SET007 Axioms: SET007+903.ax
%------------------------------------------------------------------------------
% File : SET007+903 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Inferior Limit and Superior Limit of Sequences of Real Numbers
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : rinfsup1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 110 ( 0 unt; 0 def)
% Number of atoms : 819 ( 63 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 734 ( 25 ~; 1 |; 346 &)
% ( 28 <=>; 334 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 0 prp; 1-3 aty)
% Number of functors : 34 ( 34 usr; 4 con; 0-4 aty)
% Number of variables : 252 ( 244 !; 8 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( ~ r1_xreal_0(C,k6_xcmplx_0(A,B))
& ~ r1_xreal_0(k2_xcmplx_0(A,B),C) )
<=> ~ r1_xreal_0(B,k18_complex1(k6_xcmplx_0(C,A))) ) ) ) ) ).
fof(d1_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k1_rinfsup1(A) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ).
fof(d2_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k2_rinfsup1(A) = k4_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ).
fof(t2_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k4_partfun3(k5_numbers,k3_partfun3(k5_numbers,A,B),B) = A ) ) ).
fof(t3_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( r2_hidden(A,k1_pscomp_1(k5_numbers,k1_numbers,B))
<=> r2_hidden(k4_xcmplx_0(A),k1_pscomp_1(k5_numbers,k1_numbers,k6_partfun3(k5_numbers,B))) ) ) ) ).
fof(t4_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k1_pscomp_1(k5_numbers,k1_numbers,k6_partfun3(k5_numbers,A)) = k5_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ).
fof(t5_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
<=> v1_seq_4(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ) ).
fof(t6_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
<=> v2_seq_4(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ) ).
fof(t7_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_seq_2(B)
=> ( A = k1_rinfsup1(B)
<=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),A) )
& ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,D),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) ).
fof(t8_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v2_seq_2(B)
=> ( A = k2_rinfsup1(B)
<=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(A,k2_seq_1(k5_numbers,k1_numbers,B,C)) )
& ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,D)) ) ) ) ) ) ) ) ) ).
fof(t9_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),A) )
<=> ( v1_seq_2(B)
& r1_xreal_0(k1_rinfsup1(B),A) ) ) ) ) ).
fof(t10_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(A,k2_seq_1(k5_numbers,k1_numbers,B,C)) )
<=> ( v2_seq_2(B)
& r1_xreal_0(A,k2_rinfsup1(B)) ) ) ) ) ).
fof(t11_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
<=> v2_seq_2(k6_partfun3(k5_numbers,A)) ) ) ).
fof(t12_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
<=> v1_seq_2(k6_partfun3(k5_numbers,A)) ) ) ).
fof(t13_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
=> k1_rinfsup1(A) = k1_real_1(k2_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) ).
fof(t14_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
=> k2_rinfsup1(A) = k1_real_1(k1_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) ).
fof(t15_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(A)
& v2_seq_2(B) )
=> r1_xreal_0(k3_real_1(k2_rinfsup1(A),k2_rinfsup1(B)),k2_rinfsup1(k3_partfun3(k5_numbers,A,B))) ) ) ) ).
fof(t16_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(A)
& v1_seq_2(B) )
=> r1_xreal_0(k1_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k1_rinfsup1(A),k1_rinfsup1(B))) ) ) ) ).
fof(d3_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_partfun3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t17_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v4_partfun3(B)
=> v4_partfun3(k1_seqm_3(B,A)) ) ) ) ).
fof(t18_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(A)
& v4_partfun3(A) )
=> r1_xreal_0(np__0,k2_rinfsup1(A)) ) ) ).
fof(t19_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(A)
& v4_partfun3(A) )
=> r1_xreal_0(np__0,k1_rinfsup1(A)) ) ) ).
fof(t20_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(A)
& v4_partfun3(A)
& v2_seq_2(B)
& v4_partfun3(B) )
=> ( v2_seq_2(k5_partfun3(k5_numbers,A,B))
& r1_xreal_0(k4_real_1(k2_rinfsup1(A),k2_rinfsup1(B)),k2_rinfsup1(k5_partfun3(k5_numbers,A,B))) ) ) ) ) ).
fof(t21_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(A)
& v4_partfun3(A)
& v1_seq_2(B)
& v4_partfun3(B) )
=> ( v1_seq_2(k5_partfun3(k5_numbers,A,B))
& r1_xreal_0(k1_rinfsup1(k5_partfun3(k5_numbers,A,B)),k4_real_1(k1_rinfsup1(A),k1_rinfsup1(B))) ) ) ) ) ).
fof(t22_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(A)
& v1_seq_2(A) )
=> v3_seq_2(A) ) ) ).
