TSTP Solution File: ITP117^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP117^1 : 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 03:18:23 EDT 2023
% Result : Timeout 299.94s 300.13s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.18 % Problem : ITP117^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.19 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n031.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 16:00:24 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.27/0.60 %----Proving TH0
% 0.27/0.61 %------------------------------------------------------------------------------
% 0.27/0.61 % File : ITP117^1 : TPTP v8.1.2. Released v7.5.0.
% 0.27/0.61 % Domain : Interactive Theorem Proving
% 0.27/0.61 % Problem : Sledgehammer Minkowskis_Theorem problem prob_290__6248976_1
% 0.27/0.61 % Version : Especial.
% 0.27/0.61 % English :
% 0.27/0.61
% 0.27/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.61 % Source : [Des21]
% 0.27/0.61 % Names : Minkowskis_Theorem/prob_290__6248976_1 [Des21]
% 0.27/0.61
% 0.27/0.61 % Status : Theorem
% 0.27/0.61 % Rating : 0.38 v8.1.0, 0.36 v7.5.0
% 0.27/0.61 % Syntax : Number of formulae : 487 ( 187 unt; 133 typ; 0 def)
% 0.27/0.61 % Number of atoms : 807 ( 345 equ; 0 cnn)
% 0.27/0.61 % Maximal formula atoms : 6 ( 2 avg)
% 0.27/0.61 % Number of connectives : 3013 ( 72 ~; 3 |; 79 &;2559 @)
% 0.27/0.61 % ( 0 <=>; 300 =>; 0 <=; 0 <~>)
% 0.27/0.61 % Maximal formula depth : 14 ( 6 avg)
% 0.27/0.61 % Number of types : 19 ( 18 usr)
% 0.27/0.61 % Number of type conns : 541 ( 541 >; 0 *; 0 +; 0 <<)
% 0.27/0.61 % Number of symbols : 117 ( 115 usr; 16 con; 0-2 aty)
% 0.27/0.61 % Number of variables : 1094 ( 122 ^; 923 !; 49 ?;1094 :)
% 0.27/0.61 % SPC : TH0_THM_EQU_NAR
% 0.27/0.61
% 0.27/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:47:06.896
% 0.27/0.61 %------------------------------------------------------------------------------
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% 0.27/0.61 % \<open>\<And>a. T' a \<in> sets lebesgue\<close>
% 0.27/0.61 thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % \<open>\<And>a. T a \<in> sets lebesgue\<close>
% 0.27/0.61 thf(fact_3_calculation,axiom,
% 0.27/0.61 ( sums_E1192373732nnreal
% 0.27/0.61 @ ^ [N: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ N ) ) )
% 0.27/0.61 @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) ) ).
% 0.27/0.61
% 0.27/0.61 % calculation
% 0.27/0.61 thf(fact_4_assms_I1_J,axiom,
% 0.27/0.61 member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ).
% 0.27/0.61
% 0.27/0.61 % assms(1)
% 0.27/0.61 thf(fact_5_emeasure__T__Int,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n,B: finite964658038_int_n] :
% 0.27/0.61 ( ( A != B )
% 0.27/0.61 => ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( inf_in1974387902real_n @ ( t2 @ A ) @ ( t2 @ B ) ) )
% 0.27/0.61 = zero_z1963244097nnreal ) ) ).
% 0.27/0.61
% 0.27/0.61 % emeasure_T_Int
% 0.27/0.61 thf(fact_6_T__Int,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n,B: finite964658038_int_n] :
% 0.27/0.61 ( ( A != B )
% 0.27/0.61 => ( member223413699real_n @ ( inf_in1974387902real_n @ ( t2 @ A ) @ ( t2 @ B ) ) @ ( measur1402256771real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % T_Int
% 0.27/0.61 thf(fact_7_assms_I2_J,axiom,
% 0.27/0.61 ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) ).
% 0.27/0.61
% 0.27/0.61 % assms(2)
% 0.27/0.61 thf(fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % \<open>\<And>a. R a \<in> sets lebesgue\<close>
% 0.27/0.61 thf(fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062,axiom,
% 0.27/0.61 ( sums_E1192373732nnreal
% 0.27/0.61 @ ^ [N: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ N ) ) )
% 0.27/0.61 @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
% 0.27/0.61 @ ( comple825005695real_n
% 0.27/0.61 @ ( image_1856576259real_n
% 0.27/0.61 @ ^ [N: nat] : ( t2 @ ( f @ N ) )
% 0.27/0.61 @ top_top_set_nat ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % \<open>(\<lambda>n. emeasure lebesgue (T (f n))) sums emeasure lebesgue (\<Union>n. T (f n))\<close>
% 0.27/0.61 thf(fact_10_T_H__def,axiom,
% 0.27/0.61 ( t
% 0.27/0.61 = ( ^ [A2: finite964658038_int_n] :
% 0.27/0.61 ( image_439535603real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ ( minkow1134813771n_real @ A2 ) )
% 0.27/0.61 @ ( t2 @ A2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % T'_def
% 0.27/0.61 thf(fact_11_f__def,axiom,
% 0.27/0.61 ( f
% 0.27/0.61 = ( counta1142393929_int_n @ top_to131672412_int_n ) ) ).
% 0.27/0.61
% 0.27/0.61 % f_def
% 0.27/0.61 thf(fact_12_T_H__altdef,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n] :
% 0.27/0.61 ( ( t @ A )
% 0.27/0.61 = ( vimage1233683625real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) )
% 0.27/0.61 @ ( t2 @ A ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % T'_altdef
% 0.27/0.61 thf(fact_13_of__int__vec__eq__iff,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n,B: finite964658038_int_n] :
% 0.27/0.61 ( ( ( minkow1134813771n_real @ A )
% 0.27/0.61 = ( minkow1134813771n_real @ B ) )
% 0.27/0.61 = ( A = B ) ) ).
% 0.27/0.61
% 0.27/0.61 % of_int_vec_eq_iff
% 0.27/0.61 thf(fact_14_T__def,axiom,
% 0.27/0.61 ( t2
% 0.27/0.61 = ( ^ [A2: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % T_def
% 0.27/0.61 thf(fact_15_R__Int,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n,B: finite964658038_int_n] :
% 0.27/0.61 ( ( A != B )
% 0.27/0.61 => ( member223413699real_n @ ( inf_in1974387902real_n @ ( r @ A ) @ ( r @ B ) ) @ ( measur1402256771real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % R_Int
% 0.27/0.61 thf(fact_16_sums__emeasure_H,axiom,
% 0.27/0.61 ! [B2: nat > set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.27/0.61 ( ! [X2: nat] : ( member223413699real_n @ ( B2 @ X2 ) @ ( sigma_1235138647real_n @ M ) )
% 0.27/0.61 => ( ! [X2: nat,Y: nat] :
% 0.27/0.61 ( ( X2 != Y )
% 0.27/0.61 => ( ( sigma_1536574303real_n @ M @ ( inf_in1974387902real_n @ ( B2 @ X2 ) @ ( B2 @ Y ) ) )
% 0.27/0.61 = zero_z1963244097nnreal ) )
% 0.27/0.61 => ( sums_E1192373732nnreal
% 0.27/0.61 @ ^ [X: nat] : ( sigma_1536574303real_n @ M @ ( B2 @ X ) )
% 0.27/0.61 @ ( sigma_1536574303real_n @ M @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ top_top_set_nat ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % sums_emeasure'
% 0.27/0.61 thf(fact_17_null__sets__UN,axiom,
% 0.27/0.61 ! [N2: nat > set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.27/0.61 ( ! [I: nat] : ( member223413699real_n @ ( N2 @ I ) @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n @ ( comple825005695real_n @ ( image_1856576259real_n @ N2 @ top_top_set_nat ) ) @ ( measur1402256771real_n @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets_UN
% 0.27/0.61 thf(fact_18_null__sets__UN,axiom,
% 0.27/0.61 ! [N2: finite964658038_int_n > set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.27/0.61 ( ! [I: finite964658038_int_n] : ( member223413699real_n @ ( N2 @ I ) @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n @ ( comple825005695real_n @ ( image_355963305real_n @ N2 @ top_to131672412_int_n ) ) @ ( measur1402256771real_n @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets_UN
% 0.27/0.61 thf(fact_19_null__setsI,axiom,
% 0.27/0.61 ! [M: sigma_1466784463real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( ( sigma_1536574303real_n @ M @ A3 )
% 0.27/0.61 = zero_z1963244097nnreal )
% 0.27/0.61 => ( ( member223413699real_n @ A3 @ ( sigma_1235138647real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n @ A3 @ ( measur1402256771real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_setsI
% 0.27/0.61 thf(fact_20_image__vimage__eq,axiom,
% 0.27/0.61 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( image_439535603real_n @ F @ ( vimage1233683625real_n @ F @ A3 ) )
% 0.27/0.61 = ( inf_in1974387902real_n @ A3 @ ( image_439535603real_n @ F @ top_to1292442332real_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_vimage_eq
% 0.27/0.61 thf(fact_21_image__vimage__eq,axiom,
% 0.27/0.61 ! [F: nat > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.61 ( ( image_1856576259real_n @ F @ ( vimage3210681real_n @ F @ A3 ) )
% 0.27/0.61 = ( inf_in632889204real_n @ A3 @ ( image_1856576259real_n @ F @ top_top_set_nat ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_vimage_eq
% 0.27/0.61 thf(fact_22_image__vimage__eq,axiom,
% 0.27/0.61 ! [F: nat > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( image_183184717real_n @ F @ ( vimage1860757507real_n @ F @ A3 ) )
% 0.27/0.61 = ( inf_in1974387902real_n @ A3 @ ( image_183184717real_n @ F @ top_top_set_nat ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_vimage_eq
% 0.27/0.61 thf(fact_23_image__vimage__eq,axiom,
% 0.27/0.61 ! [F: finite964658038_int_n > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.61 ( ( image_355963305real_n @ F @ ( vimage464515423real_n @ F @ A3 ) )
% 0.27/0.61 = ( inf_in632889204real_n @ A3 @ ( image_355963305real_n @ F @ top_to131672412_int_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_vimage_eq
% 0.27/0.61 thf(fact_24_image__vimage__eq,axiom,
% 0.27/0.61 ! [F: finite964658038_int_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( image_2058828787real_n @ F @ ( vimage1276736425real_n @ F @ A3 ) )
% 0.27/0.61 = ( inf_in1974387902real_n @ A3 @ ( image_2058828787real_n @ F @ top_to131672412_int_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_vimage_eq
% 0.27/0.61 thf(fact_25__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n] :
% 0.27/0.61 ( ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 0.27/0.61 => ( member223413699real_n
% 0.27/0.61 @ ( inf_in1974387902real_n
% 0.27/0.61 @ ( vimage1233683625real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) )
% 0.27/0.61 @ ( t2 @ A ) )
% 0.27/0.61 @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 0.27/0.61 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % \<open>\<And>a. T a \<in> sets lebesgue \<Longrightarrow> (\<lambda>x. x + of_int_vec a) -` T a \<inter> space lebesgue \<in> sets lebesgue\<close>
% 0.27/0.61 thf(fact_26_surj__diff__right,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n] :
% 0.27/0.61 ( ( image_1278151539_int_n
% 0.27/0.61 @ ^ [X: finite964658038_int_n] : ( minus_1196255695_int_n @ X @ A )
% 0.27/0.61 @ top_to131672412_int_n )
% 0.27/0.61 = top_to131672412_int_n ) ).
% 0.27/0.61
% 0.27/0.61 % surj_diff_right
% 0.27/0.61 thf(fact_27_surj__diff__right,axiom,
% 0.27/0.61 ! [A: finite1489363574real_n] :
% 0.27/0.61 ( ( image_439535603real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.27/0.61 @ top_to1292442332real_n )
% 0.27/0.61 = top_to1292442332real_n ) ).
% 0.27/0.61
% 0.27/0.61 % surj_diff_right
% 0.27/0.61 thf(fact_28__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062,axiom,
% 0.27/0.61 ( ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) )
% 0.27/0.61 = ( comple825005695real_n
% 0.27/0.61 @ ( image_1856576259real_n
% 0.27/0.61 @ ^ [N: nat] : ( t2 @ ( f @ N ) )
% 0.27/0.61 @ top_top_set_nat ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % \<open>\<Union> (range T) = (\<Union>n. T (f n))\<close>
% 0.27/0.61 thf(fact_29_Sup__UNIV,axiom,
% 0.27/0.61 ( ( comple1682161881et_nat @ top_top_set_set_nat )
% 0.27/0.61 = top_top_set_nat ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_UNIV
% 0.27/0.61 thf(fact_30_Sup__UNIV,axiom,
% 0.27/0.61 ( ( comple970917503_int_n @ top_to1587634578_int_n )
% 0.27/0.61 = top_to131672412_int_n ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_UNIV
% 0.27/0.61 thf(fact_31_Sup__UNIV,axiom,
% 0.27/0.61 ( ( comple825005695real_n @ top_to20708754real_n )
% 0.27/0.61 = top_to1292442332real_n ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_UNIV
% 0.27/0.61 thf(fact_32_Sup__UNIV,axiom,
% 0.27/0.61 ( ( complete_Sup_Sup_o @ top_top_set_o )
% 0.27/0.61 = top_top_o ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_UNIV
% 0.27/0.61 thf(fact_33_Sup__eq__top__iff,axiom,
% 0.27/0.61 ! [A3: set_Ex113815278nnreal] :
% 0.27/0.61 ( ( ( comple1413366923nnreal @ A3 )
% 0.27/0.61 = top_to1845833192nnreal )
% 0.27/0.61 = ( ! [X: extend1728876344nnreal] :
% 0.27/0.61 ( ( ord_le2133614988nnreal @ X @ top_to1845833192nnreal )
% 0.27/0.61 => ? [Y2: extend1728876344nnreal] :
% 0.27/0.61 ( ( member1217042383nnreal @ Y2 @ A3 )
% 0.27/0.61 & ( ord_le2133614988nnreal @ X @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_eq_top_iff
% 0.27/0.61 thf(fact_34_surj__plus,axiom,
% 0.27/0.61 ! [A: finite1489363574real_n] :
% 0.27/0.61 ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ top_to1292442332real_n )
% 0.27/0.61 = top_to1292442332real_n ) ).
% 0.27/0.61
% 0.27/0.61 % surj_plus
% 0.27/0.61 thf(fact_35_surj__plus,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n] :
% 0.27/0.61 ( ( image_1278151539_int_n @ ( plus_p1654784127_int_n @ A ) @ top_to131672412_int_n )
% 0.27/0.61 = top_to131672412_int_n ) ).
% 0.27/0.61
% 0.27/0.61 % surj_plus
% 0.27/0.61 thf(fact_36_diff__numeral__special_I9_J,axiom,
% 0.27/0.61 ( ( minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n )
% 0.27/0.61 = zero_z200130687real_n ) ).
% 0.27/0.61
% 0.27/0.61 % diff_numeral_special(9)
% 0.27/0.61 thf(fact_37_image__eqI,axiom,
% 0.27/0.61 ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,X3: finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member1352538125real_n @ X3 @ A3 )
% 0.27/0.61 => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_38_image__eqI,axiom,
% 0.27/0.61 ! [B: set_Fi1058188332real_n,F: nat > set_Fi1058188332real_n,X3: nat,A3: set_nat] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member_nat @ X3 @ A3 )
% 0.27/0.61 => ( member223413699real_n @ B @ ( image_1856576259real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_39_image__eqI,axiom,
% 0.27/0.61 ! [B: set_Fi1058188332real_n,F: finite964658038_int_n > set_Fi1058188332real_n,X3: finite964658038_int_n,A3: set_Fi160064172_int_n] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member27055245_int_n @ X3 @ A3 )
% 0.27/0.61 => ( member223413699real_n @ B @ ( image_355963305real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_40_image__eqI,axiom,
% 0.27/0.61 ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,X3: set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.61 => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_41_image__eqI,axiom,
% 0.27/0.61 ! [B: $o,F: set_Fi1058188332real_n > $o,X3: set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.61 => ( member_o @ B @ ( image_1648361637al_n_o @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_42_image__eqI,axiom,
% 0.27/0.61 ! [B: set_Fi1058188332real_n,F: $o > set_Fi1058188332real_n,X3: $o,A3: set_o] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member_o @ X3 @ A3 )
% 0.27/0.61 => ( member223413699real_n @ B @ ( image_1759008383real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_43_image__eqI,axiom,
% 0.27/0.61 ! [B: $o,F: $o > $o,X3: $o,A3: set_o] :
% 0.27/0.61 ( ( B
% 0.27/0.61 = ( F @ X3 ) )
% 0.27/0.61 => ( ( member_o @ X3 @ A3 )
% 0.27/0.61 => ( member_o @ B @ ( image_o_o @ F @ A3 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % image_eqI
% 0.27/0.61 thf(fact_44_UNIV__I,axiom,
% 0.27/0.61 ! [X3: set_Fi1058188332real_n] : ( member223413699real_n @ X3 @ top_to20708754real_n ) ).
% 0.27/0.61
% 0.27/0.61 % UNIV_I
% 0.27/0.61 thf(fact_45_UNIV__I,axiom,
% 0.27/0.61 ! [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ).
% 0.27/0.61
% 0.27/0.61 % UNIV_I
% 0.27/0.61 thf(fact_46_UNIV__I,axiom,
% 0.27/0.61 ! [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).
% 0.27/0.61
% 0.27/0.61 % UNIV_I
% 0.27/0.61 thf(fact_47_UNIV__I,axiom,
% 0.27/0.61 ! [X3: finite964658038_int_n] : ( member27055245_int_n @ X3 @ top_to131672412_int_n ) ).
% 0.27/0.61
% 0.27/0.61 % UNIV_I
% 0.27/0.61 thf(fact_48_Int__iff,axiom,
% 0.27/0.61 ! [C: set_Fi1058188332real_n,A3: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.27/0.61 ( ( member223413699real_n @ C @ ( inf_in632889204real_n @ A3 @ B2 ) )
% 0.27/0.61 = ( ( member223413699real_n @ C @ A3 )
% 0.27/0.61 & ( member223413699real_n @ C @ B2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_iff
% 0.27/0.61 thf(fact_49_Int__iff,axiom,
% 0.27/0.61 ! [C: $o,A3: set_o,B2: set_o] :
% 0.27/0.61 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 0.27/0.61 = ( ( member_o @ C @ A3 )
% 0.27/0.61 & ( member_o @ C @ B2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_iff
% 0.27/0.61 thf(fact_50_Int__iff,axiom,
% 0.27/0.61 ! [C: finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A3 @ B2 ) )
% 0.27/0.61 = ( ( member1352538125real_n @ C @ A3 )
% 0.27/0.61 & ( member1352538125real_n @ C @ B2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_iff
% 0.27/0.61 thf(fact_51_IntI,axiom,
% 0.27/0.61 ! [C: set_Fi1058188332real_n,A3: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.27/0.61 ( ( member223413699real_n @ C @ A3 )
% 0.27/0.61 => ( ( member223413699real_n @ C @ B2 )
% 0.27/0.61 => ( member223413699real_n @ C @ ( inf_in632889204real_n @ A3 @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % IntI
% 0.27/0.61 thf(fact_52_IntI,axiom,
% 0.27/0.61 ! [C: $o,A3: set_o,B2: set_o] :
% 0.27/0.61 ( ( member_o @ C @ A3 )
% 0.27/0.61 => ( ( member_o @ C @ B2 )
% 0.27/0.61 => ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % IntI
% 0.27/0.61 thf(fact_53_IntI,axiom,
% 0.27/0.61 ! [C: finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ C @ A3 )
% 0.27/0.61 => ( ( member1352538125real_n @ C @ B2 )
% 0.27/0.61 => ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A3 @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % IntI
% 0.27/0.61 thf(fact_54_Union__iff,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n,C2: set_se820660888real_n] :
% 0.27/0.61 ( ( member223413699real_n @ A3 @ ( comple1917283637real_n @ C2 ) )
% 0.27/0.61 = ( ? [X: set_se2111327970real_n] :
% 0.27/0.61 ( ( member1475136633real_n @ X @ C2 )
% 0.27/0.61 & ( member223413699real_n @ A3 @ X ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Union_iff
% 0.27/0.61 thf(fact_55_Union__iff,axiom,
% 0.27/0.61 ! [A3: $o,C2: set_set_o] :
% 0.27/0.61 ( ( member_o @ A3 @ ( comple1665300069_set_o @ C2 ) )
% 0.27/0.61 = ( ? [X: set_o] :
% 0.27/0.61 ( ( member_set_o @ X @ C2 )
% 0.27/0.61 & ( member_o @ A3 @ X ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Union_iff
% 0.27/0.61 thf(fact_56_Union__iff,axiom,
% 0.27/0.61 ! [A3: finite1489363574real_n,C2: set_se2111327970real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ A3 @ ( comple825005695real_n @ C2 ) )
% 0.27/0.61 = ( ? [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ C2 )
% 0.27/0.61 & ( member1352538125real_n @ A3 @ X ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Union_iff
% 0.27/0.61 thf(fact_57_UnionI,axiom,
% 0.27/0.61 ! [X4: set_se2111327970real_n,C2: set_se820660888real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member1475136633real_n @ X4 @ C2 )
% 0.27/0.61 => ( ( member223413699real_n @ A3 @ X4 )
% 0.27/0.61 => ( member223413699real_n @ A3 @ ( comple1917283637real_n @ C2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UnionI
% 0.27/0.61 thf(fact_58_UnionI,axiom,
% 0.27/0.61 ! [X4: set_o,C2: set_set_o,A3: $o] :
% 0.27/0.61 ( ( member_set_o @ X4 @ C2 )
% 0.27/0.61 => ( ( member_o @ A3 @ X4 )
% 0.27/0.61 => ( member_o @ A3 @ ( comple1665300069_set_o @ C2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UnionI
% 0.27/0.61 thf(fact_59_UnionI,axiom,
% 0.27/0.61 ! [X4: set_Fi1058188332real_n,C2: set_se2111327970real_n,A3: finite1489363574real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X4 @ C2 )
% 0.27/0.61 => ( ( member1352538125real_n @ A3 @ X4 )
% 0.27/0.61 => ( member1352538125real_n @ A3 @ ( comple825005695real_n @ C2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UnionI
% 0.27/0.61 thf(fact_60_UN__ball__bex__simps_I1_J,axiom,
% 0.27/0.61 ! [A3: set_se2111327970real_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ! [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ A3 ) )
% 0.27/0.61 => ( P @ X ) ) )
% 0.27/0.61 = ( ! [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ A3 )
% 0.27/0.61 => ! [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ X )
% 0.27/0.61 => ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_ball_bex_simps(1)
% 0.27/0.61 thf(fact_61_UN__ball__bex__simps_I3_J,axiom,
% 0.27/0.61 ! [A3: set_se2111327970real_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ? [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ A3 ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 = ( ? [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ A3 )
% 0.27/0.61 & ? [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ X )
% 0.27/0.61 & ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_ball_bex_simps(3)
% 0.27/0.61 thf(fact_62_null__sets_ODiff,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ A @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( ( member223413699real_n @ B @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n @ ( minus_1686442501real_n @ A @ B ) @ ( measur1402256771real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.Diff
% 0.27/0.61 thf(fact_63_vimage__eq,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.61 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) )
% 0.27/0.61 = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_eq
% 0.27/0.61 thf(fact_64_vimage__eq,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > $o,B2: set_o] :
% 0.27/0.61 ( ( member223413699real_n @ A @ ( vimage851190895al_n_o @ F @ B2 ) )
% 0.27/0.61 = ( member_o @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_eq
% 0.27/0.61 thf(fact_65_vimage__eq,axiom,
% 0.27/0.61 ! [A: $o,F: $o > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.61 ( ( member_o @ A @ ( vimage961837641real_n @ F @ B2 ) )
% 0.27/0.61 = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_eq
% 0.27/0.61 thf(fact_66_vimage__eq,axiom,
% 0.27/0.61 ! [A: $o,F: $o > $o,B2: set_o] :
% 0.27/0.61 ( ( member_o @ A @ ( vimage_o_o @ F @ B2 ) )
% 0.27/0.61 = ( member_o @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_eq
% 0.27/0.61 thf(fact_67_vimage__eq,axiom,
% 0.27/0.61 ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) )
% 0.27/0.61 = ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_eq
% 0.27/0.61 thf(fact_68_vimageI,axiom,
% 0.27/0.61 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.61 ( ( ( F @ A )
% 0.27/0.61 = B )
% 0.27/0.61 => ( ( member223413699real_n @ B @ B2 )
% 0.27/0.61 => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimageI
% 0.27/0.61 thf(fact_69_vimageI,axiom,
% 0.27/0.61 ! [F: $o > set_Fi1058188332real_n,A: $o,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.61 ( ( ( F @ A )
% 0.27/0.61 = B )
% 0.27/0.61 => ( ( member223413699real_n @ B @ B2 )
% 0.27/0.61 => ( member_o @ A @ ( vimage961837641real_n @ F @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimageI
% 0.27/0.61 thf(fact_70_vimageI,axiom,
% 0.27/0.61 ! [F: set_Fi1058188332real_n > $o,A: set_Fi1058188332real_n,B: $o,B2: set_o] :
% 0.27/0.61 ( ( ( F @ A )
% 0.27/0.61 = B )
% 0.27/0.61 => ( ( member_o @ B @ B2 )
% 0.27/0.61 => ( member223413699real_n @ A @ ( vimage851190895al_n_o @ F @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimageI
% 0.27/0.61 thf(fact_71_vimageI,axiom,
% 0.27/0.61 ! [F: $o > $o,A: $o,B: $o,B2: set_o] :
% 0.27/0.61 ( ( ( F @ A )
% 0.27/0.61 = B )
% 0.27/0.61 => ( ( member_o @ B @ B2 )
% 0.27/0.61 => ( member_o @ A @ ( vimage_o_o @ F @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimageI
% 0.27/0.61 thf(fact_72_vimageI,axiom,
% 0.27/0.61 ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( ( F @ A )
% 0.27/0.61 = B )
% 0.27/0.61 => ( ( member1352538125real_n @ B @ B2 )
% 0.27/0.61 => ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimageI
% 0.27/0.61 thf(fact_73_image__ident,axiom,
% 0.27/0.61 ! [Y3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( image_439535603real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : X
% 0.27/0.61 @ Y3 )
% 0.27/0.61 = Y3 ) ).
