ITP001 Axioms: ITP026_7.ax
%------------------------------------------------------------------------------
% File : ITP026_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 : bit.ax [Gau19]
% : HL4026_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 294 ( 98 unt; 100 typ; 0 def)
% Number of atoms : 347 ( 179 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 186 ( 33 ~; 5 |; 32 &)
% ( 38 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 90 ( 48 >; 42 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 97 ( 97 usr; 41 con; 0-4 aty)
% Number of variables : 545 ( 516 !; 5 ?; 545 :)
% ( 24 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $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_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_2Ebit_2EBIT_2E0,type,
c_2Ebit_2EBIT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Ebit_2EBIT_2E1,type,
c_2Ebit_2EBIT_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Ebit_2EBIT_2E2,type,
c_2Ebit_2EBIT_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EBITS_2E0,type,
c_2Ebit_2EBITS_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Ebit_2EBITS_2E3,type,
c_2Ebit_2EBITS_2E3: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EBITV_2E0,type,
c_2Ebit_2EBITV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebit_2EBITV_2E2,type,
c_2Ebit_2EBITV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EBITWISE_2E0,type,
c_2Ebit_2EBITWISE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))) ).
tff(c_2Ebit_2EBITWISE_2E4,type,
c_2Ebit_2EBITWISE_2E4: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) * tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EBIT__MODIFY_2E0,type,
c_2Ebit_2EBIT__MODIFY_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Ebit_2EBIT__MODIFY_2E3,type,
c_2Ebit_2EBIT__MODIFY_2E3: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EBIT__REVERSE_2E0,type,
c_2Ebit_2EBIT__REVERSE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebit_2EBIT__REVERSE_2E2,type,
c_2Ebit_2EBIT__REVERSE_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EDIVMOD__2EXP_2E0,type,
c_2Ebit_2EDIVMOD__2EXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Ebit_2EDIVMOD__2EXP_2E2,type,
c_2Ebit_2EDIVMOD__2EXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Ebit_2EDIV__2EXP_2E0,type,
c_2Ebit_2EDIV__2EXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebit_2EDIV__2EXP_2E2,type,
c_2Ebit_2EDIV__2EXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ewhile_2ELEAST_2E0,type,
c_2Ewhile_2ELEAST_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Ewhile_2ELEAST_2E1,type,
c_2Ewhile_2ELEAST_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Elogroot_2ELOG_2E0,type,
c_2Elogroot_2ELOG_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Elogroot_2ELOG_2E1,type,
c_2Elogroot_2ELOG_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Ebit_2ELOG2_2E0,type,
c_2Ebit_2ELOG2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Ebit_2ELOG2_2E1,type,
c_2Ebit_2ELOG2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebit_2ELOWEST__SET__BIT_2E0,type,
c_2Ebit_2ELOWEST__SET__BIT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Ebit_2ELOWEST__SET__BIT_2E1,type,
c_2Ebit_2ELOWEST__SET__BIT_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EMIN_2E0,type,
c_2Earithmetic_2EMIN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMIN_2E2,type,
c_2Earithmetic_2EMIN_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EMOD__2EXP_2E0,type,
c_2Ebit_2EMOD__2EXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebit_2EMOD__2EXP_2E2,type,
c_2Ebit_2EMOD__2EXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2EMOD__2EXP__EQ_2E0,type,
c_2Ebit_2EMOD__2EXP__EQ_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).
tff(c_2Ebit_2EMOD__2EXP__EQ_2E3,type,
c_2Ebit_2EMOD__2EXP__EQ_2E3: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Ebit_2EMOD__2EXP__MAX_2E0,type,
c_2Ebit_2EMOD__2EXP__MAX_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Ebit_2EMOD__2EXP__MAX_2E2,type,
c_2Ebit_2EMOD__2EXP__MAX_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
tff(c_2Ebit_2ESBIT_2E0,type,
c_2Ebit_2ESBIT_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebit_2ESBIT_2E2,type,
c_2Ebit_2ESBIT_2E2: ( tyop_2Emin_2Ebool * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2ESIGN__EXTEND_2E0,type,
c_2Ebit_2ESIGN__EXTEND_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Ebit_2ESIGN__EXTEND_2E3,type,
c_2Ebit_2ESIGN__EXTEND_2E3: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebit_2ESLICE_2E0,type,
c_2Ebit_2ESLICE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Ebit_2ESLICE_2E3,type,
c_2Ebit_2ESLICE_2E3: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebit_2ETIMES__2EXP_2E0,type,
c_2Ebit_2ETIMES__2EXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebit_2ETIMES__2EXP_2E2,type,
c_2Ebit_2ETIMES__2EXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
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_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_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_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_2Ebit_2EBIT_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebit_2EBIT_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EBIT_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebit_2EBIT_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebit_2EBITS_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EBITV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Ebit_2EBITWISE_2E4,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Enum_2Enum,X3_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITWISE_2E4(X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBITWISE_2E0,X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Ebit_2EBIT__MODIFY_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT__MODIFY_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EBIT__REVERSE_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT__REVERSE_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EDIVMOD__2EXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EDIVMOD__2EXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EDIVMOD__2EXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EDIV__2EXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EDIV__2EXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIV__2EXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ewhile_2ELEAST_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ewhile_2ELEAST_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elogroot_2ELOG_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Elogroot_2ELOG_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebit_2ELOG2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ELOG2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebit_2ELOWEST__SET__BIT_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ELOWEST__SET__BIT_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMIN_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EMOD__2EXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EMOD__2EXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EMOD__2EXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebit_2EMOD__2EXP__EQ_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EMOD__2EXP__EQ_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebit_2EMOD__2EXP__EQ_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2EMOD__2EXP__MAX_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EMOD__2EXP__MAX_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebit_2EMOD__2EXP__MAX_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EODD_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2ESBIT_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESBIT_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebit_2ESIGN__EXTEND_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESIGN__EXTEND_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESIGN__EXTEND_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebit_2ESLICE_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESLICE_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebit_2ETIMES__2EXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ETIMES__2EXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ETIMES__2EXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_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_2Ebit_2EMOD__2EXP__def,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EMOD__2EXP_2E2(V0x_2E0,V1n_2E0) = c_2Earithmetic_2EMOD_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)) ) ).