fof(t23_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(A)
& v2_seq_2(A) )
=> v3_seq_2(A) ) ) ).
fof(t24_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(A)
& v1_seq_2(A) )
=> k2_seq_2(A) = k1_rinfsup1(A) ) ) ).
fof(t25_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(A)
& v2_seq_2(A) )
=> k2_seq_2(A) = k2_rinfsup1(A) ) ) ).
fof(t26_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_seq_2(B)
=> v1_seq_2(k1_seqm_3(B,A)) ) ) ) ).
fof(t27_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v2_seq_2(B)
=> v2_seq_2(k1_seqm_3(B,A)) ) ) ) ).
fof(t28_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> v3_seq_2(k1_seqm_3(B,A)) ) ) ) ).
fof(t38_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k2_rinfsup1(k1_seqm_3(B,A)) ) ) ).
fof(t39_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k1_rinfsup1(k1_seqm_3(B,A)) ) ) ).
fof(t40_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
=> k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(A),np__0) = k2_rinfsup1(A) ) ) ).
fof(t41_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
=> k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(A),np__0) = k1_rinfsup1(A) ) ) ).
fof(t42_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v2_seq_2(C)
=> ( B = k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)
<=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D))) )
& ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_xcmplx_0(B,D),k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,E))) ) ) ) ) ) ) ) ) ) ).
fof(t43_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v1_seq_2(C)
=> ( B = k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A)
<=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D)),B) )
& ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,E)),k6_xcmplx_0(B,D)) ) ) ) ) ) ) ) ) ) ).
fof(t44_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v2_seq_2(C)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D))) )
<=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)) ) ) ) ) ) ).
fof(t45_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v2_seq_2(C)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,D)
=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,C,D)) ) )
<=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)) ) ) ) ) ) ).
fof(t46_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v1_seq_2(C)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D)),B) )
<=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A),B) ) ) ) ) ) ).
fof(t47_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v1_seq_2(C)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,D)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,D),B) ) )
<=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A),B) ) ) ) ) ) ).
fof(t48_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v2_seq_2(B)
=> k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k3_square_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) ).
fof(t49_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_seq_2(B)
=> k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k4_square_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) ).
fof(t50_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v2_seq_2(B)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1))) ) ) ) ).
fof(t51_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_seq_2(B)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A)) ) ) ) ).
fof(t52_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
=> v3_seqm_3(k3_rinfsup1(A)) ) ) ).
fof(t53_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
=> v4_seqm_3(k4_rinfsup1(A)) ) ) ).
fof(t54_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A)) ) ) ) ).
fof(t55_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_rinfsup1(k4_rinfsup1(B))) ) ) ) ).
fof(t56_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> r1_xreal_0(k1_rinfsup1(k3_rinfsup1(B)),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A)) ) ) ) ).
fof(t57_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> r1_xreal_0(k1_rinfsup1(k3_rinfsup1(A)),k2_rinfsup1(k4_rinfsup1(A))) ) ) ).
fof(t58_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> ( v3_seq_2(k4_rinfsup1(A))
& v3_seq_2(k3_rinfsup1(A)) ) ) ) ).
fof(t59_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> ( v4_seq_2(k3_rinfsup1(A))
& k2_seq_2(k3_rinfsup1(A)) = k1_rinfsup1(k3_rinfsup1(A)) ) ) ) ).
fof(t60_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> ( v4_seq_2(k4_rinfsup1(A))
& k2_seq_2(k4_rinfsup1(A)) = k2_rinfsup1(k4_rinfsup1(A)) ) ) ) ).
fof(t61_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v2_seq_2(B)
=> k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k1_real_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(k6_partfun3(k5_numbers,B)),A)) ) ) ) ).
fof(t62_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_seq_2(B)
=> k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k1_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k6_partfun3(k5_numbers,B)),A)) ) ) ) ).
fof(t63_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
=> k3_rinfsup1(A) = k6_partfun3(k5_numbers,k4_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) ).
fof(t64_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
=> k4_rinfsup1(A) = k6_partfun3(k5_numbers,k3_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) ).
fof(t65_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(B)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1))) ) ) ) ).
fof(t66_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
=> k3_rinfsup1(A) = A ) ) ).
fof(t67_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(B)
& v1_seq_2(B) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1))) ) ) ) ).
fof(t68_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(B)
& v1_seq_2(B) )
=> k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)) ) ) ) ).
fof(t69_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(B)
& v1_seq_2(B) )
=> ( k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k1_rinfsup1(B)
& v5_seqm_3(k4_rinfsup1(B)) ) ) ) ) ).