% 0.27/0.61
% 0.27/0.61 % image_ident
% 0.27/0.61 thf(fact_74_vimage__Collect__eq,axiom,
% 0.27/0.61 ! [F: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) )
% 0.27/0.61 = ( collec321817931real_n
% 0.27/0.61 @ ^ [Y2: finite1489363574real_n] : ( P @ ( F @ Y2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_Collect_eq
% 0.27/0.61 thf(fact_75_vimage__ident,axiom,
% 0.27/0.61 ! [Y3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( vimage1233683625real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : X
% 0.27/0.61 @ Y3 )
% 0.27/0.61 = Y3 ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_ident
% 0.27/0.61 thf(fact_76_Int__UNIV,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( ( inf_in1974387902real_n @ A3 @ B2 )
% 0.27/0.61 = top_to1292442332real_n )
% 0.27/0.61 = ( ( A3 = top_to1292442332real_n )
% 0.27/0.61 & ( B2 = top_to1292442332real_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_UNIV
% 0.27/0.61 thf(fact_77_Int__UNIV,axiom,
% 0.27/0.61 ! [A3: set_nat,B2: set_nat] :
% 0.27/0.61 ( ( ( inf_inf_set_nat @ A3 @ B2 )
% 0.27/0.61 = top_top_set_nat )
% 0.27/0.61 = ( ( A3 = top_top_set_nat )
% 0.27/0.61 & ( B2 = top_top_set_nat ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_UNIV
% 0.27/0.61 thf(fact_78_Int__UNIV,axiom,
% 0.27/0.61 ! [A3: set_Fi160064172_int_n,B2: set_Fi160064172_int_n] :
% 0.27/0.61 ( ( ( inf_in1108485182_int_n @ A3 @ B2 )
% 0.27/0.61 = top_to131672412_int_n )
% 0.27/0.61 = ( ( A3 = top_to131672412_int_n )
% 0.27/0.61 & ( B2 = top_to131672412_int_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_UNIV
% 0.27/0.61 thf(fact_79_ball__UN,axiom,
% 0.27/0.61 ! [B2: nat > set_Fi1058188332real_n,A3: set_nat,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ! [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) )
% 0.27/0.61 => ( P @ X ) ) )
% 0.27/0.61 = ( ! [X: nat] :
% 0.27/0.61 ( ( member_nat @ X @ A3 )
% 0.27/0.61 => ! [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 => ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % ball_UN
% 0.27/0.61 thf(fact_80_ball__UN,axiom,
% 0.27/0.61 ! [B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ! [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) )
% 0.27/0.61 => ( P @ X ) ) )
% 0.27/0.61 = ( ! [X: finite964658038_int_n] :
% 0.27/0.61 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.61 => ! [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 => ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % ball_UN
% 0.27/0.61 thf(fact_81_mem__Collect__eq,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] :
% 0.27/0.61 ( ( member223413699real_n @ A @ ( collec452821761real_n @ P ) )
% 0.27/0.61 = ( P @ A ) ) ).
% 0.27/0.61
% 0.27/0.61 % mem_Collect_eq
% 0.27/0.61 thf(fact_82_mem__Collect__eq,axiom,
% 0.27/0.61 ! [A: $o,P: $o > $o] :
% 0.27/0.61 ( ( member_o @ A @ ( collect_o @ P ) )
% 0.27/0.61 = ( P @ A ) ) ).
% 0.27/0.61
% 0.27/0.61 % mem_Collect_eq
% 0.27/0.61 thf(fact_83_Collect__mem__eq,axiom,
% 0.27/0.61 ! [A3: set_se2111327970real_n] :
% 0.27/0.61 ( ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A3 ) )
% 0.27/0.61 = A3 ) ).
% 0.27/0.61
% 0.27/0.61 % Collect_mem_eq
% 0.27/0.61 thf(fact_84_Collect__mem__eq,axiom,
% 0.27/0.61 ! [A3: set_o] :
% 0.27/0.61 ( ( collect_o
% 0.27/0.61 @ ^ [X: $o] : ( member_o @ X @ A3 ) )
% 0.27/0.61 = A3 ) ).
% 0.27/0.61
% 0.27/0.61 % Collect_mem_eq
% 0.27/0.61 thf(fact_85_bex__UN,axiom,
% 0.27/0.61 ! [B2: nat > set_Fi1058188332real_n,A3: set_nat,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ? [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 = ( ? [X: nat] :
% 0.27/0.61 ( ( member_nat @ X @ A3 )
% 0.27/0.61 & ? [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 & ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % bex_UN
% 0.27/0.61 thf(fact_86_bex__UN,axiom,
% 0.27/0.61 ! [B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ? [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 = ( ? [X: finite964658038_int_n] :
% 0.27/0.61 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.61 & ? [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 & ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % bex_UN
% 0.27/0.61 thf(fact_87_UN__ball__bex__simps_I2_J,axiom,
% 0.27/0.61 ! [B2: nat > set_Fi1058188332real_n,A3: set_nat,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ! [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) )
% 0.27/0.61 => ( P @ X ) ) )
% 0.27/0.61 = ( ! [X: nat] :
% 0.27/0.61 ( ( member_nat @ X @ A3 )
% 0.27/0.61 => ! [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 => ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_ball_bex_simps(2)
% 0.27/0.61 thf(fact_88_UN__ball__bex__simps_I2_J,axiom,
% 0.27/0.61 ! [B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ! [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) )
% 0.27/0.61 => ( P @ X ) ) )
% 0.27/0.61 = ( ! [X: finite964658038_int_n] :
% 0.27/0.61 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.61 => ! [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 => ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_ball_bex_simps(2)
% 0.27/0.61 thf(fact_89_UN__ball__bex__simps_I4_J,axiom,
% 0.27/0.61 ! [B2: nat > set_Fi1058188332real_n,A3: set_nat,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ? [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 = ( ? [X: nat] :
% 0.27/0.61 ( ( member_nat @ X @ A3 )
% 0.27/0.61 & ? [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 & ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_ball_bex_simps(4)
% 0.27/0.61 thf(fact_90_UN__ball__bex__simps_I4_J,axiom,
% 0.27/0.61 ! [B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( ? [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 = ( ? [X: finite964658038_int_n] :
% 0.27/0.61 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.61 & ? [Y2: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ Y2 @ ( B2 @ X ) )
% 0.27/0.61 & ( P @ Y2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_ball_bex_simps(4)
% 0.27/0.61 thf(fact_91_vimage__UNIV,axiom,
% 0.27/0.61 ! [F: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.61 ( ( vimage1233683625real_n @ F @ top_to1292442332real_n )
% 0.27/0.61 = top_to1292442332real_n ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_UNIV
% 0.27/0.61 thf(fact_92_vimage__UNIV,axiom,
% 0.27/0.61 ! [F: nat > nat] :
% 0.27/0.61 ( ( vimage_nat_nat @ F @ top_top_set_nat )
% 0.27/0.61 = top_top_set_nat ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_UNIV
% 0.27/0.61 thf(fact_93_vimage__UNIV,axiom,
% 0.27/0.61 ! [F: finite964658038_int_n > nat] :
% 0.27/0.61 ( ( vimage1398021123_n_nat @ F @ top_top_set_nat )
% 0.27/0.61 = top_to131672412_int_n ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_UNIV
% 0.27/0.61 thf(fact_94_vimage__UNIV,axiom,
% 0.27/0.61 ! [F: nat > finite964658038_int_n] :
% 0.27/0.61 ( ( vimage714719107_int_n @ F @ top_to131672412_int_n )
% 0.27/0.61 = top_top_set_nat ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_UNIV
% 0.27/0.61 thf(fact_95_vimage__UNIV,axiom,
% 0.27/0.61 ! [F: finite964658038_int_n > finite964658038_int_n] :
% 0.27/0.61 ( ( vimage1122713129_int_n @ F @ top_to131672412_int_n )
% 0.27/0.61 = top_to131672412_int_n ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_UNIV
% 0.27/0.61 thf(fact_96_null__sets_OInt,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ A @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( ( member223413699real_n @ B @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( measur1402256771real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.Int
% 0.27/0.61 thf(fact_97_vimage__Int,axiom,
% 0.27/0.61 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( vimage1233683625real_n @ F @ ( inf_in1974387902real_n @ A3 @ B2 ) )
% 0.27/0.61 = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A3 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_Int
% 0.27/0.61 thf(fact_98_SUP__identity__eq,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( comple2042271945real_n
% 0.27/0.61 @ ( image_439535603real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : X
% 0.27/0.61 @ A3 ) )
% 0.27/0.61 = ( comple2042271945real_n @ A3 ) ) ).
% 0.27/0.61
% 0.27/0.61 % SUP_identity_eq
% 0.27/0.61 thf(fact_99_SUP__identity__eq,axiom,
% 0.27/0.61 ! [A3: set_se2111327970real_n] :
% 0.27/0.61 ( ( comple825005695real_n
% 0.27/0.61 @ ( image_1661509983real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] : X
% 0.27/0.61 @ A3 ) )
% 0.27/0.61 = ( comple825005695real_n @ A3 ) ) ).
% 0.27/0.61
% 0.27/0.61 % SUP_identity_eq
% 0.27/0.61 thf(fact_100_SUP__identity__eq,axiom,
% 0.27/0.61 ! [A3: set_o] :
% 0.27/0.61 ( ( complete_Sup_Sup_o
% 0.27/0.61 @ ( image_o_o
% 0.27/0.61 @ ^ [X: $o] : X
% 0.27/0.61 @ A3 ) )
% 0.27/0.61 = ( complete_Sup_Sup_o @ A3 ) ) ).
% 0.27/0.61
% 0.27/0.61 % SUP_identity_eq
% 0.27/0.61 thf(fact_101_UN__iff,axiom,
% 0.27/0.61 ! [B: finite1489363574real_n,B2: nat > set_Fi1058188332real_n,A3: set_nat] :
% 0.27/0.61 ( ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) )
% 0.27/0.61 = ( ? [X: nat] :
% 0.27/0.61 ( ( member_nat @ X @ A3 )
% 0.27/0.61 & ( member1352538125real_n @ B @ ( B2 @ X ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_iff
% 0.27/0.61 thf(fact_102_UN__iff,axiom,
% 0.27/0.61 ! [B: finite1489363574real_n,B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n] :
% 0.27/0.61 ( ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) )
% 0.27/0.61 = ( ? [X: finite964658038_int_n] :
% 0.27/0.61 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.61 & ( member1352538125real_n @ B @ ( B2 @ X ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_iff
% 0.27/0.61 thf(fact_103_UN__I,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,A3: set_se2111327970real_n,B: set_Fi1058188332real_n,B2: set_Fi1058188332real_n > set_se2111327970real_n] :
% 0.27/0.61 ( ( member223413699real_n @ A @ A3 )
% 0.27/0.61 => ( ( member223413699real_n @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member223413699real_n @ B @ ( comple1917283637real_n @ ( image_797440021real_n @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_104_UN__I,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,A3: set_se2111327970real_n,B: $o,B2: set_Fi1058188332real_n > set_o] :
% 0.27/0.61 ( ( member223413699real_n @ A @ A3 )
% 0.27/0.61 => ( ( member_o @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member_o @ B @ ( comple1665300069_set_o @ ( image_1687589765_set_o @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_105_UN__I,axiom,
% 0.27/0.61 ! [A: $o,A3: set_o,B: set_Fi1058188332real_n,B2: $o > set_se2111327970real_n] :
% 0.27/0.61 ( ( member_o @ A @ A3 )
% 0.27/0.61 => ( ( member223413699real_n @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member223413699real_n @ B @ ( comple1917283637real_n @ ( image_452144437real_n @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_106_UN__I,axiom,
% 0.27/0.61 ! [A: $o,A3: set_o,B: $o,B2: $o > set_o] :
% 0.27/0.61 ( ( member_o @ A @ A3 )
% 0.27/0.61 => ( ( member_o @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member_o @ B @ ( comple1665300069_set_o @ ( image_o_set_o @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_107_UN__I,axiom,
% 0.27/0.61 ! [A: nat,A3: set_nat,B: finite1489363574real_n,B2: nat > set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member_nat @ A @ A3 )
% 0.27/0.61 => ( ( member1352538125real_n @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_108_UN__I,axiom,
% 0.27/0.61 ! [A: finite964658038_int_n,A3: set_Fi160064172_int_n,B: finite1489363574real_n,B2: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member27055245_int_n @ A @ A3 )
% 0.27/0.61 => ( ( member1352538125real_n @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_109_UN__I,axiom,
% 0.27/0.61 ! [A: set_Fi1058188332real_n,A3: set_se2111327970real_n,B: finite1489363574real_n,B2: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ A @ A3 )
% 0.27/0.61 => ( ( member1352538125real_n @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1661509983real_n @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_110_UN__I,axiom,
% 0.27/0.61 ! [A: $o,A3: set_o,B: finite1489363574real_n,B2: $o > set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member_o @ A @ A3 )
% 0.27/0.61 => ( ( member1352538125real_n @ B @ ( B2 @ A ) )
% 0.27/0.61 => ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1759008383real_n @ B2 @ A3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % UN_I
% 0.27/0.61 thf(fact_111_S__decompose,axiom,
% 0.27/0.61 ( s
% 0.27/0.61 = ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % S_decompose
% 0.27/0.61 thf(fact_112_image__add__0,axiom,
% 0.27/0.61 ! [S: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ S )
% 0.27/0.61 = S ) ).
% 0.27/0.61
% 0.27/0.61 % image_add_0
% 0.27/0.61 thf(fact_113_image__add__0,axiom,
% 0.27/0.61 ! [S: set_Ex113815278nnreal] :
% 0.27/0.61 ( ( image_2066995319nnreal @ ( plus_p1763960001nnreal @ zero_z1963244097nnreal ) @ S )
% 0.27/0.61 = S ) ).
% 0.27/0.61
% 0.27/0.61 % image_add_0
% 0.27/0.61 thf(fact_114_null__sets_OInt__space__eq2,axiom,
% 0.27/0.61 ! [X3: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X3 @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( ( inf_in1974387902real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 = X3 ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.Int_space_eq2
% 0.27/0.61 thf(fact_115_null__sets_OInt__space__eq1,axiom,
% 0.27/0.61 ! [X3: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X3 @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ M ) @ X3 )
% 0.27/0.61 = X3 ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.Int_space_eq1
% 0.27/0.61 thf(fact_116_in__sets__SUP,axiom,
% 0.27/0.61 ! [I2: set_Fi1058188332real_n,I3: set_se2111327970real_n,M: set_Fi1058188332real_n > sigma_1466784463real_n,Y3: set_Fi1058188332real_n,X4: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ I2 @ I3 )
% 0.27/0.61 => ( ! [I: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ I @ I3 )
% 0.27/0.61 => ( ( sigma_476185326real_n @ ( M @ I ) )
% 0.27/0.61 = Y3 ) )
% 0.27/0.61 => ( ( member223413699real_n @ X4 @ ( sigma_1235138647real_n @ ( M @ I2 ) ) )
% 0.27/0.61 => ( member223413699real_n @ X4 @ ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ M @ I3 ) ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % in_sets_SUP
% 0.27/0.61 thf(fact_117_in__sets__SUP,axiom,
% 0.27/0.61 ! [I2: $o,I3: set_o,M: $o > sigma_1466784463real_n,Y3: set_Fi1058188332real_n,X4: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member_o @ I2 @ I3 )
% 0.27/0.61 => ( ! [I: $o] :
% 0.27/0.61 ( ( member_o @ I @ I3 )
% 0.27/0.61 => ( ( sigma_476185326real_n @ ( M @ I ) )
% 0.27/0.61 = Y3 ) )
% 0.27/0.61 => ( ( member223413699real_n @ X4 @ ( sigma_1235138647real_n @ ( M @ I2 ) ) )
% 0.27/0.61 => ( member223413699real_n @ X4 @ ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ M @ I3 ) ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % in_sets_SUP
% 0.27/0.61 thf(fact_118_in__sets__Sup,axiom,
% 0.27/0.61 ! [M: set_Si1125517487real_n,X4: set_Fi1058188332real_n,M2: sigma_1466784463real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.61 ( ! [M3: sigma_1466784463real_n] :
% 0.27/0.61 ( ( member1000184real_n @ M3 @ M )
% 0.27/0.61 => ( ( sigma_476185326real_n @ M3 )
% 0.27/0.61 = X4 ) )
% 0.27/0.61 => ( ( member1000184real_n @ M2 @ M )
% 0.27/0.61 => ( ( member223413699real_n @ A3 @ ( sigma_1235138647real_n @ M2 ) )
% 0.27/0.61 => ( member223413699real_n @ A3 @ ( sigma_1235138647real_n @ ( comple488165692real_n @ M ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % in_sets_Sup
% 0.27/0.61 thf(fact_119_sets__SUP__cong,axiom,
% 0.27/0.61 ! [I3: set_se2111327970real_n,M: set_Fi1058188332real_n > sigma_1466784463real_n,N2: set_Fi1058188332real_n > sigma_1466784463real_n] :
% 0.27/0.61 ( ! [I: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ I @ I3 )
% 0.27/0.61 => ( ( sigma_1235138647real_n @ ( M @ I ) )
% 0.27/0.61 = ( sigma_1235138647real_n @ ( N2 @ I ) ) ) )
% 0.27/0.61 => ( ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ M @ I3 ) ) )
% 0.27/0.61 = ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ N2 @ I3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % sets_SUP_cong
% 0.27/0.61 thf(fact_120_sets__SUP__cong,axiom,
% 0.27/0.61 ! [I3: set_o,M: $o > sigma_1466784463real_n,N2: $o > sigma_1466784463real_n] :
% 0.27/0.61 ( ! [I: $o] :
% 0.27/0.61 ( ( member_o @ I @ I3 )
% 0.27/0.61 => ( ( sigma_1235138647real_n @ ( M @ I ) )
% 0.27/0.61 = ( sigma_1235138647real_n @ ( N2 @ I ) ) ) )
% 0.27/0.61 => ( ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ M @ I3 ) ) )
% 0.27/0.61 = ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ N2 @ I3 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % sets_SUP_cong
% 0.27/0.61 thf(fact_121_Sup__set__def,axiom,
% 0.27/0.61 ( comple1917283637real_n
% 0.27/0.61 = ( ^ [A4: set_se820660888real_n] :
% 0.27/0.61 ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] : ( complete_Sup_Sup_o @ ( image_1681970287al_n_o @ ( member223413699real_n @ X ) @ A4 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_set_def
% 0.27/0.61 thf(fact_122_Sup__set__def,axiom,
% 0.27/0.61 ( comple1665300069_set_o
% 0.27/0.61 = ( ^ [A4: set_set_o] :
% 0.27/0.61 ( collect_o
% 0.27/0.61 @ ^ [X: $o] : ( complete_Sup_Sup_o @ ( image_set_o_o @ ( member_o @ X ) @ A4 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_set_def
% 0.27/0.61 thf(fact_123_Sup__set__def,axiom,
% 0.27/0.61 ( comple825005695real_n
% 0.27/0.61 = ( ^ [A4: set_se2111327970real_n] :
% 0.27/0.61 ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] : ( complete_Sup_Sup_o @ ( image_1648361637al_n_o @ ( member1352538125real_n @ X ) @ A4 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Sup_set_def
% 0.27/0.61 thf(fact_124_space__Sup__eq__UN,axiom,
% 0.27/0.61 ! [M: set_Si1125517487real_n] :
% 0.27/0.61 ( ( sigma_476185326real_n @ ( comple488165692real_n @ M ) )
% 0.27/0.61 = ( comple825005695real_n @ ( image_1298280374real_n @ sigma_476185326real_n @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % space_Sup_eq_UN
% 0.27/0.61 thf(fact_125_top__set__def,axiom,
% 0.27/0.61 ( top_top_set_nat
% 0.27/0.61 = ( collect_nat @ top_top_nat_o ) ) ).
% 0.27/0.61
% 0.27/0.61 % top_set_def
% 0.27/0.61 thf(fact_126_top__set__def,axiom,
% 0.27/0.61 ( top_to131672412_int_n
% 0.27/0.61 = ( collec1941932235_int_n @ top_to287930409nt_n_o ) ) ).
