ITP001 Axioms: ITP077_7.ax
%------------------------------------------------------------------------------
% File : ITP077_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : topology.ax [Gau19]
% : HL4077_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 195 ( 54 unt; 76 typ; 0 def)
% Number of atoms : 283 ( 85 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 170 ( 6 ~; 3 |; 50 &)
% ( 31 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 59 ( 37 >; 22 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 74 ( 74 usr; 6 con; 0-4 aty)
% Number of variables : 495 ( 413 !; 9 ?; 495 :)
% ( 73 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Etopology_2Etopology,type,
tyop_2Etopology_2Etopology: $tType > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EBIGINTER_2E0,type,
c_2Epred__set_2EBIGINTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EBIGINTER_2E1,type,
c_2Epred__set_2EBIGINTER_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EBIGUNION_2E0,type,
c_2Epred__set_2EBIGUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EBIGUNION_2E1,type,
c_2Epred__set_2EBIGUNION_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2ECOMPL_2E0,type,
c_2Epred__set_2ECOMPL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ECOMPL_2E1,type,
c_2Epred__set_2ECOMPL_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EINTER_2E0,type,
c_2Epred__set_2EINTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINTER_2E2,type,
c_2Epred__set_2EINTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Etopology_2Eclosed_2E0,type,
c_2Etopology_2Eclosed_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Etopology_2Eclosed_2E1,type,
c_2Etopology_2Eclosed_2E1:
!>[A_27a: $tType] : ( tyop_2Etopology_2Etopology(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Eclosed__in_2E0,type,
c_2Etopology_2Eclosed__in_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Etopology_2Eclosed__in_2E2,type,
c_2Etopology_2Eclosed__in_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etopology_2Etopology(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Ehull_2E0,type,
c_2Etopology_2Ehull_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Etopology_2Ehull_2E2,type,
c_2Etopology_2Ehull_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Etopology_2Eistopology_2E0,type,
c_2Etopology_2Eistopology_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Etopology_2Eistopology_2E1,type,
c_2Etopology_2Eistopology_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Elimpt_2E0,type,
c_2Etopology_2Elimpt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Etopology_2Elimpt_2E3,type,
c_2Etopology_2Elimpt_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etopology_2Etopology(A_27a) * A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Eneigh_2E0,type,
c_2Etopology_2Eneigh_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Etopology_2Eneigh_2E2,type,
c_2Etopology_2Eneigh_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etopology_2Etopology(A_27a) * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Eopen_2E0,type,
c_2Etopology_2Eopen_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Etopology_2Eopen_2E1,type,
c_2Etopology_2Eopen_2E1:
!>[A_27a: $tType] : ( tyop_2Etopology_2Etopology(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Eopen__in_2E0,type,
c_2Etopology_2Eopen__in_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Etopology_2Eopen__in_2E1,type,
c_2Etopology_2Eopen__in_2E1:
!>[A_27a: $tType] : ( tyop_2Etopology_2Etopology(A_27a) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).
tff(c_2Etopology_2Eopen__in_2E2,type,
c_2Etopology_2Eopen__in_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etopology_2Etopology(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etopology_2Etopology_2E0,type,
c_2Etopology_2Etopology_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Etopology_2Etopology(A_27a)) ).
tff(c_2Etopology_2Etopology_2E1,type,
c_2Etopology_2Etopology_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Etopology_2Etopology(A_27a) ) ).
tff(c_2Etopology_2Etopspace_2E0,type,
c_2Etopology_2Etopspace_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Etopology_2Etopspace_2E1,type,
c_2Etopology_2Etopspace_2E1:
!>[A_27a: $tType] : ( tyop_2Etopology_2Etopology(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Etopology_2Etopology_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Etopology_2Etopology(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Etopology_2Etopology(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Etopology_2Eclosed_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Eclosed_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Ebool,c_2Etopology_2Eclosed_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Etopology_2Eclosed__in_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Eclosed__in_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eclosed__in_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Etopology_2Ehull_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Ehull_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Etopology_2Ehull_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Etopology_2Eistopology_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Etopology_2Eistopology_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Etopology_2Eistopology_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etopology_2Elimpt_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Elimpt_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Etopology_2Elimpt_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Etopology_2Eneigh_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a),X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)] : ( c_2Etopology_2Eneigh_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool),c_2Etopology_2Eneigh_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Etopology_2Eopen_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Eopen_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Ebool,c_2Etopology_2Eopen_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etopology_2Eopen__in_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Eopen__in_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eopen__in_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Etopology_2Eopen__in_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Eopen__in_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eopen__in_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Etopology_2Etopology_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Etopology_2Etopology_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Etopology_2Etopology(A_27a),c_2Etopology_2Etopology_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etopology_2Etopspace_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Etopspace_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Etopology_2Eistopology,axiom,
! [A_27a: $tType,V0L_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eistopology_2E1(A_27a,V0L_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),V0L_2E0))
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,V0L_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,V0L_2E0)) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0),V0L_2E0)) )
& ! [V3k_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3k_2E0,V0L_2E0))
=> p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(A_27a,V3k_2E0),V0L_2E0)) ) ) ) ).
