ITP001 Axioms: ITP011_7.ax
%------------------------------------------------------------------------------
% File : ITP011_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 : relation.ax [Gau19]
% : HL4011_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 532 ( 186 unt; 156 typ; 0 def)
% Number of atoms : 863 ( 242 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 501 ( 14 ~; 19 |; 145 &)
% ( 83 <=>; 240 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 162 ( 85 >; 77 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 154 ( 154 usr; 6 con; 0-7 aty)
% Number of variables : 1682 (1458 !; 20 ?;1682 :)
% ( 204 !>; 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(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_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_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Erelation_2ECR_2E0,type,
c_2Erelation_2ECR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2ECR_2E1,type,
c_2Erelation_2ECR_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EEMPTY__REL_2E0,type,
c_2Erelation_2EEMPTY__REL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2EEMPTY__REL_2E2,type,
c_2Erelation_2EEMPTY__REL_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EEQC_2E0,type,
c_2Erelation_2EEQC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2EEQC_2E1,type,
c_2Erelation_2EEQC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2EEQC_2E3,type,
c_2Erelation_2EEQC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Erelation_2EIDEM_2E0,type,
c_2Erelation_2EIDEM_2E0:
!>[A_27z: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EIDEM_2E1,type,
c_2Erelation_2EIDEM_2E1:
!>[A_27z: $tType] : ( tyop_2Emin_2Efun(A_27z,A_27z) > 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_2Erelation_2EINDUCTIVE__INVARIANT_2E0,type,
c_2Erelation_2EINDUCTIVE__INVARIANT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2EINDUCTIVE__INVARIANT_2E3,type,
c_2Erelation_2EINDUCTIVE__INVARIANT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E0,type,
c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4,type,
c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EINVOL_2E0,type,
c_2Erelation_2EINVOL_2E0:
!>[A_27z: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EINVOL_2E1,type,
c_2Erelation_2EINVOL_2E1:
!>[A_27z: $tType] : ( tyop_2Emin_2Efun(A_27z,A_27z) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ELinearOrder_2E0,type,
c_2Erelation_2ELinearOrder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2ELinearOrder_2E1,type,
c_2Erelation_2ELinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EO_2E0,type,
c_2Erelation_2EO_2E0:
!>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2EO_2E2,type,
c_2Erelation_2EO_2E2:
!>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : ( ( tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2EO_2E4,type,
c_2Erelation_2EO_2E4:
!>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : ( ( tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)) * A_27g * A_27k ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EOrder_2E0,type,
c_2Erelation_2EOrder_2E0:
!>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EOrder_2E1,type,
c_2Erelation_2EOrder_2E1:
!>[A_27g: $tType] : ( tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EPreOrder_2E0,type,
c_2Erelation_2EPreOrder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EPreOrder_2E1,type,
c_2Erelation_2EPreOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERC_2E0,type,
c_2Erelation_2ERC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ERC_2E1,type,
c_2Erelation_2ERC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERC_2E3,type,
c_2Erelation_2ERC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERCOMPL_2E0,type,
c_2Erelation_2ERCOMPL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ERCOMPL_2E1,type,
c_2Erelation_2ERCOMPL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERCOMPL_2E3,type,
c_2Erelation_2ERCOMPL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERDOM_2E0,type,
c_2Erelation_2ERDOM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2ERDOM_2E1,type,
c_2Erelation_2ERDOM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Erelation_2ERDOM_2E2,type,
c_2Erelation_2ERDOM_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERDOM__DELETE_2E0,type,
c_2Erelation_2ERDOM__DELETE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2ERDOM__DELETE_2E2,type,
c_2Erelation_2ERDOM__DELETE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERDOM__DELETE_2E4,type,
c_2Erelation_2ERDOM__DELETE_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a * A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERESTRICT_2E0,type,
c_2Erelation_2ERESTRICT_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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))) ).
tff(c_2Erelation_2ERESTRICT_2E3,type,
c_2Erelation_2ERESTRICT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Erelation_2ERESTRICT_2E4,type,
c_2Erelation_2ERESTRICT_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > A_27b ) ).
tff(c_2Erelation_2ERINTER_2E0,type,
c_2Erelation_2ERINTER_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2ERINTER_2E2,type,
c_2Erelation_2ERINTER_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERINTER_2E4,type,
c_2Erelation_2ERINTER_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERRANGE_2E0,type,
c_2Erelation_2ERRANGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2ERRANGE_2E1,type,
c_2Erelation_2ERRANGE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Erelation_2ERRANGE_2E2,type,
c_2Erelation_2ERRANGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERRESTRICT_2E0,type,
c_2Erelation_2ERRESTRICT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2ERRESTRICT_2E2,type,
c_2Erelation_2ERRESTRICT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERRESTRICT_2E4,type,
c_2Erelation_2ERRESTRICT_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERSUBSET_2E0,type,
c_2Erelation_2ERSUBSET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2ERSUBSET_2E2,type,
c_2Erelation_2ERSUBSET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERTC_2E0,type,
c_2Erelation_2ERTC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ERTC_2E1,type,
c_2Erelation_2ERTC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERTC_2E3,type,
c_2Erelation_2ERTC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERUNION_2E0,type,
c_2Erelation_2ERUNION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2ERUNION_2E2,type,
c_2Erelation_2ERUNION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERUNION_2E4,type,
c_2Erelation_2ERUNION_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERUNIV_2E0,type,
c_2Erelation_2ERUNIV_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2ERUNIV_2E2,type,
c_2Erelation_2ERUNIV_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ESC_2E0,type,
c_2Erelation_2ESC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ESC_2E1,type,
c_2Erelation_2ESC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ESC_2E3,type,
c_2Erelation_2ESC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ESN_2E0,type,
c_2Erelation_2ESN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2ESN_2E1,type,
c_2Erelation_2ESN_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ESTRORD_2E0,type,
c_2Erelation_2ESTRORD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ESTRORD_2E1,type,
c_2Erelation_2ESTRORD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ESTRORD_2E3,type,
c_2Erelation_2ESTRORD_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EStrongLinearOrder_2E0,type,
c_2Erelation_2EStrongLinearOrder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EStrongLinearOrder_2E1,type,
c_2Erelation_2EStrongLinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EStrongOrder_2E0,type,
c_2Erelation_2EStrongOrder_2E0:
!>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EStrongOrder_2E1,type,
c_2Erelation_2EStrongOrder_2E1:
!>[A_27g: $tType] : ( tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Erelation_2ETC_2E0,type,
c_2Erelation_2ETC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ETC_2E1,type,
c_2Erelation_2ETC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ETC_2E3,type,
c_2Erelation_2ETC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWCR_2E0,type,
c_2Erelation_2EWCR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWCR_2E1,type,
c_2Erelation_2EWCR_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWFP_2E0,type,
c_2Erelation_2EWFP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2EWFP_2E2,type,
c_2Erelation_2EWFP_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Erelation_2EWFREC_2E3,type,
c_2Erelation_2EWFREC_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) * A_27a ) > A_27b ) ).
tff(c_2Erelation_2EWeakLinearOrder_2E0,type,
c_2Erelation_2EWeakLinearOrder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWeakLinearOrder_2E1,type,
c_2Erelation_2EWeakLinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWeakOrder_2E0,type,
c_2Erelation_2EWeakOrder_2E0:
!>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWeakOrder_2E1,type,
c_2Erelation_2EWeakOrder_2E1:
!>[A_27g: $tType] : ( tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)) > 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_2Erelation_2Eantisymmetric_2E0,type,
c_2Erelation_2Eantisymmetric_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Eantisymmetric_2E1,type,
c_2Erelation_2Eantisymmetric_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Eapprox_2E0,type,
c_2Erelation_2Eapprox_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2Eapprox_2E4,type,
c_2Erelation_2Eapprox_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) * A_27a * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Ediag_2E0,type,
c_2Erelation_2Ediag_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2Ediag_2E1,type,
c_2Erelation_2Ediag_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2Ediag_2E3,type,
c_2Erelation_2Ediag_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Ediamond_2E0,type,
c_2Erelation_2Ediamond_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Ediamond_2E1,type,
c_2Erelation_2Ediamond_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Eequivalence_2E0,type,
c_2Erelation_2Eequivalence_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Eequivalence_2E1,type,
c_2Erelation_2Eequivalence_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Einv_2E0,type,
c_2Erelation_2Einv_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2Einv_2E1,type,
c_2Erelation_2Einv_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2Einv_2E3,type,
c_2Erelation_2Einv_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27b * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Einv__image_2E0,type,
c_2Erelation_2Einv__image_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2Einv__image_2E2,type,
c_2Erelation_2Einv__image_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2Einv__image_2E4,type,
c_2Erelation_2Einv__image_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Eirreflexive_2E0,type,
c_2Erelation_2Eirreflexive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Eirreflexive_2E1,type,
c_2Erelation_2Eirreflexive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Enf_2E0,type,
c_2Erelation_2Enf_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2Enf_2E2,type,
c_2Erelation_2Enf_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Erelation_2Ercdiamond_2E0,type,
c_2Erelation_2Ercdiamond_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Ercdiamond_2E1,type,
c_2Erelation_2Ercdiamond_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Ereflexive_2E0,type,
c_2Erelation_2Ereflexive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Ereflexive_2E1,type,
c_2Erelation_2Ereflexive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Esymmetric_2E0,type,
c_2Erelation_2Esymmetric_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Esymmetric_2E1,type,
c_2Erelation_2Esymmetric_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Ethe__fun_2E0,type,
c_2Erelation_2Ethe__fun_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))) ).
