ITP001 Axioms: ITP091^7.ax
%------------------------------------------------------------------------------
% File : ITP091^7 : 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 : EncodeVar.ax [Gau19]
% : HL4091^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 58 ( 7 unt; 38 typ; 0 def)
% Number of atoms : 54 ( 5 equ; 1 cnn)
% Maximal formula atoms : 5 ( 0 avg)
% Number of connectives : 450 ( 1 ~; 1 |; 6 &; 422 @)
% ( 13 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg; 422 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 3 con; 0-6 aty)
% Number of variables : 91 ( 8 ^ 57 !; 3 ?; 91 :)
% ( 23 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Elist_2ELENGTH,type,
c_2Elist_2ELENGTH:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ERES__EXISTS,type,
c_2Ebool_2ERES__EXISTS:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2ERES__FORALL,type,
c_2Ebool_2ERES__FORALL:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > $o ) ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2ECoder_2Ebnum__coder,type,
c_2ECoder_2Ebnum__coder: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o ) > ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2ECoder_2Ebool__coder,type,
c_2ECoder_2Ebool__coder: ( $o > $o ) > ( tyop_2Epair_2Eprod @ ( $o > $o ) @ ( tyop_2Epair_2Eprod @ ( $o > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2ECoder_2Edecoder,type,
c_2ECoder_2Edecoder:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > A_27a ) ).
thf(c_2ECoder_2Edomain,type,
c_2ECoder_2Edomain:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > A_27a > $o ) ).
thf(c_2ECoder_2Eencoder,type,
c_2ECoder_2Eencoder:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > A_27a > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncodeVar_2Efixed__width,type,
c_2EEncodeVar_2Efixed__width:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > $o ) ).
thf(c_2EEncodeVar_2Eof__length,type,
c_2EEncodeVar_2Eof__length:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2ECoder_2Eprod__coder,type,
c_2ECoder_2Eprod__coder:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Esum__coder,type,
c_2ECoder_2Esum__coder:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Esum_2Esum @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Eunit__coder,type,
c_2ECoder_2Eunit__coder: ( tyop_2Eone_2Eone > $o ) > ( tyop_2Epair_2Eprod @ ( tyop_2Eone_2Eone > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eone_2Eone > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2ECoder_2Ewf__coder,type,
c_2ECoder_2Ewf__coder:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > $o ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2EEncodeVar_2Efixed__width @ A_27a @ V0n @ V1c )
<=> ! [V2x: A_27a] :
( ( c_2ECoder_2Edomain @ A_27a @ V1c @ V2x )
=> ( ( c_2Elist_2ELENGTH @ $o @ ( c_2ECoder_2Eencoder @ A_27a @ V1c @ V2x ) )
= V0n ) ) ) ).
thf(thm_2EEncodeVar_2Eof__length__def,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l @ ( c_2EEncodeVar_2Eof__length @ A_27a @ V1n ) )
<=> ( ( c_2Elist_2ELENGTH @ A_27a @ V0l )
= V1n ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__univ,axiom,
! [A_27a: $tType,V0phi: A_27a > $o,V1c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V2n: tyop_2Enum_2Enum] :
( ( ( c_2ECoder_2Ewf__coder @ A_27a @ V1c )
& ( c_2EEncodeVar_2Efixed__width @ A_27a @ V2n @ V1c ) )
=> ( ! [V3x: A_27a] :
( ( c_2ECoder_2Edomain @ A_27a @ V1c @ V3x )
=> ( V0phi @ V3x ) )
<=> ( c_2Ebool_2ERES__FORALL @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2EEncodeVar_2Eof__length @ $o @ V2n )
@ ^ [V4w: tyop_2Elist_2Elist @ $o] : ( V0phi @ ( c_2ECoder_2Edecoder @ A_27a @ V1c @ V4w ) ) ) ) ) ).
thf(thm_2EEncodeVar_2Eof__length__univ__suc,axiom,
! [A_27a: $tType,V0phi: ( tyop_2Elist_2Elist @ A_27a ) > $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebool_2ERES__FORALL @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncodeVar_2Eof__length @ A_27a @ ( c_2Enum_2ESUC @ V1n ) )
@ ^ [V2w: tyop_2Elist_2Elist @ A_27a] : ( V0phi @ V2w ) )
<=> ! [V3x: A_27a] :
( c_2Ebool_2ERES__FORALL @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncodeVar_2Eof__length @ A_27a @ V1n )
@ ^ [V4w: tyop_2Elist_2Elist @ A_27a] : ( V0phi @ ( c_2Elist_2ECONS @ A_27a @ V3x @ V4w ) ) ) ) ).