% 0.27/0.61
% 0.27/0.61 % top_set_def
% 0.27/0.61 thf(fact_127_Diff__Int__distrib2,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( inf_in1974387902real_n @ ( minus_1686442501real_n @ A3 @ B2 ) @ C2 )
% 0.27/0.61 = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A3 @ C2 ) @ ( inf_in1974387902real_n @ B2 @ C2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Diff_Int_distrib2
% 0.27/0.61 thf(fact_128_Diff__Int__distrib,axiom,
% 0.27/0.61 ! [C2: set_Fi1058188332real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( inf_in1974387902real_n @ C2 @ ( minus_1686442501real_n @ A3 @ B2 ) )
% 0.27/0.61 = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ C2 @ A3 ) @ ( inf_in1974387902real_n @ C2 @ B2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Diff_Int_distrib
% 0.27/0.61 thf(fact_129_Diff__Diff__Int,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( minus_1686442501real_n @ A3 @ ( minus_1686442501real_n @ A3 @ B2 ) )
% 0.27/0.61 = ( inf_in1974387902real_n @ A3 @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % Diff_Diff_Int
% 0.27/0.61 thf(fact_130_Diff__Int2,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n,C2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A3 @ C2 ) @ ( inf_in1974387902real_n @ B2 @ C2 ) )
% 0.27/0.61 = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A3 @ C2 ) @ B2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % Diff_Int2
% 0.27/0.61 thf(fact_131_Int__Diff,axiom,
% 0.27/0.61 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A3 @ B2 ) @ C2 )
% 0.27/0.61 = ( inf_in1974387902real_n @ A3 @ ( minus_1686442501real_n @ B2 @ C2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Int_Diff
% 0.27/0.61 thf(fact_132_vimage__Diff,axiom,
% 0.27/0.61 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( vimage1233683625real_n @ F @ ( minus_1686442501real_n @ A3 @ B2 ) )
% 0.27/0.61 = ( minus_1686442501real_n @ ( vimage1233683625real_n @ F @ A3 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % vimage_Diff
% 0.27/0.61 thf(fact_133_null__sets_Osets__Collect__disj,axiom,
% 0.27/0.61 ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 0.27/0.61 ( ( member1475136633real_n
% 0.27/0.61 @ ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measur2126959417real_n @ M ) )
% 0.27/0.61 => ( ( member1475136633real_n
% 0.27/0.61 @ ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.27/0.61 & ( Q @ X ) ) )
% 0.27/0.61 @ ( measur2126959417real_n @ M ) )
% 0.27/0.61 => ( member1475136633real_n
% 0.27/0.61 @ ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.27/0.61 & ( ( Q @ X )
% 0.27/0.61 | ( P @ X ) ) ) )
% 0.27/0.61 @ ( measur2126959417real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.sets_Collect_disj
% 0.27/0.61 thf(fact_134_null__sets_Osets__Collect__disj,axiom,
% 0.27/0.61 ! [M: sigma_measure_o,P: $o > $o,Q: $o > $o] :
% 0.27/0.61 ( ( member_set_o
% 0.27/0.61 @ ( collect_o
% 0.27/0.61 @ ^ [X: $o] :
% 0.27/0.61 ( ( member_o @ X @ ( sigma_space_o @ M ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measure_null_sets_o @ M ) )
% 0.27/0.61 => ( ( member_set_o
% 0.27/0.61 @ ( collect_o
% 0.27/0.61 @ ^ [X: $o] :
% 0.27/0.61 ( ( member_o @ X @ ( sigma_space_o @ M ) )
% 0.27/0.61 & ( Q @ X ) ) )
% 0.27/0.61 @ ( measure_null_sets_o @ M ) )
% 0.27/0.61 => ( member_set_o
% 0.27/0.61 @ ( collect_o
% 0.27/0.61 @ ^ [X: $o] :
% 0.27/0.61 ( ( member_o @ X @ ( sigma_space_o @ M ) )
% 0.27/0.61 & ( ( Q @ X )
% 0.27/0.61 | ( P @ X ) ) ) )
% 0.27/0.61 @ ( measure_null_sets_o @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.sets_Collect_disj
% 0.27/0.61 thf(fact_135_null__sets_Osets__Collect__disj,axiom,
% 0.27/0.61 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( member223413699real_n
% 0.27/0.61 @ ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( ( member223413699real_n
% 0.27/0.61 @ ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 & ( Q @ X ) ) )
% 0.27/0.61 @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n
% 0.27/0.61 @ ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 & ( ( Q @ X )
% 0.27/0.61 | ( P @ X ) ) ) )
% 0.27/0.61 @ ( measur1402256771real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.sets_Collect_disj
% 0.27/0.61 thf(fact_136_null__sets_Osets__Collect__conj,axiom,
% 0.27/0.61 ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 0.27/0.61 ( ( member1475136633real_n
% 0.27/0.61 @ ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measur2126959417real_n @ M ) )
% 0.27/0.61 => ( ( member1475136633real_n
% 0.27/0.61 @ ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.27/0.61 & ( Q @ X ) ) )
% 0.27/0.61 @ ( measur2126959417real_n @ M ) )
% 0.27/0.61 => ( member1475136633real_n
% 0.27/0.61 @ ( collec452821761real_n
% 0.27/0.61 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.27/0.61 & ( Q @ X )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measur2126959417real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.sets_Collect_conj
% 0.27/0.61 thf(fact_137_null__sets_Osets__Collect__conj,axiom,
% 0.27/0.61 ! [M: sigma_measure_o,P: $o > $o,Q: $o > $o] :
% 0.27/0.61 ( ( member_set_o
% 0.27/0.61 @ ( collect_o
% 0.27/0.61 @ ^ [X: $o] :
% 0.27/0.61 ( ( member_o @ X @ ( sigma_space_o @ M ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measure_null_sets_o @ M ) )
% 0.27/0.61 => ( ( member_set_o
% 0.27/0.61 @ ( collect_o
% 0.27/0.61 @ ^ [X: $o] :
% 0.27/0.61 ( ( member_o @ X @ ( sigma_space_o @ M ) )
% 0.27/0.61 & ( Q @ X ) ) )
% 0.27/0.61 @ ( measure_null_sets_o @ M ) )
% 0.27/0.61 => ( member_set_o
% 0.27/0.61 @ ( collect_o
% 0.27/0.61 @ ^ [X: $o] :
% 0.27/0.61 ( ( member_o @ X @ ( sigma_space_o @ M ) )
% 0.27/0.61 & ( Q @ X )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measure_null_sets_o @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.sets_Collect_conj
% 0.27/0.61 thf(fact_138_null__sets_Osets__Collect__conj,axiom,
% 0.27/0.61 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.27/0.61 ( ( member223413699real_n
% 0.27/0.61 @ ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( ( member223413699real_n
% 0.27/0.61 @ ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 & ( Q @ X ) ) )
% 0.27/0.61 @ ( measur1402256771real_n @ M ) )
% 0.27/0.61 => ( member223413699real_n
% 0.27/0.61 @ ( collec321817931real_n
% 0.27/0.61 @ ^ [X: finite1489363574real_n] :
% 0.27/0.61 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.27/0.61 & ( Q @ X )
% 0.27/0.61 & ( P @ X ) ) )
% 0.27/0.61 @ ( measur1402256771real_n @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % null_sets.sets_Collect_conj
% 0.27/0.61 thf(fact_139_translation__diff,axiom,
% 0.27/0.61 ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T: set_Fi1058188332real_n] :
% 0.27/0.61 ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( minus_1686442501real_n @ S2 @ T ) )
% 0.27/0.61 = ( minus_1686442501real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % translation_diff
% 0.27/0.62 thf(fact_140_null__set__Diff,axiom,
% 0.27/0.62 ! [B2: set_Fi1058188332real_n,M: sigma_1466784463real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ B2 @ ( measur1402256771real_n @ M ) )
% 0.27/0.62 => ( ( member223413699real_n @ A3 @ ( sigma_1235138647real_n @ M ) )
% 0.27/0.62 => ( member223413699real_n @ ( minus_1686442501real_n @ B2 @ A3 ) @ ( measur1402256771real_n @ M ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % null_set_Diff
% 0.27/0.62 thf(fact_141_Int__Union2,axiom,
% 0.27/0.62 ! [B2: set_se2111327970real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ ( comple825005695real_n @ B2 ) @ A3 )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1661509983real_n
% 0.27/0.62 @ ^ [C3: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ C3 @ A3 )
% 0.27/0.62 @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_Union2
% 0.27/0.62 thf(fact_142_Int__Union,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ A3 @ ( comple825005695real_n @ B2 ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_1661509983real_n @ ( inf_in1974387902real_n @ A3 ) @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_Union
% 0.27/0.62 thf(fact_143_vimage__Union,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( vimage1233683625real_n @ F @ ( comple825005695real_n @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_1661509983real_n @ ( vimage1233683625real_n @ F ) @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimage_Union
% 0.27/0.62 thf(fact_144_UN__extend__simps_I6_J,axiom,
% 0.27/0.62 ! [A3: nat > set_Fi1058188332real_n,C2: set_nat,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( minus_1686442501real_n @ ( comple825005695real_n @ ( image_1856576259real_n @ A3 @ C2 ) ) @ B2 )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( minus_1686442501real_n @ ( A3 @ X ) @ B2 )
% 0.27/0.62 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_extend_simps(6)
% 0.27/0.62 thf(fact_145_UN__extend__simps_I6_J,axiom,
% 0.27/0.62 ! [A3: finite964658038_int_n > set_Fi1058188332real_n,C2: set_Fi160064172_int_n,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( minus_1686442501real_n @ ( comple825005695real_n @ ( image_355963305real_n @ A3 @ C2 ) ) @ B2 )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( minus_1686442501real_n @ ( A3 @ X ) @ B2 )
% 0.27/0.62 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_extend_simps(6)
% 0.27/0.62 thf(fact_146_emeasure__Diff__null__set,axiom,
% 0.27/0.62 ! [B2: set_Fi1058188332real_n,M: sigma_1466784463real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ B2 @ ( measur1402256771real_n @ M ) )
% 0.27/0.62 => ( ( member223413699real_n @ A3 @ ( sigma_1235138647real_n @ M ) )
% 0.27/0.62 => ( ( sigma_1536574303real_n @ M @ ( minus_1686442501real_n @ A3 @ B2 ) )
% 0.27/0.62 = ( sigma_1536574303real_n @ M @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % emeasure_Diff_null_set
% 0.27/0.62 thf(fact_147_Sup_OSUP__cong,axiom,
% 0.27/0.62 ! [A3: set_nat,B2: set_nat,C2: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n,Sup: set_se2111327970real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: nat] :
% 0.27/0.62 ( ( member_nat @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( Sup @ ( image_1856576259real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( Sup @ ( image_1856576259real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Sup.SUP_cong
% 0.27/0.62 thf(fact_148_Sup_OSUP__cong,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,Sup: set_Fi1058188332real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( Sup @ ( image_439535603real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( Sup @ ( image_439535603real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Sup.SUP_cong
% 0.27/0.62 thf(fact_149_Sup_OSUP__cong,axiom,
% 0.27/0.62 ! [A3: set_Fi160064172_int_n,B2: set_Fi160064172_int_n,C2: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n,Sup: set_se2111327970real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( Sup @ ( image_355963305real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( Sup @ ( image_355963305real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Sup.SUP_cong
% 0.27/0.62 thf(fact_150_Inf_OINF__cong,axiom,
% 0.27/0.62 ! [A3: set_nat,B2: set_nat,C2: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n,Inf: set_se2111327970real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: nat] :
% 0.27/0.62 ( ( member_nat @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( Inf @ ( image_1856576259real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( Inf @ ( image_1856576259real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Inf.INF_cong
% 0.27/0.62 thf(fact_151_Inf_OINF__cong,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,Inf: set_Fi1058188332real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( Inf @ ( image_439535603real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( Inf @ ( image_439535603real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Inf.INF_cong
% 0.27/0.62 thf(fact_152_Inf_OINF__cong,axiom,
% 0.27/0.62 ! [A3: set_Fi160064172_int_n,B2: set_Fi160064172_int_n,C2: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n,Inf: set_se2111327970real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( Inf @ ( image_355963305real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( Inf @ ( image_355963305real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Inf.INF_cong
% 0.27/0.62 thf(fact_153_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: finite1489363574real_n,A3: set_Fi1058188332real_n,B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_154_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: nat,A3: set_nat,B: set_Fi1058188332real_n,F: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member_nat @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member223413699real_n @ B @ ( image_1856576259real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_155_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: finite964658038_int_n,A3: set_Fi160064172_int_n,B: set_Fi1058188332real_n,F: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member223413699real_n @ B @ ( image_355963305real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_156_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: set_Fi1058188332real_n,A3: set_se2111327970real_n,B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_157_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: set_Fi1058188332real_n,A3: set_se2111327970real_n,B: $o,F: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member_o @ B @ ( image_1648361637al_n_o @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_158_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: $o,A3: set_o,B: set_Fi1058188332real_n,F: $o > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member_o @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member223413699real_n @ B @ ( image_1759008383real_n @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_159_rev__image__eqI,axiom,
% 0.27/0.62 ! [X3: $o,A3: set_o,B: $o,F: $o > $o] :
% 0.27/0.62 ( ( member_o @ X3 @ A3 )
% 0.27/0.62 => ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member_o @ B @ ( image_o_o @ F @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_image_eqI
% 0.27/0.62 thf(fact_160_ball__imageD,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,A3: set_nat,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X2 @ ( image_1856576259real_n @ F @ A3 ) )
% 0.27/0.62 => ( P @ X2 ) )
% 0.27/0.62 => ! [X5: nat] :
% 0.27/0.62 ( ( member_nat @ X5 @ A3 )
% 0.27/0.62 => ( P @ ( F @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ball_imageD
% 0.27/0.62 thf(fact_161_ball__imageD,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.27/0.62 ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X2 @ ( image_439535603real_n @ F @ A3 ) )
% 0.27/0.62 => ( P @ X2 ) )
% 0.27/0.62 => ! [X5: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X5 @ A3 )
% 0.27/0.62 => ( P @ ( F @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ball_imageD
% 0.27/0.62 thf(fact_162_ball__imageD,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X2 @ ( image_355963305real_n @ F @ A3 ) )
% 0.27/0.62 => ( P @ X2 ) )
% 0.27/0.62 => ! [X5: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X5 @ A3 )
% 0.27/0.62 => ( P @ ( F @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ball_imageD
% 0.27/0.62 thf(fact_163_image__cong,axiom,
% 0.27/0.62 ! [M: set_nat,N2: set_nat,F: nat > set_Fi1058188332real_n,G: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( M = N2 )
% 0.27/0.62 => ( ! [X2: nat] :
% 0.27/0.62 ( ( member_nat @ X2 @ N2 )
% 0.27/0.62 => ( ( F @ X2 )
% 0.27/0.62 = ( G @ X2 ) ) )
% 0.27/0.62 => ( ( image_1856576259real_n @ F @ M )
% 0.27/0.62 = ( image_1856576259real_n @ G @ N2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_cong
% 0.27/0.62 thf(fact_164_image__cong,axiom,
% 0.27/0.62 ! [M: set_Fi1058188332real_n,N2: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( M = N2 )
% 0.27/0.62 => ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X2 @ N2 )
% 0.27/0.62 => ( ( F @ X2 )
% 0.27/0.62 = ( G @ X2 ) ) )
% 0.27/0.62 => ( ( image_439535603real_n @ F @ M )
% 0.27/0.62 = ( image_439535603real_n @ G @ N2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_cong
% 0.27/0.62 thf(fact_165_image__cong,axiom,
% 0.27/0.62 ! [M: set_Fi160064172_int_n,N2: set_Fi160064172_int_n,F: finite964658038_int_n > set_Fi1058188332real_n,G: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( M = N2 )
% 0.27/0.62 => ( ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X2 @ N2 )
% 0.27/0.62 => ( ( F @ X2 )
% 0.27/0.62 = ( G @ X2 ) ) )
% 0.27/0.62 => ( ( image_355963305real_n @ F @ M )
% 0.27/0.62 = ( image_355963305real_n @ G @ N2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_cong
% 0.27/0.62 thf(fact_166_bex__imageD,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,A3: set_nat,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ? [X5: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X5 @ ( image_1856576259real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X5 ) )
% 0.27/0.62 => ? [X2: nat] :
% 0.27/0.62 ( ( member_nat @ X2 @ A3 )
% 0.27/0.62 & ( P @ ( F @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bex_imageD
% 0.27/0.62 thf(fact_167_bex__imageD,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.27/0.62 ( ? [X5: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X5 @ ( image_439535603real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X5 ) )
% 0.27/0.62 => ? [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X2 @ A3 )
% 0.27/0.62 & ( P @ ( F @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bex_imageD
% 0.27/0.62 thf(fact_168_bex__imageD,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ? [X5: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X5 @ ( image_355963305real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X5 ) )
% 0.27/0.62 => ? [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X2 @ A3 )
% 0.27/0.62 & ( P @ ( F @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bex_imageD
% 0.27/0.62 thf(fact_169_image__iff,axiom,
% 0.27/0.62 ! [Z: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ Z @ ( image_439535603real_n @ F @ A3 ) )
% 0.27/0.62 = ( ? [X: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X @ A3 )
% 0.27/0.62 & ( Z
% 0.27/0.62 = ( F @ X ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_iff
% 0.27/0.62 thf(fact_170_image__iff,axiom,
% 0.27/0.62 ! [Z: set_Fi1058188332real_n,F: nat > set_Fi1058188332real_n,A3: set_nat] :
% 0.27/0.62 ( ( member223413699real_n @ Z @ ( image_1856576259real_n @ F @ A3 ) )
% 0.27/0.62 = ( ? [X: nat] :
% 0.27/0.62 ( ( member_nat @ X @ A3 )
% 0.27/0.62 & ( Z
% 0.27/0.62 = ( F @ X ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_iff
% 0.27/0.62 thf(fact_171_image__iff,axiom,
% 0.27/0.62 ! [Z: set_Fi1058188332real_n,F: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( member223413699real_n @ Z @ ( image_355963305real_n @ F @ A3 ) )
% 0.27/0.62 = ( ? [X: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.62 & ( Z
% 0.27/0.62 = ( F @ X ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_iff
% 0.27/0.62 thf(fact_172_imageI,axiom,
% 0.27/0.62 ! [X3: finite1489363574real_n,A3: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X3 @ A3 )
% 0.27/0.62 => ( member1352538125real_n @ ( F @ X3 ) @ ( image_439535603real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_173_imageI,axiom,
% 0.27/0.62 ! [X3: nat,A3: set_nat,F: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member_nat @ X3 @ A3 )
% 0.27/0.62 => ( member223413699real_n @ ( F @ X3 ) @ ( image_1856576259real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_174_imageI,axiom,
% 0.27/0.62 ! [X3: finite964658038_int_n,A3: set_Fi160064172_int_n,F: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X3 @ A3 )
% 0.27/0.62 => ( member223413699real_n @ ( F @ X3 ) @ ( image_355963305real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_175_imageI,axiom,
% 0.27/0.62 ! [X3: set_Fi1058188332real_n,A3: set_se2111327970real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.62 => ( member223413699real_n @ ( F @ X3 ) @ ( image_1661509983real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_176_imageI,axiom,
% 0.27/0.62 ! [X3: set_Fi1058188332real_n,A3: set_se2111327970real_n,F: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.62 => ( member_o @ ( F @ X3 ) @ ( image_1648361637al_n_o @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_177_imageI,axiom,
% 0.27/0.62 ! [X3: $o,A3: set_o,F: $o > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member_o @ X3 @ A3 )
% 0.27/0.62 => ( member223413699real_n @ ( F @ X3 ) @ ( image_1759008383real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_178_imageI,axiom,
% 0.27/0.62 ! [X3: $o,A3: set_o,F: $o > $o] :
% 0.27/0.62 ( ( member_o @ X3 @ A3 )
% 0.27/0.62 => ( member_o @ ( F @ X3 ) @ ( image_o_o @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageI
% 0.27/0.62 thf(fact_179_is__num__normalize_I1_J,axiom,
% 0.27/0.62 ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
% 0.27/0.62 ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C )
% 0.27/0.62 = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % is_num_normalize(1)
% 0.27/0.62 thf(fact_180_UNIV__witness,axiom,
% 0.27/0.62 ? [X2: set_Fi1058188332real_n] : ( member223413699real_n @ X2 @ top_to20708754real_n ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_witness
% 0.27/0.62 thf(fact_181_UNIV__witness,axiom,
% 0.27/0.62 ? [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_witness
% 0.27/0.62 thf(fact_182_UNIV__witness,axiom,
% 0.27/0.62 ? [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_witness
% 0.27/0.62 thf(fact_183_UNIV__witness,axiom,
% 0.27/0.62 ? [X2: finite964658038_int_n] : ( member27055245_int_n @ X2 @ top_to131672412_int_n ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_witness
% 0.27/0.62 thf(fact_184_UNIV__eq__I,axiom,
% 0.27/0.62 ! [A3: set_se2111327970real_n] :
% 0.27/0.62 ( ! [X2: set_Fi1058188332real_n] : ( member223413699real_n @ X2 @ A3 )
% 0.27/0.62 => ( top_to20708754real_n = A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_eq_I
% 0.27/0.62 thf(fact_185_UNIV__eq__I,axiom,
% 0.27/0.62 ! [A3: set_o] :
% 0.27/0.62 ( ! [X2: $o] : ( member_o @ X2 @ A3 )
% 0.27/0.62 => ( top_top_set_o = A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_eq_I
% 0.27/0.62 thf(fact_186_UNIV__eq__I,axiom,
% 0.27/0.62 ! [A3: set_nat] :
% 0.27/0.62 ( ! [X2: nat] : ( member_nat @ X2 @ A3 )
% 0.27/0.62 => ( top_top_set_nat = A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_eq_I
% 0.27/0.62 thf(fact_187_UNIV__eq__I,axiom,
% 0.27/0.62 ! [A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ! [X2: finite964658038_int_n] : ( member27055245_int_n @ X2 @ A3 )
% 0.27/0.62 => ( top_to131672412_int_n = A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_eq_I
% 0.27/0.62 thf(fact_188_Int__left__commute,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ A3 @ ( inf_in1974387902real_n @ B2 @ C2 ) )
% 0.27/0.62 = ( inf_in1974387902real_n @ B2 @ ( inf_in1974387902real_n @ A3 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_left_commute
% 0.27/0.62 thf(fact_189_Int__left__absorb,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ A3 @ ( inf_in1974387902real_n @ A3 @ B2 ) )
% 0.27/0.62 = ( inf_in1974387902real_n @ A3 @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_left_absorb
% 0.27/0.62 thf(fact_190_Int__commute,axiom,
% 0.27/0.62 ( inf_in1974387902real_n
% 0.27/0.62 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B3 @ A4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_commute
% 0.27/0.62 thf(fact_191_Int__absorb,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ A3 @ A3 )
% 0.27/0.62 = A3 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_absorb
% 0.27/0.62 thf(fact_192_Int__assoc,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A3 @ B2 ) @ C2 )
% 0.27/0.62 = ( inf_in1974387902real_n @ A3 @ ( inf_in1974387902real_n @ B2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_assoc
% 0.27/0.62 thf(fact_193_IntD2,axiom,
% 0.27/0.62 ! [C: set_Fi1058188332real_n,A3: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ C @ ( inf_in632889204real_n @ A3 @ B2 ) )
% 0.27/0.62 => ( member223413699real_n @ C @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntD2
% 0.27/0.62 thf(fact_194_IntD2,axiom,
% 0.27/0.62 ! [C: $o,A3: set_o,B2: set_o] :
% 0.27/0.62 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 0.27/0.62 => ( member_o @ C @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntD2
% 0.27/0.62 thf(fact_195_IntD2,axiom,
% 0.27/0.62 ! [C: finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A3 @ B2 ) )
% 0.27/0.62 => ( member1352538125real_n @ C @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntD2
% 0.27/0.62 thf(fact_196_IntD1,axiom,
% 0.27/0.62 ! [C: set_Fi1058188332real_n,A3: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ C @ ( inf_in632889204real_n @ A3 @ B2 ) )
% 0.27/0.62 => ( member223413699real_n @ C @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntD1
% 0.27/0.62 thf(fact_197_IntD1,axiom,
% 0.27/0.62 ! [C: $o,A3: set_o,B2: set_o] :
% 0.27/0.62 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 0.27/0.62 => ( member_o @ C @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntD1
% 0.27/0.62 thf(fact_198_IntD1,axiom,
% 0.27/0.62 ! [C: finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A3 @ B2 ) )
% 0.27/0.62 => ( member1352538125real_n @ C @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntD1
% 0.27/0.62 thf(fact_199_IntE,axiom,
% 0.27/0.62 ! [C: set_Fi1058188332real_n,A3: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ C @ ( inf_in632889204real_n @ A3 @ B2 ) )
% 0.27/0.62 => ~ ( ( member223413699real_n @ C @ A3 )
% 0.27/0.62 => ~ ( member223413699real_n @ C @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntE
% 0.27/0.62 thf(fact_200_IntE,axiom,
% 0.27/0.62 ! [C: $o,A3: set_o,B2: set_o] :
% 0.27/0.62 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 0.27/0.62 => ~ ( ( member_o @ C @ A3 )
% 0.27/0.62 => ~ ( member_o @ C @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntE
% 0.27/0.62 thf(fact_201_IntE,axiom,
% 0.27/0.62 ! [C: finite1489363574real_n,A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A3 @ B2 ) )
% 0.27/0.62 => ~ ( ( member1352538125real_n @ C @ A3 )
% 0.27/0.62 => ~ ( member1352538125real_n @ C @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % IntE
% 0.27/0.62 thf(fact_202_UnionE,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,C2: set_se820660888real_n] :
% 0.27/0.62 ( ( member223413699real_n @ A3 @ ( comple1917283637real_n @ C2 ) )
% 0.27/0.62 => ~ ! [X6: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ A3 @ X6 )
% 0.27/0.62 => ~ ( member1475136633real_n @ X6 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UnionE
% 0.27/0.62 thf(fact_203_UnionE,axiom,
% 0.27/0.62 ! [A3: $o,C2: set_set_o] :
% 0.27/0.62 ( ( member_o @ A3 @ ( comple1665300069_set_o @ C2 ) )
% 0.27/0.62 => ~ ! [X6: set_o] :
% 0.27/0.62 ( ( member_o @ A3 @ X6 )
% 0.27/0.62 => ~ ( member_set_o @ X6 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UnionE
% 0.27/0.62 thf(fact_204_UnionE,axiom,
% 0.27/0.62 ! [A3: finite1489363574real_n,C2: set_se2111327970real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ A3 @ ( comple825005695real_n @ C2 ) )
% 0.27/0.62 => ~ ! [X6: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ A3 @ X6 )
% 0.27/0.62 => ~ ( member223413699real_n @ X6 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UnionE
% 0.27/0.62 thf(fact_205_vimage__Collect,axiom,
% 0.27/0.62 ! [P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,Q: finite1489363574real_n > $o] :
% 0.27/0.62 ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( P @ ( F @ X2 ) )
% 0.27/0.62 = ( Q @ X2 ) )
% 0.27/0.62 => ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) )
% 0.27/0.62 = ( collec321817931real_n @ Q ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimage_Collect
% 0.27/0.62 thf(fact_206_vimageI2,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ ( F @ A ) @ A3 )
% 0.27/0.62 => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageI2
% 0.27/0.62 thf(fact_207_vimageI2,axiom,
% 0.27/0.62 ! [F: $o > set_Fi1058188332real_n,A: $o,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ ( F @ A ) @ A3 )
% 0.27/0.62 => ( member_o @ A @ ( vimage961837641real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageI2
% 0.27/0.62 thf(fact_208_vimageI2,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > $o,A: set_Fi1058188332real_n,A3: set_o] :
% 0.27/0.62 ( ( member_o @ ( F @ A ) @ A3 )
% 0.27/0.62 => ( member223413699real_n @ A @ ( vimage851190895al_n_o @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageI2