tff(c_2Erelation_2Ethe__fun_2E3,type,
c_2Erelation_2Ethe__fun_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) * A_27a ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Erelation_2Etotal_2E0,type,
c_2Erelation_2Etotal_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Etotal_2E1,type,
c_2Erelation_2Etotal_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Etransitive_2E0,type,
c_2Erelation_2Etransitive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Etransitive_2E1,type,
c_2Erelation_2Etransitive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Etrichotomous_2E0,type,
c_2Erelation_2Etrichotomous_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Etrichotomous_2E1,type,
c_2Erelation_2Etrichotomous_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > 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_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_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,A_27b),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ECR_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ECR_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EEMPTY__REL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : ( c_2Erelation_2EEMPTY__REL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2EEMPTY__REL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EEQC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EEQC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2EEQC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2EEQC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EIDEM_2E1_2Emono_2EA_27z,axiom,
! [A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] : ( c_2Erelation_2EIDEM_2E1(A_27z,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E0(A_27z),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EIDEM_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Erelation_2EIDEM_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_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(arityeq3_2Ec_2Erelation_2EINDUCTIVE__INVARIANT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Erelation_2EINDUCTIVE__INVARIANT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2EA_27z,axiom,
! [A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] : ( c_2Erelation_2EINVOL_2E1(A_27z,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E0(A_27z),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2Erelation_2EINVOL_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Erelation_2EINVOL_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ELinearOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ELinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2ELinearOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27b,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27b,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27d,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27d,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27d,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27d,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2EO_2E4_2Emono_2EA_27g_20mono_2EA_27h_20mono_2EA_27k,axiom,
! [A_27g: $tType,A_27h: $tType,A_27k: $tType,X0_2E0: tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X2_2E0: A_27g,X3_2E0: A_27k] : ( c_2Erelation_2EO_2E4(A_27g,A_27h,A_27k,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27k,tyop_2Emin_2Ebool,app_2E2(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27g,A_27h,A_27k),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EOrder_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E0(A_27g),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EPreOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EPreOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EPreOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ERC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ERC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERCOMPL_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERCOMPL_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERCOMPL_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ERCOMPL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27b] : ( c_2Erelation_2ERCOMPL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERCOMPL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERDOM_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERDOM_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Erelation_2ERDOM_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERDOM__DELETE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Erelation_2ERDOM__DELETE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERDOM__DELETE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2ERDOM__DELETE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a,X3_2E0: A_27b] : ( c_2Erelation_2ERDOM__DELETE_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERDOM__DELETE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ERESTRICT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0: A_27a] : ( c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2ERESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2ERESTRICT_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Erelation_2ERESTRICT_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2ERESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERINTER_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERINTER_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERINTER_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERINTER_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2ERINTER_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: A_27a,X3_2E0: A_27b] : ( c_2Erelation_2ERINTER_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERINTER_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERRANGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27b] : ( c_2Erelation_2ERRANGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERRANGE_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erelation_2ERRESTRICT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERRESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2ERRESTRICT_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a,X3_2E0: A_27b] : ( c_2Erelation_2ERRESTRICT_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERRESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ERSUBSET_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ERSUBSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERSUBSET_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ERSUBSET_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERSUBSET_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ERSUBSET_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERTC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ERTC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERUNION_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERUNION_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERUNION_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERUNION_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2ERUNION_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: A_27a,X3_2E0: A_27b] : ( c_2Erelation_2ERUNION_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERUNION_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERUNIV_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Erelation_2ERUNIV_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Erelation_2ERUNIV_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ESC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ESC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ESC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ESN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESTRORD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ESTRORD_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ESTRORD_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongLinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongOrder_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E0(A_27g),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ETC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ETC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWCR_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWCR_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFP_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Erelation_2EWFP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2EWFP_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2Erelation_2EWFREC_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Erelation_2EWFREC_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2EWFREC_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0: A_27a] : ( c_2Erelation_2EWFREC_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Erelation_2EWFREC_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWeakLinearOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakLinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakOrder_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E0(A_27g),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWeakOrder_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_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_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eantisymmetric_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eantisymmetric_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E0(A_27g),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eantisymmetric_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2Eapprox_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0: A_27a,X3_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Erelation_2Eapprox_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Erelation_2Eapprox_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Ediag_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erelation_2Ediag_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2Ediag_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2Ediag_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Ediamond_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ediamond_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eequivalence_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eequivalence_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2Einv_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27b,X2_2E0: A_27a] : ( c_2Erelation_2Einv_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Erelation_2Einv__image_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Erelation_2Einv__image_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Erelation_2Einv__image_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Erelation_2Einv__image_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E0(A_27g),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2Enf_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Erelation_2Enf_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2Enf_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27z_20mono_2EA_27z_20mono_2EA_27z,axiom,
! [A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(A_27z,A_27z),X1_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] : ( c_2Ecombin_2Eo_2E2(A_27z,A_27z,A_27z,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(A_27z,A_27z),app_2E2(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(A_27z,A_27z)),c_2Ecombin_2Eo_2E0(A_27z,A_27z,A_27z),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Ercdiamond_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ercdiamond_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ereflexive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ereflexive_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ereflexive_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E0(A_27g),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Esymmetric_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Esymmetric_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E0(A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2Ethe__fun_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0: A_27a] : ( c_2Erelation_2Ethe__fun_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2Ethe__fun_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etotal_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etotal_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27g,axiom,
! [A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27g,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27g),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etrichotomous_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etrichotomous_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_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_2Erelation_2Etransitive__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V3z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0)) ) ) ).
tff(thm_2Erelation_2Ereflexive__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V1x_2E0)) ) ).
tff(thm_2Erelation_2Eirreflexive__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a] : ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V1x_2E0)) ) ).
tff(thm_2Erelation_2Esymmetric__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0) ) ) ).
tff(thm_2Erelation_2Eantisymmetric__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0)) )
=> ( V1x_2E0 = V2y_2E0 ) ) ) ).
tff(thm_2Erelation_2Eequivalence__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Eequivalence_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2Etotal__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0)) ) ) ).
tff(thm_2Erelation_2Etrichotomous,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0))
<=> ! [V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1a_2E0),V2b_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2b_2E0),V1a_2E0))
| ( V1a_2E0 = V2b_2E0 ) ) ) ).
tff(thm_2Erelation_2ETC__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1a_2E0,V2b_2E0))
<=> ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V4x_2E0),V5y_2E0)) )
& ! [V6x_2E0: A_27a,V7y_2E0: A_27a,V8z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V6x_2E0),V7y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V7y_2E0),V8z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V6x_2E0),V8z_2E0)) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V1a_2E0),V2b_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1a_2E0,V2b_2E0))
<=> ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V4x_2E0),V4x_2E0))
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a,V7z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V6y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V6y_2E0),V7z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V5x_2E0),V7z_2E0)) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0,V1a_2E0),V2b_2E0)) ) ) ).
tff(thm_2Erelation_2ERC__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ( ( V1x_2E0 = V2y_2E0 )
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) ) ) ).
tff(thm_2Erelation_2ESC__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ESC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0)) ) ) ).