tff(thm_2Ebit_2EDIV__2EXP__def,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EDIV__2EXP_2E2(V0x_2E0,V1n_2E0) = c_2Earithmetic_2EDIV_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)) ) ).
tff(thm_2Ebit_2ETIMES__2EXP__def,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ETIMES__2EXP_2E2(V0x_2E0,V1n_2E0) = c_2Earithmetic_2E_2A_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)) ) ).
tff(thm_2Ebit_2EDIVMOD__2EXP__def,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EDIVMOD__2EXP_2E2(V0x_2E0,V1n_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)),c_2Earithmetic_2EMOD_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0))) ) ).
tff(thm_2Ebit_2ESBIT__def,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESBIT_2E2(V0b_2E0,V1n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V0b_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0),c_2Enum_2E0_2E0) ) ).
tff(thm_2Ebit_2EBITS__def,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Ebit_2EMOD__2EXP_2E2(c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0),c_2Ebit_2EDIV__2EXP_2E2(V1l_2E0,V2n_2E0)) ) ).
tff(thm_2Ebit_2EBITV__def,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITV_2E2(V0n_2E0,V1b_2E0) = c_2Ebit_2EBITS_2E3(V1b_2E0,V1b_2E0,V0n_2E0) ) ).
tff(thm_2Ebit_2EBIT__def,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(V0b_2E0,V1n_2E0))
<=> ( c_2Ebit_2EBITS_2E3(V0b_2E0,V0b_2E0,V1n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Ebit_2ESLICE__def,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESLICE_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Earithmetic_2E_2D_2E2(c_2Ebit_2EMOD__2EXP_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V2n_2E0),c_2Ebit_2EMOD__2EXP_2E2(V1l_2E0,V2n_2E0)) ) ).
tff(thm_2Ebit_2ELOG2__def,axiom,
c_2Ebit_2ELOG2_2E0 = c_2Elogroot_2ELOG_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) ).
tff(thm_2Ebit_2ELOWEST__SET__BIT__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0n_2E0),V1i_2E0) = c_2Ebit_2EBIT_2E2(V1i_2E0,V0n_2E0) )
=> ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ELOWEST__SET__BIT_2E1(V0n_2E0) = c_2Ewhile_2ELEAST_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0n_2E0)) ) ) ).
tff(thm_2Ebit_2EBIT__REVERSE__def,axiom,
( ! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT__REVERSE_2E2(c_2Enum_2E0_2E0,V0x_2E0) = c_2Enum_2E0_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT__REVERSE_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V2x_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Ebit_2EBIT__REVERSE_2E2(V1n_2E0,V2x_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebit_2ESBIT_2E2(c_2Ebit_2EBIT_2E2(V1n_2E0,V2x_2E0),c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2Ebit_2EBITWISE__def,axiom,
( ! [V0op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1x_2E0: tyop_2Enum_2Enum,V2y_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITWISE_2E4(c_2Enum_2E0_2E0,V0op_2E0,V1x_2E0,V2y_2E0) = c_2Enum_2E0_2E0 )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V5x_2E0: tyop_2Enum_2Enum,V6y_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITWISE_2E4(c_2Enum_2ESUC_2E1(V3n_2E0),V4op_2E0,V5x_2E0,V6y_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Ebit_2EBITWISE_2E4(V3n_2E0,V4op_2E0,V5x_2E0,V6y_2E0),c_2Ebit_2ESBIT_2E2(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4op_2E0,c_2Ebit_2EBIT_2E2(V3n_2E0,V5x_2E0)),c_2Ebit_2EBIT_2E2(V3n_2E0,V6y_2E0)),V3n_2E0)) ) ) ).
tff(thm_2Ebit_2EBIT__MODIFY__def,axiom,
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1x_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT__MODIFY_2E3(c_2Enum_2E0_2E0,V0f_2E0,V1x_2E0) = c_2Enum_2E0_2E0 )
& ! [V2n_2E0: tyop_2Enum_2Enum,V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4x_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT__MODIFY_2E3(c_2Enum_2ESUC_2E1(V2n_2E0),V3f_2E0,V4x_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Ebit_2EBIT__MODIFY_2E3(V2n_2E0,V3f_2E0,V4x_2E0),c_2Ebit_2ESBIT_2E2(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3f_2E0,V2n_2E0),c_2Ebit_2EBIT_2E2(V2n_2E0,V4x_2E0)),V2n_2E0)) ) ) ).
tff(thm_2Ebit_2ESIGN__EXTEND__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))] :
( ! [V0l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0,V0l_2E0),V2n_2E0),V1h_2E0),V3m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2D_2E2(V0l_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2n_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1h_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0l_2E0)),V3m_2E0),V3m_2E0) )
=> ! [V0l_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESIGN__EXTEND_2E3(V0l_2E0,V1h_2E0,V2n_2E0) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0,V0l_2E0),V2n_2E0),V1h_2E0),c_2Earithmetic_2EMOD_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0l_2E0))) ) ) ).
tff(thm_2Ebit_2EMOD__2EXP__EQ__def,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EMOD__2EXP__EQ_2E3(V0n_2E0,V1a_2E0,V2b_2E0))
<=> ( c_2Ebit_2EMOD__2EXP_2E2(V0n_2E0,V1a_2E0) = c_2Ebit_2EMOD__2EXP_2E2(V0n_2E0,V2b_2E0) ) ) ).
tff(thm_2Ebit_2EMOD__2EXP__MAX__def,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EMOD__2EXP__MAX_2E2(V0n_2E0,V1a_2E0))
<=> ( c_2Ebit_2EMOD__2EXP_2E2(V0n_2E0,V1a_2E0) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Ebit_2ELESS__MULT__MONO2,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum,V3y_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V0a_2E0,V2x_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V1b_2E0,V3y_2E0)) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2E_2A_2E2(V0a_2E0,V1b_2E0),c_2Earithmetic_2E_2A_2E2(V2x_2E0,V3y_2E0))) ) ).