% 0.27/0.62 thf(fact_209_vimageI2,axiom,
% 0.27/0.62 ! [F: $o > $o,A: $o,A3: set_o] :
% 0.27/0.62 ( ( member_o @ ( F @ A ) @ A3 )
% 0.27/0.62 => ( member_o @ A @ ( vimage_o_o @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageI2
% 0.27/0.62 thf(fact_210_vimageI2,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ ( F @ A ) @ A3 )
% 0.27/0.62 => ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageI2
% 0.27/0.62 thf(fact_211_vimageE,axiom,
% 0.27/0.62 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) )
% 0.27/0.62 => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageE
% 0.27/0.62 thf(fact_212_vimageE,axiom,
% 0.27/0.62 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > $o,B2: set_o] :
% 0.27/0.62 ( ( member223413699real_n @ A @ ( vimage851190895al_n_o @ F @ B2 ) )
% 0.27/0.62 => ( member_o @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageE
% 0.27/0.62 thf(fact_213_vimageE,axiom,
% 0.27/0.62 ! [A: $o,F: $o > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.27/0.62 ( ( member_o @ A @ ( vimage961837641real_n @ F @ B2 ) )
% 0.27/0.62 => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageE
% 0.27/0.62 thf(fact_214_vimageE,axiom,
% 0.27/0.62 ! [A: $o,F: $o > $o,B2: set_o] :
% 0.27/0.62 ( ( member_o @ A @ ( vimage_o_o @ F @ B2 ) )
% 0.27/0.62 => ( member_o @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageE
% 0.27/0.62 thf(fact_215_vimageE,axiom,
% 0.27/0.62 ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) )
% 0.27/0.62 => ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageE
% 0.27/0.62 thf(fact_216_vimageD,axiom,
% 0.27/0.62 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A3 ) )
% 0.27/0.62 => ( member223413699real_n @ ( F @ A ) @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageD
% 0.27/0.62 thf(fact_217_vimageD,axiom,
% 0.27/0.62 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > $o,A3: set_o] :
% 0.27/0.62 ( ( member223413699real_n @ A @ ( vimage851190895al_n_o @ F @ A3 ) )
% 0.27/0.62 => ( member_o @ ( F @ A ) @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageD
% 0.27/0.62 thf(fact_218_vimageD,axiom,
% 0.27/0.62 ! [A: $o,F: $o > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member_o @ A @ ( vimage961837641real_n @ F @ A3 ) )
% 0.27/0.62 => ( member223413699real_n @ ( F @ A ) @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageD
% 0.27/0.62 thf(fact_219_vimageD,axiom,
% 0.27/0.62 ! [A: $o,F: $o > $o,A3: set_o] :
% 0.27/0.62 ( ( member_o @ A @ ( vimage_o_o @ F @ A3 ) )
% 0.27/0.62 => ( member_o @ ( F @ A ) @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageD
% 0.27/0.62 thf(fact_220_vimageD,axiom,
% 0.27/0.62 ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A3 ) )
% 0.27/0.62 => ( member1352538125real_n @ ( F @ A ) @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimageD
% 0.27/0.62 thf(fact_221_Sup_OSUP__identity__eq,axiom,
% 0.27/0.62 ! [Sup: set_Fi1058188332real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( Sup
% 0.27/0.62 @ ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : X
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 = ( Sup @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % Sup.SUP_identity_eq
% 0.27/0.62 thf(fact_222_Inf_OINF__identity__eq,axiom,
% 0.27/0.62 ! [Inf: set_Fi1058188332real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( Inf
% 0.27/0.62 @ ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : X
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 = ( Inf @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % Inf.INF_identity_eq
% 0.27/0.62 thf(fact_223_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.27/0.62 ( ( collec321817931real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X @ ( image_439535603real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_439535603real_n @ F
% 0.27/0.62 @ ( collec321817931real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_224_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,A3: set_nat,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ ( image_1856576259real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_1856576259real_n @ F
% 0.27/0.62 @ ( collect_nat
% 0.27/0.62 @ ^ [X: nat] :
% 0.27/0.62 ( ( member_nat @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_225_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ ( image_355963305real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_355963305real_n @ F
% 0.27/0.62 @ ( collec1941932235_int_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_226_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A3: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ ( image_1661509983real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_1661509983real_n @ F
% 0.27/0.62 @ ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_227_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: $o > set_Fi1058188332real_n,A3: set_o,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ ( image_1759008383real_n @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_1759008383real_n @ F
% 0.27/0.62 @ ( collect_o
% 0.27/0.62 @ ^ [X: $o] :
% 0.27/0.62 ( ( member_o @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_228_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > $o,A3: set_se2111327970real_n,P: $o > $o] :
% 0.27/0.62 ( ( collect_o
% 0.27/0.62 @ ^ [X: $o] :
% 0.27/0.62 ( ( member_o @ X @ ( image_1648361637al_n_o @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_1648361637al_n_o @ F
% 0.27/0.62 @ ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_229_Compr__image__eq,axiom,
% 0.27/0.62 ! [F: $o > $o,A3: set_o,P: $o > $o] :
% 0.27/0.62 ( ( collect_o
% 0.27/0.62 @ ^ [X: $o] :
% 0.27/0.62 ( ( member_o @ X @ ( image_o_o @ F @ A3 ) )
% 0.27/0.62 & ( P @ X ) ) )
% 0.27/0.62 = ( image_o_o @ F
% 0.27/0.62 @ ( collect_o
% 0.27/0.62 @ ^ [X: $o] :
% 0.27/0.62 ( ( member_o @ X @ A3 )
% 0.27/0.62 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Compr_image_eq
% 0.27/0.62 thf(fact_230_image__image,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,G: nat > set_Fi1058188332real_n,A3: set_nat] :
% 0.27/0.62 ( ( image_1661509983real_n @ F @ ( image_1856576259real_n @ G @ A3 ) )
% 0.27/0.62 = ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_231_image__image,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,G: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( image_1661509983real_n @ F @ ( image_355963305real_n @ G @ A3 ) )
% 0.27/0.62 = ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_232_image__image,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,G: nat > nat,A3: set_nat] :
% 0.27/0.62 ( ( image_1856576259real_n @ F @ ( image_nat_nat @ G @ A3 ) )
% 0.27/0.62 = ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_233_image__image,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,G: finite964658038_int_n > nat,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( image_1856576259real_n @ F @ ( image_497739341_n_nat @ G @ A3 ) )
% 0.27/0.62 = ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_234_image__image,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( image_439535603real_n @ F @ ( image_439535603real_n @ G @ A3 ) )
% 0.27/0.62 = ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_235_image__image,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,G: nat > finite964658038_int_n,A3: set_nat] :
% 0.27/0.62 ( ( image_355963305real_n @ F @ ( image_1961920973_int_n @ G @ A3 ) )
% 0.27/0.62 = ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_236_image__image,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,G: finite964658038_int_n > finite964658038_int_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( image_355963305real_n @ F @ ( image_1278151539_int_n @ G @ A3 ) )
% 0.27/0.62 = ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_image
% 0.27/0.62 thf(fact_237_imageE,axiom,
% 0.27/0.62 ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member1352538125real_n @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_238_imageE,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: nat > set_Fi1058188332real_n,A3: set_nat] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( image_1856576259real_n @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member_nat @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_239_imageE,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( image_355963305real_n @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member27055245_int_n @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_240_imageE,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member223413699real_n @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_241_imageE,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: $o > set_Fi1058188332real_n,A3: set_o] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( image_1759008383real_n @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: $o] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member_o @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_242_imageE,axiom,
% 0.27/0.62 ! [B: $o,F: set_Fi1058188332real_n > $o,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member_o @ B @ ( image_1648361637al_n_o @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member223413699real_n @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_243_imageE,axiom,
% 0.27/0.62 ! [B: $o,F: $o > $o,A3: set_o] :
% 0.27/0.62 ( ( member_o @ B @ ( image_o_o @ F @ A3 ) )
% 0.27/0.62 => ~ ! [X2: $o] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X2 ) )
% 0.27/0.62 => ~ ( member_o @ X2 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % imageE
% 0.27/0.62 thf(fact_244_UNIV__def,axiom,
% 0.27/0.62 ( top_top_set_nat
% 0.27/0.62 = ( collect_nat
% 0.27/0.62 @ ^ [X: nat] : $true ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_def
% 0.27/0.62 thf(fact_245_UNIV__def,axiom,
% 0.27/0.62 ( top_to131672412_int_n
% 0.27/0.62 = ( collec1941932235_int_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : $true ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_def
% 0.27/0.62 thf(fact_246_Collect__conj__eq,axiom,
% 0.27/0.62 ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.27/0.62 ( ( collec321817931real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] :
% 0.27/0.62 ( ( P @ X )
% 0.27/0.62 & ( Q @ X ) ) )
% 0.27/0.62 = ( inf_in1974387902real_n @ ( collec321817931real_n @ P ) @ ( collec321817931real_n @ Q ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_conj_eq
% 0.27/0.62 thf(fact_247_Int__Collect,axiom,
% 0.27/0.62 ! [X3: set_Fi1058188332real_n,A3: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( member223413699real_n @ X3 @ ( inf_in632889204real_n @ A3 @ ( collec452821761real_n @ P ) ) )
% 0.27/0.62 = ( ( member223413699real_n @ X3 @ A3 )
% 0.27/0.62 & ( P @ X3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_Collect
% 0.27/0.62 thf(fact_248_Int__Collect,axiom,
% 0.27/0.62 ! [X3: $o,A3: set_o,P: $o > $o] :
% 0.27/0.62 ( ( member_o @ X3 @ ( inf_inf_set_o @ A3 @ ( collect_o @ P ) ) )
% 0.27/0.62 = ( ( member_o @ X3 @ A3 )
% 0.27/0.62 & ( P @ X3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_Collect
% 0.27/0.62 thf(fact_249_Int__Collect,axiom,
% 0.27/0.62 ! [X3: finite1489363574real_n,A3: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.27/0.62 ( ( member1352538125real_n @ X3 @ ( inf_in1974387902real_n @ A3 @ ( collec321817931real_n @ P ) ) )
% 0.27/0.62 = ( ( member1352538125real_n @ X3 @ A3 )
% 0.27/0.62 & ( P @ X3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_Collect
% 0.27/0.62 thf(fact_250_Int__def,axiom,
% 0.27/0.62 ( inf_in632889204real_n
% 0.27/0.62 = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 0.27/0.62 ( collec452821761real_n
% 0.27/0.62 @ ^ [X: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X @ A4 )
% 0.27/0.62 & ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_def
% 0.27/0.62 thf(fact_251_Int__def,axiom,
% 0.27/0.62 ( inf_inf_set_o
% 0.27/0.62 = ( ^ [A4: set_o,B3: set_o] :
% 0.27/0.62 ( collect_o
% 0.27/0.62 @ ^ [X: $o] :
% 0.27/0.62 ( ( member_o @ X @ A4 )
% 0.27/0.62 & ( member_o @ X @ B3 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_def
% 0.27/0.62 thf(fact_252_Int__def,axiom,
% 0.27/0.62 ( inf_in1974387902real_n
% 0.27/0.62 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 0.27/0.62 ( collec321817931real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X @ A4 )
% 0.27/0.62 & ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Int_def
% 0.27/0.62 thf(fact_253_vimage__def,axiom,
% 0.27/0.62 ( vimage1233683625real_n
% 0.27/0.62 = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,B3: set_Fi1058188332real_n] :
% 0.27/0.62 ( collec321817931real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimage_def
% 0.27/0.62 thf(fact_254_less__numeral__extra_I3_J,axiom,
% 0.27/0.62 ~ ( ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal ) ).
% 0.27/0.62
% 0.27/0.62 % less_numeral_extra(3)
% 0.27/0.62 thf(fact_255_less__numeral__extra_I4_J,axiom,
% 0.27/0.62 ~ ( ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal ) ).
% 0.27/0.62
% 0.27/0.62 % less_numeral_extra(4)
% 0.27/0.62 thf(fact_256_range__eqI,axiom,
% 0.27/0.62 ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,X3: finite1489363574real_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ top_to1292442332real_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_eqI
% 0.27/0.62 thf(fact_257_range__eqI,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: nat > set_Fi1058188332real_n,X3: nat] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member223413699real_n @ B @ ( image_1856576259real_n @ F @ top_top_set_nat ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_eqI
% 0.27/0.62 thf(fact_258_range__eqI,axiom,
% 0.27/0.62 ! [B: $o,F: nat > $o,X3: nat] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_eqI
% 0.27/0.62 thf(fact_259_range__eqI,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: finite964658038_int_n > set_Fi1058188332real_n,X3: finite964658038_int_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member223413699real_n @ B @ ( image_355963305real_n @ F @ top_to131672412_int_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_eqI
% 0.27/0.62 thf(fact_260_range__eqI,axiom,
% 0.27/0.62 ! [B: $o,F: finite964658038_int_n > $o,X3: finite964658038_int_n] :
% 0.27/0.62 ( ( B
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( member_o @ B @ ( image_216309723nt_n_o @ F @ top_to131672412_int_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_eqI
% 0.27/0.62 thf(fact_261_surj__def,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( ( image_439535603real_n @ F @ top_to1292442332real_n )
% 0.27/0.62 = top_to1292442332real_n )
% 0.27/0.62 = ( ! [Y2: finite1489363574real_n] :
% 0.27/0.62 ? [X: finite1489363574real_n] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_262_surj__def,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( ( image_1856576259real_n @ F @ top_top_set_nat )
% 0.27/0.62 = top_to20708754real_n )
% 0.27/0.62 = ( ! [Y2: set_Fi1058188332real_n] :
% 0.27/0.62 ? [X: nat] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_263_surj__def,axiom,
% 0.27/0.62 ! [F: nat > nat] :
% 0.27/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.27/0.62 = top_top_set_nat )
% 0.27/0.62 = ( ! [Y2: nat] :
% 0.27/0.62 ? [X: nat] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_264_surj__def,axiom,
% 0.27/0.62 ! [F: nat > finite964658038_int_n] :
% 0.27/0.62 ( ( ( image_1961920973_int_n @ F @ top_top_set_nat )
% 0.27/0.62 = top_to131672412_int_n )
% 0.27/0.62 = ( ! [Y2: finite964658038_int_n] :
% 0.27/0.62 ? [X: nat] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_265_surj__def,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( ( image_355963305real_n @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_to20708754real_n )
% 0.27/0.62 = ( ! [Y2: set_Fi1058188332real_n] :
% 0.27/0.62 ? [X: finite964658038_int_n] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_266_surj__def,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > nat] :
% 0.27/0.62 ( ( ( image_497739341_n_nat @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_top_set_nat )
% 0.27/0.62 = ( ! [Y2: nat] :
% 0.27/0.62 ? [X: finite964658038_int_n] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_267_surj__def,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > finite964658038_int_n] :
% 0.27/0.62 ( ( ( image_1278151539_int_n @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_to131672412_int_n )
% 0.27/0.62 = ( ! [Y2: finite964658038_int_n] :
% 0.27/0.62 ? [X: finite964658038_int_n] :
% 0.27/0.62 ( Y2
% 0.27/0.62 = ( F @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surj_def
% 0.27/0.62 thf(fact_268_rangeI,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,X3: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X3 ) @ ( image_439535603real_n @ F @ top_to1292442332real_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeI
% 0.27/0.62 thf(fact_269_rangeI,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,X3: nat] : ( member223413699real_n @ ( F @ X3 ) @ ( image_1856576259real_n @ F @ top_top_set_nat ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeI
% 0.27/0.62 thf(fact_270_rangeI,axiom,
% 0.27/0.62 ! [F: nat > $o,X3: nat] : ( member_o @ ( F @ X3 ) @ ( image_nat_o @ F @ top_top_set_nat ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeI
% 0.27/0.62 thf(fact_271_rangeI,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,X3: finite964658038_int_n] : ( member223413699real_n @ ( F @ X3 ) @ ( image_355963305real_n @ F @ top_to131672412_int_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeI
% 0.27/0.62 thf(fact_272_rangeI,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > $o,X3: finite964658038_int_n] : ( member_o @ ( F @ X3 ) @ ( image_216309723nt_n_o @ F @ top_to131672412_int_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeI
% 0.27/0.62 thf(fact_273_surjI,axiom,
% 0.27/0.62 ! [G: finite1489363574real_n > finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_439535603real_n @ G @ top_to1292442332real_n )
% 0.27/0.62 = top_to1292442332real_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_274_surjI,axiom,
% 0.27/0.62 ! [G: nat > set_Fi1058188332real_n,F: set_Fi1058188332real_n > nat] :
% 0.27/0.62 ( ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_1856576259real_n @ G @ top_top_set_nat )
% 0.27/0.62 = top_to20708754real_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_275_surjI,axiom,
% 0.27/0.62 ! [G: nat > nat,F: nat > nat] :
% 0.27/0.62 ( ! [X2: nat] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.27/0.62 = top_top_set_nat ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_276_surjI,axiom,
% 0.27/0.62 ! [G: nat > finite964658038_int_n,F: finite964658038_int_n > nat] :
% 0.27/0.62 ( ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_1961920973_int_n @ G @ top_top_set_nat )
% 0.27/0.62 = top_to131672412_int_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_277_surjI,axiom,
% 0.27/0.62 ! [G: finite964658038_int_n > set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite964658038_int_n] :
% 0.27/0.62 ( ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_355963305real_n @ G @ top_to131672412_int_n )
% 0.27/0.62 = top_to20708754real_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_278_surjI,axiom,
% 0.27/0.62 ! [G: finite964658038_int_n > nat,F: nat > finite964658038_int_n] :
% 0.27/0.62 ( ! [X2: nat] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_497739341_n_nat @ G @ top_to131672412_int_n )
% 0.27/0.62 = top_top_set_nat ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_279_surjI,axiom,
% 0.27/0.62 ! [G: finite964658038_int_n > finite964658038_int_n,F: finite964658038_int_n > finite964658038_int_n] :
% 0.27/0.62 ( ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( G @ ( F @ X2 ) )
% 0.27/0.62 = X2 )
% 0.27/0.62 => ( ( image_1278151539_int_n @ G @ top_to131672412_int_n )
% 0.27/0.62 = top_to131672412_int_n ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjI
% 0.27/0.62 thf(fact_280_surjE,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,Y4: finite1489363574real_n] :
% 0.27/0.62 ( ( ( image_439535603real_n @ F @ top_to1292442332real_n )
% 0.27/0.62 = top_to1292442332real_n )
% 0.27/0.62 => ~ ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_281_surjE,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,Y4: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( ( image_1856576259real_n @ F @ top_top_set_nat )
% 0.27/0.62 = top_to20708754real_n )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_282_surjE,axiom,
% 0.27/0.62 ! [F: nat > nat,Y4: nat] :
% 0.27/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.27/0.62 = top_top_set_nat )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_283_surjE,axiom,
% 0.27/0.62 ! [F: nat > finite964658038_int_n,Y4: finite964658038_int_n] :
% 0.27/0.62 ( ( ( image_1961920973_int_n @ F @ top_top_set_nat )
% 0.27/0.62 = top_to131672412_int_n )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_284_surjE,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,Y4: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( ( image_355963305real_n @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_to20708754real_n )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_285_surjE,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > nat,Y4: nat] :
% 0.27/0.62 ( ( ( image_497739341_n_nat @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_top_set_nat )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_286_surjE,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > finite964658038_int_n,Y4: finite964658038_int_n] :
% 0.27/0.62 ( ( ( image_1278151539_int_n @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_to131672412_int_n )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjE
% 0.27/0.62 thf(fact_287_surjD,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,Y4: finite1489363574real_n] :
% 0.27/0.62 ( ( ( image_439535603real_n @ F @ top_to1292442332real_n )
% 0.27/0.62 = top_to1292442332real_n )
% 0.27/0.62 => ? [X2: finite1489363574real_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_288_surjD,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,Y4: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( ( image_1856576259real_n @ F @ top_top_set_nat )
% 0.27/0.62 = top_to20708754real_n )
% 0.27/0.62 => ? [X2: nat] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_289_surjD,axiom,
% 0.27/0.62 ! [F: nat > nat,Y4: nat] :
% 0.27/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.27/0.62 = top_top_set_nat )
% 0.27/0.62 => ? [X2: nat] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_290_surjD,axiom,
% 0.27/0.62 ! [F: nat > finite964658038_int_n,Y4: finite964658038_int_n] :
% 0.27/0.62 ( ( ( image_1961920973_int_n @ F @ top_top_set_nat )
% 0.27/0.62 = top_to131672412_int_n )
% 0.27/0.62 => ? [X2: nat] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_291_surjD,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,Y4: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( ( image_355963305real_n @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_to20708754real_n )
% 0.27/0.62 => ? [X2: finite964658038_int_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_292_surjD,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > nat,Y4: nat] :
% 0.27/0.62 ( ( ( image_497739341_n_nat @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_top_set_nat )
% 0.27/0.62 => ? [X2: finite964658038_int_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_293_surjD,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > finite964658038_int_n,Y4: finite964658038_int_n] :
% 0.27/0.62 ( ( ( image_1278151539_int_n @ F @ top_to131672412_int_n )
% 0.27/0.62 = top_to131672412_int_n )
% 0.27/0.62 => ? [X2: finite964658038_int_n] :
% 0.27/0.62 ( Y4
% 0.27/0.62 = ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % surjD
% 0.27/0.62 thf(fact_294_less__Sup__iff,axiom,
% 0.27/0.62 ! [A: extend1728876344nnreal,S: set_Ex113815278nnreal] :
% 0.27/0.62 ( ( ord_le2133614988nnreal @ A @ ( comple1413366923nnreal @ S ) )
% 0.27/0.62 = ( ? [X: extend1728876344nnreal] :
% 0.27/0.62 ( ( member1217042383nnreal @ X @ S )
% 0.27/0.62 & ( ord_le2133614988nnreal @ A @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_Sup_iff
% 0.27/0.62 thf(fact_295_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C2: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( comple2042271945real_n @ ( image_439535603real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( comple2042271945real_n @ ( image_439535603real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_296_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_nat,B2: set_nat,C2: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: nat] :
% 0.27/0.62 ( ( member_nat @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( comple825005695real_n @ ( image_1856576259real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_1856576259real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_297_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_Fi160064172_int_n,B2: set_Fi160064172_int_n,C2: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( comple825005695real_n @ ( image_355963305real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_355963305real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_298_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_se2111327970real_n,B2: set_se2111327970real_n,C2: set_Fi1058188332real_n > set_Fi1058188332real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( comple825005695real_n @ ( image_1661509983real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_1661509983real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_299_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_o,B2: set_o,C2: $o > set_Fi1058188332real_n,D: $o > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: $o] :
% 0.27/0.62 ( ( member_o @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( comple825005695real_n @ ( image_1759008383real_n @ C2 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_1759008383real_n @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_300_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_se2111327970real_n,B2: set_se2111327970real_n,C2: set_Fi1058188332real_n > $o,D: set_Fi1058188332real_n > $o] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( complete_Sup_Sup_o @ ( image_1648361637al_n_o @ C2 @ A3 ) )
% 0.27/0.62 = ( complete_Sup_Sup_o @ ( image_1648361637al_n_o @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_301_SUP__cong,axiom,
% 0.27/0.62 ! [A3: set_o,B2: set_o,C2: $o > $o,D: $o > $o] :
% 0.27/0.62 ( ( A3 = B2 )
% 0.27/0.62 => ( ! [X2: $o] :
% 0.27/0.62 ( ( member_o @ X2 @ B2 )
% 0.27/0.62 => ( ( C2 @ X2 )
% 0.27/0.62 = ( D @ X2 ) ) )
% 0.27/0.62 => ( ( complete_Sup_Sup_o @ ( image_o_o @ C2 @ A3 ) )
% 0.27/0.62 = ( complete_Sup_Sup_o @ ( image_o_o @ D @ B2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_cong
% 0.27/0.62 thf(fact_302_Int__UNIV__right,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ A3 @ top_to1292442332real_n )
% 0.27/0.62 = A3 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_UNIV_right
% 0.27/0.62 thf(fact_303_Int__UNIV__right,axiom,
% 0.27/0.62 ! [A3: set_nat] :
% 0.27/0.62 ( ( inf_inf_set_nat @ A3 @ top_top_set_nat )
% 0.27/0.62 = A3 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_UNIV_right
% 0.27/0.62 thf(fact_304_Int__UNIV__right,axiom,
% 0.27/0.62 ! [A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( inf_in1108485182_int_n @ A3 @ top_to131672412_int_n )
% 0.27/0.62 = A3 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_UNIV_right
% 0.27/0.62 thf(fact_305_Int__UNIV__left,axiom,
% 0.27/0.62 ! [B2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( inf_in1974387902real_n @ top_to1292442332real_n @ B2 )
% 0.27/0.62 = B2 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_UNIV_left
% 0.27/0.62 thf(fact_306_Int__UNIV__left,axiom,
% 0.27/0.62 ! [B2: set_nat] :
% 0.27/0.62 ( ( inf_inf_set_nat @ top_top_set_nat @ B2 )
% 0.27/0.62 = B2 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_UNIV_left
% 0.27/0.62 thf(fact_307_Int__UNIV__left,axiom,
% 0.27/0.62 ! [B2: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( inf_in1108485182_int_n @ top_to131672412_int_n @ B2 )
% 0.27/0.62 = B2 ) ).
% 0.27/0.62
% 0.27/0.62 % Int_UNIV_left
% 0.27/0.62 thf(fact_308_Union__UNIV,axiom,
% 0.27/0.62 ( ( comple1682161881et_nat @ top_top_set_set_nat )
% 0.27/0.62 = top_top_set_nat ) ).
% 0.27/0.62
% 0.27/0.62 % Union_UNIV
% 0.27/0.62 thf(fact_309_Union__UNIV,axiom,
% 0.27/0.62 ( ( comple970917503_int_n @ top_to1587634578_int_n )
% 0.27/0.62 = top_to131672412_int_n ) ).