tff(thm_2Erelation_2EEQC__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) = c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,c_2Erelation_2ESC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2EWF__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
<=> ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V2w_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1B_2E0,V2w_2E0))
=> ? [V3min_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1B_2E0,V3min_2E0))
& ! [V4b_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4b_2E0),V3min_2E0))
=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1B_2E0,V4b_2E0)) ) ) ) ) ).
tff(thm_2Erelation_2EEMPTY__REL__DEF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] : ( c_2Erelation_2EEMPTY__REL_2E2(A_27a,V0x_2E0,V1y_2E0) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2Erelation_2Einv__image__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a,V3x_27_2E0: A_27a] : ( c_2Erelation_2Einv__image_2E4(A_27a,A_27b,V0R_2E0,V1f_2E0,V2x_2E0,V3x_27_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0)),app_2E2(A_27a,A_27b,V1f_2E0,V3x_27_2E0)) ) ).
tff(thm_2Erelation_2ERESTRICT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2x_2E0: A_27a,V3x_27_2E0: A_27a] : ( c_2Erelation_2ERESTRICT_2E4(A_27a,A_27b,V0f_2E0,V1R_2E0,V2x_2E0,V3x_27_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V3x_27_2E0),V2x_2E0),app_2E2(A_27a,A_27b,V0f_2E0,V3x_27_2E0),c_2Ebool_2EARB_2E0(A_27b)) ) ).
tff(thm_2Erelation_2Eapprox__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))))] :
( ! [V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0,V1M_2E0),V3f_2E0),V0R_2E0),V4y_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1M_2E0,c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,V3f_2E0,V0R_2E0,V4y_2E0)),V4y_2E0) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2x_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Erelation_2Eapprox_2E4(A_27a,A_27b,V0R_2E0,V1M_2E0,V2x_2E0,V3f_2E0))
<=> ( V3f_2E0 = c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0,V1M_2E0),V3f_2E0),V0R_2E0),V0R_2E0,V2x_2E0) ) ) ) ).
tff(thm_2Erelation_2Ethe__fun__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2x_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1M_2E0),V2x_2E0),V3f_2E0) = c_2Erelation_2Eapprox_2E4(A_27a,A_27b,V0R_2E0,V1M_2E0,V2x_2E0,V3f_2E0) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2x_2E0: A_27a] : ( c_2Erelation_2Ethe__fun_2E3(A_27a,A_27b,V0R_2E0,V1M_2E0,V2x_2E0) = c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1M_2E0),V2x_2E0)) ) ) ).
tff(thm_2Erelation_2EWFREC__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))))] :
( ! [V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4v_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0,V1M_2E0),V0R_2E0),V3f_2E0),V4v_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1M_2E0,c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,V3f_2E0,V0R_2E0,V4v_2E0)),V4v_2E0) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2x_2E0: A_27a] : ( c_2Erelation_2EWFREC_2E3(A_27a,A_27b,V0R_2E0,V1M_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1M_2E0,c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,c_2Erelation_2Ethe__fun_2E3(A_27a,A_27b,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0,V1M_2E0),V0R_2E0),V2x_2E0),V0R_2E0,V2x_2E0)),V2x_2E0) ) ) ).
tff(thm_2Erelation_2EWFP__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a] :
( p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V1a_2E0))
<=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] :
( ! [V4y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4y_2E0),V3x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V1a_2E0)) ) ) ).
tff(thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
( p(c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(A_27a,A_27b,V0R_2E0,V1P_2E0,V2M_2E0))
<=> ! [V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_2E0: A_27a] :
( ! [V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5y_2E0),V4x_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V5y_2E0),app_2E2(A_27a,A_27b,V3f_2E0,V5y_2E0))) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V2M_2E0,V3f_2E0),V4x_2E0))) ) ) ).
tff(thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1D_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
( p(c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(A_27a,A_27b,V0R_2E0,V1D_2E0,V2P_2E0,V3M_2E0))
<=> ! [V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5x_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1D_2E0,V5x_2E0))
& ! [V6y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1D_2E0,V6y_2E0))
=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V6y_2E0),V5x_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,V6y_2E0),app_2E2(A_27a,A_27b,V4f_2E0,V6y_2E0))) ) ) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,V5x_2E0),app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V3M_2E0,V4f_2E0),V5x_2E0))) ) ) ).
tff(thm_2Erelation_2Einv__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27b,V2y_2E0: A_27a] : ( c_2Erelation_2Einv_2E3(A_27a,A_27b,V0R_2E0,V1x_2E0,V2y_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0) ) ).
tff(thm_2Erelation_2EINVOL__DEF,axiom,
! [A_27z: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] :
( p(c_2Erelation_2EINVOL_2E1(A_27z,V0f_2E0))
<=> ( c_2Ecombin_2Eo_2E2(A_27z,A_27z,A_27z,V0f_2E0,V0f_2E0) = c_2Ecombin_2EI_2E0(A_27z) ) ) ).
tff(thm_2Erelation_2EIDEM__DEF,axiom,
! [A_27z: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] :
( p(c_2Erelation_2EIDEM_2E1(A_27z,V0f_2E0))
<=> ( c_2Ecombin_2Eo_2E2(A_27z,A_27z,A_27z,V0f_2E0,V0f_2E0) = V0f_2E0 ) ) ).
tff(thm_2Erelation_2EO__DEF,axiom,
! [A_27g: $tType,A_27h: $tType,A_27k: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V2x_2E0: A_27g,V3z_2E0: A_27k] :
( p(c_2Erelation_2EO_2E4(A_27g,A_27h,A_27k,V0R1_2E0,V1R2_2E0,V2x_2E0,V3z_2E0))
<=> ? [V4y_2E0: A_27h] :
( p(app_2E2(A_27h,tyop_2Emin_2Ebool,app_2E2(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),V1R2_2E0,V2x_2E0),V4y_2E0))
& p(app_2E2(A_27k,tyop_2Emin_2Ebool,app_2E2(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool),V0R1_2E0,V4y_2E0),V3z_2E0)) ) ) ).
tff(thm_2Erelation_2ERSUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V0R1_2E0,V1R2_2E0))
<=> ! [V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R1_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R2_2E0,V2x_2E0),V3y_2E0)) ) ) ).
tff(thm_2Erelation_2ERUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Erelation_2ERUNION_2E4(A_27a,A_27b,V0R1_2E0,V1R2_2E0,V2x_2E0,V3y_2E0))
<=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R1_2E0,V2x_2E0),V3y_2E0))
| p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R2_2E0,V2x_2E0),V3y_2E0)) ) ) ).
tff(thm_2Erelation_2ERINTER,axiom,
! [A_27a: $tType,A_27b: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Erelation_2ERINTER_2E4(A_27a,A_27b,V0R1_2E0,V1R2_2E0,V2x_2E0,V3y_2E0))
<=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R1_2E0,V2x_2E0),V3y_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R2_2E0,V2x_2E0),V3y_2E0)) ) ) ).
tff(thm_2Erelation_2ERCOMPL,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27b] :
( p(c_2Erelation_2ERCOMPL_2E3(A_27a,A_27b,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ~ p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) ) ).
tff(thm_2Erelation_2EPreOrder,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EPreOrder_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2EOrder,axiom,
! [A_27g: $tType,V0Z_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EOrder_2E1(A_27g,V0Z_2E0))
<=> ( p(c_2Erelation_2Eantisymmetric_2E1(A_27g,V0Z_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27g,V0Z_2E0)) ) ) ).
tff(thm_2Erelation_2EWeakOrder,axiom,
! [A_27g: $tType,V0Z_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakOrder_2E1(A_27g,V0Z_2E0))
<=> ( p(c_2Erelation_2Ereflexive_2E1(A_27g,V0Z_2E0))
& p(c_2Erelation_2Eantisymmetric_2E1(A_27g,V0Z_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27g,V0Z_2E0)) ) ) ).
tff(thm_2Erelation_2EStrongOrder,axiom,
! [A_27g: $tType,V0Z_2E0: tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongOrder_2E1(A_27g,V0Z_2E0))
<=> ( p(c_2Erelation_2Eirreflexive_2E1(A_27g,V0Z_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27g,V0Z_2E0)) ) ) ).