tff(thm_2Ebit_2ELOG2__UNIQUE,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1p_2E0),V0n_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V1p_2E0)))) )
=> ( c_2Ebit_2ELOG2_2E1(V0n_2E0) = V1p_2E0 ) ) ).
tff(thm_2Ebit_2ELOG2__TWOEXP,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ELOG2_2E1(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)) = V0n_2E0 ) ).
tff(thm_2Ebit_2EDIVMOD__2EXP,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EDIVMOD__2EXP_2E2(V0x_2E0,V1n_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(V0x_2E0,V1n_2E0),c_2Ebit_2EMOD__2EXP_2E2(V0x_2E0,V1n_2E0)) ) ).
tff(thm_2Ebit_2ESUC__SUB,axiom,
! [V0a_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V0a_2E0),V0a_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ).
tff(thm_2Ebit_2EDIV__MULT__1,axiom,
! [V0r_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,V1n_2E0))
=> ( c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0r_2E0),V1n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Ebit_2ENOT__ZERO__ADD1,axiom,
! [V0m_2E0: tyop_2Enum_2Enum] :
( ( V0m_2E0 != c_2Enum_2E0_2E0 )
=> ? [V1p_2E0: tyop_2Enum_2Enum] : ( V0m_2E0 = c_2Enum_2ESUC_2E1(V1p_2E0) ) ) ).
tff(thm_2Ebit_2EZERO__LT__TWOEXP,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0))) ).
tff(thm_2Ebit_2EONE__LE__TWOEXP,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0))) ).
tff(thm_2Ebit_2ETWOEXP__NOT__ZERO,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0) != c_2Enum_2E0_2E0 ) ).
tff(thm_2Ebit_2EMOD__2EXP__LT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1k_2E0: tyop_2Enum_2Enum] : p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EMOD_2E2(V1k_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0))) ).
tff(thm_2Ebit_2ETWOEXP__DIVISION,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1k_2E0: tyop_2Enum_2Enum] : ( V1k_2E0 = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EDIV_2E2(V1k_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)),c_2Earithmetic_2EMOD_2E2(V1k_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0))) ) ).
tff(thm_2Ebit_2ETWOEXP__MONO,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0a_2E0,V1b_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0a_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0))) ) ).
tff(thm_2Ebit_2ETWOEXP__MONO2,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0a_2E0,V1b_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0a_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0))) ) ).
tff(thm_2Ebit_2EEXP__SUB__LESS__EQ,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(V0a_2E0,V1b_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0a_2E0))) ).
tff(thm_2Ebit_2EMOD__LEQ,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V1b_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EMOD_2E2(V0a_2E0,V1b_2E0),V0a_2E0)) ) ).
tff(thm_2Ebit_2EBITS__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2EDIV_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0))) ) ).
tff(thm_2Ebit_2EBITSLT__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : p(c_2Eprim__rec_2E_3C_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0)))) ).
tff(thm_2Ebit_2EBITSLT__THM2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : p(c_2Eprim__rec_2E_3C_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0)))) ).
tff(thm_2Ebit_2EBITS__THM2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2EMOD_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0))),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0)) ) ).
tff(thm_2Ebit_2EBITS__LEQ,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0),V2n_2E0)) ).
tff(thm_2Ebit_2EBITS__COMP__THM,axiom,
! [V0h1_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Enum_2Enum,V2h2_2E0: tyop_2Enum_2Enum,V3l2_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V2h2_2E0,V1l1_2E0),V0h1_2E0))
=> ( c_2Ebit_2EBITS_2E3(V2h2_2E0,V3l2_2E0,c_2Ebit_2EBITS_2E3(V0h1_2E0,V1l1_2E0,V4n_2E0)) = c_2Ebit_2EBITS_2E3(c_2Earithmetic_2E_2B_2E2(V2h2_2E0,V1l1_2E0),c_2Earithmetic_2E_2B_2E2(V3l2_2E0,V1l1_2E0),V4n_2E0) ) ) ).
tff(thm_2Ebit_2EBITS__DIV__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2x_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V3n_2E0)) = c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Earithmetic_2E_2B_2E2(V1l_2E0,V3n_2E0),V2x_2E0) ) ).
tff(thm_2Ebit_2EBITS__LT__HIGH,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0))))
=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Earithmetic_2EDIV_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0)) ) ) ).
tff(thm_2Ebit_2EBITS__ZERO,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0h_2E0,V1l_2E0))
=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2EBITS__ZERO2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 ) ).
tff(thm_2Ebit_2EBITS__ZERO3,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,V1n_2E0) = c_2Earithmetic_2EMOD_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0))) ) ).
tff(thm_2Ebit_2EBITS__ZERO4,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1l_2E0,V0h_2E0))
=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,c_2Earithmetic_2E_2A_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0))) = c_2Ebit_2EBITS_2E3(c_2Earithmetic_2E_2D_2E2(V0h_2E0,V1l_2E0),c_2Enum_2E0_2E0,V2a_2E0) ) ) ).
tff(thm_2Ebit_2EBITS__ZEROL,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0))))
=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,V1a_2E0) = V1a_2E0 ) ) ).
tff(thm_2Ebit_2EBITS__LOG2__ZERO__ID,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ( c_2Ebit_2EBITS_2E3(c_2Ebit_2ELOG2_2E1(V0n_2E0),c_2Enum_2E0_2E0,V0n_2E0) = V0n_2E0 ) ) ).
tff(thm_2Ebit_2EBITS__LT__LOW,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0)))
=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2EBIT__ZERO,axiom,
! [V0b_2E0: tyop_2Enum_2Enum] : ~ p(c_2Ebit_2EBIT_2E2(V0b_2E0,c_2Enum_2E0_2E0)) ).
tff(thm_2Ebit_2EBIT__B,axiom,
! [V0b_2E0: tyop_2Enum_2Enum] : p(c_2Ebit_2EBIT_2E2(V0b_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0b_2E0))) ).