fof(t70_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(A)
& v1_seq_2(A) )
=> k2_rinfsup1(k4_rinfsup1(A)) = k1_rinfsup1(A) ) ) ).
fof(t71_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(B)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) ).
fof(t72_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
=> k4_rinfsup1(A) = A ) ) ).
fof(t73_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(B)
& v2_seq_2(B) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) ).
fof(t74_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(B)
& v2_seq_2(B) )
=> k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1)) ) ) ) ).
fof(t75_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(B)
& v2_seq_2(B) )
=> ( k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k2_rinfsup1(B)
& v5_seqm_3(k3_rinfsup1(B)) ) ) ) ) ).
fof(t76_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(A)
& v2_seq_2(A) )
=> k1_rinfsup1(k3_rinfsup1(A)) = k2_rinfsup1(A) ) ) ).
fof(t77_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& v3_seq_2(B)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,B,C)) ) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(A),C),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),C)) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(A),C),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),C)) ) ) ) ) ) ).
fof(t78_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(B)
& v2_seq_2(C) )
=> r1_xreal_0(k3_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k3_partfun3(k5_numbers,B,C)),A)) ) ) ) ) ).
fof(t79_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(B)
& v1_seq_2(C) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(k3_partfun3(k5_numbers,B,C)),A),k3_real_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A))) ) ) ) ) ).
fof(t80_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(B)
& v4_partfun3(B)
& v2_seq_2(C)
& v4_partfun3(C) )
=> r1_xreal_0(k4_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k5_partfun3(k5_numbers,B,C)),A)) ) ) ) ) ).
fof(t81_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(B)
& v4_partfun3(B)
& v2_seq_2(C)
& v4_partfun3(C) )
=> r1_xreal_0(k4_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k5_partfun3(k5_numbers,B,C)),A)) ) ) ) ) ).
fof(t82_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(B)
& v4_partfun3(B)
& v1_seq_2(C)
& v4_partfun3(C) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(k5_partfun3(k5_numbers,B,C)),A),k4_real_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A))) ) ) ) ) ).
fof(d6_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k5_rinfsup1(A) = k2_rinfsup1(k4_rinfsup1(A)) ) ).
fof(d7_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k6_rinfsup1(A) = k1_rinfsup1(k3_rinfsup1(A)) ) ).
fof(t83_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> ( r1_xreal_0(k6_rinfsup1(B),A)
<=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(C,np__0)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) ) ) ) ) ) ) ) ).
fof(t84_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> ( r1_xreal_0(A,k6_rinfsup1(B))
<=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) ).
fof(t85_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> ( A = k6_rinfsup1(B)
<=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(C,np__0)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) )
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) ) ).
fof(t86_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> ( r1_xreal_0(A,k5_rinfsup1(B))
<=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(C,np__0)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) ).
fof(t87_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> ( r1_xreal_0(k5_rinfsup1(B),A)
<=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) ) ) ) ) ) ) ) ).
fof(t88_rinfsup1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v3_seq_2(B)
=> ( A = k5_rinfsup1(B)
<=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(C,np__0)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) )
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) ) ) ) ) ) ) ) ) ).
fof(t89_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> r1_xreal_0(k6_rinfsup1(A),k5_rinfsup1(A)) ) ) ).
fof(t90_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& k5_rinfsup1(A) = k6_rinfsup1(A) )
<=> v4_seq_2(A) ) ) ).
fof(t91_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seq_2(A)
=> ( k2_seq_2(A) = k5_rinfsup1(A)
& k2_seq_2(A) = k6_rinfsup1(A) ) ) ) ).
fof(t92_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> ( k5_rinfsup1(k6_partfun3(k5_numbers,A)) = k1_real_1(k6_rinfsup1(A))
& k6_rinfsup1(k6_partfun3(k5_numbers,A)) = k1_real_1(k5_rinfsup1(A)) ) ) ) ).
fof(t93_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& v3_seq_2(B)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,B,C)) ) )
=> ( r1_xreal_0(k5_rinfsup1(A),k5_rinfsup1(B))
& r1_xreal_0(k6_rinfsup1(A),k6_rinfsup1(B)) ) ) ) ) ).