tff(thm_2Erelation_2ESTRORD,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(c_2Erelation_2ESTRORD_2E3(A_27a,V0R_2E0,V1a_2E0,V2b_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1a_2E0),V2b_2E0))
& ( V1a_2E0 != V2b_2E0 ) ) ) ).
tff(thm_2Erelation_2ELinearOrder,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2ELinearOrder_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Erelation_2EOrder_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2EStrongLinearOrder,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Erelation_2EStrongOrder_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2EWeakLinearOrder,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakLinearOrder_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Erelation_2EWeakOrder_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2Ediag__def,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2Ediag_2E3(A_27a,V0A_2E0,V1x_2E0,V2y_2E0))
<=> ( ( V1x_2E0 = V2y_2E0 )
& p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0A_2E0)) ) ) ).
tff(thm_2Erelation_2ERDOM__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] :
( p(c_2Erelation_2ERDOM_2E2(A_27a,A_27b,V0R_2E0,V1x_2E0))
<=> ? [V2y_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) ) ).
tff(thm_2Erelation_2ERRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1y_2E0: A_27b] :
( p(c_2Erelation_2ERRANGE_2E2(A_27a,A_27b,V0R_2E0,V1y_2E0))
<=> ? [V2x_2E0: A_27a] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V1y_2E0)) ) ).
tff(thm_2Erelation_2ERUNIV,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( c_2Erelation_2ERUNIV_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Erelation_2ERRESTRICT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Erelation_2ERRESTRICT_2E4(A_27a,A_27b,V0R_2E0,V1s_2E0,V2x_2E0,V3y_2E0))
<=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0)) ) ) ).
tff(thm_2Erelation_2ERDOM__DELETE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2u_2E0: A_27a,V3v_2E0: A_27b] :
( p(c_2Erelation_2ERDOM__DELETE_2E4(A_27a,A_27b,V0R_2E0,V1x_2E0,V2u_2E0,V3v_2E0))
<=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2u_2E0),V3v_2E0))
& ( V2u_2E0 != V1x_2E0 ) ) ) ).
tff(thm_2Erelation_2Ediamond__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ediamond_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0)) )
=> ? [V4u_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V4u_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3z_2E0),V4u_2E0)) ) ) ) ).
tff(thm_2Erelation_2Ercdiamond__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ercdiamond_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0)) )
=> ? [V4u_2E0: A_27a] :
( p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V2y_2E0,V4u_2E0))
& p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V3z_2E0,V4u_2E0)) ) ) ) ).
tff(thm_2Erelation_2ECR__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ECR_2E1(A_27a,V0R_2E0) = c_2Erelation_2Ediamond_2E1(A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2EWCR__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWCR_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0)) )
=> ? [V4u_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2y_2E0,V4u_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3z_2E0,V4u_2E0)) ) ) ) ).
tff(thm_2Erelation_2ESN__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESN_2E1(A_27a,V0R_2E0) = c_2Erelation_2EWF_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2Enf__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] :
( p(c_2Erelation_2Enf_2E2(A_27a,A_27b,V0R_2E0,V1x_2E0))
<=> ! [V2y_2E0: A_27b] : ~ p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) ) ).
tff(thm_2Erelation_2ESC__SYMMETRIC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Esymmetric_2E1(A_27a,c_2Erelation_2ESC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2ETC__TRANSITIVE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2ERTC__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V2x_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a,V5z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4y_2E0),V5z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),V5z_2E0)) ) )
=> ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V6x_2E0,V7y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V6x_2E0),V7y_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__RULES,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) )
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a,V5z_2E0: A_27a] :
( ( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V3x_2E0,V4y_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V4y_2E0,V5z_2E0)) )
=> p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V3x_2E0,V5z_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__RULES,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a] : p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V1x_2E0))
& ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V4z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3y_2E0,V4z_2E0)) )
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2x_2E0,V4z_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__REFL,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2ERTC_2E3(A_27a,V1R_2E0,V0x_2E0,V0x_2E0)) ).
tff(thm_2Erelation_2ERTC__SINGLE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ERTC__STRONG__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V2x_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a,V5z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V4y_2E0,V5z_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4y_2E0),V5z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),V5z_2E0)) ) )
=> ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V6x_2E0,V7y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V6x_2E0),V7y_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__RTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
=> ! [V3z_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2y_2E0,V3z_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V3z_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__TRANSITIVE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2Etransitive__RTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2ERTC__REFLEXIVE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2Ereflexive__RTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2ERC__REFLEXIVE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2Ereflexive__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2ERC__lifts__monotonicities,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V2x_2E0)),app_2E2(A_27a,A_27a,V0f_2E0,V3y_2E0))) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ERC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> p(c_2Erelation_2ERC_2E3(A_27a,V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V4x_2E0),app_2E2(A_27a,A_27a,V0f_2E0,V5y_2E0))) ) ) ).
tff(thm_2Erelation_2ERC__MONOTONE,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0,V4x_2E0),V5y_2E0)) )
=> ( p(c_2Erelation_2ERC_2E3(A_27a,V2R_2E0,V1x_2E0,V0y_2E0))
=> p(c_2Erelation_2ERC_2E3(A_27a,V3Q_2E0,V1x_2E0,V0y_2E0)) ) ) ).
tff(thm_2Erelation_2ERC__lifts__invariants,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0))
& p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V4x_2E0,V5y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V5y_2E0)) ) ) ).
tff(thm_2Erelation_2ERC__lifts__equalities,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ERC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) ) ) ).
tff(thm_2Erelation_2ESC__lifts__monotonicities,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V2x_2E0)),app_2E2(A_27a,A_27a,V0f_2E0,V3y_2E0))) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ESC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> p(c_2Erelation_2ESC_2E3(A_27a,V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V4x_2E0),app_2E2(A_27a,A_27a,V0f_2E0,V5y_2E0))) ) ) ).
tff(thm_2Erelation_2ESC__lifts__equalities,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ESC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) ) ) ).
tff(thm_2Erelation_2ESC__MONOTONE,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0,V4x_2E0),V5y_2E0)) )
=> ( p(c_2Erelation_2ESC_2E3(A_27a,V2R_2E0,V1x_2E0,V0y_2E0))
=> p(c_2Erelation_2ESC_2E3(A_27a,V3Q_2E0,V1x_2E0,V0y_2E0)) ) ) ).
tff(thm_2Erelation_2Esymmetric__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Esymmetric_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Eantisymmetric__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eantisymmetric_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Etransitive__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2ETC__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ERTC__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ERC__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ERC__RTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ETC__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V5y_2E0),V6z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V6z_2E0)) ) )
=> ! [V7u_2E0: A_27a,V8v_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V7u_2E0,V8v_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7u_2E0),V8v_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__INDUCT__LEFT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V5y_2E0),V6z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V6z_2E0)) ) )
=> ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V7x_2E0,V8y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7x_2E0),V8y_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__INDUCT__RIGHT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5y_2E0),V6z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V6z_2E0)) ) )
=> ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V7x_2E0,V8y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7x_2E0),V8y_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__STRONG__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V5y_2E0),V6z_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V4x_2E0,V5y_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V5y_2E0,V6z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V6z_2E0)) ) )
=> ! [V7u_2E0: A_27a,V8v_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V7u_2E0,V8v_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7u_2E0),V8v_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V5y_2E0),V6z_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V5y_2E0,V6z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V6z_2E0)) ) )
=> ! [V7u_2E0: A_27a,V8v_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V7u_2E0,V8v_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7u_2E0),V8v_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V5y_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V4x_2E0,V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5y_2E0),V6z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V6z_2E0)) ) )
=> ! [V7u_2E0: A_27a,V8v_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V7u_2E0,V8v_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7u_2E0),V8v_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__INDUCT__ALT__LEFT,axiom,
! [A_27a: $tType,V0b_2E0: A_27a,V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V3x_2E0),V0b_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V3x_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V5y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V4x_2E0)) ) )
=> ! [V6a_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V1R_2E0,V6a_2E0,V0b_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V6a_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__INDUCT__ALT__RIGHT,axiom,
! [A_27a: $tType,V0a_2E0: A_27a,V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V0a_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V3y_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V4x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V4x_2E0),V5y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V5y_2E0)) ) )
=> ! [V6b_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V1R_2E0,V0a_2E0,V6b_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2Q_2E0,V6b_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__lifts__monotonicities,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V2x_2E0)),app_2E2(A_27a,A_27a,V0f_2E0,V3y_2E0))) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> p(c_2Erelation_2ETC_2E3(A_27a,V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V4x_2E0),app_2E2(A_27a,A_27a,V0f_2E0,V5y_2E0))) ) ) ).