% 0.27/0.62
% 0.27/0.62 % Union_UNIV
% 0.27/0.62 thf(fact_310_Union__UNIV,axiom,
% 0.27/0.62 ( ( comple825005695real_n @ top_to20708754real_n )
% 0.27/0.62 = top_to1292442332real_n ) ).
% 0.27/0.62
% 0.27/0.62 % Union_UNIV
% 0.27/0.62 thf(fact_311_null__setsD2,axiom,
% 0.27/0.62 ! [A3: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.27/0.62 ( ( member223413699real_n @ A3 @ ( measur1402256771real_n @ M ) )
% 0.27/0.62 => ( member223413699real_n @ A3 @ ( sigma_1235138647real_n @ M ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % null_setsD2
% 0.27/0.62 thf(fact_312_vimage__inter__cong,axiom,
% 0.27/0.62 ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,Y4: set_Fi1058188332real_n] :
% 0.27/0.62 ( ! [W: finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ W @ S )
% 0.27/0.62 => ( ( F @ W )
% 0.27/0.62 = ( G @ W ) ) )
% 0.27/0.62 => ( ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ Y4 ) @ S )
% 0.27/0.62 = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ G @ Y4 ) @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % vimage_inter_cong
% 0.27/0.62 thf(fact_313_translation__subtract__diff,axiom,
% 0.27/0.62 ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.27/0.62 @ ( minus_1686442501real_n @ S2 @ T ) )
% 0.27/0.62 = ( minus_1686442501real_n
% 0.27/0.62 @ ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.27/0.62 @ S2 )
% 0.27/0.62 @ ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.27/0.62 @ T ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % translation_subtract_diff
% 0.27/0.62 thf(fact_314_range__composition,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( image_439535603real_n
% 0.27/0.62 @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_to1292442332real_n )
% 0.27/0.62 = ( image_439535603real_n @ F @ ( image_439535603real_n @ G @ top_to1292442332real_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_315_range__composition,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,G: nat > finite1489363574real_n] :
% 0.27/0.62 ( ( image_183184717real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_top_set_nat )
% 0.27/0.62 = ( image_439535603real_n @ F @ ( image_183184717real_n @ G @ top_top_set_nat ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_316_range__composition,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,G: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_top_set_nat )
% 0.27/0.62 = ( image_1661509983real_n @ F @ ( image_1856576259real_n @ G @ top_top_set_nat ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_317_range__composition,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,G: nat > nat] :
% 0.27/0.62 ( ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_top_set_nat )
% 0.27/0.62 = ( image_1856576259real_n @ F @ ( image_nat_nat @ G @ top_top_set_nat ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_318_range__composition,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,G: nat > finite964658038_int_n] :
% 0.27/0.62 ( ( image_1856576259real_n
% 0.27/0.62 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_top_set_nat )
% 0.27/0.62 = ( image_355963305real_n @ F @ ( image_1961920973_int_n @ G @ top_top_set_nat ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_319_range__composition,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,G: finite964658038_int_n > finite1489363574real_n] :
% 0.27/0.62 ( ( image_2058828787real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_to131672412_int_n )
% 0.27/0.62 = ( image_439535603real_n @ F @ ( image_2058828787real_n @ G @ top_to131672412_int_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_320_range__composition,axiom,
% 0.27/0.62 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,G: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_to131672412_int_n )
% 0.27/0.62 = ( image_1661509983real_n @ F @ ( image_355963305real_n @ G @ top_to131672412_int_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_321_range__composition,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,G: finite964658038_int_n > nat] :
% 0.27/0.62 ( ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_to131672412_int_n )
% 0.27/0.62 = ( image_1856576259real_n @ F @ ( image_497739341_n_nat @ G @ top_to131672412_int_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_322_range__composition,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,G: finite964658038_int_n > finite964658038_int_n] :
% 0.27/0.62 ( ( image_355963305real_n
% 0.27/0.62 @ ^ [X: finite964658038_int_n] : ( F @ ( G @ X ) )
% 0.27/0.62 @ top_to131672412_int_n )
% 0.27/0.62 = ( image_355963305real_n @ F @ ( image_1278151539_int_n @ G @ top_to131672412_int_n ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % range_composition
% 0.27/0.62 thf(fact_323_rangeE,axiom,
% 0.27/0.62 ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ top_to1292442332real_n ) )
% 0.27/0.62 => ~ ! [X2: finite1489363574real_n] :
% 0.27/0.62 ( B
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeE
% 0.27/0.62 thf(fact_324_rangeE,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: nat > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( image_1856576259real_n @ F @ top_top_set_nat ) )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( B
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeE
% 0.27/0.62 thf(fact_325_rangeE,axiom,
% 0.27/0.62 ! [B: $o,F: nat > $o] :
% 0.27/0.62 ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( B
% 0.27/0.62 = ( ~ ( F @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeE
% 0.27/0.62 thf(fact_326_rangeE,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,F: finite964658038_int_n > set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( image_355963305real_n @ F @ top_to131672412_int_n ) )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( B
% 0.27/0.62 != ( F @ X2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeE
% 0.27/0.62 thf(fact_327_rangeE,axiom,
% 0.27/0.62 ! [B: $o,F: finite964658038_int_n > $o] :
% 0.27/0.62 ( ( member_o @ B @ ( image_216309723nt_n_o @ F @ top_to131672412_int_n ) )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( B
% 0.27/0.62 = ( ~ ( F @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rangeE
% 0.27/0.62 thf(fact_328_SUP__commute,axiom,
% 0.27/0.62 ! [F: nat > nat > set_Fi1058188332real_n,B2: set_nat,A3: set_nat] :
% 0.27/0.62 ( ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [I4: nat] : ( comple825005695real_n @ ( image_1856576259real_n @ ( F @ I4 ) @ B2 ) )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [J: nat] :
% 0.27/0.62 ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [I4: nat] : ( F @ I4 @ J )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_commute
% 0.27/0.62 thf(fact_329_SUP__commute,axiom,
% 0.27/0.62 ! [F: nat > finite964658038_int_n > set_Fi1058188332real_n,B2: set_Fi160064172_int_n,A3: set_nat] :
% 0.27/0.62 ( ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [I4: nat] : ( comple825005695real_n @ ( image_355963305real_n @ ( F @ I4 ) @ B2 ) )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [J: finite964658038_int_n] :
% 0.27/0.62 ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [I4: nat] : ( F @ I4 @ J )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_commute
% 0.27/0.62 thf(fact_330_SUP__commute,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > nat > set_Fi1058188332real_n,B2: set_nat,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [I4: finite964658038_int_n] : ( comple825005695real_n @ ( image_1856576259real_n @ ( F @ I4 ) @ B2 ) )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [J: nat] :
% 0.27/0.62 ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [I4: finite964658038_int_n] : ( F @ I4 @ J )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_commute
% 0.27/0.62 thf(fact_331_SUP__commute,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > finite964658038_int_n > set_Fi1058188332real_n,B2: set_Fi160064172_int_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [I4: finite964658038_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ ( F @ I4 ) @ B2 ) )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [J: finite964658038_int_n] :
% 0.27/0.62 ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [I4: finite964658038_int_n] : ( F @ I4 @ J )
% 0.27/0.62 @ A3 ) )
% 0.27/0.62 @ B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SUP_commute
% 0.27/0.62 thf(fact_332_image__Union,axiom,
% 0.27/0.62 ! [F: nat > set_Fi1058188332real_n,S: set_set_nat] :
% 0.27/0.62 ( ( image_1856576259real_n @ F @ ( comple1682161881et_nat @ S ) )
% 0.27/0.62 = ( comple1917283637real_n @ ( image_1587769199real_n @ ( image_1856576259real_n @ F ) @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_Union
% 0.27/0.62 thf(fact_333_image__Union,axiom,
% 0.27/0.62 ! [F: finite964658038_int_n > set_Fi1058188332real_n,S: set_se944069346_int_n] :
% 0.27/0.62 ( ( image_355963305real_n @ F @ ( comple970917503_int_n @ S ) )
% 0.27/0.62 = ( comple1917283637real_n @ ( image_1054146965real_n @ ( image_355963305real_n @ F ) @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_Union
% 0.27/0.62 thf(fact_334_image__Union,axiom,
% 0.27/0.62 ! [F: finite1489363574real_n > finite1489363574real_n,S: set_se2111327970real_n] :
% 0.27/0.62 ( ( image_439535603real_n @ F @ ( comple825005695real_n @ S ) )
% 0.27/0.62 = ( comple825005695real_n @ ( image_1661509983real_n @ ( image_439535603real_n @ F ) @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_Union
% 0.27/0.62 thf(fact_335_UN__UN__flatten,axiom,
% 0.27/0.62 ! [C2: nat > set_Fi1058188332real_n,B2: nat > set_nat,A3: set_nat] :
% 0.27/0.62 ( ( comple825005695real_n @ ( image_1856576259real_n @ C2 @ ( comple1682161881et_nat @ ( image_nat_set_nat @ B2 @ A3 ) ) ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [Y2: nat] : ( comple825005695real_n @ ( image_1856576259real_n @ C2 @ ( B2 @ Y2 ) ) )
% 0.27/0.62 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_UN_flatten
% 0.27/0.62 thf(fact_336_UN__UN__flatten,axiom,
% 0.27/0.62 ! [C2: nat > set_Fi1058188332real_n,B2: finite964658038_int_n > set_nat,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( comple825005695real_n @ ( image_1856576259real_n @ C2 @ ( comple1682161881et_nat @ ( image_1085873667et_nat @ B2 @ A3 ) ) ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [Y2: finite964658038_int_n] : ( comple825005695real_n @ ( image_1856576259real_n @ C2 @ ( B2 @ Y2 ) ) )
% 0.27/0.62 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_UN_flatten
% 0.27/0.62 thf(fact_337_UN__UN__flatten,axiom,
% 0.27/0.62 ! [C2: finite964658038_int_n > set_Fi1058188332real_n,B2: nat > set_Fi160064172_int_n,A3: set_nat] :
% 0.27/0.62 ( ( comple825005695real_n @ ( image_355963305real_n @ C2 @ ( comple970917503_int_n @ ( image_968789251_int_n @ B2 @ A3 ) ) ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [Y2: nat] : ( comple825005695real_n @ ( image_355963305real_n @ C2 @ ( B2 @ Y2 ) ) )
% 0.27/0.62 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_UN_flatten
% 0.27/0.62 thf(fact_338_UN__UN__flatten,axiom,
% 0.27/0.62 ! [C2: finite964658038_int_n > set_Fi1058188332real_n,B2: finite964658038_int_n > set_Fi160064172_int_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( comple825005695real_n @ ( image_355963305real_n @ C2 @ ( comple970917503_int_n @ ( image_1819506345_int_n @ B2 @ A3 ) ) ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [Y2: finite964658038_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ C2 @ ( B2 @ Y2 ) ) )
% 0.27/0.62 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_UN_flatten
% 0.27/0.62 thf(fact_339_UN__UN__flatten,axiom,
% 0.27/0.62 ! [C2: finite1489363574real_n > set_Fi1058188332real_n,B2: nat > set_Fi1058188332real_n,A3: set_nat] :
% 0.27/0.62 ( ( comple825005695real_n @ ( image_545463721real_n @ C2 @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_1856576259real_n
% 0.27/0.62 @ ^ [Y2: nat] : ( comple825005695real_n @ ( image_545463721real_n @ C2 @ ( B2 @ Y2 ) ) )
% 0.27/0.62 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_UN_flatten
% 0.27/0.62 thf(fact_340_UN__UN__flatten,axiom,
% 0.27/0.62 ! [C2: finite1489363574real_n > set_Fi1058188332real_n,B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( comple825005695real_n @ ( image_545463721real_n @ C2 @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) ) )
% 0.27/0.62 = ( comple825005695real_n
% 0.27/0.62 @ ( image_355963305real_n
% 0.27/0.62 @ ^ [Y2: finite964658038_int_n] : ( comple825005695real_n @ ( image_545463721real_n @ C2 @ ( B2 @ Y2 ) ) )
% 0.27/0.62 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_UN_flatten
% 0.27/0.62 thf(fact_341_UN__E,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,B2: set_Fi1058188332real_n > set_se2111327970real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( comple1917283637real_n @ ( image_797440021real_n @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X2 @ A3 )
% 0.27/0.62 => ~ ( member223413699real_n @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_E
% 0.27/0.62 thf(fact_342_UN__E,axiom,
% 0.27/0.62 ! [B: set_Fi1058188332real_n,B2: $o > set_se2111327970real_n,A3: set_o] :
% 0.27/0.62 ( ( member223413699real_n @ B @ ( comple1917283637real_n @ ( image_452144437real_n @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: $o] :
% 0.27/0.62 ( ( member_o @ X2 @ A3 )
% 0.27/0.62 => ~ ( member223413699real_n @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_E
% 0.27/0.62 thf(fact_343_UN__E,axiom,
% 0.27/0.62 ! [B: $o,B2: set_Fi1058188332real_n > set_o,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member_o @ B @ ( comple1665300069_set_o @ ( image_1687589765_set_o @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: set_Fi1058188332real_n] :
% 0.27/0.62 ( ( member223413699real_n @ X2 @ A3 )
% 0.27/0.62 => ~ ( member_o @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_E
% 0.27/0.62 thf(fact_344_UN__E,axiom,
% 0.27/0.62 ! [B: $o,B2: $o > set_o,A3: set_o] :
% 0.27/0.62 ( ( member_o @ B @ ( comple1665300069_set_o @ ( image_o_set_o @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: $o] :
% 0.27/0.62 ( ( member_o @ X2 @ A3 )
% 0.27/0.62 => ~ ( member_o @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_E
% 0.27/0.62 thf(fact_345_UN__E,axiom,
% 0.27/0.62 ! [B: finite1489363574real_n,B2: nat > set_Fi1058188332real_n,A3: set_nat] :
% 0.27/0.62 ( ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: nat] :
% 0.27/0.62 ( ( member_nat @ X2 @ A3 )
% 0.27/0.62 => ~ ( member1352538125real_n @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_E
% 0.27/0.62 thf(fact_346_UN__E,axiom,
% 0.27/0.62 ! [B: finite1489363574real_n,B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_Fi160064172_int_n] :
% 0.27/0.62 ( ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_355963305real_n @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: finite964658038_int_n] :
% 0.27/0.62 ( ( member27055245_int_n @ X2 @ A3 )
% 0.27/0.62 => ~ ( member1352538125real_n @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % UN_E
% 0.27/0.62 thf(fact_347_UN__E,axiom,
% 0.27/0.62 ! [B: finite1489363574real_n,B2: set_Fi1058188332real_n > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.62 ( ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1661509983real_n @ B2 @ A3 ) ) )
% 0.27/0.62 => ~ ! [X2: set_Fi1058188332real_n] :
% 0.27/0.71 ( ( member223413699real_n @ X2 @ A3 )
% 0.27/0.71 => ~ ( member1352538125real_n @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % UN_E
% 0.27/0.71 thf(fact_348_UN__E,axiom,
% 0.27/0.71 ! [B: finite1489363574real_n,B2: $o > set_Fi1058188332real_n,A3: set_o] :
% 0.27/0.71 ( ( member1352538125real_n @ B @ ( comple825005695real_n @ ( image_1759008383real_n @ B2 @ A3 ) ) )
% 0.27/0.71 => ~ ! [X2: $o] :
% 0.27/0.71 ( ( member_o @ X2 @ A3 )
% 0.27/0.71 => ~ ( member1352538125real_n @ B @ ( B2 @ X2 ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % UN_E
% 0.27/0.71 thf(fact_349_UN__extend__simps_I8_J,axiom,
% 0.27/0.71 ! [B2: nat > set_Fi1058188332real_n,A3: set_set_nat] :
% 0.27/0.71 ( ( comple825005695real_n
% 0.27/0.71 @ ( image_933134521real_n
% 0.27/0.71 @ ^ [Y2: set_nat] : ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ Y2 ) )
% 0.27/0.71 @ A3 ) )
% 0.27/0.71 = ( comple825005695real_n @ ( image_1856576259real_n @ B2 @ ( comple1682161881et_nat @ A3 ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % UN_extend_simps(8)
% 0.27/0.71 thf(fact_350_UN__extend__simps_I8_J,axiom,
% 0.27/0.71 ! [B2: finite964658038_int_n > set_Fi1058188332real_n,A3: set_se944069346_int_n] :
% 0.27/0.71 ( ( comple825005695real_n
% 0.27/0.71 @ ( image_792439519real_n
% 0.27/0.71 @ ^ [Y2: set_Fi160064172_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ B2 @ Y2 ) )
% 0.27/0.71 @ A3 ) )
% 0.27/0.71 = ( comple825005695real_n @ ( image_355963305real_n @ B2 @ ( comple970917503_int_n @ A3 ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % UN_extend_simps(8)
% 0.27/0.71 thf(fact_351_UN__extend__simps_I8_J,axiom,
% 0.27/0.71 ! [B2: finite1489363574real_n > set_Fi1058188332real_n,A3: set_se2111327970real_n] :
% 0.27/0.71 ( ( comple825005695real_n
% 0.27/0.71 @ ( image_1661509983real_n
% 0.27/0.71 @ ^ [Y2: set_Fi1058188332real_n] : ( comple825005695real_n @ ( image_545463721real_n @ B2 @ Y2 ) )
% 0.27/0.71 @ A3 ) )
% 0.27/0.71 = ( comple825005695real_n @ ( image_545463721real_n @ B2 @ ( comple825005695real_n @ A3 ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % UN_extend_simps(8)
% 0.27/0.71 thf(fact_352_Sup__bool__def,axiom,
% 0.27/0.71 ( complete_Sup_Sup_o
% 0.27/0.71 = ( member_o @ $true ) ) ).
% 0.27/0.71
% 0.27/0.71 % Sup_bool_def
% 0.27/0.71
% 0.27/0.71 % Conjectures (1)
% 0.27/0.71 thf(conj_0,conjecture,
% 0.27/0.71 ( ( ^ [N: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ N ) ) ) )
% 0.27/0.71 = ( ^ [N: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ N ) ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 %------------------------------------------------------------------------------
% 0.27/0.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.LoqAwcRKjZ/cvc5---1.0.5_23224.p...
