) (A1 tptp.extended_ereal)) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 X5)) (@ tptp.extended_ereal2 Y3))) (=> (forall ((X_1 tptp.extended_ereal)) (@ (@ P tptp.extend1289208545_ereal) X_1)) (=> (forall ((A4 tptp.extended_ereal)) (@ (@ P A4) (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (=> (forall ((X5 tptp.real)) (@ (@ P (@ tptp.extended_ereal2 X5)) tptp.extend1289208545_ereal)) (=> (forall ((R2 tptp.real)) (@ (@ P (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (@ tptp.extended_ereal2 R2))) (=> (@ (@ P (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) tptp.extend1289208545_ereal) (@ (@ P A0) A1)))))))))
% 0.25/0.71 (assert (forall ((P (-> tptp.extended_ereal Bool)) (A0 tptp.extended_ereal)) (=> (forall ((R2 tptp.real)) (@ P (@ tptp.extended_ereal2 R2))) (=> (@ P (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (=> (@ P tptp.extend1289208545_ereal) (@ P A0))))))
% 0.25/0.71 (assert (= (lambda ((P4 (-> tptp.extended_ereal Bool))) (forall ((X6 tptp.extended_ereal)) (@ P4 X6))) (lambda ((P5 (-> tptp.extended_ereal Bool))) (and (@ P5 tptp.extend1289208545_ereal) (forall ((X tptp.real)) (@ P5 (@ tptp.extended_ereal2 X))) (@ P5 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (=> (forall ((R2 tptp.real)) (not (= X2 (@ tptp.extended_ereal2 R2)))) (=> (not (= X2 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= X2 tptp.extend1289208545_ereal)))))
% 0.25/0.71 (assert (= (lambda ((P4 (-> tptp.extended_ereal Bool))) (exists ((X6 tptp.extended_ereal)) (@ P4 X6))) (lambda ((P5 (-> tptp.extended_ereal Bool))) (or (@ P5 tptp.extend1289208545_ereal) (exists ((X tptp.real)) (@ P5 (@ tptp.extended_ereal2 X))) (@ P5 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Xa3 tptp.extended_ereal) (Xb tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (let ((_let_2 (not (= Xb _let_1)))) (let ((_let_3 (= Xa3 _let_1))) (let ((_let_4 (=> _let_3 _let_2))) (let ((_let_5 (= X2 _let_1))) (let ((_let_6 (not (= Xb tptp.extend1289208545_ereal)))) (let ((_let_7 (=> _let_3 _let_6))) (let ((_let_8 (= Xa3 tptp.extend1289208545_ereal))) (let ((_let_9 (=> _let_8 _let_2))) (let ((_let_10 (=> _let_8 _let_6))) (let ((_let_11 (= X2 tptp.extend1289208545_ereal))) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) (=> (exists ((Ra tptp.real)) (= Xa3 (@ tptp.extended_ereal2 Ra))) (forall ((Rb tptp.real)) (not (= Xb (@ tptp.extended_ereal2 Rb)))))) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) (=> (exists ((Ra tptp.real)) (= Xa3 (@ tptp.extended_ereal2 Ra))) _let_6)) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) (=> (exists ((Ra tptp.real)) (= Xa3 (@ tptp.extended_ereal2 Ra))) _let_2)) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) (=> _let_8 (forall ((Ra tptp.real)) (not (= Xb (@ tptp.extended_ereal2 Ra)))))) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_10) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_9) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) (=> _let_3 (forall ((Ra tptp.real)) (not (= Xb (@ tptp.extended_ereal2 Ra)))))) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_7) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_4) (=> (=> _let_11 (=> (exists ((R2 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 R2))) (forall ((Ra tptp.real)) (not (= Xb (@ tptp.extended_ereal2 Ra)))))) (=> (=> _let_11 (=> (exists ((R2 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 R2))) _let_6)) (=> (=> _let_11 (=> (exists ((R2 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 R2))) _let_2)) (=> (=> _let_11 (=> _let_8 (forall ((R2 tptp.real)) (not (= Xb (@ tptp.extended_ereal2 R2)))))) (=> (=> _let_11 _let_10) (=> (=> _let_11 _let_9) (=> (=> _let_11 (=> _let_3 (forall ((R2 tptp.real)) (not (= Xb (@ tptp.extended_ereal2 R2)))))) (=> (=> _let_11 _let_7) (=> (=> _let_11 _let_4) (=> (=> _let_5 (=> (exists ((R2 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 R2))) (forall ((Ra tptp.real)) (not (= Xb (@ tptp.extended_ereal2 Ra)))))) (=> (=> _let_5 (=> (exists ((R2 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 R2))) _let_6)) (=> (=> _let_5 (=> (exists ((R2 