tff(thm_2Erelation_2ETC__lifts__invariants,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V4x_2E0,V5y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V5y_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__lifts__equalities,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) ) ) ).
tff(thm_2Erelation_2ETC__lifts__transitive__relations,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V3x_2E0),V4y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0)),app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0))) )
& p(c_2Erelation_2Etransitive_2E1(A_27b,V2Q_2E0)) )
=> ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V1R_2E0,V5x_2E0,V6y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0)),app_2E2(A_27a,A_27b,V0f_2E0,V6y_2E0))) ) ) ).
tff(thm_2Erelation_2ETC__implies__one__step,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
& ( V1x_2E0 != V2y_2E0 ) )
=> ? [V3z_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0))
& ( V1x_2E0 != V3z_2E0 ) ) ) ).
tff(thm_2Erelation_2ETC__RTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ERTC__TC__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
=> ( p(c_2Erelation_2ERC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
| p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__RC__EQNS,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2ETC_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0) ) ) ).
tff(thm_2Erelation_2ERTC__ALT__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1a_2E0,V2b_2E0))
<=> ! [V3Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V2b_2E0))
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V5y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V5y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V4x_2E0)) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V1a_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__ALT__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2b_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) )
=> ! [V5x_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V5x_2E0,V2b_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V5x_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__ALT__RIGHT__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1a_2E0,V2b_2E0))
<=> ! [V3Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V1a_2E0))
& ! [V4y_2E0: A_27a,V5z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4y_2E0),V5z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V5z_2E0)) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3Q_2E0,V2b_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2a_2E0))
& ! [V3y_2E0: A_27a,V4z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V4z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4z_2E0)) ) )
=> ! [V5z_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2a_2E0,V5z_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V5z_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__INDUCT__RIGHT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V2x_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a,V5z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4y_2E0),V5z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),V5z_2E0)) ) )
=> ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V6x_2E0,V7y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V6x_2E0),V7y_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__RULES__RIGHT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a] : p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V1x_2E0))
& ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V4z_2E0: A_27a] :
( ( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2x_2E0,V3y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V4z_2E0)) )
=> p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2x_2E0,V4z_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V2x_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a,V5z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),V4y_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3x_2E0,V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4y_2E0),V5z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),V5z_2E0)) ) )
=> ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V6x_2E0,V7y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V6x_2E0),V7y_2E0)) ) ) ).
tff(thm_2Erelation_2EEXTEND__RTC__TC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V2y_2E0,V3z_2E0)) )
=> p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V3z_2E0)) ) ).
tff(thm_2Erelation_2EEXTEND__RTC__TC__EQN,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2z_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2z_2E0))
<=> ? [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3y_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3y_2E0,V2z_2E0)) ) ) ).
tff(thm_2Erelation_2Ereflexive__RC__identity,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2ERC_2E1(A_27a,V0R_2E0) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2Esymmetric__SC__identity,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2ESC_2E1(A_27a,V0R_2E0) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2Etransitive__TC__identity,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2ETC_2E1(A_27a,V0R_2E0) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2ERC__IDEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERC_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2ESC__IDEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESC_2E1(A_27a,c_2Erelation_2ESC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ESC_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2ETC__IDEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ETC_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ETC_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2ERC__MOVES__OUT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Erelation_2ESC_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ESC_2E1(A_27a,V0R_2E0)) )
& ( c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2ETC_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2Esymmetric__TC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Esymmetric_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2Ereflexive__TC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2EEQC__EQUIVALENCE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Eequivalence_2E1(A_27a,c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2EEQC__IDEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EEQC_2E1(A_27a,c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2ERTC__IDEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERTC_2E1(A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2ERTC__CASES1,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ( ( V1x_2E0 = V2y_2E0 )
| ? [V3u_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3u_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3u_2E0,V2y_2E0)) ) ) ) ).
tff(thm_2Erelation_2ERTC__CASES__TC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ( ( V1x_2E0 = V2y_2E0 )
| p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__CASES2,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ( ( V1x_2E0 = V2y_2E0 )
| ? [V3u_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V3u_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3u_2E0),V2y_2E0)) ) ) ) ).
tff(thm_2Erelation_2ERTC__CASES__RTC__TWICE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
<=> ? [V3u_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V3u_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3u_2E0,V2y_2E0)) ) ) ).
tff(thm_2Erelation_2ETC__CASES1__E,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2z_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2z_2E0))
=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2z_2E0))
| ? [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3y_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V3y_2E0,V2z_2E0)) ) ) ) ).
tff(thm_2Erelation_2ETC__CASES1,axiom,
! [A_27a: $tType,V0z_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2ETC_2E3(A_27a,V2R_2E0,V1x_2E0,V0z_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V1x_2E0),V0z_2E0))
| ? [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V1x_2E0),V3y_2E0))
& p(c_2Erelation_2ETC_2E3(A_27a,V2R_2E0,V3y_2E0,V0z_2E0)) ) ) ) ).
tff(thm_2Erelation_2ETC__CASES2__E,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2z_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V2z_2E0))
=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2z_2E0))
| ? [V3y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V0R_2E0,V1x_2E0,V3y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V2z_2E0)) ) ) ) ).
tff(thm_2Erelation_2ETC__CASES2,axiom,
! [A_27a: $tType,V0z_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2ETC_2E3(A_27a,V2R_2E0,V1x_2E0,V0z_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V1x_2E0),V0z_2E0))
| ? [V3y_2E0: A_27a] :
( p(c_2Erelation_2ETC_2E3(A_27a,V2R_2E0,V1x_2E0,V3y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3y_2E0),V0z_2E0)) ) ) ) ).
tff(thm_2Erelation_2ETC__MONOTONE,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0,V4x_2E0),V5y_2E0)) )
=> ( p(c_2Erelation_2ETC_2E3(A_27a,V2R_2E0,V1x_2E0,V0y_2E0))
=> p(c_2Erelation_2ETC_2E3(A_27a,V3Q_2E0,V1x_2E0,V0y_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__MONOTONE,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0,V4x_2E0),V5y_2E0)) )
=> ( p(c_2Erelation_2ERTC_2E3(A_27a,V2R_2E0,V1x_2E0,V0y_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V3Q_2E0,V1x_2E0,V0y_2E0)) ) ) ).
tff(thm_2Erelation_2EEQC__INDUCTION,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V4x_2E0))
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V5x_2E0),V6y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V6y_2E0),V5x_2E0)) )
& ! [V7x_2E0: A_27a,V8y_2E0: A_27a,V9z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7x_2E0),V8y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V8y_2E0),V9z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7x_2E0),V9z_2E0)) ) )
=> ! [V10x_2E0: A_27a,V11y_2E0: A_27a] :
( p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V10x_2E0,V11y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V10x_2E0),V11y_2E0)) ) ) ).
tff(thm_2Erelation_2EEQC__REFL,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] : p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V1x_2E0,V1x_2E0)) ).
tff(thm_2Erelation_2EEQC__R,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2EEQC__SYM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
=> p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V2y_2E0,V1x_2E0)) ) ).
tff(thm_2Erelation_2EEQC__TRANS,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
& p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V2y_2E0,V3z_2E0)) )
=> p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V1x_2E0,V3z_2E0)) ) ).
tff(thm_2Erelation_2Etransitive__EQC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2Esymmetric__EQC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Esymmetric_2E1(A_27a,c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2Ereflexive__EQC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0))) ).
tff(thm_2Erelation_2EEQC__MOVES__IN,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Erelation_2EEQC_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2EEQC_2E1(A_27a,c_2Erelation_2ESC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2EEQC_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) ) ) ).
tff(thm_2Erelation_2ESTRONG__EQC__INDUCTION,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0)) )
& ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),V4x_2E0))
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( ( p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V5x_2E0,V6y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V5x_2E0),V6y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V6y_2E0),V5x_2E0)) )
& ! [V7x_2E0: A_27a,V8y_2E0: A_27a,V9z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7x_2E0),V8y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V8y_2E0),V9z_2E0))
& p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V7x_2E0,V8y_2E0))
& p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V8y_2E0,V9z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V7x_2E0),V9z_2E0)) ) )
=> ! [V10x_2E0: A_27a,V11y_2E0: A_27a] :
( p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V10x_2E0,V11y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V10x_2E0),V11y_2E0)) ) ) ).