% 0.27/0.71 (declare-sort $$unsorted 0)
% 0.27/0.71 (declare-sort tptp.sigma_1422848389real_n 0)
% 0.27/0.71 (declare-sort tptp.set_Si1125517487real_n 0)
% 0.27/0.71 (declare-sort tptp.set_se820660888real_n 0)
% 0.27/0.71 (declare-sort tptp.sigma_1466784463real_n 0)
% 0.27/0.71 (declare-sort tptp.set_se2111327970real_n 0)
% 0.27/0.71 (declare-sort tptp.set_se944069346_int_n 0)
% 0.27/0.71 (declare-sort tptp.set_Fi1058188332real_n 0)
% 0.27/0.71 (declare-sort tptp.set_Fi160064172_int_n 0)
% 0.27/0.71 (declare-sort tptp.finite1489363574real_n 0)
% 0.27/0.71 (declare-sort tptp.finite964658038_int_n 0)
% 0.27/0.71 (declare-sort tptp.set_Ex113815278nnreal 0)
% 0.27/0.71 (declare-sort tptp.set_set_nat 0)
% 0.27/0.71 (declare-sort tptp.extend1728876344nnreal 0)
% 0.27/0.71 (declare-sort tptp.sigma_measure_o 0)
% 0.27/0.71 (declare-sort tptp.set_set_o 0)
% 0.27/0.71 (declare-sort tptp.set_nat 0)
% 0.27/0.71 (declare-sort tptp.set_o 0)
% 0.27/0.71 (declare-sort tptp.nat 0)
% 0.27/0.71 (declare-fun tptp.complete_Sup_Sup_o (tptp.set_o) Bool)
% 0.27/0.71 (declare-fun tptp.comple1413366923nnreal (tptp.set_Ex113815278nnreal) tptp.extend1728876344nnreal)
% 0.27/0.71 (declare-fun tptp.comple2042271945real_n (tptp.set_Fi1058188332real_n) tptp.finite1489363574real_n)
% 0.27/0.71 (declare-fun tptp.comple1665300069_set_o (tptp.set_set_o) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.comple970917503_int_n (tptp.set_se944069346_int_n) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.comple825005695real_n (tptp.set_se2111327970real_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.comple1682161881et_nat (tptp.set_set_nat) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.comple1917283637real_n (tptp.set_se820660888real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.comple488165692real_n (tptp.set_Si1125517487real_n) tptp.sigma_1466784463real_n)
% 0.27/0.71 (declare-fun tptp.comple230862828real_n (tptp.sigma_1466784463real_n) tptp.sigma_1466784463real_n)
% 0.27/0.71 (declare-fun tptp.counta1142393929_int_n (tptp.set_Fi160064172_int_n tptp.nat) tptp.finite964658038_int_n)
% 0.27/0.71 (declare-fun tptp.minus_1196255695_int_n (tptp.finite964658038_int_n tptp.finite964658038_int_n) tptp.finite964658038_int_n)
% 0.27/0.71 (declare-fun tptp.minus_1037315151real_n (tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)
% 0.27/0.71 (declare-fun tptp.minus_1686442501real_n (tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.one_on705384445nnreal () tptp.extend1728876344nnreal)
% 0.27/0.71 (declare-fun tptp.one_on1253059131real_n () tptp.finite1489363574real_n)
% 0.27/0.71 (declare-fun tptp.plus_p1763960001nnreal (tptp.extend1728876344nnreal tptp.extend1728876344nnreal) tptp.extend1728876344nnreal)
% 0.27/0.71 (declare-fun tptp.plus_p1654784127_int_n (tptp.finite964658038_int_n tptp.finite964658038_int_n) tptp.finite964658038_int_n)
% 0.27/0.71 (declare-fun tptp.plus_p585657087real_n (tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)
% 0.27/0.71 (declare-fun tptp.zero_z1963244097nnreal () tptp.extend1728876344nnreal)
% 0.27/0.71 (declare-fun tptp.zero_z200130687real_n () tptp.finite1489363574real_n)
% 0.27/0.71 (declare-fun tptp.inf_inf_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.inf_in1108485182_int_n (tptp.set_Fi160064172_int_n tptp.set_Fi160064172_int_n) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.inf_in1974387902real_n (tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.inf_in632889204real_n (tptp.set_se2111327970real_n tptp.set_se2111327970real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.lebesg260170249real_n () tptp.sigma_1466784463real_n)
% 0.27/0.71 (declare-fun tptp.measure_null_sets_o (tptp.sigma_measure_o) tptp.set_set_o)
% 0.27/0.71 (declare-fun tptp.measur1402256771real_n (tptp.sigma_1466784463real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.measur2126959417real_n (tptp.sigma_1422848389real_n) tptp.set_se820660888real_n)
% 0.27/0.71 (declare-fun tptp.minkow1134813771n_real (tptp.finite964658038_int_n) tptp.finite1489363574real_n)
% 0.27/0.71 (declare-fun tptp.ord_le2133614988nnreal (tptp.extend1728876344nnreal tptp.extend1728876344nnreal) Bool)
% 0.27/0.71 (declare-fun tptp.top_to287930409nt_n_o (tptp.finite964658038_int_n) Bool)
% 0.27/0.71 (declare-fun tptp.top_top_nat_o (tptp.nat) Bool)
% 0.27/0.71 (declare-fun tptp.top_top_o () Bool)
% 0.27/0.71 (declare-fun tptp.top_to1845833192nnreal () tptp.extend1728876344nnreal)
% 0.27/0.71 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 0.27/0.71 (declare-fun tptp.top_to131672412_int_n () tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.top_to1292442332real_n () tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.top_to1587634578_int_n () tptp.set_se944069346_int_n)
% 0.27/0.71 (declare-fun tptp.top_to20708754real_n () tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.top_top_set_set_nat () tptp.set_set_nat)
% 0.27/0.71 (declare-fun tptp.sums_E1192373732nnreal ((-> tptp.nat tptp.extend1728876344nnreal) tptp.extend1728876344nnreal) Bool)
% 0.27/0.71 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.collec1941932235_int_n ((-> tptp.finite964658038_int_n Bool)) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.collec321817931real_n ((-> tptp.finite1489363574real_n Bool)) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.collec452821761real_n ((-> tptp.set_Fi1058188332real_n Bool)) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_o_o ((-> Bool Bool) tptp.set_o) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.image_o_set_o ((-> Bool tptp.set_o) tptp.set_o) tptp.set_set_o)
% 0.27/0.71 (declare-fun tptp.image_1759008383real_n ((-> Bool tptp.set_Fi1058188332real_n) tptp.set_o) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_452144437real_n ((-> Bool tptp.set_se2111327970real_n) tptp.set_o) tptp.set_se820660888real_n)
% 0.27/0.71 (declare-fun tptp.image_1599934780real_n ((-> Bool tptp.sigma_1466784463real_n) tptp.set_o) tptp.set_Si1125517487real_n)
% 0.27/0.71 (declare-fun tptp.image_2066995319nnreal ((-> tptp.extend1728876344nnreal tptp.extend1728876344nnreal) tptp.set_Ex113815278nnreal) tptp.set_Ex113815278nnreal)
% 0.27/0.71 (declare-fun tptp.image_216309723nt_n_o ((-> tptp.finite964658038_int_n Bool) tptp.set_Fi160064172_int_n) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.image_1278151539_int_n ((-> tptp.finite964658038_int_n tptp.finite964658038_int_n) tptp.set_Fi160064172_int_n) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.image_2058828787real_n ((-> tptp.finite964658038_int_n tptp.finite1489363574real_n) tptp.set_Fi160064172_int_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.image_497739341_n_nat ((-> tptp.finite964658038_int_n tptp.nat) tptp.set_Fi160064172_int_n) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.image_1819506345_int_n ((-> tptp.finite964658038_int_n tptp.set_Fi160064172_int_n) tptp.set_Fi160064172_int_n) tptp.set_se944069346_int_n)
% 0.27/0.71 (declare-fun tptp.image_355963305real_n ((-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n) tptp.set_Fi160064172_int_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_1085873667et_nat ((-> tptp.finite964658038_int_n tptp.set_nat) tptp.set_Fi160064172_int_n) tptp.set_set_nat)
% 0.27/0.71 (declare-fun tptp.image_439535603real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.image_545463721real_n ((-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_nat_o ((-> tptp.nat Bool) tptp.set_nat) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.image_1961920973_int_n ((-> tptp.nat tptp.finite964658038_int_n) tptp.set_nat) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.image_183184717real_n ((-> tptp.nat tptp.finite1489363574real_n) tptp.set_nat) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.image_968789251_int_n ((-> tptp.nat tptp.set_Fi160064172_int_n) tptp.set_nat) tptp.set_se944069346_int_n)
% 0.27/0.71 (declare-fun tptp.image_1856576259real_n ((-> tptp.nat tptp.set_Fi1058188332real_n) tptp.set_nat) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 0.27/0.71 (declare-fun tptp.image_set_o_o ((-> tptp.set_o Bool) tptp.set_set_o) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.image_792439519real_n ((-> tptp.set_Fi160064172_int_n tptp.set_Fi1058188332real_n) tptp.set_se944069346_int_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_1054146965real_n ((-> tptp.set_Fi160064172_int_n tptp.set_se2111327970real_n) tptp.set_se944069346_int_n) tptp.set_se820660888real_n)
% 0.27/0.71 (declare-fun tptp.image_1648361637al_n_o ((-> tptp.set_Fi1058188332real_n Bool) tptp.set_se2111327970real_n) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.image_1687589765_set_o ((-> tptp.set_Fi1058188332real_n tptp.set_o) tptp.set_se2111327970real_n) tptp.set_set_o)
% 0.27/0.71 (declare-fun tptp.image_1661509983real_n ((-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_797440021real_n ((-> tptp.set_Fi1058188332real_n tptp.set_se2111327970real_n) tptp.set_se2111327970real_n) tptp.set_se820660888real_n)
% 0.27/0.71 (declare-fun tptp.image_987430492real_n ((-> tptp.set_Fi1058188332real_n tptp.sigma_1466784463real_n) tptp.set_se2111327970real_n) tptp.set_Si1125517487real_n)
% 0.27/0.71 (declare-fun tptp.image_933134521real_n ((-> tptp.set_nat tptp.set_Fi1058188332real_n) tptp.set_set_nat) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.image_1587769199real_n ((-> tptp.set_nat tptp.set_se2111327970real_n) tptp.set_set_nat) tptp.set_se820660888real_n)
% 0.27/0.71 (declare-fun tptp.image_1681970287al_n_o ((-> tptp.set_se2111327970real_n Bool) tptp.set_se820660888real_n) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.image_1298280374real_n ((-> tptp.sigma_1466784463real_n tptp.set_Fi1058188332real_n) tptp.set_Si1125517487real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.vimage_o_o ((-> Bool Bool) tptp.set_o) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.vimage961837641real_n ((-> Bool tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.vimage1122713129_int_n ((-> tptp.finite964658038_int_n tptp.finite964658038_int_n) tptp.set_Fi160064172_int_n) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.vimage1276736425real_n ((-> tptp.finite964658038_int_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.vimage1398021123_n_nat ((-> tptp.finite964658038_int_n tptp.nat) tptp.set_nat) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.vimage464515423real_n ((-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_Fi160064172_int_n)
% 0.27/0.71 (declare-fun tptp.vimage1233683625real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.vimage714719107_int_n ((-> tptp.nat tptp.finite964658038_int_n) tptp.set_Fi160064172_int_n) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.vimage1860757507real_n ((-> tptp.nat tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.vimage3210681real_n ((-> tptp.nat tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_nat)
% 0.27/0.71 (declare-fun tptp.vimage851190895al_n_o ((-> tptp.set_Fi1058188332real_n Bool) tptp.set_o) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.vimage784510485real_n ((-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.sigma_1536574303real_n (tptp.sigma_1466784463real_n tptp.set_Fi1058188332real_n) tptp.extend1728876344nnreal)
% 0.27/0.71 (declare-fun tptp.sigma_1235138647real_n (tptp.sigma_1466784463real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.sigma_space_o (tptp.sigma_measure_o) tptp.set_o)
% 0.27/0.71 (declare-fun tptp.sigma_476185326real_n (tptp.sigma_1466784463real_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.sigma_607186084real_n (tptp.sigma_1422848389real_n) tptp.set_se2111327970real_n)
% 0.27/0.71 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 0.27/0.71 (declare-fun tptp.member1217042383nnreal (tptp.extend1728876344nnreal tptp.set_Ex113815278nnreal) Bool)
% 0.27/0.71 (declare-fun tptp.member27055245_int_n (tptp.finite964658038_int_n tptp.set_Fi160064172_int_n) Bool)
% 0.27/0.71 (declare-fun tptp.member1352538125real_n (tptp.finite1489363574real_n tptp.set_Fi1058188332real_n) Bool)
% 0.27/0.71 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.27/0.71 (declare-fun tptp.member_set_o (tptp.set_o tptp.set_set_o) Bool)
% 0.27/0.71 (declare-fun tptp.member223413699real_n (tptp.set_Fi1058188332real_n tptp.set_se2111327970real_n) Bool)
% 0.27/0.71 (declare-fun tptp.member1475136633real_n (tptp.set_se2111327970real_n tptp.set_se820660888real_n) Bool)
% 0.27/0.71 (declare-fun tptp.member1000184real_n (tptp.sigma_1466784463real_n tptp.set_Si1125517487real_n) Bool)
% 0.27/0.71 (declare-fun tptp.r (tptp.finite964658038_int_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.s () tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.t (tptp.finite964658038_int_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.t2 (tptp.finite964658038_int_n) tptp.set_Fi1058188332real_n)
% 0.27/0.71 (declare-fun tptp.f (tptp.nat) tptp.finite964658038_int_n)
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (let ((_let_1 (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))) (= (@ _let_1 (@ tptp.t A)) (@ _let_1 (@ tptp.t2 A))))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ tptp.t A)) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ tptp.t2 A)) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))))
% 0.27/0.71 (assert (@ (@ tptp.sums_E1192373732nnreal (lambda ((N tptp.nat)) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) (@ tptp.t2 (@ tptp.f N))))) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) tptp.s)))
% 0.27/0.71 (assert (@ (@ tptp.member223413699real_n tptp.s) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n) (B tptp.finite964658038_int_n)) (=> (not (= A B)) (= (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) (@ (@ tptp.inf_in1974387902real_n (@ tptp.t2 A)) (@ tptp.t2 B))) tptp.zero_z1963244097nnreal))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n) (B tptp.finite964658038_int_n)) (=> (not (= A B)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ tptp.t2 A)) (@ tptp.t2 B))) (@ tptp.measur1402256771real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))))))
% 0.27/0.71 (assert (@ (@ tptp.ord_le2133614988nnreal tptp.one_on705384445nnreal) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) tptp.s)))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ tptp.r A)) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))))
% 0.27/0.71 (assert (@ (@ tptp.sums_E1192373732nnreal (lambda ((N tptp.nat)) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) (@ tptp.t2 (@ tptp.f N))))) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((N tptp.nat)) (@ tptp.t2 (@ tptp.f N)))) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (= tptp.t (lambda ((A2 tptp.finite964658038_int_n)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) (@ tptp.minkow1134813771n_real A2)))) (@ tptp.t2 A2)))))
% 0.27/0.71 (assert (= tptp.f (@ tptp.counta1142393929_int_n tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (= (@ tptp.t A) (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n X) (@ tptp.minkow1134813771n_real A)))) (@ tptp.t2 A)))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n) (B tptp.finite964658038_int_n)) (= (= (@ tptp.minkow1134813771n_real A) (@ tptp.minkow1134813771n_real B)) (= A B))))
% 0.27/0.71 (assert (= tptp.t2 (lambda ((A2 tptp.finite964658038_int_n)) (@ (@ tptp.inf_in1974387902real_n tptp.s) (@ tptp.r A2)))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n) (B tptp.finite964658038_int_n)) (=> (not (= A B)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ tptp.r A)) (@ tptp.r B))) (@ tptp.measur1402256771real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (M tptp.sigma_1466784463real_n)) (=> (forall ((X2 tptp.nat)) (@ (@ tptp.member223413699real_n (@ B2 X2)) (@ tptp.sigma_1235138647real_n M))) (=> (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (= (@ (@ tptp.sigma_1536574303real_n M) (@ (@ tptp.inf_in1974387902real_n (@ B2 X2)) (@ B2 Y))) tptp.zero_z1963244097nnreal))) (@ (@ tptp.sums_E1192373732nnreal (lambda ((X tptp.nat)) (@ (@ tptp.sigma_1536574303real_n M) (@ B2 X)))) (@ (@ tptp.sigma_1536574303real_n M) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) tptp.top_top_set_nat))))))))
% 0.27/0.71 (assert (forall ((N2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (M tptp.sigma_1466784463real_n)) (=> (forall ((I tptp.nat)) (@ (@ tptp.member223413699real_n (@ N2 I)) (@ tptp.measur1402256771real_n M))) (@ (@ tptp.member223413699real_n (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n N2) tptp.top_top_set_nat))) (@ tptp.measur1402256771real_n M)))))
% 0.27/0.71 (assert (forall ((N2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (M tptp.sigma_1466784463real_n)) (=> (forall ((I tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ N2 I)) (@ tptp.measur1402256771real_n M))) (@ (@ tptp.member223413699real_n (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n N2) tptp.top_to131672412_int_n))) (@ tptp.measur1402256771real_n M)))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_1466784463real_n) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n A3))) (=> (= (@ (@ tptp.sigma_1536574303real_n M) A3) tptp.zero_z1963244097nnreal) (=> (@ _let_1 (@ tptp.sigma_1235138647real_n M)) (@ _let_1 (@ tptp.measur1402256771real_n M)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_439535603real_n F))) (= (@ _let_1 (@ (@ tptp.vimage1233683625real_n F) A3)) (@ (@ tptp.inf_in1974387902real_n A3) (@ _let_1 tptp.top_to1292442332real_n))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.image_1856576259real_n F))) (= (@ _let_1 (@ (@ tptp.vimage3210681real_n F) A3)) (@ (@ tptp.inf_in632889204real_n A3) (@ _let_1 tptp.top_top_set_nat))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_183184717real_n F))) (= (@ _let_1 (@ (@ tptp.vimage1860757507real_n F) A3)) (@ (@ tptp.inf_in1974387902real_n A3) (@ _let_1 tptp.top_top_set_nat))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.image_355963305real_n F))) (= (@ _let_1 (@ (@ tptp.vimage464515423real_n F) A3)) (@ (@ tptp.inf_in632889204real_n A3) (@ _let_1 tptp.top_to131672412_int_n))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_2058828787real_n F))) (= (@ _let_1 (@ (@ tptp.vimage1276736425real_n F) A3)) (@ (@ tptp.inf_in1974387902real_n A3) (@ _let_1 tptp.top_to131672412_int_n))))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (let ((_let_1 (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))) (let ((_let_2 (@ tptp.sigma_1235138647real_n _let_1))) (let ((_let_3 (@ tptp.t2 A))) (=> (@ (@ tptp.member223413699real_n _let_3) _let_2) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n X) (@ tptp.minkow1134813771n_real A)))) _let_3)) (@ tptp.sigma_476185326real_n _let_1))) _let_2)))))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (= (@ (@ tptp.image_1278151539_int_n (lambda ((X tptp.finite964658038_int_n)) (@ (@ tptp.minus_1196255695_int_n X) A))) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n)))
% 0.27/0.71 (assert (= (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n tptp.t2) tptp.top_to131672412_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((N tptp.nat)) (@ tptp.t2 (@ tptp.f N)))) tptp.top_top_set_nat))))
% 0.27/0.71 (assert (= (@ tptp.comple1682161881et_nat tptp.top_top_set_set_nat) tptp.top_top_set_nat))
% 0.27/0.71 (assert (= (@ tptp.comple970917503_int_n tptp.top_to1587634578_int_n) tptp.top_to131672412_int_n))
% 0.27/0.71 (assert (= (@ tptp.comple825005695real_n tptp.top_to20708754real_n) tptp.top_to1292442332real_n))
% 0.27/0.71 (assert (= (@ tptp.complete_Sup_Sup_o tptp.top_top_set_o) tptp.top_top_o))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Ex113815278nnreal)) (= (= (@ tptp.comple1413366923nnreal A3) tptp.top_to1845833192nnreal) (forall ((X tptp.extend1728876344nnreal)) (=> (@ (@ tptp.ord_le2133614988nnreal X) tptp.top_to1845833192nnreal) (exists ((Y2 tptp.extend1728876344nnreal)) (and (@ (@ tptp.member1217042383nnreal Y2) A3) (@ (@ tptp.ord_le2133614988nnreal X) Y2))))))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n)))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n)) (= (@ (@ tptp.image_1278151539_int_n (@ tptp.plus_p1654784127_int_n A)) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (= (@ (@ tptp.minus_1037315151real_n tptp.one_on1253059131real_n) tptp.one_on1253059131real_n) tptp.zero_z200130687real_n))
% 0.27/0.71 (assert (forall ((B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X3 tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member1352538125real_n X3) A3) (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) A3))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.nat tptp.set_Fi1058188332real_n)) (X3 tptp.nat) (A3 tptp.set_nat)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1856576259real_n F) A3))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (X3 tptp.finite964658038_int_n) (A3 tptp.set_Fi160064172_int_n)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member27055245_int_n X3) A3) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_355963305real_n F) A3))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member223413699real_n X3) A3) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1661509983real_n F) A3))))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> tptp.set_Fi1058188332real_n Bool)) (X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member223413699real_n X3) A3) (@ (@ tptp.member_o B) (@ (@ tptp.image_1648361637al_n_o F) A3))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> Bool tptp.set_Fi1058188332real_n)) (X3 Bool) (A3 tptp.set_o)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1759008383real_n F) A3))))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> Bool Bool)) (X3 Bool) (A3 tptp.set_o)) (=> (= B (@ F X3)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o F) A3))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X3) tptp.top_to20708754real_n)))
% 0.27/0.71 (assert (forall ((X3 Bool)) (@ (@ tptp.member_o X3) tptp.top_top_set_o)))
% 0.27/0.71 (assert (forall ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) tptp.top_top_set_nat)))
% 0.27/0.71 (assert (forall ((X3 tptp.finite964658038_int_n)) (@ (@ tptp.member27055245_int_n X3) tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (forall ((C tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C))) (= (@ _let_1 (@ (@ tptp.inf_in632889204real_n A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((C tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((C tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in632889204real_n A3) B2)))))))
% 0.27/0.71 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)))))))
% 0.27/0.71 (assert (forall ((C tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (C2 tptp.set_se820660888real_n)) (= (@ (@ tptp.member223413699real_n A3) (@ tptp.comple1917283637real_n C2)) (exists ((X tptp.set_se2111327970real_n)) (and (@ (@ tptp.member1475136633real_n X) C2) (@ (@ tptp.member223413699real_n A3) X))))))
% 0.27/0.71 (assert (forall ((A3 Bool) (C2 tptp.set_set_o)) (= (@ (@ tptp.member_o A3) (@ tptp.comple1665300069_set_o C2)) (exists ((X tptp.set_o)) (and (@ (@ tptp.member_set_o X) C2) (@ (@ tptp.member_o A3) X))))))
% 0.27/0.71 (assert (forall ((A3 tptp.finite1489363574real_n) (C2 tptp.set_se2111327970real_n)) (= (@ (@ tptp.member1352538125real_n A3) (@ tptp.comple825005695real_n C2)) (exists ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) C2) (@ (@ tptp.member1352538125real_n A3) X))))))
% 0.27/0.71 (assert (forall ((X4 tptp.set_se2111327970real_n) (C2 tptp.set_se820660888real_n) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n A3))) (=> (@ (@ tptp.member1475136633real_n X4) C2) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.comple1917283637real_n C2)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.set_o) (C2 tptp.set_set_o) (A3 Bool)) (let ((_let_1 (@ tptp.member_o A3))) (=> (@ (@ tptp.member_set_o X4) C2) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.comple1665300069_set_o C2)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.set_Fi1058188332real_n) (C2 tptp.set_se2111327970real_n) (A3 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.member1352538125real_n A3))) (=> (@ (@ tptp.member223413699real_n X4) C2) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.comple825005695real_n C2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (forall ((X tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n A3)) (@ P X))) (forall ((X tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X) A3) (forall ((Y2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n Y2) X) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n A3)) (@ P X))) (exists ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) A3) (exists ((Y2 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n Y2) X) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.measur1402256771real_n M))) (=> (@ (@ tptp.member223413699real_n A) _let_1) (=> (@ (@ tptp.member223413699real_n B) _let_1) (@ (@ tptp.member223413699real_n (@ (@ tptp.minus_1686442501real_n A) B)) _let_1))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (= (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n Bool)) (B2 tptp.set_o)) (= (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage851190895al_n_o F) B2)) (@ (@ tptp.member_o (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A Bool) (F (-> Bool tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (= (@ (@ tptp.member_o A) (@ (@ tptp.vimage961837641real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A Bool) (F (-> Bool Bool)) (B2 tptp.set_o)) (= (@ (@ tptp.member_o A) (@ (@ tptp.vimage_o_o F) B2)) (@ (@ tptp.member_o (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) B2)) (@ (@ tptp.member1352538125real_n (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n) (B2 tptp.set_se2111327970real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member223413699real_n B) B2) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) B2))))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.set_Fi1058188332real_n)) (A Bool) (B tptp.set_Fi1058188332real_n) (B2 tptp.set_se2111327970real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member223413699real_n B) B2) (@ (@ tptp.member_o A) (@ (@ tptp.vimage961837641real_n F) B2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n Bool)) (A tptp.set_Fi1058188332real_n) (B Bool) (B2 tptp.set_o)) (=> (= (@ F A) B) (=> (@ (@ tptp.member_o B) B2) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage851190895al_n_o F) B2))))))
% 0.27/0.71 (assert (forall ((F (-> Bool Bool)) (A Bool) (B Bool) (B2 tptp.set_o)) (=> (= (@ F A) B) (=> (@ (@ tptp.member_o B) B2) (@ (@ tptp.member_o A) (@ (@ tptp.vimage_o_o F) B2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (B2 tptp.set_Fi1058188332real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member1352538125real_n B) B2) (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) B2))))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) X)) Y3) Y3)))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (P (-> tptp.finite1489363574real_n Bool))) (= (@ (@ tptp.vimage1233683625real_n F) (@ tptp.collec321817931real_n P)) (@ tptp.collec321817931real_n (lambda ((Y2 tptp.finite1489363574real_n)) (@ P (@ F Y2)))))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) X)) Y3) Y3)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (= (= (@ (@ tptp.inf_in1974387902real_n A3) B2) tptp.top_to1292442332real_n) (and (= A3 tptp.top_to1292442332real_n) (= B2 tptp.top_to1292442332real_n)))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.top_top_set_nat) (and (= A3 tptp.top_top_set_nat) (= B2 tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi160064172_int_n) (B2 tptp.set_Fi160064172_int_n)) (= (= (@ (@ tptp.inf_in1108485182_int_n A3) B2) tptp.top_to131672412_int_n) (and (= A3 tptp.top_to131672412_int_n) (= B2 tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.finite1489363574real_n Bool))) (= (forall ((X tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))) (@ P X))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A3) (forall ((Y2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.finite1489363574real_n Bool))) (= (forall ((X tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))) (@ P X))) (forall ((X tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X) A3) (forall ((Y2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ (@ tptp.member223413699real_n A) (@ tptp.collec452821761real_n P)) (@ P A))))
% 0.27/0.71 (assert (forall ((A Bool) (P (-> Bool Bool))) (= (@ (@ tptp.member_o A) (@ tptp.collect_o P)) (@ P A))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n)) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) A3))) A3)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_o)) (= (@ tptp.collect_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A3))) A3)))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.finite1489363574real_n Bool))) (= (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))) (@ P X))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (exists ((Y2 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.finite1489363574real_n Bool))) (= (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))) (@ P X))) (exists ((X tptp.finite964658038_int_n)) (and (@ (@ tptp.member27055245_int_n X) A3) (exists ((Y2 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.finite1489363574real_n Bool))) (= (forall ((X tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))) (@ P X))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A3) (forall ((Y2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.finite1489363574real_n Bool))) (= (forall ((X tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))) (@ P X))) (forall ((X tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X) A3) (forall ((Y2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.finite1489363574real_n Bool))) (= (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))) (@ P X))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (exists ((Y2 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.finite1489363574real_n Bool))) (= (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))) (@ P X))) (exists ((X tptp.finite964658038_int_n)) (and (@ (@ tptp.member27055245_int_n X) A3) (exists ((Y2 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n Y2) (@ B2 X)) (@ P Y2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (= (@ (@ tptp.vimage1233683625real_n F) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n)))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.vimage_nat_nat F) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.nat))) (= (@ (@ tptp.vimage1398021123_n_nat F) tptp.top_top_set_nat) tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.finite964658038_int_n))) (= (@ (@ tptp.vimage714719107_int_n F) tptp.top_to131672412_int_n) tptp.top_top_set_nat)))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.finite964658038_int_n))) (= (@ (@ tptp.vimage1122713129_int_n F) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.measur1402256771real_n M))) (=> (@ (@ tptp.member223413699real_n A) _let_1) (=> (@ (@ tptp.member223413699real_n B) _let_1) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n A) B)) _let_1))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.vimage1233683625real_n F))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) B2)) (@ (@ tptp.inf_in1974387902real_n (@ _let_1 A3)) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n)) (= (@ tptp.comple2042271945real_n (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) X)) A3)) (@ tptp.comple2042271945real_n A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n (lambda ((X tptp.set_Fi1058188332real_n)) X)) A3)) (@ tptp.comple825005695real_n A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_o)) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_o_o (lambda ((X Bool)) X)) A3)) (@ tptp.complete_Sup_Sup_o A3))))