fof(t94_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& v3_seq_2(B) )
=> ( r1_xreal_0(k3_real_1(k6_rinfsup1(A),k6_rinfsup1(B)),k6_rinfsup1(k3_partfun3(k5_numbers,A,B)))
& r1_xreal_0(k6_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k6_rinfsup1(A),k5_rinfsup1(B)))
& r1_xreal_0(k6_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k5_rinfsup1(A),k6_rinfsup1(B)))
& r1_xreal_0(k3_real_1(k6_rinfsup1(A),k5_rinfsup1(B)),k5_rinfsup1(k3_partfun3(k5_numbers,A,B)))
& r1_xreal_0(k3_real_1(k5_rinfsup1(A),k6_rinfsup1(B)),k5_rinfsup1(k3_partfun3(k5_numbers,A,B)))
& r1_xreal_0(k5_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k5_rinfsup1(A),k5_rinfsup1(B)))
& ( ( v4_seq_2(A)
| v4_seq_2(B) )
=> ( k6_rinfsup1(k3_partfun3(k5_numbers,A,B)) = k3_real_1(k6_rinfsup1(A),k6_rinfsup1(B))
& k5_rinfsup1(k3_partfun3(k5_numbers,A,B)) = k3_real_1(k5_rinfsup1(A),k5_rinfsup1(B)) ) ) ) ) ) ) ).
fof(t95_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& v4_partfun3(A)
& v3_seq_2(B)
& v4_partfun3(B) )
=> ( r1_xreal_0(k4_real_1(k6_rinfsup1(A),k6_rinfsup1(B)),k6_rinfsup1(k5_partfun3(k5_numbers,A,B)))
& r1_xreal_0(k5_rinfsup1(k5_partfun3(k5_numbers,A,B)),k4_real_1(k5_rinfsup1(A),k5_rinfsup1(B))) ) ) ) ) ).
fof(dt_k1_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> m1_subset_1(k1_rinfsup1(A),k1_numbers) ) ).
fof(dt_k2_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> m1_subset_1(k2_rinfsup1(A),k1_numbers) ) ).
fof(dt_k3_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k3_rinfsup1(A))
& v1_funct_2(k3_rinfsup1(A),k5_numbers,k1_numbers)
& m2_relset_1(k3_rinfsup1(A),k5_numbers,k1_numbers) ) ) ).
fof(dt_k4_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k4_rinfsup1(A))
& v1_funct_2(k4_rinfsup1(A),k5_numbers,k1_numbers)
& m2_relset_1(k4_rinfsup1(A),k5_numbers,k1_numbers) ) ) ).
fof(dt_k5_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> m1_subset_1(k5_rinfsup1(A),k1_numbers) ) ).
fof(dt_k6_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> m1_subset_1(k6_rinfsup1(A),k1_numbers) ) ).
fof(t29_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> m1_subset_1(a_2_0_rinfsup1(A,B),k1_zfmisc_1(k1_numbers)) ) ) ).
fof(t30_rinfsup1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k1_pscomp_1(k5_numbers,k1_numbers,k1_seqm_3(B,A)) = a_2_1_rinfsup1(A,B) ) ) ).
fof(t31_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seq_2(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( C = a_2_0_rinfsup1(A,B)
=> v1_seq_4(C) ) ) ) ) ) ).
fof(t32_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seq_2(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( C = a_2_0_rinfsup1(A,B)
=> v2_seq_4(C) ) ) ) ) ) ).
fof(t33_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_2(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( C = a_2_0_rinfsup1(A,B)
=> v3_seq_4(C) ) ) ) ) ) ).
fof(t34_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( C = a_2_0_rinfsup1(A,B)
=> k4_pscomp_1(C) = k2_seq_1(k5_numbers,k1_numbers,A,B) ) ) ) ) ) ).
fof(t35_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( C = a_2_0_rinfsup1(A,B)
=> k3_pscomp_1(C) = k2_seq_1(k5_numbers,k1_numbers,A,B) ) ) ) ) ) ).
fof(t36_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
=> ( D = a_2_0_rinfsup1(A,C)
=> k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_pscomp_1(D) ) ) ) ) ) ).
fof(t37_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
=> ( D = a_2_0_rinfsup1(A,C)
=> k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_pscomp_1(D) ) ) ) ) ) ).
fof(d4_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( B = k3_rinfsup1(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
=> ( D = a_2_0_rinfsup1(A,C)
=> k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_pscomp_1(D) ) ) ) ) ) ) ).
fof(d5_rinfsup1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( B = k4_rinfsup1(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
=> ( D = a_2_0_rinfsup1(A,C)
=> k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_pscomp_1(D) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_rinfsup1,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_rinfsup1(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_seq_1(k5_numbers,k1_numbers,B,D)
& r1_xreal_0(C,D) ) ) ) ).
fof(fraenkel_a_2_1_rinfsup1,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( r2_hidden(A,a_2_1_rinfsup1(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_seq_1(k5_numbers,k1_numbers,C,D)
& r1_xreal_0(B,D) ) ) ) ).
%------------------------------------------------------------------------------