tff(thm_2Ebit_2EBIT__TWO__POW,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(V0n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0)))
<=> ( V1m_2E0 = V0n_2E0 ) ) ).
tff(thm_2Ebit_2EBIT__B__NEQ,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( ( V0a_2E0 != V1b_2E0 )
=> ~ p(c_2Ebit_2EBIT_2E2(V0a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0))) ) ).
tff(thm_2Ebit_2EBITS__COMP__THM2,axiom,
! [V0h1_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Enum_2Enum,V2h2_2E0: tyop_2Enum_2Enum,V3l2_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V2h2_2E0,V3l2_2E0,c_2Ebit_2EBITS_2E3(V0h1_2E0,V1l1_2E0,V4n_2E0)) = c_2Ebit_2EBITS_2E3(c_2Earithmetic_2EMIN_2E2(V0h1_2E0,c_2Earithmetic_2E_2B_2E2(V2h2_2E0,V1l1_2E0)),c_2Earithmetic_2E_2B_2E2(V3l2_2E0,V1l1_2E0),V4n_2E0) ) ).
tff(thm_2Ebit_2ENOT__MOD2__LEM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) != c_2Enum_2E0_2E0 )
<=> ( c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Ebit_2ENOT__MOD2__LEM2,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) != c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
<=> ( c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2EODD__MOD2__LEM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2EODD_2E1(V0n_2E0))
<=> ( c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Ebit_2EDIV__MULT__THM,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EDIV_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)) = c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2EMOD_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0))) ) ).
tff(thm_2Ebit_2EDIV__MULT__THM2,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2EDIV_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).
tff(thm_2Ebit_2ELESS__EQ__EXP__MULT,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0a_2E0,V1b_2E0))
=> ? [V2p_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0) = c_2Earithmetic_2E_2A_2E2(V2p_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0a_2E0)) ) ) ).
tff(thm_2Ebit_2ESLICE__THM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESLICE_2E3(V1h_2E0,V2l_2E0,V0n_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Ebit_2EBITS_2E3(V1h_2E0,V2l_2E0,V0n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2l_2E0)) ) ).
tff(thm_2Ebit_2ESLICELT__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : p(c_2Eprim__rec_2E_3C_2E2(c_2Ebit_2ESLICE_2E3(V0h_2E0,V1l_2E0,V2n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0)))) ).
tff(thm_2Ebit_2EBITS__SLICE__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,c_2Ebit_2ESLICE_2E3(V0h_2E0,V1l_2E0,V2n_2E0)) = c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0) ) ).
tff(thm_2Ebit_2EBITS__SLICE__THM2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1h2_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0h_2E0,V1h2_2E0))
=> ( c_2Ebit_2EBITS_2E3(V1h2_2E0,V2l_2E0,c_2Ebit_2ESLICE_2E3(V0h_2E0,V2l_2E0,V3n_2E0)) = c_2Ebit_2EBITS_2E3(V0h_2E0,V2l_2E0,V3n_2E0) ) ) ).
tff(thm_2Ebit_2ESLICE__ZERO__THM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESLICE_2E3(V1h_2E0,c_2Enum_2E0_2E0,V0n_2E0) = c_2Ebit_2EBITS_2E3(V1h_2E0,c_2Enum_2E0_2E0,V0n_2E0) ) ).
tff(thm_2Ebit_2EMOD__2EXP__MONO,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2l_2E0,V1h_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2l_2E0)),c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V1h_2E0))))) ) ).
tff(thm_2Ebit_2ESLICE__COMP__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V1m_2E0),V0h_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V2l_2E0,V1m_2E0)) )
=> ( c_2Earithmetic_2E_2B_2E2(c_2Ebit_2ESLICE_2E3(V0h_2E0,c_2Enum_2ESUC_2E1(V1m_2E0),V3n_2E0),c_2Ebit_2ESLICE_2E3(V1m_2E0,V2l_2E0,V3n_2E0)) = c_2Ebit_2ESLICE_2E3(V0h_2E0,V2l_2E0,V3n_2E0) ) ) ).
tff(thm_2Ebit_2ESLICE__COMP__RWT,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1m_27_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum,V3l_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V3l_2E0,V2m_2E0))
& ( V1m_27_2E0 = c_2Earithmetic_2E_2B_2E2(V2m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
& p(c_2Eprim__rec_2E_3C_2E2(V2m_2E0,V0h_2E0)) )
=> ( c_2Earithmetic_2E_2B_2E2(c_2Ebit_2ESLICE_2E3(V0h_2E0,V1m_27_2E0,V4n_2E0),c_2Ebit_2ESLICE_2E3(V2m_2E0,V3l_2E0,V4n_2E0)) = c_2Ebit_2ESLICE_2E3(V0h_2E0,V3l_2E0,V4n_2E0) ) ) ).
tff(thm_2Ebit_2ESLICE__ZERO,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0h_2E0,V1l_2E0))
=> ( c_2Ebit_2ESLICE_2E3(V0h_2E0,V1l_2E0,V2n_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2ESLICE__ZERO2,axiom,
! [V0l_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESLICE_2E3(V1h_2E0,V0l_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 ) ).
tff(thm_2Ebit_2EBITS__SUM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V3b_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0)))
=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0)),V3b_2E0)) = c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,c_2Earithmetic_2E_2A_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1l_2E0))) ) ) ).
tff(thm_2Ebit_2EBITS__SUM2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0h_2E0))),V3b_2E0)) = c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V3b_2E0) ) ).
tff(thm_2Ebit_2ESLICE__COMP__THM2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum,V3y_2E0: tyop_2Enum_2Enum,V4n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0h_2E0,V2x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3y_2E0,V1l_2E0)) )
=> ( c_2Ebit_2ESLICE_2E3(V0h_2E0,V1l_2E0,c_2Ebit_2ESLICE_2E3(V2x_2E0,V3y_2E0,V4n_2E0)) = c_2Ebit_2ESLICE_2E3(V0h_2E0,V1l_2E0,V4n_2E0) ) ) ).