tff(thm_2Erelation_2EALT__equivalence,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Eequivalence_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
<=> ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0) ) ) ) ).
tff(thm_2Erelation_2EEQC__MONOTONE,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2R_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3R_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_27_2E0,V4x_2E0),V5y_2E0)) )
=> ( p(c_2Erelation_2EEQC_2E3(A_27a,V3R_2E0,V1x_2E0,V0y_2E0))
=> p(c_2Erelation_2EEQC_2E3(A_27a,V2R_27_2E0,V1x_2E0,V0y_2E0)) ) ) ).
tff(thm_2Erelation_2ERTC__EQC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0))
=> p(c_2Erelation_2EEQC_2E3(A_27a,V0R_2E0,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Erelation_2ERTC__lifts__monotonicities,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V2x_2E0)),app_2E2(A_27a,A_27a,V0f_2E0,V3y_2E0))) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> p(c_2Erelation_2ERTC_2E3(A_27a,V1R_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V4x_2E0),app_2E2(A_27a,A_27a,V0f_2E0,V5y_2E0))) ) ) ).
tff(thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V3x_2E0),V4y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0)),app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0))) )
& p(c_2Erelation_2Ereflexive_2E1(A_27b,V2Q_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27b,V2Q_2E0)) )
=> ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V1R_2E0,V5x_2E0,V6y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0)),app_2E2(A_27a,A_27b,V0f_2E0,V6y_2E0))) ) ) ).
tff(thm_2Erelation_2ERTC__lifts__equalities,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V3y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,V1R_2E0,V4x_2E0,V5y_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) ) ) ).
tff(thm_2Erelation_2ERTC__lifts__invariants,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V4x_2E0,V5y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V5y_2E0)) ) ) ).
tff(thm_2Erelation_2EWF__INDUCTION__THM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( ! [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
=> ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0)) ) ) ).
tff(thm_2Erelation_2EINDUCTION__WF__THM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( ! [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
=> ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0)) )
=> p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2EWF__EQ__INDUCTION__THM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
<=> ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( ! [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
=> ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0)) ) ) ).
tff(thm_2Erelation_2EWF__NOT__REFL,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> ( V1x_2E0 != V2y_2E0 ) ) ) ).
tff(thm_2Erelation_2EWF__irreflexive,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2EWF__EMPTY__REL,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EWF_2E1(A_27a,c_2Erelation_2EEMPTY__REL_2E0(A_27a))) ).
tff(thm_2Erelation_2EWF__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
& ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0,V2x_2E0),V3y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0)) ) )
=> p(c_2Erelation_2EWF_2E1(A_27a,V1P_2E0)) ) ).
tff(thm_2Erelation_2EWF__TC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2EWF_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2EWF__TC__EQN,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2EWF_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2EWF__noloops,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V2R_2E0))
=> ( p(c_2Erelation_2ETC_2E3(A_27a,V2R_2E0,V1x_2E0,V0y_2E0))
=> ( V1x_2E0 != V0y_2E0 ) ) ) ).
tff(thm_2Erelation_2EWF__antisymmetric,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2Einv__image__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27a] : ( c_2Erelation_2Einv__image_2E4(A_27a,A_27b,V0R_2E0,V1f_2E0,V2x_2E0,V3y_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0)),app_2E2(A_27a,A_27b,V1f_2E0,V3y_2E0)) ) ).
tff(thm_2Erelation_2EWF__inv__image,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Erelation_2EWF_2E1(A_27b,V0R_2E0))
=> p(c_2Erelation_2EWF_2E1(A_27a,c_2Erelation_2Einv__image_2E2(A_27a,A_27b,V0R_2E0,V1f_2E0))) ) ).
tff(thm_2Erelation_2Etotal__inv__image,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Etotal_2E1(A_27b,c_2Erelation_2Einv__image_2E2(A_27b,A_27a,V0R_2E0,V1f_2E0))) ) ).
tff(thm_2Erelation_2Ereflexive__inv__image,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Ereflexive_2E1(A_27b,c_2Erelation_2Einv__image_2E2(A_27b,A_27a,V0R_2E0,V1f_2E0))) ) ).
tff(thm_2Erelation_2Esymmetric__inv__image,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Esymmetric_2E1(A_27b,c_2Erelation_2Einv__image_2E2(A_27b,A_27a,V0R_2E0,V1f_2E0))) ) ).
tff(thm_2Erelation_2Etransitive__inv__image,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Etransitive_2E1(A_27b,c_2Erelation_2Einv__image_2E2(A_27b,A_27a,V0R_2E0,V1f_2E0))) ) ).
tff(thm_2Erelation_2ERESTRICT__LEMMA,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2y_2E0: A_27a,V3z_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2y_2E0),V3z_2E0))
=> ( c_2Erelation_2ERESTRICT_2E4(A_27a,A_27b,V0f_2E0,V1R_2E0,V3z_2E0,V2y_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0) ) ) ).
tff(thm_2Erelation_2EWFREC__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> ! [V2x_2E0: A_27a] : ( c_2Erelation_2EWFREC_2E3(A_27a,A_27b,V0R_2E0,V1M_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1M_2E0,c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,c_2Erelation_2EWFREC_2E2(A_27a,A_27b,V0R_2E0,V1M_2E0),V0R_2E0,V2x_2E0)),V2x_2E0) ) ) ).
tff(thm_2Erelation_2EWFREC__COROLLARY,axiom,
! [A_27a: $tType,A_27b: $tType,V0M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V2f_2E0 = c_2Erelation_2EWFREC_2E2(A_27a,A_27b,V1R_2E0,V0M_2E0) )
=> ( p(c_2Erelation_2EWF_2E1(A_27a,V1R_2E0))
=> ! [V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0,c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,V2f_2E0,V1R_2E0,V3x_2E0)),V3x_2E0) ) ) ) ).
tff(thm_2Erelation_2EWF__RECURSION__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))] :
( ! [V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0,V1M_2E0),V0R_2E0),V2f_2E0))
<=> ! [V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),V1M_2E0,c_2Erelation_2ERESTRICT_2E3(A_27a,A_27b,V2f_2E0,V0R_2E0,V3x_2E0)),V3x_2E0) ) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
=> ! [V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] : p(c_2Ebool_2E_3F_21_2E1(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0,V1M_2E0),V0R_2E0))) ) ) ).
tff(thm_2Erelation_2EWFP__RULES,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] :
( ! [V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0))
=> p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V2y_2E0)) )
=> p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V1x_2E0)) ) ).
tff(thm_2Erelation_2EWFP__INDUCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( ! [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3y_2E0),V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
=> ! [V4x_2E0: A_27a] :
( p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V4x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V4x_2E0)) ) ) ).
tff(thm_2Erelation_2EWFP__CASES,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] :
( p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V1x_2E0))
<=> ! [V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0))
=> p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V2y_2E0)) ) ) ).
tff(thm_2Erelation_2EWFP__STRONG__INDUCT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a] :
( ( p(c_2Erelation_2EWFP_2E2(A_27a,V1R_2E0,V2x_2E0))
& ! [V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V3y_2E0),V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3y_2E0)) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
=> ! [V4x_2E0: A_27a] :
( p(c_2Erelation_2EWFP_2E2(A_27a,V1R_2E0,V4x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) ) ) ).
tff(thm_2Erelation_2EWF__EQ__WFP,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a] : p(c_2Erelation_2EWFP_2E2(A_27a,V0R_2E0,V1x_2E0)) ) ).
tff(thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
( ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(A_27a,A_27b,V0R_2E0,V1P_2E0,V2M_2E0)) )
=> ! [V3x_2E0: A_27a] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V3x_2E0),c_2Erelation_2EWFREC_2E3(A_27a,A_27b,V0R_2E0,V2M_2E0,V3x_2E0))) ) ).
tff(thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V4x_2E0: A_27a] :
( ( ( V0f_2E0 = c_2Erelation_2EWFREC_2E2(A_27a,A_27b,V1R_2E0,V3M_2E0) )
& p(c_2Erelation_2EWF_2E1(A_27a,V1R_2E0))
& p(c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(A_27a,A_27b,V1R_2E0,V2P_2E0,V3M_2E0)) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,V4x_2E0),app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0))) ) ).