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 R2))) _let_2)) (=> (=> _let_5 (=> _let_8 (forall ((R2 tptp.real)) (not (= Xb (@ tptp.extended_ereal2 R2)))))) (=> (=> _let_5 _let_10) (=> (=> _let_5 _let_9) (=> (=> _let_5 (=> _let_3 (forall ((R2 tptp.real)) (not (= Xb (@ tptp.extended_ereal2 R2)))))) (=> (=> _let_5 _let_7) (not (=> _let_5 _let_4)))))))))))))))))))))))))))))))))))))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal) (Xa3 tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (let ((_let_2 (not (= Xa3 _let_1)))) (let ((_let_3 (= X2 _let_1))) (let ((_let_4 (not (= Xa3 tptp.extend1289208545_ereal)))) (let ((_let_5 (= X2 tptp.extend1289208545_ereal))) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) (forall ((Ra tptp.real)) (not (= Xa3 (@ tptp.extended_ereal2 Ra))))) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_4) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_2) (=> (=> _let_5 (forall ((R2 tptp.real)) (not (= Xa3 (@ tptp.extended_ereal2 R2))))) (=> (=> _let_5 _let_4) (=> (=> _let_5 _let_2) (=> (=> _let_3 (forall ((R2 tptp.real)) (not (= Xa3 (@ tptp.extended_ereal2 R2))))) (=> (=> _let_3 _let_4) (not (=> _let_3 _let_2)))))))))))))))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (=> (forall ((R2 tptp.real)) (not (= X2 (@ tptp.extended_ereal2 R2)))) (=> (not (= X2 tptp.extend1289208545_ereal)) (= X2 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (forall ((R tptp.real)) (not (= (@ tptp.extended_ereal2 R) (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (=> (forall ((B6 tptp.real)) (@ (@ tptp.ord_le824540014_ereal (@ tptp.extended_ereal2 B6)) X2)) (= X2 tptp.extend1289208545_ereal))))
% 0.25/0.71 (assert (forall ((X2 tptp.extended_ereal)) (=> (forall ((B6 tptp.real)) (@ (@ tptp.ord_le824540014_ereal X2) (@ tptp.extended_ereal2 B6))) (= X2 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)))))
% 0.25/0.71 (assert (forall ((F2 (-> tptp.nat tptp.extended_ereal)) (L tptp.extended_ereal) (B5 tptp.real)) (=> (@ (@ (@ tptp.filter1531173832_ereal F2) (@ tptp.topolo2140997059_ereal L)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le824540014_ereal (@ F2 N2)) (@ tptp.extended_ereal2 B5))) (not (= L tptp.extend1289208545_ereal))))))
% 0.25/0.71 (assert (@ (@ (@ tptp.filter1531173832_ereal (lambda ((X tptp.nat)) (@ tptp.extended_ereal2 (@ tptp.uminus_uminus_real (@ tptp.semiri2110766477t_real X))))) (@ tptp.topolo2140997059_ereal (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) tptp.at_top_nat))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (= tptp.extend1289208545_ereal (@ (@ tptp.plus_p2118002693_ereal A) B)) (or (= A tptp.extend1289208545_ereal) (= B tptp.extend1289208545_ereal)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (= (= (@ (@ tptp.plus_p2118002693_ereal A) B) tptp.extend1289208545_ereal) (or (= A tptp.extend1289208545_ereal) (= B tptp.extend1289208545_ereal)))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (= _let_1 (@ (@ tptp.plus_p2118002693_ereal A) B)) (or (and (= A _let_1) (not (= B tptp.extend1289208545_ereal))) (and (= B _let_1) (not (= A tptp.extend1289208545_ereal))))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (= (@ (@ tptp.plus_p2118002693_ereal A) B) _let_1) (and (or (= A _let_1) (= B _let_1)) (not (= A tptp.extend1289208545_ereal)) (not (= B tptp.extend1289208545_ereal)))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal)) (= (@ (@ tptp.plus_p2118002693_ereal tptp.extend1289208545_ereal) A) tptp.extend1289208545_ereal)))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal)) (= (@ (@ tptp.plus_p2118002693_ereal A) tptp.extend1289208545_ereal) tptp.extend1289208545_ereal)))
% 0.25/0.71 (assert (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (@ (@ tptp.plus_p2118002693_ereal _let_1) _let_1) _let_1)))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (C tptp.extended_ereal)) (let ((_let_1 (@ tptp.plus_p2118002693_ereal A))) (=> (not (= A (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (= (@ _let_1 B) (@ _let_1 C)) (or (= A tptp.extend1289208545_ereal) (= B C)))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (B tptp.extended_ereal) (C tptp.extended_ereal)) (=> (not (= A (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (= (@ (@ tptp.plus_p2118002693_ereal B) A) (@ (@ tptp.plus_p2118002693_ereal C) A)) (or (= A tptp.extend1289208545_ereal) (= B C))))))