tff(thm_2Ebit_2EBITS__SUM3,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,c_2Earithmetic_2E_2B_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,V1a_2E0),c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,V2b_2E0))) = c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,c_2Earithmetic_2E_2B_2E2(V1a_2E0,V2b_2E0)) ) ).
tff(thm_2Ebit_2EBITS__MUL,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,c_2Earithmetic_2E_2A_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,V1a_2E0),c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,V2b_2E0))) = c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2E0_2E0,c_2Earithmetic_2E_2A_2E2(V1a_2E0,V2b_2E0)) ) ).
tff(thm_2Ebit_2EBIT__COMP__THM3,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V1m_2E0),V0h_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V2l_2E0,V1m_2E0)) )
=> ( c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Ebit_2EBITS_2E3(V0h_2E0,c_2Enum_2ESUC_2E1(V1m_2E0),V3n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V1m_2E0),V2l_2E0))),c_2Ebit_2EBITS_2E3(V1m_2E0,V2l_2E0,V3n_2E0)) = c_2Ebit_2EBITS_2E3(V0h_2E0,V2l_2E0,V3n_2E0) ) ) ).
tff(thm_2Ebit_2ENOT__BIT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( ~ p(c_2Ebit_2EBIT_2E2(V0n_2E0,V1a_2E0))
<=> ( c_2Ebit_2EBITS_2E3(V0n_2E0,V0n_2E0,V1a_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2ENOT__BITS,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( ( c_2Ebit_2EBITS_2E3(V0n_2E0,V0n_2E0,V1a_2E0) != c_2Enum_2E0_2E0 )
<=> ( c_2Ebit_2EBITS_2E3(V0n_2E0,V0n_2E0,V1a_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Ebit_2ENOT__BITS2,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( ( c_2Ebit_2EBITS_2E3(V0n_2E0,V0n_2E0,V1a_2E0) != c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
<=> ( c_2Ebit_2EBITS_2E3(V0n_2E0,V0n_2E0,V1a_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2EBIT__SLICE,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] :
( ( c_2Ebit_2EBIT_2E2(V0n_2E0,V1a_2E0) = c_2Ebit_2EBIT_2E2(V0n_2E0,V2b_2E0) )
<=> ( c_2Ebit_2ESLICE_2E3(V0n_2E0,V0n_2E0,V1a_2E0) = c_2Ebit_2ESLICE_2E3(V0n_2E0,V0n_2E0,V2b_2E0) ) ) ).
tff(thm_2Ebit_2EBIT__SLICE__LEM,axiom,
! [V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESBIT_2E2(c_2Ebit_2EBIT_2E2(V1x_2E0,V2n_2E0),c_2Earithmetic_2E_2B_2E2(V1x_2E0,V0y_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Ebit_2ESLICE_2E3(V1x_2E0,V1x_2E0,V2n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0y_2E0)) ) ).
tff(thm_2Ebit_2EBIT__SLICE__THM,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2ESBIT_2E2(c_2Ebit_2EBIT_2E2(V0x_2E0,V1n_2E0),V0x_2E0) = c_2Ebit_2ESLICE_2E3(V0x_2E0,V0x_2E0,V1n_2E0) ) ).
tff(thm_2Ebit_2EBIT__SLICE__THM2,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(V0b_2E0,V1n_2E0))
<=> ( c_2Ebit_2ESLICE_2E3(V0b_2E0,V0b_2E0,V1n_2E0) = c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0b_2E0) ) ) ).
tff(thm_2Ebit_2EBIT__SLICE__THM3,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ~ p(c_2Ebit_2EBIT_2E2(V0b_2E0,V1n_2E0))
<=> ( c_2Ebit_2ESLICE_2E3(V0b_2E0,V0b_2E0,V1n_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2EBIT__SLICE__THM4,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(V0b_2E0,c_2Ebit_2ESLICE_2E3(V1h_2E0,V2l_2E0,V3n_2E0)))
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V2l_2E0,V0b_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V0b_2E0,V1h_2E0))
& p(c_2Ebit_2EBIT_2E2(V0b_2E0,V3n_2E0)) ) ) ).
tff(thm_2Ebit_2ESBIT__DIV,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,V1m_2E0))
=> ( c_2Ebit_2ESBIT_2E2(V0b_2E0,c_2Earithmetic_2E_2D_2E2(V1m_2E0,V2n_2E0)) = c_2Earithmetic_2EDIV_2E2(c_2Ebit_2ESBIT_2E2(V0b_2E0,V1m_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2n_2E0)) ) ) ).
tff(thm_2Ebit_2EBITS__SUC,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1l_2E0,c_2Enum_2ESUC_2E1(V0h_2E0)))
=> ( c_2Earithmetic_2E_2B_2E2(c_2Ebit_2ESBIT_2E2(c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V2n_2E0),c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0)),c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0)) = c_2Ebit_2EBITS_2E3(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0,V2n_2E0) ) ) ).
tff(thm_2Ebit_2EBITS__SUC__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0,V2n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0),c_2Enum_2E0_2E0,c_2Earithmetic_2E_2B_2E2(c_2Ebit_2ESBIT_2E2(c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V2n_2E0),c_2Earithmetic_2E_2D_2E2(c_2Enum_2ESUC_2E1(V0h_2E0),V1l_2E0)),c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2n_2E0))) ) ).
tff(thm_2Ebit_2EBIT__BITS__THM,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] :
( ! [V4x_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1l_2E0,V4x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V4x_2E0,V0h_2E0)) )
=> ( c_2Ebit_2EBIT_2E2(V4x_2E0,V2a_2E0) = c_2Ebit_2EBIT_2E2(V4x_2E0,V3b_2E0) ) )
<=> ( c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V2a_2E0) = c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V3b_2E0) ) ) ).
tff(thm_2Ebit_2EBITS__ZERO5,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ! [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2i_2E0,V0n_2E0))
=> ~ p(c_2Ebit_2EBIT_2E2(V2i_2E0,V1m_2E0)) )
=> ( c_2Ebit_2EBITS_2E3(V0n_2E0,c_2Enum_2E0_2E0,V1m_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ebit_2EBIT0__ODD,axiom,
c_2Ebit_2EBIT_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2EODD_2E0 ).