% 0.27/0.71 (assert (forall ((B tptp.finite1489363574real_n) (B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat)) (= (@ (@ tptp.member1352538125real_n B) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member1352538125real_n B) (@ B2 X)))))))
% 0.27/0.71 (assert (forall ((B tptp.finite1489363574real_n) (B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.member1352538125real_n B) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))) (exists ((X tptp.finite964658038_int_n)) (and (@ (@ tptp.member27055245_int_n X) A3) (@ (@ tptp.member1352538125real_n B) (@ B2 X)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B tptp.set_Fi1058188332real_n) (B2 (-> tptp.set_Fi1058188332real_n tptp.set_se2111327970real_n))) (let ((_let_1 (@ tptp.member223413699real_n B))) (=> (@ (@ tptp.member223413699real_n A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple1917283637real_n (@ (@ tptp.image_797440021real_n B2) A3))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B Bool) (B2 (-> tptp.set_Fi1058188332real_n tptp.set_o))) (let ((_let_1 (@ tptp.member_o B))) (=> (@ (@ tptp.member223413699real_n A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple1665300069_set_o (@ (@ tptp.image_1687589765_set_o B2) A3))))))))
% 0.27/0.71 (assert (forall ((A Bool) (A3 tptp.set_o) (B tptp.set_Fi1058188332real_n) (B2 (-> Bool tptp.set_se2111327970real_n))) (let ((_let_1 (@ tptp.member223413699real_n B))) (=> (@ (@ tptp.member_o A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple1917283637real_n (@ (@ tptp.image_452144437real_n B2) A3))))))))
% 0.27/0.71 (assert (forall ((A Bool) (A3 tptp.set_o) (B Bool) (B2 (-> Bool tptp.set_o))) (let ((_let_1 (@ tptp.member_o B))) (=> (@ (@ tptp.member_o A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple1665300069_set_o (@ (@ tptp.image_o_set_o B2) A3))))))))
% 0.27/0.71 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B tptp.finite1489363574real_n) (B2 (-> tptp.nat tptp.set_Fi1058188332real_n))) (let ((_let_1 (@ tptp.member1352538125real_n B))) (=> (@ (@ tptp.member_nat A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))))))))
% 0.27/0.71 (assert (forall ((A tptp.finite964658038_int_n) (A3 tptp.set_Fi160064172_int_n) (B tptp.finite1489363574real_n) (B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (let ((_let_1 (@ tptp.member1352538125real_n B))) (=> (@ (@ tptp.member27055245_int_n A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B tptp.finite1489363574real_n) (B2 (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (let ((_let_1 (@ tptp.member1352538125real_n B))) (=> (@ (@ tptp.member223413699real_n A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n B2) A3))))))))
% 0.27/0.71 (assert (forall ((A Bool) (A3 tptp.set_o) (B tptp.finite1489363574real_n) (B2 (-> Bool tptp.set_Fi1058188332real_n))) (let ((_let_1 (@ tptp.member1352538125real_n B))) (=> (@ (@ tptp.member_o A) A3) (=> (@ _let_1 (@ B2 A)) (@ _let_1 (@ tptp.comple825005695real_n (@ (@ tptp.image_1759008383real_n B2) A3))))))))
% 0.27/0.71 (assert (= tptp.s (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n tptp.t2) tptp.top_to131672412_int_n))))
% 0.27/0.71 (assert (forall ((S tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n tptp.zero_z200130687real_n)) S) S)))
% 0.27/0.71 (assert (forall ((S tptp.set_Ex113815278nnreal)) (= (@ (@ tptp.image_2066995319nnreal (@ tptp.plus_p1763960001nnreal tptp.zero_z1963244097nnreal)) S) S)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n X3) (@ tptp.measur1402256771real_n M)) (= (@ (@ tptp.inf_in1974387902real_n X3) (@ tptp.sigma_476185326real_n M)) X3))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n X3) (@ tptp.measur1402256771real_n M)) (= (@ (@ tptp.inf_in1974387902real_n (@ tptp.sigma_476185326real_n M)) X3) X3))))
% 0.27/0.71 (assert (forall ((I2 tptp.set_Fi1058188332real_n) (I3 tptp.set_se2111327970real_n) (M (-> tptp.set_Fi1058188332real_n tptp.sigma_1466784463real_n)) (Y3 tptp.set_Fi1058188332real_n) (X4 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n X4))) (=> (@ (@ tptp.member223413699real_n I2) I3) (=> (forall ((I tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n I) I3) (= (@ tptp.sigma_476185326real_n (@ M I)) Y3))) (=> (@ _let_1 (@ tptp.sigma_1235138647real_n (@ M I2))) (@ _let_1 (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n (@ (@ tptp.image_987430492real_n M) I3))))))))))
% 0.27/0.71 (assert (forall ((I2 Bool) (I3 tptp.set_o) (M (-> Bool tptp.sigma_1466784463real_n)) (Y3 tptp.set_Fi1058188332real_n) (X4 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n X4))) (=> (@ (@ tptp.member_o I2) I3) (=> (forall ((I Bool)) (=> (@ (@ tptp.member_o I) I3) (= (@ tptp.sigma_476185326real_n (@ M I)) Y3))) (=> (@ _let_1 (@ tptp.sigma_1235138647real_n (@ M I2))) (@ _let_1 (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n (@ (@ tptp.image_1599934780real_n M) I3))))))))))
% 0.27/0.71 (assert (forall ((M tptp.set_Si1125517487real_n) (X4 tptp.set_Fi1058188332real_n) (M2 tptp.sigma_1466784463real_n) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n A3))) (=> (forall ((M3 tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member1000184real_n M3) M) (= (@ tptp.sigma_476185326real_n M3) X4))) (=> (@ (@ tptp.member1000184real_n M2) M) (=> (@ _let_1 (@ tptp.sigma_1235138647real_n M2)) (@ _let_1 (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n M)))))))))
% 0.27/0.71 (assert (forall ((I3 tptp.set_se2111327970real_n) (M (-> tptp.set_Fi1058188332real_n tptp.sigma_1466784463real_n)) (N2 (-> tptp.set_Fi1058188332real_n tptp.sigma_1466784463real_n))) (=> (forall ((I tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n I) I3) (= (@ tptp.sigma_1235138647real_n (@ M I)) (@ tptp.sigma_1235138647real_n (@ N2 I))))) (= (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n (@ (@ tptp.image_987430492real_n M) I3))) (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n (@ (@ tptp.image_987430492real_n N2) I3)))))))
% 0.27/0.71 (assert (forall ((I3 tptp.set_o) (M (-> Bool tptp.sigma_1466784463real_n)) (N2 (-> Bool tptp.sigma_1466784463real_n))) (=> (forall ((I Bool)) (=> (@ (@ tptp.member_o I) I3) (= (@ tptp.sigma_1235138647real_n (@ M I)) (@ tptp.sigma_1235138647real_n (@ N2 I))))) (= (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n (@ (@ tptp.image_1599934780real_n M) I3))) (@ tptp.sigma_1235138647real_n (@ tptp.comple488165692real_n (@ (@ tptp.image_1599934780real_n N2) I3)))))))
% 0.27/0.71 (assert (= tptp.comple1917283637real_n (lambda ((A4 tptp.set_se820660888real_n)) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_1681970287al_n_o (@ tptp.member223413699real_n X)) A4)))))))
% 0.27/0.71 (assert (= tptp.comple1665300069_set_o (lambda ((A4 tptp.set_set_o)) (@ tptp.collect_o (lambda ((X Bool)) (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_set_o_o (@ tptp.member_o X)) A4)))))))
% 0.27/0.71 (assert (= tptp.comple825005695real_n (lambda ((A4 tptp.set_se2111327970real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_1648361637al_n_o (@ tptp.member1352538125real_n X)) A4)))))))
% 0.27/0.71 (assert (forall ((M tptp.set_Si1125517487real_n)) (= (@ tptp.sigma_476185326real_n (@ tptp.comple488165692real_n M)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1298280374real_n tptp.sigma_476185326real_n) M)))))
% 0.27/0.71 (assert (= tptp.top_top_set_nat (@ tptp.collect_nat tptp.top_top_nat_o)))
% 0.27/0.71 (assert (= tptp.top_to131672412_int_n (@ tptp.collec1941932235_int_n tptp.top_to287930409nt_n_o)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.minus_1686442501real_n A3) B2)) C2) (@ (@ tptp.minus_1686442501real_n (@ (@ tptp.inf_in1974387902real_n A3) C2)) (@ (@ tptp.inf_in1974387902real_n B2) C2)))))
% 0.27/0.71 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n C2))) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n A3) B2)) (@ (@ tptp.minus_1686442501real_n (@ _let_1 A3)) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.minus_1686442501real_n A3))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.inf_in1974387902real_n A3) B2)))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.minus_1686442501real_n (@ (@ tptp.inf_in1974387902real_n A3) C2)))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n B2) C2)) (@ _let_1 B2)))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A3))) (= (@ (@ tptp.minus_1686442501real_n (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.minus_1686442501real_n B2) C2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.vimage1233683625real_n F))) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n A3) B2)) (@ (@ tptp.minus_1686442501real_n (@ _let_1 A3)) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool)) (Q (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.measur2126959417real_n M))) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (or (@ Q X) (@ P X)))))) _let_1))))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_measure_o) (P (-> Bool Bool)) (Q (-> Bool Bool))) (let ((_let_1 (@ tptp.measure_null_sets_o M))) (=> (@ (@ tptp.member_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.sigma_space_o M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.sigma_space_o M)) (@ Q X))))) _let_1) (@ (@ tptp.member_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.sigma_space_o M)) (or (@ Q X) (@ P X)))))) _let_1))))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.measur1402256771real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (or (@ Q X) (@ P X)))))) _let_1))))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool)) (Q (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.measur2126959417real_n M))) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ Q X) (@ P X))))) _let_1))))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_measure_o) (P (-> Bool Bool)) (Q (-> Bool Bool))) (let ((_let_1 (@ tptp.measure_null_sets_o M))) (=> (@ (@ tptp.member_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.sigma_space_o M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.sigma_space_o M)) (@ Q X))))) _let_1) (@ (@ tptp.member_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.sigma_space_o M)) (@ Q X) (@ P X))))) _let_1))))))
% 0.27/0.71 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.measur1402256771real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ Q X) (@ P X))))) _let_1))))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n) (S2 tptp.set_Fi1058188332real_n) (T tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)))) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n S2) T)) (@ (@ tptp.minus_1686442501real_n (@ _let_1 S2)) (@ _let_1 T))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.measur1402256771real_n M))) (=> (@ (@ tptp.member223413699real_n B2) _let_1) (=> (@ (@ tptp.member223413699real_n A3) (@ tptp.sigma_1235138647real_n M)) (@ (@ tptp.member223413699real_n (@ (@ tptp.minus_1686442501real_n B2) A3)) _let_1))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_se2111327970real_n) (A3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n (@ tptp.comple825005695real_n B2)) A3) (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n (lambda ((C3 tptp.set_Fi1058188332real_n)) (@ (@ tptp.inf_in1974387902real_n C3) A3))) B2)))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A3))) (= (@ _let_1 (@ tptp.comple825005695real_n B2)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n _let_1) B2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.vimage1233683625real_n F))) (= (@ _let_1 (@ tptp.comple825005695real_n A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n _let_1) A3))))))
% 0.27/0.71 (assert (forall ((A3 (-> tptp.nat tptp.set_Fi1058188332real_n)) (C2 tptp.set_nat) (B2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.minus_1686442501real_n (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n A3) C2))) B2) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ (@ tptp.minus_1686442501real_n (@ A3 X)) B2))) C2)))))
% 0.27/0.71 (assert (forall ((A3 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (C2 tptp.set_Fi160064172_int_n) (B2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.minus_1686442501real_n (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n A3) C2))) B2) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ (@ tptp.minus_1686442501real_n (@ A3 X)) B2))) C2)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (A3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.sigma_1536574303real_n M))) (=> (@ (@ tptp.member223413699real_n B2) (@ tptp.measur1402256771real_n M)) (=> (@ (@ tptp.member223413699real_n A3) (@ tptp.sigma_1235138647real_n M)) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n A3) B2)) (@ _let_1 A3)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (D (-> tptp.nat tptp.set_Fi1058188332real_n)) (Sup (-> tptp.set_se2111327970real_n tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ Sup (@ (@ tptp.image_1856576259real_n C2) A3)) (@ Sup (@ (@ tptp.image_1856576259real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (D (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Sup (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ Sup (@ (@ tptp.image_439535603real_n C2) A3)) (@ Sup (@ (@ tptp.image_439535603real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi160064172_int_n) (B2 tptp.set_Fi160064172_int_n) (C2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (D (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (Sup (-> tptp.set_se2111327970real_n tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ Sup (@ (@ tptp.image_355963305real_n C2) A3)) (@ Sup (@ (@ tptp.image_355963305real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (D (-> tptp.nat tptp.set_Fi1058188332real_n)) (Inf (-> tptp.set_se2111327970real_n tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ Inf (@ (@ tptp.image_1856576259real_n C2) A3)) (@ Inf (@ (@ tptp.image_1856576259real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (D (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Inf (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ Inf (@ (@ tptp.image_439535603real_n C2) A3)) (@ Inf (@ (@ tptp.image_439535603real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi160064172_int_n) (B2 tptp.set_Fi160064172_int_n) (C2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (D (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (Inf (-> tptp.set_se2111327970real_n tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ Inf (@ (@ tptp.image_355963305real_n C2) A3)) (@ Inf (@ (@ tptp.image_355963305real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((X3 tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1352538125real_n X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) A3))))))
% 0.27/0.71 (assert (forall ((X3 tptp.nat) (A3 tptp.set_nat) (B tptp.set_Fi1058188332real_n) (F (-> tptp.nat tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member_nat X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1856576259real_n F) A3))))))
% 0.27/0.71 (assert (forall ((X3 tptp.finite964658038_int_n) (A3 tptp.set_Fi160064172_int_n) (B tptp.set_Fi1058188332real_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member27055245_int_n X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_355963305real_n F) A3))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1661509983real_n F) A3))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B Bool) (F (-> tptp.set_Fi1058188332real_n Bool))) (=> (@ (@ tptp.member223413699real_n X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member_o B) (@ (@ tptp.image_1648361637al_n_o F) A3))))))
% 0.27/0.71 (assert (forall ((X3 Bool) (A3 tptp.set_o) (B tptp.set_Fi1058188332real_n) (F (-> Bool tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member_o X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1759008383real_n F) A3))))))
% 0.27/0.71 (assert (forall ((X3 Bool) (A3 tptp.set_o) (B Bool) (F (-> Bool Bool))) (=> (@ (@ tptp.member_o X3) A3) (=> (= B (@ F X3)) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o F) A3))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) (@ (@ tptp.image_1856576259real_n F) A3)) (@ P X2))) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ P (@ F X5)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (forall ((X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X2) (@ (@ tptp.image_439535603real_n F) A3)) (@ P X2))) (forall ((X5 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X5) A3) (@ P (@ F X5)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) (@ (@ tptp.image_355963305real_n F) A3)) (@ P X2))) (forall ((X5 tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X5) A3) (@ P (@ F X5)))))))
% 0.27/0.71 (assert (forall ((M tptp.set_nat) (N2 tptp.set_nat) (F (-> tptp.nat tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.set_Fi1058188332real_n))) (=> (= M N2) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N2) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.image_1856576259real_n F) M) (@ (@ tptp.image_1856576259real_n G) N2))))))
% 0.27/0.71 (assert (forall ((M tptp.set_Fi1058188332real_n) (N2 tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (= M N2) (=> (forall ((X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X2) N2) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.image_439535603real_n F) M) (@ (@ tptp.image_439535603real_n G) N2))))))
% 0.27/0.71 (assert (forall ((M tptp.set_Fi160064172_int_n) (N2 tptp.set_Fi160064172_int_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (=> (= M N2) (=> (forall ((X2 tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X2) N2) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.image_355963305real_n F) M) (@ (@ tptp.image_355963305real_n G) N2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (exists ((X5 tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X5) (@ (@ tptp.image_1856576259real_n F) A3)) (@ P X5))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A3) (@ P (@ F X2)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (exists ((X5 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X5) (@ (@ tptp.image_439535603real_n F) A3)) (@ P X5))) (exists ((X2 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X2) A3) (@ P (@ F X2)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (exists ((X5 tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X5) (@ (@ tptp.image_355963305real_n F) A3)) (@ P X5))) (exists ((X2 tptp.finite964658038_int_n)) (and (@ (@ tptp.member27055245_int_n X2) A3) (@ P (@ F X2)))))))
% 0.27/0.71 (assert (forall ((Z tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.member1352538125real_n Z) (@ (@ tptp.image_439535603real_n F) A3)) (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) A3) (= Z (@ F X)))))))
% 0.27/0.71 (assert (forall ((Z tptp.set_Fi1058188332real_n) (F (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat)) (= (@ (@ tptp.member223413699real_n Z) (@ (@ tptp.image_1856576259real_n F) A3)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (= Z (@ F X)))))))
% 0.27/0.71 (assert (forall ((Z tptp.set_Fi1058188332real_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.member223413699real_n Z) (@ (@ tptp.image_355963305real_n F) A3)) (exists ((X tptp.finite964658038_int_n)) (and (@ (@ tptp.member27055245_int_n X) A3) (= Z (@ F X)))))))
% 0.27/0.71 (assert (forall ((X3 tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1352538125real_n X3) A3) (@ (@ tptp.member1352538125real_n (@ F X3)) (@ (@ tptp.image_439535603real_n F) A3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member223413699real_n (@ F X3)) (@ (@ tptp.image_1856576259real_n F) A3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.finite964658038_int_n) (A3 tptp.set_Fi160064172_int_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member27055245_int_n X3) A3) (@ (@ tptp.member223413699real_n (@ F X3)) (@ (@ tptp.image_355963305real_n F) A3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n X3) A3) (@ (@ tptp.member223413699real_n (@ F X3)) (@ (@ tptp.image_1661509983real_n F) A3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (F (-> tptp.set_Fi1058188332real_n Bool))) (=> (@ (@ tptp.member223413699real_n X3) A3) (@ (@ tptp.member_o (@ F X3)) (@ (@ tptp.image_1648361637al_n_o F) A3)))))
% 0.27/0.71 (assert (forall ((X3 Bool) (A3 tptp.set_o) (F (-> Bool tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member223413699real_n (@ F X3)) (@ (@ tptp.image_1759008383real_n F) A3)))))
% 0.27/0.71 (assert (forall ((X3 Bool) (A3 tptp.set_o) (F (-> Bool Bool))) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member_o (@ F X3)) (@ (@ tptp.image_o_o F) A3)))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (@ (@ tptp.plus_p585657087real_n (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p585657087real_n B) C))))))
% 0.27/0.71 (assert (exists ((X2 tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X2) tptp.top_to20708754real_n)))
% 0.27/0.71 (assert (exists ((X2 Bool)) (@ (@ tptp.member_o X2) tptp.top_top_set_o)))
% 0.27/0.71 (assert (exists ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.top_top_set_nat)))
% 0.27/0.71 (assert (exists ((X2 tptp.finite964658038_int_n)) (@ (@ tptp.member27055245_int_n X2) tptp.top_to131672412_int_n)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n)) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X2) A3)) (= tptp.top_to20708754real_n A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_o)) (=> (forall ((X2 Bool)) (@ (@ tptp.member_o X2) A3)) (= tptp.top_top_set_o A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A3)) (= tptp.top_top_set_nat A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi160064172_int_n)) (=> (forall ((X2 tptp.finite964658038_int_n)) (@ (@ tptp.member27055245_int_n X2) A3)) (= tptp.top_to131672412_int_n A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A3))) (let ((_let_2 (@ tptp.inf_in1974387902real_n B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A3))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.27/0.71 (assert (= tptp.inf_in1974387902real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ (@ tptp.inf_in1974387902real_n B3) A4))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n A3) A3) A3)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A3))) (= (@ (@ tptp.inf_in1974387902real_n (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n B2) C2))))))
% 0.27/0.71 (assert (forall ((C tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C))) (=> (@ _let_1 (@ (@ tptp.inf_in632889204real_n A3) B2)) (@ _let_1 B2)))))
% 0.27/0.71 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (@ _let_1 B2)))))
% 0.27/0.71 (assert (forall ((C tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C))) (=> (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) B2)) (@ _let_1 B2)))))
% 0.27/0.71 (assert (forall ((C tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C))) (=> (@ _let_1 (@ (@ tptp.inf_in632889204real_n A3) B2)) (@ _let_1 A3)))))
% 0.27/0.71 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (@ _let_1 A3)))))
% 0.27/0.71 (assert (forall ((C tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C))) (=> (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) B2)) (@ _let_1 A3)))))
% 0.27/0.71 (assert (forall ((C tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C))) (=> (@ _let_1 (@ (@ tptp.inf_in632889204real_n A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 0.27/0.71 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 0.27/0.71 (assert (forall ((C tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C))) (=> (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (C2 tptp.set_se820660888real_n)) (=> (@ (@ tptp.member223413699real_n A3) (@ tptp.comple1917283637real_n C2)) (not (forall ((X6 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n A3) X6) (not (@ (@ tptp.member1475136633real_n X6) C2))))))))
% 0.27/0.71 (assert (forall ((A3 Bool) (C2 tptp.set_set_o)) (=> (@ (@ tptp.member_o A3) (@ tptp.comple1665300069_set_o C2)) (not (forall ((X6 tptp.set_o)) (=> (@ (@ tptp.member_o A3) X6) (not (@ (@ tptp.member_set_o X6) C2))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.finite1489363574real_n) (C2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1352538125real_n A3) (@ tptp.comple825005695real_n C2)) (not (forall ((X6 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n A3) X6) (not (@ (@ tptp.member223413699real_n X6) C2))))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.finite1489363574real_n Bool)) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Q (-> tptp.finite1489363574real_n Bool))) (=> (forall ((X2 tptp.finite1489363574real_n)) (= (@ P (@ F X2)) (@ Q X2))) (= (@ (@ tptp.vimage1233683625real_n F) (@ tptp.collec321817931real_n P)) (@ tptp.collec321817931real_n Q)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n (@ F A)) A3) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) A3)))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.set_Fi1058188332real_n)) (A Bool) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n (@ F A)) A3) (@ (@ tptp.member_o A) (@ (@ tptp.vimage961837641real_n F) A3)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n Bool)) (A tptp.set_Fi1058188332real_n) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o (@ F A)) A3) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage851190895al_n_o F) A3)))))
% 0.27/0.71 (assert (forall ((F (-> Bool Bool)) (A Bool) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o (@ F A)) A3) (@ (@ tptp.member_o A) (@ (@ tptp.vimage_o_o F) A3)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n (@ F A)) A3) (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) A3)))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n Bool)) (B2 tptp.set_o)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage851190895al_n_o F) B2)) (@ (@ tptp.member_o (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A Bool) (F (-> Bool tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.vimage961837641real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A Bool) (F (-> Bool Bool)) (B2 tptp.set_o)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.vimage_o_o F) B2)) (@ (@ tptp.member_o (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) B2)) (@ (@ tptp.member1352538125real_n (@ F A)) B2))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) A3)) (@ (@ tptp.member223413699real_n (@ F A)) A3))))
% 0.27/0.71 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n Bool)) (A3 tptp.set_o)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage851190895al_n_o F) A3)) (@ (@ tptp.member_o (@ F A)) A3))))
% 0.27/0.71 (assert (forall ((A Bool) (F (-> Bool tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.vimage961837641real_n F) A3)) (@ (@ tptp.member223413699real_n (@ F A)) A3))))
% 0.27/0.71 (assert (forall ((A Bool) (F (-> Bool Bool)) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.vimage_o_o F) A3)) (@ (@ tptp.member_o (@ F A)) A3))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) A3)) (@ (@ tptp.member1352538125real_n (@ F A)) A3))))
% 0.27/0.71 (assert (forall ((Sup (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (= (@ Sup (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) X)) A3)) (@ Sup A3))))
% 0.27/0.71 (assert (forall ((Inf (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (= (@ Inf (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) X)) A3)) (@ Inf A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ (@ tptp.image_439535603real_n F) A3)) (@ P X)))) (@ (@ tptp.image_439535603real_n F) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_1856576259real_n F) A3)) (@ P X)))) (@ (@ tptp.image_1856576259real_n F) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_355963305real_n F) A3)) (@ P X)))) (@ (@ tptp.image_355963305real_n F) (@ tptp.collec1941932235_int_n (lambda ((X tptp.finite964658038_int_n)) (and (@ (@ tptp.member27055245_int_n X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_1661509983real_n F) A3)) (@ P X)))) (@ (@ tptp.image_1661509983real_n F) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.set_Fi1058188332real_n)) (A3 tptp.set_o) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_1759008383real_n F) A3)) (@ P X)))) (@ (@ tptp.image_1759008383real_n F) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n Bool)) (A3 tptp.set_se2111327970real_n) (P (-> Bool Bool))) (= (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ (@ tptp.image_1648361637al_n_o F) A3)) (@ P X)))) (@ (@ tptp.image_1648361637al_n_o F) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> Bool Bool)) (A3 tptp.set_o) (P (-> Bool Bool))) (= (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) (@ (@ tptp.image_o_o F) A3)) (@ P X)))) (@ (@ tptp.image_o_o F) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ P (@ F X)))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_1661509983real_n F) (@ (@ tptp.image_1856576259real_n G) A3)) (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.image_1661509983real_n F) (@ (@ tptp.image_355963305real_n G) A3)) (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_1856576259real_n F) (@ (@ tptp.image_nat_nat G) A3)) (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.nat)) (A3 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.image_1856576259real_n F) (@ (@ tptp.image_497739341_n_nat G) A3)) (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n F) (@ (@ tptp.image_439535603real_n G) A3)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.finite964658038_int_n)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_355963305real_n F) (@ (@ tptp.image_1961920973_int_n G) A3)) (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.finite964658038_int_n)) (A3 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.image_355963305real_n F) (@ (@ tptp.image_1278151539_int_n G) A3)) (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) A3))))