% 0.25/0.71 (assert (forall ((P2 tptp.real)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (@ (@ tptp.plus_p2118002693_ereal _let_1) (@ tptp.extended_ereal2 P2)) _let_1))))
% 0.25/0.71 (assert (forall ((R tptp.real)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (= (@ (@ tptp.plus_p2118002693_ereal (@ tptp.extended_ereal2 R)) _let_1) _let_1))))
% 0.25/0.71 (assert (forall ((C tptp.extended_ereal) (A tptp.extended_ereal) (B tptp.extended_ereal)) (let ((_let_1 (@ tptp.plus_p2118002693_ereal C))) (= (@ (@ tptp.ord_le824540014_ereal (@ _let_1 A)) (@ _let_1 B)) (or (@ (@ tptp.ord_le824540014_ereal A) B) (= C tptp.extend1289208545_ereal) (and (= C (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (not (= A tptp.extend1289208545_ereal)) (not (= B tptp.extend1289208545_ereal))))))))
% 0.25/0.71 (assert (forall ((A tptp.extended_ereal) (C tptp.extended_ereal) (B tptp.extended_ereal)) (= (@ (@ tptp.ord_le824540014_ereal (@ (@ tptp.plus_p2118002693_ereal A) C)) (@ (@ tptp.plus_p2118002693_ereal B) C)) (or (@ (@ tptp.ord_le824540014_ereal A) B) (= C tptp.extend1289208545_ereal) (and (= C (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal)) (not (= A tptp.extend1289208545_ereal)) (not (= B tptp.extend1289208545_ereal)))))))
% 0.25/0.71 (assert (@ (@ (@ tptp.filter1531173832_ereal (lambda ((X tptp.nat)) (@ tptp.extended_ereal2 (@ tptp.semiri2110766477t_real X)))) (@ tptp.topolo2140997059_ereal tptp.extend1289208545_ereal)) tptp.at_top_nat))
% 0.25/0.71 (assert (forall ((U (-> tptp.nat tptp.extended_ereal)) (V (-> tptp.nat tptp.extended_ereal))) (let ((_let_1 (@ tptp.liminf1045857232_ereal tptp.at_top_nat))) (let ((_let_2 (@ _let_1 V))) (let ((_let_3 (@ _let_1 U))) (let ((_let_4 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (=> (not (or (and (= _let_3 tptp.extend1289208545_ereal) (= _let_2 _let_4)) (and (= _let_3 _let_4) (= _let_2 tptp.extend1289208545_ereal)))) (@ (@ tptp.ord_le824540014_ereal (@ (@ tptp.plus_p2118002693_ereal _let_3) _let_2)) (@ _let_1 (lambda ((N tptp.nat)) (@ (@ tptp.plus_p2118002693_ereal (@ U N)) (@ V N))))))))))))
% 0.25/0.71 (assert (forall ((K tptp.nat) (M5 tptp.nat) (N7 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M5)) (@ _let_1 N7)) (@ (@ tptp.ord_less_eq_nat M5) N7)))))
% 0.25/0.71 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int A3)) (@ tptp.semiri2019852685at_int B2)))))
% 0.25/0.71 (assert (forall ((M5 tptp.nat) (K tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M5) K)) N7) (not (=> (@ (@ tptp.ord_less_eq_nat M5) N7) (not (@ (@ tptp.ord_less_eq_nat K) N7)))))))
% 0.25/0.71 (assert (forall ((N7 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N7) (@ (@ tptp.plus_plus_nat N7) M5))))
% 0.25/0.71 (assert (forall ((N7 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N7) (@ (@ tptp.plus_plus_nat M5) N7))))
% 0.25/0.71 (assert (forall ((M5 tptp.nat) (K tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M5) K)) N7) (@ (@ tptp.ord_less_eq_nat M5) N7))))
% 0.25/0.71 (assert (forall ((M5 tptp.nat) (K tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M5) K)) N7) (@ (@ tptp.ord_less_eq_nat K) N7))))
% 0.25/0.71 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))))
% 0.25/0.71 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.25/0.71 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.25/0.71 (assert (forall ((I tptp.nat) (J tptp.nat) (M5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M5))))))
% 0.25/0.71 (assert (forall ((I tptp.nat) (J tptp.nat) (M5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M5) J))))))
% 0.25/0.71 (assert (= tptp.ord_less_eq_nat (lambda ((M4 tptp.nat) (N tptp.nat)) (exists ((K2 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M4) K2))))))
% 0.25/0.71 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int A3)) (@ tptp.semiri2019852685at_int B2)))))