tff(thm_2Ebit_2EBITV__THM,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITV_2E2(V1n_2E0,V0b_2E0) = c_2Ebit_2ESBIT_2E2(c_2Ebit_2EBIT_2E2(V0b_2E0,V1n_2E0),c_2Enum_2E0_2E0) ) ).
tff(thm_2Ebit_2EADD__BIT0,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0)))
<=> ( c_2Ebit_2EBIT_2E2(c_2Enum_2E0_2E0,V0m_2E0) != c_2Ebit_2EBIT_2E2(c_2Enum_2E0_2E0,V1n_2E0) ) ) ).
tff(thm_2Ebit_2EADD__BITS__SUC,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITS_2E3(c_2Enum_2ESUC_2E1(V0n_2E0),c_2Enum_2ESUC_2E1(V0n_2E0),c_2Earithmetic_2E_2B_2E2(V1a_2E0,V2b_2E0)) = c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Ebit_2EBITS_2E3(c_2Enum_2ESUC_2E1(V0n_2E0),c_2Enum_2ESUC_2E1(V0n_2E0),V1a_2E0),c_2Ebit_2EBITS_2E3(c_2Enum_2ESUC_2E1(V0n_2E0),c_2Enum_2ESUC_2E1(V0n_2E0),V2b_2E0)),c_2Ebit_2EBITS_2E3(c_2Enum_2ESUC_2E1(V0n_2E0),c_2Enum_2ESUC_2E1(V0n_2E0),c_2Earithmetic_2E_2B_2E2(c_2Ebit_2EBITS_2E3(V0n_2E0,c_2Enum_2E0_2E0,V1a_2E0),c_2Ebit_2EBITS_2E3(V0n_2E0,c_2Enum_2E0_2E0,V2b_2E0)))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Ebit_2EADD__BIT__SUC,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1a_2E0),V2b_2E0))
<=> ( c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0n_2E0),V1a_2E0) = c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0n_2E0),V2b_2E0) ) )
=> ( ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0,F0_2E0),V0n_2E0),V1a_2E0),V2b_2E0))
<=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1a_2E0),V2b_2E0)) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0n_2E0),c_2Earithmetic_2E_2B_2E2(V1a_2E0,V2b_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0n_2E0),c_2Earithmetic_2E_2B_2E2(c_2Ebit_2EBITS_2E3(V0n_2E0,c_2Enum_2E0_2E0,V1a_2E0),c_2Ebit_2EBITS_2E3(V0n_2E0,c_2Enum_2E0_2E0,V2b_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1a_2E0),V2b_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0,F0_2E0),V0n_2E0),V1a_2E0),V2b_2E0)) ) ) ) ).
tff(thm_2Ebit_2EBITWISE__LT__2EXP,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] : p(c_2Eprim__rec_2E_3C_2E2(c_2Ebit_2EBITWISE_2E4(V0n_2E0,V1op_2E0,V2a_2E0,V3b_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0))) ).
tff(thm_2Ebit_2EBITWISE__THM,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3a_2E0: tyop_2Enum_2Enum,V4b_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,V1n_2E0))
=> ( c_2Ebit_2EBIT_2E2(V0x_2E0,c_2Ebit_2EBITWISE_2E4(V1n_2E0,V2op_2E0,V3a_2E0,V4b_2E0)) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V2op_2E0,c_2Ebit_2EBIT_2E2(V0x_2E0,V3a_2E0)),c_2Ebit_2EBIT_2E2(V0x_2E0,V4b_2E0)) ) ) ).
tff(thm_2Ebit_2EBITWISE__COR,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3a_2E0: tyop_2Enum_2Enum,V4b_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,V1n_2E0))
=> ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V2op_2E0,c_2Ebit_2EBIT_2E2(V0x_2E0,V3a_2E0)),c_2Ebit_2EBIT_2E2(V0x_2E0,V4b_2E0)))
=> ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2EDIV_2E2(c_2Ebit_2EBITWISE_2E4(V1n_2E0,V2op_2E0,V3a_2E0,V4b_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ) ).
tff(thm_2Ebit_2EBITWISE__NOT__COR,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3a_2E0: tyop_2Enum_2Enum,V4b_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,V1n_2E0))
=> ( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V2op_2E0,c_2Ebit_2EBIT_2E2(V0x_2E0,V3a_2E0)),c_2Ebit_2EBIT_2E2(V0x_2E0,V4b_2E0)))
=> ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2EDIV_2E2(c_2Ebit_2EBITWISE_2E4(V1n_2E0,V2op_2E0,V3a_2E0,V4b_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Ebit_2EBITWISE__BITS,axiom,
! [V0wl_2E0: tyop_2Enum_2Enum,V1op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITWISE_2E4(c_2Enum_2ESUC_2E1(V0wl_2E0),V1op_2E0,c_2Ebit_2EBITS_2E3(V0wl_2E0,c_2Enum_2E0_2E0,V2a_2E0),c_2Ebit_2EBITS_2E3(V0wl_2E0,c_2Enum_2E0_2E0,V3b_2E0)) = c_2Ebit_2EBITWISE_2E4(c_2Enum_2ESUC_2E1(V0wl_2E0),V1op_2E0,V2a_2E0,V3b_2E0) ) ).
tff(thm_2Ebit_2ENOT__BIT__GT__TWOEXP,axiom,
! [V0i_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0i_2E0)))
=> ~ p(c_2Ebit_2EBIT_2E2(V0i_2E0,V1n_2E0)) ) ).
tff(thm_2Ebit_2EBIT__IMP__GE__TWOEXP,axiom,
! [V0i_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(V0i_2E0,V1n_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0i_2E0),V1n_2E0)) ) ).
tff(thm_2Ebit_2EBITWISE__ONE__COMP__LEM,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V3x_2E0: tyop_2Emin_2Ebool,V4y_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V4y_2E0))
<=> ~ p(V3x_2E0) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITWISE_2E4(c_2Enum_2ESUC_2E1(V0n_2E0),F0_2E0,V1a_2E0,V2b_2E0) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2ESUC_2E1(V0n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebit_2EBITS_2E3(V0n_2E0,c_2Enum_2E0_2E0,V1a_2E0)) ) ) ).