tff(thm_2Etopology_2Etopology__TY__DEF,axiom,
! [A_27a: $tType] :
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Etopology_2Etopology(A_27a),c_2Etopology_2Eistopology_2E0(A_27a),V0rep_2E0)) ).
tff(thm_2Etopology_2Etopology__tybij,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Etopology_2E1(A_27a,c_2Etopology_2Eopen__in_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eistopology_2E1(A_27a,V1r_2E0))
<=> ( c_2Etopology_2Eopen__in_2E1(A_27a,c_2Etopology_2Etopology_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Etopology_2Eopen__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Eopen_2E1(A_27a,V0s_2E0) = c_2Etopology_2Eopen__in_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) ) ).
tff(thm_2Etopology_2Etopspace,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
( ! [V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0top_2E0),V1s_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1s_2E0,c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0)) )
=> ! [V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0) = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0top_2E0))) ) ) ).
tff(thm_2Etopology_2Eneigh,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Etopology_2Eneigh_2E2(A_27a,V0top_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,V1N_2E0,V2x_2E0)))
<=> ? [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V3P_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3P_2E0,V1N_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V2x_2E0)) ) ) ).
tff(thm_2Etopology_2Eclosed__in,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1s_2E0))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0)))
& p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0),V1s_2E0))) ) ) ).
tff(thm_2Etopology_2Eclosed__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Etopology_2Etopology(A_27a)] : ( c_2Etopology_2Eclosed_2E1(A_27a,V0s_2E0) = c_2Etopology_2Eclosed__in_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) ) ).
tff(thm_2Etopology_2Elimpt,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1x_2E0: A_27a,V2S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Elimpt_2E3(A_27a,V0top_2E0,V1x_2E0,V2S_27_2E0))
<=> ! [V3N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eneigh_2E2(A_27a,V0top_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,V3N_2E0,V1x_2E0)))
=> ? [V4y_2E0: A_27a] :
( ( V1x_2E0 != V4y_2E0 )
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2S_27_2E0,V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3N_2E0,V4y_2E0)) ) ) ) ).
tff(thm_2Etopology_2Ehull,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V2t_2E0),V1s_2E0))
<=> ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0)) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1s_2E0),V2t_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2t_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V2t_2E0),V1s_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0) = c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1s_2E0))) ) ) ) ).
tff(thm_2Etopology_2EISTOPOLOGY__OPEN__IN,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] : p(c_2Etopology_2Eistopology_2E1(A_27a,c_2Etopology_2Eopen__in_2E1(A_27a,V0top_2E0))) ).
tff(thm_2Etopology_2ETOPOLOGY__EQ,axiom,
! [A_27a: $tType,V0top1_2E0: tyop_2Etopology_2Etopology(A_27a),V1top2_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( ( V0top1_2E0 = V1top2_2E0 )
<=> ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Eopen__in_2E2(A_27a,V0top1_2E0,V2s_2E0) = c_2Etopology_2Eopen__in_2E2(A_27a,V1top2_2E0,V2s_2E0) ) ) ).
tff(thm_2Etopology_2Eopen__topspace,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eopen_2E1(A_27a,V0top_2E0))
=> ( c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Etopology_2EOPEN__IN__CLAUSES,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0))) )
& ! [V3k_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0,V3k_2E0))
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V4s_2E0)) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V3k_2E0))) ) ) ).
tff(thm_2Etopology_2EOPEN__IN__SUBSET,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0))) ) ).
tff(thm_2Etopology_2EOPEN__IN__EMPTY,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] : p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Etopology_2EOPEN__IN__INTER,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2EOPEN__IN__BIGUNION,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1k_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,V1k_2E0))
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V2s_2E0)) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1k_2E0))) ) ).
tff(thm_2Etopology_2EBIGUNION__2,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) = c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0) ) ).
tff(thm_2Etopology_2EOPEN__IN__UNION,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2EOPEN__IN__TOPSPACE,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] : p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0))) ).
tff(thm_2Etopology_2EOPEN__IN__BIGINTER,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))
& ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) )
& ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,V1s_2E0))
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V2t_2E0)) ) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1s_2E0))) ) ).
tff(thm_2Etopology_2EOPEN__IN__SUBOPEN,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> ? [V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V3t_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V3t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3t_2E0,V1s_2E0)) ) ) ) ).