tff(thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3D_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_2E0: A_27a] :
( ( p(c_2Erelation_2EWF_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(A_27a,A_27b,V0R_2E0,V3D_2E0,V1P_2E0,V2M_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3D_2E0,V4x_2E0)) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V4x_2E0),c_2Erelation_2EWFREC_2E3(A_27a,A_27b,V0R_2E0,V2M_2E0,V4x_2E0))) ) ).
tff(thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2D_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V5x_2E0: A_27a] :
( ( ( V0f_2E0 = c_2Erelation_2EWFREC_2E2(A_27a,A_27b,V1R_2E0,V4M_2E0) )
& p(c_2Erelation_2EWF_2E1(A_27a,V1R_2E0))
& p(c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(A_27a,A_27b,V1R_2E0,V2D_2E0,V3P_2E0,V4M_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2D_2E0,V5x_2E0)) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0,V5x_2E0),app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0))) ) ).
tff(thm_2Erelation_2Einv__inv,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27b,A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27b,V0R_2E0)) = V0R_2E0 ) ).
tff(thm_2Erelation_2Einv__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2Einv__SC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2ESC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ESC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2ESC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2ESC_2E1(A_27a,V0R_2E0) ) ) ).
tff(thm_2Erelation_2Einv__TC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ETC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2Einv__EQC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2EEQC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) ) ) ).
tff(thm_2Erelation_2Einv__MOVES__OUT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = V0R_2E0 )
& ( c_2Erelation_2ESC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2ESC_2E1(A_27a,V0R_2E0) )
& ( c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) )
& ( c_2Erelation_2ETC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0)) )
& ( c_2Erelation_2ERTC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2ERTC_2E1(A_27a,V0R_2E0)) )
& ( c_2Erelation_2EEQC_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2EEQC_2E1(A_27a,V0R_2E0) ) ) ).
tff(thm_2Erelation_2Ereflexive__inv,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ereflexive_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Eirreflexive__inv,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Esymmetric__inv,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Esymmetric_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Eantisymmetric__inv,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eantisymmetric_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Etransitive__inv,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Esymmetric__inv__identity,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2Eequivalence__inv__identity,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Eequivalence_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2EINVOL,axiom,
! [A_27z: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] :
( p(c_2Erelation_2EINVOL_2E1(A_27z,V0f_2E0))
<=> ! [V1x_2E0: A_27z] : ( app_2E2(A_27z,A_27z,V0f_2E0,app_2E2(A_27z,A_27z,V0f_2E0,V1x_2E0)) = V1x_2E0 ) ) ).
tff(thm_2Erelation_2EINVOL__ONE__ONE,axiom,
! [A_27z: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] :
( p(c_2Erelation_2EINVOL_2E1(A_27z,V0f_2E0))
=> ! [V1a_2E0: A_27z,V2b_2E0: A_27z] :
( ( app_2E2(A_27z,A_27z,V0f_2E0,V1a_2E0) = app_2E2(A_27z,A_27z,V0f_2E0,V2b_2E0) )
<=> ( V1a_2E0 = V2b_2E0 ) ) ) ).
tff(thm_2Erelation_2EINVOL__ONE__ENO,axiom,
! [A_27z: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] :
( p(c_2Erelation_2EINVOL_2E1(A_27z,V0f_2E0))
=> ! [V1a_2E0: A_27z,V2b_2E0: A_27z] :
( ( app_2E2(A_27z,A_27z,V0f_2E0,V1a_2E0) = V2b_2E0 )
<=> ( V1a_2E0 = app_2E2(A_27z,A_27z,V0f_2E0,V2b_2E0) ) ) ) ).
tff(thm_2Erelation_2ENOT__INVOL,axiom,
p(c_2Erelation_2EINVOL_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ).
tff(thm_2Erelation_2EIDEM,axiom,
! [A_27z: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27z,A_27z)] :
( p(c_2Erelation_2EIDEM_2E1(A_27z,V0f_2E0))
<=> ! [V1x_2E0: A_27z] : ( app_2E2(A_27z,A_27z,V0f_2E0,app_2E2(A_27z,A_27z,V0f_2E0,V1x_2E0)) = app_2E2(A_27z,A_27z,V0f_2E0,V1x_2E0) ) ) ).
tff(thm_2Erelation_2Einv__INVOL,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EINVOL_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27a,A_27a))) ).
tff(thm_2Erelation_2Einv__O,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_27_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27c,A_27b,c_2Erelation_2EO_2E2(A_27c,A_27a,A_27b,V0R_2E0,V1R_27_2E0)) = c_2Erelation_2EO_2E2(A_27b,A_27a,A_27c,c_2Erelation_2Einv_2E1(A_27c,A_27a,V1R_27_2E0),c_2Erelation_2Einv_2E1(A_27a,A_27b,V0R_2E0)) ) ).
tff(thm_2Erelation_2Eirreflexive__RSUBSET,axiom,
! [A_27a: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V1R2_2E0))
& p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,V0R1_2E0,V1R2_2E0)) )
=> p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R1_2E0)) ) ).
tff(thm_2Erelation_2ERUNION__COMM,axiom,
! [A_27a: $tType,A_27b: $tType,V0R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERUNION_2E2(A_27a,A_27b,V1R1_2E0,V0R2_2E0) = c_2Erelation_2ERUNION_2E2(A_27a,A_27b,V0R2_2E0,V1R1_2E0) ) ).
tff(thm_2Erelation_2ERUNION__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0R3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERUNION_2E2(A_27a,A_27b,V2R1_2E0,c_2Erelation_2ERUNION_2E2(A_27a,A_27b,V1R2_2E0,V0R3_2E0)) = c_2Erelation_2ERUNION_2E2(A_27a,A_27b,c_2Erelation_2ERUNION_2E2(A_27a,A_27b,V2R1_2E0,V1R2_2E0),V0R3_2E0) ) ).
tff(thm_2Erelation_2ERINTER__COMM,axiom,
! [A_27a: $tType,A_27b: $tType,V0R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERINTER_2E2(A_27a,A_27b,V1R1_2E0,V0R2_2E0) = c_2Erelation_2ERINTER_2E2(A_27a,A_27b,V0R2_2E0,V1R1_2E0) ) ).
tff(thm_2Erelation_2ERINTER__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0R3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERINTER_2E2(A_27a,A_27b,V2R1_2E0,c_2Erelation_2ERINTER_2E2(A_27a,A_27b,V1R2_2E0,V0R3_2E0)) = c_2Erelation_2ERINTER_2E2(A_27a,A_27b,c_2Erelation_2ERINTER_2E2(A_27a,A_27b,V2R1_2E0,V1R2_2E0),V0R3_2E0) ) ).
tff(thm_2Erelation_2Eantisymmetric__RINTER,axiom,
! [A_27a: $tType,V0R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V1R1_2E0))
=> p(c_2Erelation_2Eantisymmetric_2E1(A_27a,c_2Erelation_2ERINTER_2E2(A_27a,A_27a,V1R1_2E0,V0R2_2E0))) )
& ( p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R2_2E0))
=> p(c_2Erelation_2Eantisymmetric_2E1(A_27a,c_2Erelation_2ERINTER_2E2(A_27a,A_27a,V1R1_2E0,V0R2_2E0))) ) ) ).
tff(thm_2Erelation_2Etransitive__RINTER,axiom,
! [A_27a: $tType,V0R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V1R1_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0R2_2E0)) )
=> p(c_2Erelation_2Etransitive_2E1(A_27a,c_2Erelation_2ERINTER_2E2(A_27a,A_27a,V1R1_2E0,V0R2_2E0))) ) ).
tff(thm_2Erelation_2Ereflexive__Id__RSUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ereflexive_2E1(A_27a,V0R_2E0) = c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,c_2Emin_2E_3D_2E0(A_27a),V0R_2E0) ) ).
tff(thm_2Erelation_2Esymmetric__inv__RSUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Esymmetric_2E1(A_27a,V0R_2E0) = c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0),V0R_2E0) ) ).
tff(thm_2Erelation_2Etransitive__O__RSUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0) = c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,V0R_2E0,V0R_2E0),V0R_2E0) ) ).
tff(thm_2Erelation_2Eirrefl__trans__implies__antisym,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0)) )
=> p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2EStrongOrd__Ord,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongOrder_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2EOrder_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2EWeakOrd__Ord,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakOrder_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2EOrder_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2EWeakOrder__EQ,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakOrder_2E1(A_27a,V0R_2E0))
=> ! [V1y_2E0: A_27a,V2z_2E0: A_27a] :
( ( V1y_2E0 = V2z_2E0 )
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1y_2E0),V2z_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2z_2E0),V1y_2E0)) ) ) ) ).