tff(thm_2Ebit_2EBIT__COMPLEMENT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebit_2EBIT_2E2(V1i_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0),c_2Earithmetic_2EMOD_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)))))
<=> ( ( ( c_2Earithmetic_2EMOD_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)) = c_2Enum_2E0_2E0 )
& ( V1i_2E0 = V0n_2E0 ) )
| ( ( c_2Earithmetic_2EMOD_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)) != c_2Enum_2E0_2E0 )
& p(c_2Eprim__rec_2E_3C_2E2(V1i_2E0,V0n_2E0))
& ~ p(c_2Ebit_2EBIT_2E2(V1i_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EMOD_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ) ).
tff(thm_2Ebit_2EBIT__OF__BITS__THM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Enum_2Enum,V3a_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V2l_2E0,V0n_2E0),V1h_2E0))
=> ( c_2Ebit_2EBIT_2E2(V0n_2E0,c_2Ebit_2EBITS_2E3(V1h_2E0,V2l_2E0,V3a_2E0)) = c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2B_2E2(V2l_2E0,V0n_2E0),V3a_2E0) ) ) ).
tff(thm_2Ebit_2EBIT__SHIFT__THM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V2s_2E0),c_2Earithmetic_2E_2A_2E2(V1a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2s_2E0))) = c_2Ebit_2EBIT_2E2(V0n_2E0,V1a_2E0) ) ).
tff(thm_2Ebit_2EBIT__SHIFT__THM2,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2s_2E0,V0n_2E0))
=> ( c_2Ebit_2EBIT_2E2(V0n_2E0,c_2Earithmetic_2E_2A_2E2(V1a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2s_2E0))) = c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,V2s_2E0),V1a_2E0) ) ) ).
tff(thm_2Ebit_2EBIT__SHIFT__THM3,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V2s_2E0))
=> ~ p(c_2Ebit_2EBIT_2E2(V0n_2E0,c_2Earithmetic_2E_2A_2E2(V1a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2s_2E0)))) ) ).
tff(thm_2Ebit_2EBIT__OF__BITS__THM2,axiom,
! [V0h_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0h_2E0,c_2Earithmetic_2E_2B_2E2(V1l_2E0,V2x_2E0)))
=> ~ p(c_2Ebit_2EBIT_2E2(V2x_2E0,c_2Ebit_2EBITS_2E3(V0h_2E0,V1l_2E0,V3n_2E0))) ) ).
tff(thm_2Ebit_2EBIT__DIV2,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(V0n_2E0,c_2Earithmetic_2EDIV_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Ebit_2EBIT_2E2(c_2Enum_2ESUC_2E1(V0n_2E0),V1i_2E0) ) ).
tff(thm_2Ebit_2EBIT__SHIFT__THM4,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(V1i_2E0,c_2Earithmetic_2EDIV_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0))) = c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2B_2E2(V1i_2E0,V0n_2E0),V2a_2E0) ) ).
tff(thm_2Ebit_2EDIV__LT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0))) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EDIV_2E2(V2a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0))) ) ).
tff(thm_2Ebit_2EMOD__ZERO__GT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( ( ( V1a_2E0 != c_2Enum_2E0_2E0 )
& ( c_2Earithmetic_2EMOD_2E2(V1a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)) = c_2Enum_2E0_2E0 ) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0),V1a_2E0)) ) ).
tff(thm_2Ebit_2EDIV__GT0,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1b_2E0,V0a_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V1b_2E0)) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2EDIV_2E2(V0a_2E0,V1b_2E0))) ) ).
tff(thm_2Ebit_2EDIV__SUB1,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0),V0a_2E0))
& ( c_2Earithmetic_2EMOD_2E2(V0a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0)) = c_2Enum_2E0_2E0 ) )
=> ( c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EDIV_2E2(V0a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0)) ) ) ).
tff(thm_2Ebit_2EBIT__EXP__SUB1,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(V0b_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Eprim__rec_2E_3C_2E2(V0b_2E0,V1n_2E0) ) ).
tff(thm_2Ebit_2EBIT__SHIFT__THM5,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V3a_2E0: tyop_2Enum_2Enum,V0n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V3a_2E0),V0n_2E0))
<=> ( c_2Earithmetic_2EMOD_2E2(V3a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)) = c_2Enum_2E0_2E0 ) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Enum_2Enum,V3a_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2E_2B_2E2(V2i_2E0,V0n_2E0),V1m_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V3a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0))) )
=> ( c_2Ebit_2EBIT_2E2(V2i_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0),c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EDIV_2E2(V3a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0)),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V3a_2E0),V0n_2E0),c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0)))) = c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2B_2E2(V2i_2E0,V0n_2E0),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0),c_2Earithmetic_2EMOD_2E2(V3a_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0)))) ) ) ) ).
tff(thm_2Ebit_2ESBIT__MULT,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Ebit_2ESBIT_2E2(V0b_2E0,V2n_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0)) = c_2Ebit_2ESBIT_2E2(V0b_2E0,c_2Earithmetic_2E_2B_2E2(V2n_2E0,V1m_2E0)) ) ).
tff(thm_2Ebit_2EBITWISE__EVAL,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2a_2E0: tyop_2Enum_2Enum,V3b_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITWISE_2E4(c_2Enum_2ESUC_2E1(V0n_2E0),V1op_2E0,V2a_2E0,V3b_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Ebit_2EBITWISE_2E4(V0n_2E0,V1op_2E0,c_2Earithmetic_2EDIV_2E2(V2a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2EDIV_2E2(V3b_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebit_2ESBIT_2E2(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1op_2E0,c_2Earithmetic_2EODD_2E1(V2a_2E0)),c_2Earithmetic_2EODD_2E1(V3b_2E0)),c_2Enum_2E0_2E0)) ) ).