tff(thm_2Etopology_2EOPEN__OWN__NEIGH,axiom,
! [A_27a: $tType,V0S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1top_2E0: tyop_2Etopology_2Etopology(A_27a),V2x_2E0: A_27a] :
( ( p(c_2Etopology_2Eopen__in_2E2(A_27a,V1top_2E0,V0S_27_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0S_27_2E0,V2x_2E0)) )
=> p(c_2Etopology_2Eneigh_2E2(A_27a,V1top_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,V0S_27_2E0,V2x_2E0))) ) ).
tff(thm_2Etopology_2EOPEN__UNOPEN,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
( ! [V1top_2E0: tyop_2Etopology_2Etopology(A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V1top_2E0),V2P_2E0),V0S_27_2E0))
<=> ( p(c_2Etopology_2Eopen__in_2E2(A_27a,V1top_2E0,V2P_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2P_2E0,V0S_27_2E0)) ) )
=> ( ! [V1top_2E0: tyop_2Etopology_2Etopology(A_27a),V0S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1top_2E0),V0S_27_2E0),V2P_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2P_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V1top_2E0),V2P_2E0),V0S_27_2E0)) )
=> ! [V0S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V1top_2E0,V0S_27_2E0))
<=> ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1top_2E0),V0S_27_2E0))) = V0S_27_2E0 ) ) ) ) ).
tff(thm_2Etopology_2EOPEN__SUBOPEN,axiom,
! [A_27a: $tType,V0S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V1top_2E0,V0S_27_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0S_27_2E0,V2x_2E0))
=> ? [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V2x_2E0))
& p(c_2Etopology_2Eopen__in_2E2(A_27a,V1top_2E0,V3P_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3P_2E0,V0S_27_2E0)) ) ) ) ).
tff(thm_2Etopology_2EOPEN__NEIGH,axiom,
! [A_27a: $tType,V0S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V1top_2E0,V0S_27_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0S_27_2E0,V2x_2E0))
=> ? [V3N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eneigh_2E2(A_27a,V1top_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,V3N_2E0,V2x_2E0)))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3N_2E0,V0S_27_2E0)) ) ) ) ).
tff(thm_2Etopology_2Eclosed__topspace,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eclosed_2E1(A_27a,V0top_2E0))
=> ( c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Etopology_2ECLOSED__IN__OPEN__IN__COMPL,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eclosed_2E1(A_27a,V0top_2E0))
=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1s_2E0) = c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,V1s_2E0)) ) ) ).
tff(thm_2Etopology_2ECLOSED__IN__SUBSET,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1s_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0))) ) ).
tff(thm_2Etopology_2ECLOSED__IN__EMPTY,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] : p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Etopology_2ECLOSED__IN__TOPSPACE,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] : p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0))) ).
tff(thm_2Etopology_2ECLOSED__IN__UNION,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2ECLOSED__IN__BIGINTER,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1k_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( ( V1k_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) )
& ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,V1k_2E0))
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V2s_2E0)) ) )
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1k_2E0))) ) ).
tff(thm_2Etopology_2EBIGINTER__2,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) = c_2Epred__set_2EINTER_2E2(A_27a,V0P_2E0,V1Q_2E0) ) ).
tff(thm_2Etopology_2ECLOSED__IN__INTER,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2EOPEN__IN__CLOSED__IN__EQ,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0)))
& p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0),V1s_2E0))) ) ) ).
tff(thm_2Etopology_2EOPEN__IN__CLOSED__IN,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0)))
=> ( c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0) = c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Etopology_2Etopspace_2E1(A_27a,V0top_2E0),V1s_2E0)) ) ) ).
tff(thm_2Etopology_2EOPEN__IN__DIFF,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2ECLOSED__IN__DIFF,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1s_2E0))
& p(c_2Etopology_2Eopen__in_2E2(A_27a,V0top_2E0,V2t_2E0)) )
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2ECLOSED__IN__BIGUNION,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))
& ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,V1s_2E0))
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V2t_2E0)) ) )
=> p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1s_2E0))) ) ).
tff(thm_2Etopology_2ECLOSED__LIMPT,axiom,
! [A_27a: $tType,V0top_2E0: tyop_2Etopology_2Etopology(A_27a)] :
( p(c_2Etopology_2Eclosed_2E1(A_27a,V0top_2E0))
=> ! [V1S_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Etopology_2Eclosed__in_2E2(A_27a,V0top_2E0,V1S_27_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Etopology_2Elimpt_2E3(A_27a,V0top_2E0,V2x_2E0,V1S_27_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1S_27_2E0,V2x_2E0)) ) ) ) ).
tff(thm_2Etopology_2EHULL__P,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1s_2E0))
=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0) = V1s_2E0 ) ) ).
tff(thm_2Etopology_2EP__HULL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,V2f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3s_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V2f_2E0))) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0))) ) ).