% 0.25/0.71 (assert (forall ((R tptp.real) (P2 tptp.real)) (= (@ (@ tptp.plus_p2118002693_ereal (@ tptp.extended_ereal2 R)) (@ tptp.extended_ereal2 P2)) (@ tptp.extended_ereal2 (@ (@ tptp.plus_plus_real R) P2)))))
% 0.25/0.71 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_bot_real) tptp.at_top_real))
% 0.25/0.71 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_top_real) tptp.at_bot_real))
% 0.25/0.71 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y6 tptp.nat)) (=> (@ P Y6) (@ (@ tptp.ord_less_eq_nat Y6) X5)))))))))
% 0.25/0.71 (assert (forall ((M5 tptp.nat) (N7 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M5) N7) (@ (@ tptp.ord_less_eq_nat N7) M5))))
% 0.25/0.71 (assert (forall ((M5 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N7) (=> (@ (@ tptp.ord_less_eq_nat N7) M5) (= M5 N7)))))
% 0.25/0.71 (assert (forall ((M5 tptp.nat) (N7 tptp.nat)) (=> (= M5 N7) (@ (@ tptp.ord_less_eq_nat M5) N7))))
% 0.25/0.71 (assert (for/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 25957 Alarm clock ( read result; case "$result" in
% 299.79/300.14 unsat)
% 299.79/300.14 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.79/300.14 ;;
% 299.79/300.14 sat)
% 299.79/300.14 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.79/300.14 ;;
% 299.79/300.14 esac; exit 1 )
% 299.79/300.14 all ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 299.79/300.14 (assert (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N7) N7)))
% 299.79/300.14 (assert (forall ((X2 tptp.extended_ereal) (Xa3 tptp.extended_ereal) (Y tptp.extended_ereal)) (let ((_let_1 (@ tptp.uminus1208298309_ereal tptp.extend1289208545_ereal))) (let ((_let_2 (not (= Y _let_1)))) (let ((_let_3 (=> (= Xa3 _let_1) _let_2))) (let ((_let_4 (= X2 _let_1))) (let ((_let_5 (not (= Y tptp.extend1289208545_ereal)))) (=> (= (@ (@ tptp.plus_p2118002693_ereal X2) Xa3) Y) (=> (forall ((R2 tptp.real)) (=> (= X2 (@ tptp.extended_ereal2 R2)) (forall ((P3 tptp.real)) (=> (= Xa3 (@ tptp.extended_ereal2 P3)) (not (= Y (@ tptp.extended_ereal2 (@ (@ tptp.plus_plus_real R2) P3)))))))) (=> (=> (= X2 tptp.extend1289208545_ereal) _let_5) (=> (=> (= Xa3 tptp.extend1289208545_ereal) _let_5) (=> (=> (exists ((R2 tptp.real)) (= X2 (@ tptp.extended_ereal2 R2))) _let_3) (=> (=> _let_4 (=> (exists ((P3 tptp.real)) (= Xa3 (@ tptp.extended_ereal2 P3))) _let_2)) (not (=> _let_4 _let_3)))))))))))))))
% 299.79/300.14 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri2110766477t_real) tptp.at_top_real) tptp.at_top_nat))
% 299.79/300.14 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri2019852685at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int A)) (@ tptp.semiri2019852685at_int B)))))
% 299.79/300.14 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri2019852685at_int A3) (@ tptp.semiri2019852685at_int B2)))))
% 299.79/300.14 (assert (not (@ (@ (@ tptp.filter1531173832_ereal (lambda ((I2 tptp.nat)) (@ tptp.uminus1208298309_ereal (@ tptp.f (@ tptp.x I2))))) (@ tptp.topolo2140997059_ereal (@ tptp.uminus1208298309_ereal tptp.a2))) tptp.at_top_nat)))
% 299.79/300.14 (set-info :filename cvc5---1.0.5_25831)
% 299.79/300.14 (check-sat-assuming ( true ))
% 299.79/300.14 ------- get file name : TPTP file name is ITP112^1
% 299.79/300.14 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25831.smt2...
% 299.79/300.14 --- Run --ho-elim --full-saturate-quant at 10...
% 299.79/300.14 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 299.79/300.14 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 299.79/300.14 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 299.79/300.14 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 299.79/300.14 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 299.79/300.14 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 299.79/300.14 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 299.79/300.14 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 299.79/300.14 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.79/300.14 % cvc5---1.0.5 exiting
% 299.79/300.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------