tff(thm_2Ebit_2EMOD__PLUS__RIGHT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1j_2E0: tyop_2Enum_2Enum,V2k_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(V1j_2E0,c_2Earithmetic_2EMOD_2E2(V2k_2E0,V0n_2E0)),V0n_2E0) = c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(V1j_2E0,V2k_2E0),V0n_2E0) ) ) ).
tff(thm_2Ebit_2EMOD__PLUS__LEFT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1j_2E0: tyop_2Enum_2Enum,V2k_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EMOD_2E2(V2k_2E0,V0n_2E0),V1j_2E0),V0n_2E0) = c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(V2k_2E0,V1j_2E0),V0n_2E0) ) ) ).
tff(thm_2Ebit_2EMOD__PLUS__1,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1x_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(V1x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0n_2E0) = c_2Enum_2E0_2E0 )
<=> ( c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EMOD_2E2(V1x_2E0,V0n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0n_2E0 ) ) ) ).
tff(thm_2Ebit_2EMOD__ADD__1,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1x_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(V1x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0n_2E0) != c_2Enum_2E0_2E0 )
=> ( c_2Earithmetic_2EMOD_2E2(c_2Earithmetic_2E_2B_2E2(V1x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EMOD_2E2(V1x_2E0,V0n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ) ).
tff(thm_2Ebit_2EBIT__REVERSE__THM,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,V1n_2E0))
=> ( c_2Ebit_2EBIT_2E2(V0x_2E0,c_2Ebit_2EBIT__REVERSE_2E2(V1n_2E0,V2a_2E0)) = c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0),V2a_2E0) ) ) ).
tff(thm_2Ebit_2ELOG2__LE__MONO,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0x_2E0))
=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V0x_2E0,V1y_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Ebit_2ELOG2_2E1(V0x_2E0),c_2Ebit_2ELOG2_2E1(V1y_2E0))) ) ) ).
tff(thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2,axiom,
( ! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0),V1y_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V0x_2E0,c_2Ebit_2ELOG2_2E1(V1y_2E0))) )
& ! [V2y_2E0: tyop_2Enum_2Enum,V3x_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V3x_2E0))
=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V3x_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2y_2E0)))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Ebit_2ELOG2_2E1(V3x_2E0),V2y_2E0)) ) ) ) ).
tff(thm_2Ebit_2ENOT__BIT__GT__LOG2,axiom,
! [V0i_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Ebit_2ELOG2_2E1(V1n_2E0),V0i_2E0))
=> ~ p(c_2Ebit_2EBIT_2E2(V0i_2E0,V1n_2E0)) ) ).
tff(thm_2Ebit_2ENOT__BIT__GT__BITWISE,axiom,
! [V0i_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2op_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3a_2E0: tyop_2Enum_2Enum,V4b_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V0i_2E0))
=> ~ p(c_2Ebit_2EBIT_2E2(V0i_2E0,c_2Ebit_2EBITWISE_2E4(V1n_2E0,V2op_2E0,V3a_2E0,V4b_2E0))) ) ).
tff(thm_2Ebit_2ELT__TWOEXP,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0)))
<=> ( ( V0x_2E0 = c_2Enum_2E0_2E0 )
| p(c_2Eprim__rec_2E_3C_2E2(c_2Ebit_2ELOG2_2E1(V0x_2E0),V1n_2E0)) ) ) ).
tff(thm_2Ebit_2EBIT__MODIFY__THM,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3a_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,V1n_2E0))
=> ( c_2Ebit_2EBIT_2E2(V0x_2E0,c_2Ebit_2EBIT__MODIFY_2E3(V1n_2E0,V2f_2E0,V3a_2E0)) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V2f_2E0,V0x_2E0),c_2Ebit_2EBIT_2E2(V0x_2E0,V3a_2E0)) ) ) ).
tff(thm_2Ebit_2EBIT__SIGN__EXTEND,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( ! [V0l_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V3i_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0l_2E0),V1h_2E0),V3i_2E0))
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V0l_2E0,V1h_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V0l_2E0)) ) )
=> ( ! [V3i_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V0l_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0,V3i_2E0),V1h_2E0),V0l_2E0),V2n_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V1h_2E0))
& p(c_2Ebit_2EBIT_2E2(c_2Earithmetic_2E_2D_2E2(V0l_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2n_2E0)) ) )
=> ! [V0l_2E0: tyop_2Enum_2Enum,V1h_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V3i_2E0: tyop_2Enum_2Enum] :
( ( V0l_2E0 != c_2Enum_2E0_2E0 )
=> ( c_2Ebit_2EBIT_2E2(V3i_2E0,c_2Ebit_2ESIGN__EXTEND_2E3(V0l_2E0,V1h_2E0,V2n_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0l_2E0),V1h_2E0),V3i_2E0),c_2Ebit_2EBIT_2E2(V3i_2E0,c_2Earithmetic_2EMOD_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0l_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0,V3i_2E0),V1h_2E0),V0l_2E0),V2n_2E0)) ) ) ) ) ).
tff(thm_2Ebit_2EBIT__LOG2,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( V0n_2E0 != c_2Enum_2E0_2E0 )
=> p(c_2Ebit_2EBIT_2E2(c_2Ebit_2ELOG2_2E1(V0n_2E0),V0n_2E0)) ) ).
tff(thm_2Ebit_2EEXISTS__BIT__IN__RANGE,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( ( V2n_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0a_2E0),V2n_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1b_2E0))) )
=> ? [V3i_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0a_2E0,V3i_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V1b_2E0))
& p(c_2Ebit_2EBIT_2E2(V3i_2E0,V2n_2E0)) ) ) ).
tff(thm_2Ebit_2EEXISTS__BIT__LT,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0b_2E0))) )
=> ? [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,V0b_2E0))
& p(c_2Ebit_2EBIT_2E2(V2i_2E0,V1n_2E0)) ) ) ).
tff(thm_2Ebit_2ELEAST__THM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( ! [V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2m_2E0,V0n_2E0))
=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V2m_2E0)) )
& p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V0n_2E0)) )
=> ( c_2Ewhile_2ELEAST_2E1(V1P_2E0) = V0n_2E0 ) ) ).
%------------------------------------------------------------------------------