thf(thm_2EEncodeVar_2Eof__length__univ__zero,axiom,
! [A_27a: $tType,V0phi: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Ebool_2ERES__FORALL @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncodeVar_2Eof__length @ A_27a @ c_2Enum_2E0 )
@ ^ [V1w: tyop_2Elist_2Elist @ A_27a] : ( V0phi @ V1w ) )
= ( V0phi @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__exists,axiom,
! [A_27a: $tType,V0phi: A_27a > $o,V1c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V2n: tyop_2Enum_2Enum] :
( ( ( c_2ECoder_2Ewf__coder @ A_27a @ V1c )
& ( c_2EEncodeVar_2Efixed__width @ A_27a @ V2n @ V1c ) )
=> ( ? [V3x: A_27a] :
( ( c_2ECoder_2Edomain @ A_27a @ V1c @ V3x )
& ( V0phi @ V3x ) )
<=> ( c_2Ebool_2ERES__EXISTS @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2EEncodeVar_2Eof__length @ $o @ V2n )
@ ^ [V4w: tyop_2Elist_2Elist @ $o] : ( V0phi @ ( c_2ECoder_2Edecoder @ A_27a @ V1c @ V4w ) ) ) ) ) ).
thf(thm_2EEncodeVar_2Eof__length__exists__suc,axiom,
! [A_27a: $tType,V0phi: ( tyop_2Elist_2Elist @ A_27a ) > $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebool_2ERES__EXISTS @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncodeVar_2Eof__length @ A_27a @ ( c_2Enum_2ESUC @ V1n ) )
@ ^ [V2w: tyop_2Elist_2Elist @ A_27a] : ( V0phi @ V2w ) )
<=> ? [V3x: A_27a] :
( c_2Ebool_2ERES__EXISTS @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncodeVar_2Eof__length @ A_27a @ V1n )
@ ^ [V4w: tyop_2Elist_2Elist @ A_27a] : ( V0phi @ ( c_2Elist_2ECONS @ A_27a @ V3x @ V4w ) ) ) ) ).
thf(thm_2EEncodeVar_2Eof__length__exists__zero,axiom,
! [A_27a: $tType,V0phi: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Ebool_2ERES__EXISTS @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncodeVar_2Eof__length @ A_27a @ c_2Enum_2E0 )
@ ^ [V1w: tyop_2Elist_2Elist @ A_27a] : ( V0phi @ V1w ) )
= ( V0phi @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__unit,axiom,
! [V0p: tyop_2Eone_2Eone > $o] : ( c_2EEncodeVar_2Efixed__width @ tyop_2Eone_2Eone @ c_2Enum_2E0 @ ( c_2ECoder_2Eunit__coder @ V0p ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__bool,axiom,
! [V0p: $o > $o] : ( c_2EEncodeVar_2Efixed__width @ $o @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2ECoder_2Ebool__coder @ V0p ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__prod,axiom,
! [A_27a: $tType,A_27b: $tType,V0c1: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V1c2: tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V2n1: tyop_2Enum_2Enum,V3n2: tyop_2Enum_2Enum] :
( ( ( c_2EEncodeVar_2Efixed__width @ A_27a @ V2n1 @ V0c1 )
& ( c_2EEncodeVar_2Efixed__width @ A_27b @ V3n2 @ V1c2 ) )
=> ( c_2EEncodeVar_2Efixed__width @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Earithmetic_2E_2B @ V2n1 @ V3n2 ) @ ( c_2ECoder_2Eprod__coder @ A_27a @ A_27b @ A_27a @ A_27b @ V0c1 @ V1c2 ) ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__sum,axiom,
! [A_27a: $tType,A_27b: $tType,V0c1: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V1c2: tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V2n: tyop_2Enum_2Enum] :
( ( ( c_2EEncodeVar_2Efixed__width @ A_27a @ V2n @ V0c1 )
& ( c_2EEncodeVar_2Efixed__width @ A_27b @ V2n @ V1c2 ) )
=> ( c_2EEncodeVar_2Efixed__width @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Enum_2ESUC @ V2n ) @ ( c_2ECoder_2Esum__coder @ A_27a @ A_27b @ A_27a @ A_27b @ V0c1 @ V1c2 ) ) ) ).
thf(thm_2EEncodeVar_2Efixed__width__bnum,axiom,
! [V0m: tyop_2Enum_2Enum,V1p: tyop_2Enum_2Enum > $o] : ( c_2EEncodeVar_2Efixed__width @ tyop_2Enum_2Enum @ V0m @ ( c_2ECoder_2Ebnum__coder @ V0m @ V1p ) ) ).
%------------------------------------------------------------------------------