tff(thm_2Erelation_2ERSUBSET__ANTISYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V0R1_2E0,V1R2_2E0))
& p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V1R2_2E0,V0R1_2E0)) )
=> ( V0R1_2E0 = V1R2_2E0 ) ) ).
tff(thm_2Erelation_2ERSUBSET__antisymmetric,axiom,
! [A_27a: $tType,A_27b: $tType] : p(c_2Erelation_2Eantisymmetric_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0(A_27a,A_27b))) ).
tff(thm_2Erelation_2ERSUBSET__WeakOrder,axiom,
! [A_27a: $tType,A_27b: $tType] : p(c_2Erelation_2EWeakOrder_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0(A_27a,A_27b))) ).
tff(thm_2Erelation_2EEqIsBothRSUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( V0y_2E0 = V1z_2E0 )
<=> ( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V0y_2E0,V1z_2E0))
& p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V1z_2E0,V0y_2E0)) ) ) ).
tff(thm_2Erelation_2ESTRORD__AND__NOT__Id,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ESTRORD_2E1(A_27a,V0R_2E0) = c_2Erelation_2ERINTER_2E2(A_27a,A_27a,V0R_2E0,c_2Erelation_2ERCOMPL_2E1(A_27a,A_27a,c_2Emin_2E_3D_2E0(A_27a))) ) ).
tff(thm_2Erelation_2ERC__OR__Id,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERC_2E1(A_27a,V0R_2E0) = c_2Erelation_2ERUNION_2E2(A_27a,A_27a,V0R_2E0,c_2Emin_2E_3D_2E0(A_27a)) ) ).
tff(thm_2Erelation_2ERC__Weak,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EOrder_2E1(A_27a,V0R_2E0) = c_2Erelation_2EWeakOrder_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2ESTRORD__Strong,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EOrder_2E1(A_27a,V0R_2E0) = c_2Erelation_2EStrongOrder_2E1(A_27a,c_2Erelation_2ESTRORD_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2ESTRORD__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongOrder_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2ESTRORD_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2ERC__STRORD,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakOrder_2E1(A_27a,V0R_2E0))
=> ( c_2Erelation_2ERC_2E1(A_27a,c_2Erelation_2ESTRORD_2E1(A_27a,V0R_2E0)) = V0R_2E0 ) ) ).
tff(thm_2Erelation_2EIDEM__STRORD,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EIDEM_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E0(A_27a))) ).
tff(thm_2Erelation_2EIDEM__RC,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EIDEM_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E0(A_27a))) ).
tff(thm_2Erelation_2EIDEM__SC,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EIDEM_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E0(A_27a))) ).
tff(thm_2Erelation_2EIDEM__TC,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EIDEM_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(A_27a))) ).
tff(thm_2Erelation_2EIDEM__RTC,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EIDEM_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(A_27a))) ).
tff(thm_2Erelation_2Etrichotomous__STRORD,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etrichotomous_2E1(A_27a,c_2Erelation_2ESTRORD_2E1(A_27a,V0R_2E0)) = c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2Etrichotomous__RC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etrichotomous_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) = c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Erelation_2EWeakLinearOrder__dichotomy,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakLinearOrder_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Erelation_2EWeakOrder_2E1(A_27a,V0R_2E0))
& ! [V1a_2E0: A_27a,V2b_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1a_2E0),V2b_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2b_2E0),V1a_2E0)) ) ) ) ).
tff(thm_2Erelation_2EO__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V2R1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27c,A_27b,V2R1_2E0,c_2Erelation_2EO_2E2(A_27a,A_27d,A_27c,V1R2_2E0,V0R3_2E0)) = c_2Erelation_2EO_2E2(A_27a,A_27d,A_27b,c_2Erelation_2EO_2E2(A_27d,A_27c,A_27b,V2R1_2E0,V1R2_2E0),V0R3_2E0) ) ).
tff(thm_2Erelation_2EId__O,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27b,A_27b,c_2Emin_2E_3D_2E0(A_27b),V0R_2E0) = V0R_2E0 ) ).
tff(thm_2Erelation_2EO__Id,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27a,A_27b,V0R_2E0,c_2Emin_2E_3D_2E0(A_27a)) = V0R_2E0 ) ).
tff(thm_2Erelation_2EO__MONO,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0S2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1S1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V3R1_2E0,V2R2_2E0))
& p(c_2Erelation_2ERSUBSET_2E2(A_27c,A_27a,V1S1_2E0,V0S2_2E0)) )
=> p(c_2Erelation_2ERSUBSET_2E2(A_27c,A_27b,c_2Erelation_2EO_2E2(A_27c,A_27a,A_27b,V3R1_2E0,V1S1_2E0),c_2Erelation_2EO_2E2(A_27c,A_27a,A_27b,V2R2_2E0,V0S2_2E0))) ) ).
tff(thm_2Erelation_2Einv__Id,axiom,
! [A_27a: $tType] : ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Emin_2E_3D_2E0(A_27a)) = c_2Emin_2E_3D_2E0(A_27a) ) ).
tff(thm_2Erelation_2Einv__diag,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Erelation_2Ediag_2E1(A_27a,V0A_2E0)) = c_2Erelation_2Ediag_2E1(A_27a,V0A_2E0) ) ).
tff(thm_2Erelation_2EIN__RDOM,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,V1R_2E0)))
<=> ? [V2y_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1R_2E0,V0x_2E0),V2y_2E0)) ) ).
tff(thm_2Erelation_2EIN__RRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27a,V1R_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Erelation_2ERRANGE_2E1(A_27b,A_27a,V1R_2E0)))
<=> ? [V2x_2E0: A_27b] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V0y_2E0)) ) ).
tff(thm_2Erelation_2EIN__RDOM__RUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,c_2Erelation_2ERUNION_2E2(A_27a,A_27b,V2R1_2E0,V1R2_2E0))))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,V2R1_2E0)))
| p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,V1R2_2E0))) ) ) ).
tff(thm_2Erelation_2ERUNIV__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,c_2Erelation_2ERUNIV_2E0(A_27a,A_27b),V0R_2E0))
<=> ( V0R_2E0 = c_2Erelation_2ERUNIV_2E0(A_27a,A_27b) ) )
& p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27b,V0R_2E0,c_2Erelation_2ERUNIV_2E0(A_27a,A_27b))) ) ).
tff(thm_2Erelation_2EREMPTY__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,c_2Erelation_2EEMPTY__REL_2E0(A_27a),V0R_2E0))
& ( p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,V0R_2E0,c_2Erelation_2EEMPTY__REL_2E0(A_27a)))
<=> ( V0R_2E0 = c_2Erelation_2EEMPTY__REL_2E0(A_27a) ) ) ) ).
tff(thm_2Erelation_2EIN__RDOM__RRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,c_2Erelation_2ERRESTRICT_2E2(A_27a,A_27b,V2R_2E0,V1s_2E0))))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,V2R_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0)) ) ) ).
tff(thm_2Erelation_2EIN__RDOM__DELETE,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1k_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,c_2Erelation_2ERDOM__DELETE_2E2(A_27a,A_27b,V2R_2E0,V1k_2E0))))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27b,V2R_2E0)))
& ( V0x_2E0 != V1k_2E0 ) ) ) ).
tff(thm_2Erelation_2Ercdiamond__diamond,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Ercdiamond_2E1(A_27a,V0R_2E0) = c_2Erelation_2Ediamond_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0)) ) ).
tff(thm_2Erelation_2Ediamond__RC__diamond,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ediamond_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Ediamond_2E1(A_27a,c_2Erelation_2ERC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2Ediamond__TC__diamond,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Ediamond_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2Ediamond_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Erelation_2Eestablish__CR,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Ercdiamond_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2ECR_2E1(A_27a,V0R_2E0)) )
& ( p(c_2Erelation_2Ediamond_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2ECR_2E1(A_27a,V0R_2E0)) ) ) ).
tff(thm_2Erelation_2ENewmans__lemma,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2EWCR_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2ESN_2E1(A_27a,V0R_2E0)) )
=> p(c_2Erelation_2ECR_2E1(A_27a,V0R_2E0)) ) ).
%------------------------------------------------------------------------------