% 0.27/0.71 (assert (forall ((B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) A3)) (not (forall ((X2 tptp.finite1489363574real_n)) (=> (= B (@ F X2)) (not (@ (@ tptp.member1352538125real_n X2) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat)) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1856576259real_n F) A3)) (not (forall ((X2 tptp.nat)) (=> (= B (@ F X2)) (not (@ (@ tptp.member_nat X2) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n)) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_355963305real_n F) A3)) (not (forall ((X2 tptp.finite964658038_int_n)) (=> (= B (@ F X2)) (not (@ (@ tptp.member27055245_int_n X2) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1661509983real_n F) A3)) (not (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (= B (@ F X2)) (not (@ (@ tptp.member223413699real_n X2) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> Bool tptp.set_Fi1058188332real_n)) (A3 tptp.set_o)) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1759008383real_n F) A3)) (not (forall ((X2 Bool)) (=> (= B (@ F X2)) (not (@ (@ tptp.member_o X2) A3))))))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> tptp.set_Fi1058188332real_n Bool)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_1648361637al_n_o F) A3)) (not (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (= B (@ F X2)) (not (@ (@ tptp.member223413699real_n X2) A3))))))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> Bool Bool)) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o F) A3)) (not (forall ((X2 Bool)) (=> (= B (@ F X2)) (not (@ (@ tptp.member_o X2) A3))))))))
% 0.27/0.71 (assert (= tptp.top_top_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) true))))
% 0.27/0.71 (assert (= tptp.top_to131672412_int_n (@ tptp.collec1941932235_int_n (lambda ((X tptp.finite964658038_int_n)) true))))
% 0.27/0.71 (assert (forall ((P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_in1974387902real_n (@ tptp.collec321817931real_n P)) (@ tptp.collec321817931real_n Q)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Fi1058188332real_n) (A3 tptp.set_se2111327970real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.member223413699real_n X3))) (= (@ _let_1 (@ (@ tptp.inf_in632889204real_n A3) (@ tptp.collec452821761real_n P))) (and (@ _let_1 A3) (@ P X3))))))
% 0.27/0.71 (assert (forall ((X3 Bool) (A3 tptp.set_o) (P (-> Bool Bool))) (let ((_let_1 (@ tptp.member_o X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) (@ tptp.collect_o P))) (and (@ _let_1 A3) (@ P X3))))))
% 0.27/0.71 (assert (forall ((X3 tptp.finite1489363574real_n) (A3 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.member1352538125real_n X3))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A3) (@ tptp.collec321817931real_n P))) (and (@ _let_1 A3) (@ P X3))))))
% 0.27/0.71 (assert (= tptp.inf_in632889204real_n (lambda ((A4 tptp.set_se2111327970real_n) (B3 tptp.set_se2111327970real_n)) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n X))) (and (@ _let_1 A4) (@ _let_1 B3))))))))
% 0.27/0.71 (assert (= tptp.inf_inf_set_o (lambda ((A4 tptp.set_o) (B3 tptp.set_o)) (@ tptp.collect_o (lambda ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (and (@ _let_1 A4) (@ _let_1 B3))))))))
% 0.27/0.71 (assert (= tptp.inf_in1974387902real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.member1352538125real_n X))) (and (@ _let_1 A4) (@ _let_1 B3))))))))
% 0.27/0.71 (assert (= tptp.vimage1233683625real_n (lambda ((F2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n (@ F2 X)) B3))))))
% 0.27/0.71 (assert (not (@ (@ tptp.ord_le2133614988nnreal tptp.zero_z1963244097nnreal) tptp.zero_z1963244097nnreal)))
% 0.27/0.71 (assert (not (@ (@ tptp.ord_le2133614988nnreal tptp.one_on705384445nnreal) tptp.one_on705384445nnreal)))
% 0.27/0.71 (assert (forall ((B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X3 tptp.finite1489363574real_n)) (=> (= B (@ F X3)) (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) tptp.top_to1292442332real_n)))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.nat tptp.set_Fi1058188332real_n)) (X3 tptp.nat)) (=> (= B (@ F X3)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1856576259real_n F) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (= B (@ F X3)) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o F) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (X3 tptp.finite964658038_int_n)) (=> (= B (@ F X3)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_355963305real_n F) tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> tptp.finite964658038_int_n Bool)) (X3 tptp.finite964658038_int_n)) (=> (= B (@ F X3)) (@ (@ tptp.member_o B) (@ (@ tptp.image_216309723nt_n_o F) tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (= (= (@ (@ tptp.image_439535603real_n F) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n) (forall ((Y2 tptp.finite1489363574real_n)) (exists ((X tptp.finite1489363574real_n)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n))) (= (= (@ (@ tptp.image_1856576259real_n F) tptp.top_top_set_nat) tptp.top_to20708754real_n) (forall ((Y2 tptp.set_Fi1058188332real_n)) (exists ((X tptp.nat)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.nat))) (= (= (@ (@ tptp.image_nat_nat F) tptp.top_top_set_nat) tptp.top_top_set_nat) (forall ((Y2 tptp.nat)) (exists ((X tptp.nat)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.finite964658038_int_n))) (= (= (@ (@ tptp.image_1961920973_int_n F) tptp.top_top_set_nat) tptp.top_to131672412_int_n) (forall ((Y2 tptp.finite964658038_int_n)) (exists ((X tptp.nat)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (= (= (@ (@ tptp.image_355963305real_n F) tptp.top_to131672412_int_n) tptp.top_to20708754real_n) (forall ((Y2 tptp.set_Fi1058188332real_n)) (exists ((X tptp.finite964658038_int_n)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.nat))) (= (= (@ (@ tptp.image_497739341_n_nat F) tptp.top_to131672412_int_n) tptp.top_top_set_nat) (forall ((Y2 tptp.nat)) (exists ((X tptp.finite964658038_int_n)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.finite964658038_int_n))) (= (= (@ (@ tptp.image_1278151539_int_n F) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n) (forall ((Y2 tptp.finite964658038_int_n)) (exists ((X tptp.finite964658038_int_n)) (= Y2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X3 tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n (@ F X3)) (@ (@ tptp.image_439535603real_n F) tptp.top_to1292442332real_n))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (X3 tptp.nat)) (@ (@ tptp.member223413699real_n (@ F X3)) (@ (@ tptp.image_1856576259real_n F) tptp.top_top_set_nat))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat Bool)) (X3 tptp.nat)) (@ (@ tptp.member_o (@ F X3)) (@ (@ tptp.image_nat_o F) tptp.top_top_set_nat))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (X3 tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ F X3)) (@ (@ tptp.image_355963305real_n F) tptp.top_to131672412_int_n))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n Bool)) (X3 tptp.finite964658038_int_n)) (@ (@ tptp.member_o (@ F X3)) (@ (@ tptp.image_216309723nt_n_o F) tptp.top_to131672412_int_n))))
% 0.27/0.71 (assert (forall ((G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (forall ((X2 tptp.finite1489363574real_n)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_439535603real_n G) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n))))
% 0.27/0.71 (assert (forall ((G (-> tptp.nat tptp.set_Fi1058188332real_n)) (F (-> tptp.set_Fi1058188332real_n tptp.nat))) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_1856576259real_n G) tptp.top_top_set_nat) tptp.top_to20708754real_n))))
% 0.27/0.71 (assert (forall ((G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X2 tptp.nat)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat) tptp.top_top_set_nat))))
% 0.27/0.71 (assert (forall ((G (-> tptp.nat tptp.finite964658038_int_n)) (F (-> tptp.finite964658038_int_n tptp.nat))) (=> (forall ((X2 tptp.finite964658038_int_n)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_1961920973_int_n G) tptp.top_top_set_nat) tptp.top_to131672412_int_n))))
% 0.27/0.71 (assert (forall ((G (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (F (-> tptp.set_Fi1058188332real_n tptp.finite964658038_int_n))) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_355963305real_n G) tptp.top_to131672412_int_n) tptp.top_to20708754real_n))))
% 0.27/0.71 (assert (forall ((G (-> tptp.finite964658038_int_n tptp.nat)) (F (-> tptp.nat tptp.finite964658038_int_n))) (=> (forall ((X2 tptp.nat)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_497739341_n_nat G) tptp.top_to131672412_int_n) tptp.top_top_set_nat))))
% 0.27/0.71 (assert (forall ((G (-> tptp.finite964658038_int_n tptp.finite964658038_int_n)) (F (-> tptp.finite964658038_int_n tptp.finite964658038_int_n))) (=> (forall ((X2 tptp.finite964658038_int_n)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_1278151539_int_n G) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Y4 tptp.finite1489363574real_n)) (=> (= (@ (@ tptp.image_439535603real_n F) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n) (not (forall ((X2 tptp.finite1489363574real_n)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (Y4 tptp.set_Fi1058188332real_n)) (=> (= (@ (@ tptp.image_1856576259real_n F) tptp.top_top_set_nat) tptp.top_to20708754real_n) (not (forall ((X2 tptp.nat)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (Y4 tptp.nat)) (=> (= (@ (@ tptp.image_nat_nat F) tptp.top_top_set_nat) tptp.top_top_set_nat) (not (forall ((X2 tptp.nat)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.finite964658038_int_n)) (Y4 tptp.finite964658038_int_n)) (=> (= (@ (@ tptp.image_1961920973_int_n F) tptp.top_top_set_nat) tptp.top_to131672412_int_n) (not (forall ((X2 tptp.nat)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (Y4 tptp.set_Fi1058188332real_n)) (=> (= (@ (@ tptp.image_355963305real_n F) tptp.top_to131672412_int_n) tptp.top_to20708754real_n) (not (forall ((X2 tptp.finite964658038_int_n)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.nat)) (Y4 tptp.nat)) (=> (= (@ (@ tptp.image_497739341_n_nat F) tptp.top_to131672412_int_n) tptp.top_top_set_nat) (not (forall ((X2 tptp.finite964658038_int_n)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.finite964658038_int_n)) (Y4 tptp.finite964658038_int_n)) (=> (= (@ (@ tptp.image_1278151539_int_n F) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n) (not (forall ((X2 tptp.finite964658038_int_n)) (not (= Y4 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Y4 tptp.finite1489363574real_n)) (=> (= (@ (@ tptp.image_439535603real_n F) tptp.top_to1292442332real_n) tptp.top_to1292442332real_n) (exists ((X2 tptp.finite1489363574real_n)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (Y4 tptp.set_Fi1058188332real_n)) (=> (= (@ (@ tptp.image_1856576259real_n F) tptp.top_top_set_nat) tptp.top_to20708754real_n) (exists ((X2 tptp.nat)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (Y4 tptp.nat)) (=> (= (@ (@ tptp.image_nat_nat F) tptp.top_top_set_nat) tptp.top_top_set_nat) (exists ((X2 tptp.nat)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.finite964658038_int_n)) (Y4 tptp.finite964658038_int_n)) (=> (= (@ (@ tptp.image_1961920973_int_n F) tptp.top_top_set_nat) tptp.top_to131672412_int_n) (exists ((X2 tptp.nat)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (Y4 tptp.set_Fi1058188332real_n)) (=> (= (@ (@ tptp.image_355963305real_n F) tptp.top_to131672412_int_n) tptp.top_to20708754real_n) (exists ((X2 tptp.finite964658038_int_n)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.nat)) (Y4 tptp.nat)) (=> (= (@ (@ tptp.image_497739341_n_nat F) tptp.top_to131672412_int_n) tptp.top_top_set_nat) (exists ((X2 tptp.finite964658038_int_n)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.finite964658038_int_n)) (Y4 tptp.finite964658038_int_n)) (=> (= (@ (@ tptp.image_1278151539_int_n F) tptp.top_to131672412_int_n) tptp.top_to131672412_int_n) (exists ((X2 tptp.finite964658038_int_n)) (= Y4 (@ F X2))))))
% 0.27/0.71 (assert (forall ((A tptp.extend1728876344nnreal) (S tptp.set_Ex113815278nnreal)) (= (@ (@ tptp.ord_le2133614988nnreal A) (@ tptp.comple1413366923nnreal S)) (exists ((X tptp.extend1728876344nnreal)) (and (@ (@ tptp.member1217042383nnreal X) S) (@ (@ tptp.ord_le2133614988nnreal A) X))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (D (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.comple2042271945real_n (@ (@ tptp.image_439535603real_n C2) A3)) (@ tptp.comple2042271945real_n (@ (@ tptp.image_439535603real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (D (-> tptp.nat tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n C2) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi160064172_int_n) (B2 tptp.set_Fi160064172_int_n) (C2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (D (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n C2) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n) (C2 (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (D (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n C2) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (C2 (-> Bool tptp.set_Fi1058188332real_n)) (D (-> Bool tptp.set_Fi1058188332real_n))) (=> (= A3 B2) (=> (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1759008383real_n C2) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1759008383real_n D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n) (C2 (-> tptp.set_Fi1058188332real_n Bool)) (D (-> tptp.set_Fi1058188332real_n Bool))) (=> (= A3 B2) (=> (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_1648361637al_n_o C2) A3)) (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_1648361637al_n_o D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (C2 (-> Bool Bool)) (D (-> Bool Bool))) (=> (= A3 B2) (=> (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) B2) (= (@ C2 X2) (@ D X2)))) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_o_o C2) A3)) (@ tptp.complete_Sup_Sup_o (@ (@ tptp.image_o_o D) B2)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n A3) tptp.top_to1292442332real_n) A3)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) tptp.top_top_set_nat) A3)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.inf_in1108485182_int_n A3) tptp.top_to131672412_int_n) A3)))
% 0.27/0.71 (assert (forall ((B2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n tptp.top_to1292442332real_n) B2) B2)))
% 0.27/0.71 (assert (forall ((B2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) B2) B2)))
% 0.27/0.71 (assert (forall ((B2 tptp.set_Fi160064172_int_n)) (= (@ (@ tptp.inf_in1108485182_int_n tptp.top_to131672412_int_n) B2) B2)))
% 0.27/0.71 (assert (= (@ tptp.comple1682161881et_nat tptp.top_top_set_set_nat) tptp.top_top_set_nat))
% 0.27/0.71 (assert (= (@ tptp.comple970917503_int_n tptp.top_to1587634578_int_n) tptp.top_to131672412_int_n))
% 0.27/0.71 (assert (= (@ tptp.comple825005695real_n tptp.top_to20708754real_n) tptp.top_to1292442332real_n))
% 0.27/0.71 (assert (forall ((A3 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.member223413699real_n A3))) (=> (@ _let_1 (@ tptp.measur1402256771real_n M)) (@ _let_1 (@ tptp.sigma_1235138647real_n M))))))
% 0.27/0.71 (assert (forall ((S tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Y4 tptp.set_Fi1058188332real_n)) (=> (forall ((W tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n W) S) (= (@ F W) (@ G W)))) (= (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n F) Y4)) S) (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n G) Y4)) S)))))
% 0.27/0.71 (assert (forall ((A tptp.finite1489363574real_n) (S2 tptp.set_Fi1058188332real_n) (T tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) (@ (@ tptp.minus_1686442501real_n S2) T)) (@ (@ tptp.minus_1686442501real_n (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) S2)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) T)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ F (@ G X)))) tptp.top_to1292442332real_n) (@ (@ tptp.image_439535603real_n F) (@ (@ tptp.image_439535603real_n G) tptp.top_to1292442332real_n)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.nat tptp.finite1489363574real_n))) (= (@ (@ tptp.image_183184717real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) tptp.top_top_set_nat) (@ (@ tptp.image_439535603real_n F) (@ (@ tptp.image_183184717real_n G) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.set_Fi1058188332real_n))) (= (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) tptp.top_top_set_nat) (@ (@ tptp.image_1661509983real_n F) (@ (@ tptp.image_1856576259real_n G) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.nat))) (= (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) tptp.top_top_set_nat) (@ (@ tptp.image_1856576259real_n F) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (G (-> tptp.nat tptp.finite964658038_int_n))) (= (@ (@ tptp.image_1856576259real_n (lambda ((X tptp.nat)) (@ F (@ G X)))) tptp.top_top_set_nat) (@ (@ tptp.image_355963305real_n F) (@ (@ tptp.image_1961920973_int_n G) tptp.top_top_set_nat)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite964658038_int_n tptp.finite1489363574real_n))) (= (@ (@ tptp.image_2058828787real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) tptp.top_to131672412_int_n) (@ (@ tptp.image_439535603real_n F) (@ (@ tptp.image_2058828787real_n G) tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (= (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) tptp.top_to131672412_int_n) (@ (@ tptp.image_1661509983real_n F) (@ (@ tptp.image_355963305real_n G) tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.nat))) (= (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) tptp.top_to131672412_int_n) (@ (@ tptp.image_1856576259real_n F) (@ (@ tptp.image_497739341_n_nat G) tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (G (-> tptp.finite964658038_int_n tptp.finite964658038_int_n))) (= (@ (@ tptp.image_355963305real_n (lambda ((X tptp.finite964658038_int_n)) (@ F (@ G X)))) tptp.top_to131672412_int_n) (@ (@ tptp.image_355963305real_n F) (@ (@ tptp.image_1278151539_int_n G) tptp.top_to131672412_int_n)))))
% 0.27/0.71 (assert (forall ((B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) tptp.top_to1292442332real_n)) (not (forall ((X2 tptp.finite1489363574real_n)) (not (= B (@ F X2))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.nat tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1856576259real_n F) tptp.top_top_set_nat)) (not (forall ((X2 tptp.nat)) (not (= B (@ F X2))))))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> tptp.nat Bool))) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o F) tptp.top_top_set_nat)) (not (forall ((X2 tptp.nat)) (= B (not (@ F X2))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_355963305real_n F) tptp.top_to131672412_int_n)) (not (forall ((X2 tptp.finite964658038_int_n)) (not (= B (@ F X2))))))))
% 0.27/0.71 (assert (forall ((B Bool) (F (-> tptp.finite964658038_int_n Bool))) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_216309723nt_n_o F) tptp.top_to131672412_int_n)) (not (forall ((X2 tptp.finite964658038_int_n)) (= B (not (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.nat tptp.set_Fi1058188332real_n)) (B2 tptp.set_nat) (A3 tptp.set_nat)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((I4 tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (@ F I4)) B2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((J tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((I4 tptp.nat)) (@ (@ F I4) J))) A3)))) B2)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (B2 tptp.set_Fi160064172_int_n) (A3 tptp.set_nat)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((I4 tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (@ F I4)) B2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((J tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((I4 tptp.nat)) (@ (@ F I4) J))) A3)))) B2)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.nat tptp.set_Fi1058188332real_n)) (B2 tptp.set_nat) (A3 tptp.set_Fi160064172_int_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((I4 tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (@ F I4)) B2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((J tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((I4 tptp.finite964658038_int_n)) (@ (@ F I4) J))) A3)))) B2)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (B2 tptp.set_Fi160064172_int_n) (A3 tptp.set_Fi160064172_int_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((I4 tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (@ F I4)) B2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((J tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((I4 tptp.finite964658038_int_n)) (@ (@ F I4) J))) A3)))) B2)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.nat tptp.set_Fi1058188332real_n)) (S tptp.set_set_nat)) (let ((_let_1 (@ tptp.image_1856576259real_n F))) (= (@ _let_1 (@ tptp.comple1682161881et_nat S)) (@ tptp.comple1917283637real_n (@ (@ tptp.image_1587769199real_n _let_1) S))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (S tptp.set_se944069346_int_n)) (let ((_let_1 (@ tptp.image_355963305real_n F))) (= (@ _let_1 (@ tptp.comple970917503_int_n S)) (@ tptp.comple1917283637real_n (@ (@ tptp.image_1054146965real_n _let_1) S))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (S tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.image_439535603real_n F))) (= (@ _let_1 (@ tptp.comple825005695real_n S)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n _let_1) S))))))
% 0.27/0.71 (assert (forall ((C2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (B2 (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n C2) (@ tptp.comple1682161881et_nat (@ (@ tptp.image_nat_set_nat B2) A3)))) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((Y2 tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n C2) (@ B2 Y2))))) A3)))))
% 0.27/0.71 (assert (forall ((C2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (B2 (-> tptp.finite964658038_int_n tptp.set_nat)) (A3 tptp.set_Fi160064172_int_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n C2) (@ tptp.comple1682161881et_nat (@ (@ tptp.image_1085873667et_nat B2) A3)))) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((Y2 tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n C2) (@ B2 Y2))))) A3)))))
% 0.27/0.71 (assert (forall ((C2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (B2 (-> tptp.nat tptp.set_Fi160064172_int_n)) (A3 tptp.set_nat)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n C2) (@ tptp.comple970917503_int_n (@ (@ tptp.image_968789251_int_n B2) A3)))) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((Y2 tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n C2) (@ B2 Y2))))) A3)))))
% 0.27/0.71 (assert (forall ((C2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (B2 (-> tptp.finite964658038_int_n tptp.set_Fi160064172_int_n)) (A3 tptp.set_Fi160064172_int_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n C2) (@ tptp.comple970917503_int_n (@ (@ tptp.image_1819506345_int_n B2) A3)))) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((Y2 tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n C2) (@ B2 Y2))))) A3)))))
% 0.27/0.71 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_545463721real_n C2) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3)))) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n (lambda ((Y2 tptp.nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_545463721real_n C2) (@ B2 Y2))))) A3)))))
% 0.27/0.71 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_545463721real_n C2) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3)))) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n (lambda ((Y2 tptp.finite964658038_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_545463721real_n C2) (@ B2 Y2))))) A3)))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (B2 (-> tptp.set_Fi1058188332real_n tptp.set_se2111327970real_n)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n B) (@ tptp.comple1917283637real_n (@ (@ tptp.image_797440021real_n B2) A3))) (not (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) A3) (not (@ (@ tptp.member223413699real_n B) (@ B2 X2)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_Fi1058188332real_n) (B2 (-> Bool tptp.set_se2111327970real_n)) (A3 tptp.set_o)) (=> (@ (@ tptp.member223413699real_n B) (@ tptp.comple1917283637real_n (@ (@ tptp.image_452144437real_n B2) A3))) (not (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (not (@ (@ tptp.member223413699real_n B) (@ B2 X2)))))))))
% 0.27/0.71 (assert (forall ((B Bool) (B2 (-> tptp.set_Fi1058188332real_n tptp.set_o)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member_o B) (@ tptp.comple1665300069_set_o (@ (@ tptp.image_1687589765_set_o B2) A3))) (not (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) A3) (not (@ (@ tptp.member_o B) (@ B2 X2)))))))))
% 0.27/0.71 (assert (forall ((B Bool) (B2 (-> Bool tptp.set_o)) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o B) (@ tptp.comple1665300069_set_o (@ (@ tptp.image_o_set_o B2) A3))) (not (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (not (@ (@ tptp.member_o B) (@ B2 X2)))))))))
% 71.51/71.76 (assert (forall ((B tptp.finite1489363574real_n) (B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_nat)) (=> (@ (@ tptp.member1352538125real_n B) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) A3))) (not (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A3) (not (@ (@ tptp.member1352538125real_n B) (@ B2 X2)))))))))
% 71.51/71.76 (assert (forall ((B tptp.finite1489363574real_n) (B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_Fi160064172_int_n)) (=> (@ (@ tptp.member1352538125real_n B) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) A3))) (not (forall ((X2 tptp.finite964658038_int_n)) (=> (@ (@ tptp.member27055245_int_n X2) A3) (not (@ (@ tptp.member1352538125real_n B) (@ B2 X2)))))))))
% 71.51/71.76 (assert (forall ((B tptp.finite1489363574real_n) (B2 (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1352538125real_n B) (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n B2) A3))) (not (forall ((X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X2) A3) (not (@ (@ tptp.member1352538125real_n B) (@ B2 X2)))))))))
% 71.51/71.76 (assert (forall ((B tptp.finite1489363574real_n) (B2 (-> Bool tptp.set_Fi1058188332real_n)) (A3 tptp.set_o)) (=> (@ (@ tptp.member1352538125real_n B) (@ tptp.comple825005695real_n (@ (@ tptp.image_1759008383real_n B2) A3))) (not (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (not (@ (@ tptp.member1352538125real_n B) (@ B2 X2)))))))))
% 71.51/71.76 (assert (forall ((B2 (-> tptp.nat tptp.set_Fi1058188332real_n)) (A3 tptp.set_set_nat)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_933134521real_n (lambda ((Y2 tptp.set_nat)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) Y2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_1856576259real_n B2) (@ tptp.comple1682161881et_nat A3))))))
% 71.51/71.76 (assert (forall ((B2 (-> tptp.finite964658038_int_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se944069346_int_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_792439519real_n (lambda ((Y2 tptp.set_Fi160064172_int_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) Y2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_355963305real_n B2) (@ tptp.comple970917503_int_n A3))))))
% 71.51/71.76 (assert (forall ((B2 (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (A3 tptp.set_se2111327970real_n)) (= (@ tptp.comple825005695real_n (@ (@ tptp.image_1661509983real_n (lambda ((Y2 tptp.set_Fi1058188332real_n)) (@ tptp.comple825005695real_n (@ (@ tptp.image_545463721real_n B2) Y2)))) A3)) (@ tptp.comple825005695real_n (@ (@ tptp.image_545463721real_n B2) (@ tptp.comple825005695real_n A3))))))
% 71.51/71.76 (assert (= tptp.complete_Sup_Sup_o (@ tptp.member_o true)))
% 71.51/71.76 (assert (not (= (lambda ((N tptp.nat)) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) (@ tptp.t2 (@ tptp.f N)))) (lambda ((N tptp.nat)) (@ (@ tptp.sigma_1536574303real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) (@ tptp.t (@ tptp.f N)))))))
% 71.51/71.76 (set-info :filename cvc5---1.0.5_23224)
% 71.51/71.76 (check-sat-assuming ( true ))
% 71.51/71.76 ------- get file name : TPTP file name is ITP117^1
% 71.51/71.76 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23224.smt2...
% 71.51/71.76 --- Run --ho-elim --full-saturate-quant at 10...
% 71.51/71.76 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 71.51/71.76 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 71.51/71.76 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 71.51/71.76 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 71.51/71.76 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 71.51/71.76 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 71.51/71.76 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 71.51/71.76 --- Run --no-ho-match/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 23493 Alarm clock ( read result; case "$result" in
% 299.94/300.13 unsat)
% 299.94/300.13 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.94/300.13 ;;
% 299.94/300.13 sat)
% 299.94/300.13 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.94/300.13 ;;
% 299.94/300.13 esac; exit 1 )
% 299.94/300.14 Alarm clock
% 299.94/300.14 % cvc5---1.0.5 exiting
% 299.94/300.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------