tff(thm_2Etopology_2EHULL__EQ,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,V2f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3s_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V2f_2E0))) )
=> ( ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0) = V1s_2E0 )
<=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1s_2E0)) ) ) ).
tff(thm_2Etopology_2EHULL__HULL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0)) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0) ) ).
tff(thm_2Etopology_2EHULL__SUBSET,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0))) ).
tff(thm_2Etopology_2EHULL__MONO,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0),c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2EHULL__ANTIMONO,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V1Q_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V1Q_2E0,V2s_2E0),c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0))) ) ).
tff(thm_2Etopology_2EHULL__MINIMAL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0))
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2t_2E0)) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0),V2t_2E0)) ) ).
tff(thm_2Etopology_2ESUBSET__HULL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2t_2E0))
=> ( c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0),V2t_2E0) = c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0) ) ) ).
tff(thm_2Etopology_2EHULL__UNIQUE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0))
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2t_2E0))
& ! [V3t_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V3t_27_2E0))
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3t_27_2E0)) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V3t_27_2E0)) ) )
=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0) = V2t_2E0 ) ) ).
tff(thm_2Etopology_2EHULL__UNION__SUBSET,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0),c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2t_2E0)),c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)))) ).
tff(thm_2Etopology_2EHULL__UNION,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0),c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2EHULL__UNION__LEFT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0),V2t_2E0)) ) ).
tff(thm_2Etopology_2EHULL__UNION__RIGHT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2t_2E0))) ) ).
tff(thm_2Etopology_2EHULL__REDUNDANT__EQ,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1a_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1a_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0)))
<=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,V2s_2E0)) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0) ) ) ).
tff(thm_2Etopology_2EHULL__REDUNDANT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1a_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1a_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0)))
=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,V2s_2E0)) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0) ) ) ).
tff(thm_2Etopology_2EHULL__INDUCT,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1p_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,V1p_2E0,V4x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1p_2E0,V3x_2E0)) )
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1p_2E0)))) )
=> ! [V5x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1p_2E0,V5x_2E0)) ) ) ) ).
tff(thm_2Etopology_2EHULL__INC,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0))) ) ).
tff(thm_2Etopology_2EHULL__IMAGE__SUBSET,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0)))
& ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3s_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V3s_2E0))) ) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V2s_2E0)),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0)))) ) ).
tff(thm_2Etopology_2EHULL__IMAGE__GALOIS,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V2g_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V4s_2E0)))
& ! [V5s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V5s_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V5s_2E0))) )
& ! [V6s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V6s_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V2g_2E0,V6s_2E0))) )
& ! [V7s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,V7s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V2g_2E0,V8t_2E0)) = c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V7s_2E0),V8t_2E0) ) )
=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V3s_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V3s_2E0)) ) ) ).
tff(thm_2Etopology_2EHULL__IMAGE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V3s_2E0)))
& ! [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V4s_2E0)) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V4s_2E0) )
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27a,V1f_2E0,V5x_2E0) = app_2E2(A_27a,A_27a,V1f_2E0,V6y_2E0) )
=> ( V5x_2E0 = V6y_2E0 ) )
& ! [V7y_2E0: A_27a] :
? [V8x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,V1f_2E0,V8x_2E0) = V7y_2E0 ) )
=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V2s_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2s_2E0)) ) ) ).
tff(thm_2Etopology_2EIS__HULL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0,V2f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3s_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V2f_2E0))) )
=> ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1s_2E0))
<=> ? [V4t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( V1s_2E0 = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V4t_2E0) ) ) ) ).
tff(thm_2Etopology_2EHULLS__EQ,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0,V3f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V4s_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V3f_2E0))) )
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2t_2E0)))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0))) )
=> ( c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V1s_2E0) = c_2Etopology_2Ehull_2E2(A_27a,V0P_2E0,V2t_2E0) ) ) ).
tff(thm_2Etopology_2EHULL__P__AND__Q,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
( ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V8x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V2Q_2E0),V8x_2E0))
<=> ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,V8x_2E0))
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2Q_2E0,V8x_2E0)) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( ! [V3f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0,V3f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,V4s_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V3f_2E0))) )
& ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V6s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6s_2E0,V5f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2Q_2E0,V6s_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2Q_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V5f_2E0))) )
& ! [V7s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2Q_2E0,V7s_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2Q_2E0,c_2Etopology_2Ehull_2E2(A_27a,V1P_2E0,V7s_2E0))) ) )
=> ( c_2Etopology_2Ehull_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V2Q_2E0),V0s_2E0) = c_2Etopology_2Ehull_2E2(A_27a,V1P_2E0,c_2Etopology_2Ehull_2E2(A_27a,V2Q_2E0,V0s_2E0)) ) ) ) ).
%------------------------------------------------------------------------------