ITP001 Axioms: ITP024^7.ax
%------------------------------------------------------------------------------
% File : ITP024^7 : 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 : logroot.ax [Gau19]
% : HL4024^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 78 ( 12 unt; 37 typ; 0 def)
% Number of atoms : 119 ( 40 equ; 1 cnn)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 899 ( 1 ~; 1 |; 34 &; 826 @)
% ( 8 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg; 826 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 3 con; 0-4 aty)
% Number of variables : 116 ( 13 ^ 88 !; 3 ?; 116 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2A,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: 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_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
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_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Earithmetic_2EDIV,type,
c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EEXP,type,
c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2EFST,type,
c_2Epair_2EFST:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27a ) ).
thf(c_2Ebool_2ELET,type,
c_2Ebool_2ELET:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Elogroot_2ELOG,type,
c_2Elogroot_2ELOG: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EMOD,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Elogroot_2EROOT,type,
c_2Elogroot_2EROOT: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2ESND,type,
c_2Epair_2ESND:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27b ) ).
thf(c_2Elogroot_2ESQRTd,type,
c_2Elogroot_2ESQRTd: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ).
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_2Elogroot_2EiSQRT0,type,
c_2Elogroot_2EiSQRT0: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ).
thf(c_2Elogroot_2EiSQRT1,type,
c_2Elogroot_2EiSQRT1: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ).
thf(c_2Elogroot_2EiSQRT2,type,
c_2Elogroot_2EiSQRT2: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ).
thf(c_2Elogroot_2EiSQRT3,type,
c_2Elogroot_2EiSQRT3: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ).
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_2Elogroot_2EROOT,axiom,
! [V0r: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0r )
=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ ( c_2Elogroot_2EROOT @ V0r @ V1n ) @ V0r ) @ V1n )
& ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2EEXP @ ( c_2Enum_2ESUC @ ( c_2Elogroot_2EROOT @ V0r @ V1n ) ) @ V0r ) ) ) ) ).
thf(thm_2Elogroot_2ELOG,axiom,
! [V0a: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1n ) )
=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V0a @ ( c_2Elogroot_2ELOG @ V0a @ V1n ) ) @ V1n )
& ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2EEXP @ V0a @ ( c_2Enum_2ESUC @ ( c_2Elogroot_2ELOG @ V0a @ V1n ) ) ) ) ) ) ).
thf(thm_2Elogroot_2ESQRTd__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elogroot_2ESQRTd @ V0n )
= ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Elogroot_2EROOT @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2E_2A @ ( c_2Elogroot_2EROOT @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) @ ( c_2Elogroot_2EROOT @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ) ) ).
thf(thm_2Elogroot_2EiSQRT0__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elogroot_2EiSQRT0 @ V0n )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V1p: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V2d: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2d @ c_2Enum_2E0 ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Epair_2ESND @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2d ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
@ ( c_2Earithmetic_2E_2D @ ( c_2Epair_2ESND @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) )
@ ( c_2Elogroot_2ESQRTd @ V0n ) ) ) ).
thf(thm_2Elogroot_2EiSQRT1__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elogroot_2EiSQRT1 @ V0n )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V1p: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V2d: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2d @ c_2Enum_2E0 ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Epair_2ESND @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) ) @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ V2d @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
@ ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ ( c_2Epair_2ESND @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) )
@ ( c_2Elogroot_2ESQRTd @ V0n ) ) ) ).
thf(thm_2Elogroot_2EiSQRT2__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elogroot_2EiSQRT2 @ V0n )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V1p: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V2d: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V3c: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V4e: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V4e @ c_2Enum_2E0 ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2d @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V3c ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Enum_2ESUC @ V2d ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V4e ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
@ ( c_2Earithmetic_2E_2D @ V3c @ V2d ) )
@ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2ESND @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) ) )
@ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) )
@ ( c_2Elogroot_2ESQRTd @ V0n ) ) ) ).
thf(thm_2Elogroot_2EiSQRT3__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elogroot_2EiSQRT3 @ V0n )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V1p: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V2d: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V3c: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )
@ ^ [V4e: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V4e @ c_2Enum_2E0 ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2d @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V3c ) ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Enum_2ESUC @ V2d ) @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ V4e @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
@ ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V3c ) @ V2d ) )
@ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2ESND @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) ) )
@ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1p ) ) )
@ ( c_2Elogroot_2ESQRTd @ V0n ) ) ) ).
thf(thm_2Elogroot_2ELT__EXP__ISO,axiom,
! [V0e: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum,V2b: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0e )
=> ( ( c_2Eprim__rec_2E_3C @ V1a @ V2b )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EEXP @ V0e @ V1a ) @ ( c_2Earithmetic_2EEXP @ V0e @ V2b ) ) ) ) ).
thf(thm_2Elogroot_2ELE__EXP__ISO,axiom,
! [V0e: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum,V2b: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0e )
=> ( ( c_2Earithmetic_2E_3C_3D @ V1a @ V2b )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V0e @ V1a ) @ ( c_2Earithmetic_2EEXP @ V0e @ V2b ) ) ) ) ).
thf(thm_2Elogroot_2EEXP__LT__ISO,axiom,
! [V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum,V2r: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2r )
=> ( ( c_2Eprim__rec_2E_3C @ V0a @ V1b )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EEXP @ V0a @ V2r ) @ ( c_2Earithmetic_2EEXP @ V1b @ V2r ) ) ) ) ).
thf(thm_2Elogroot_2EEXP__LE__ISO,axiom,
! [V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum,V2r: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2r )
=> ( ( c_2Earithmetic_2E_3C_3D @ V0a @ V1b )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V0a @ V2r ) @ ( c_2Earithmetic_2EEXP @ V1b @ V2r ) ) ) ) ).
thf(thm_2Elogroot_2EROOT__exists,axiom,
! [V0r: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0r )
=> ? [V2rt: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V2rt @ V0r ) @ V1n )
& ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2EEXP @ ( c_2Enum_2ESUC @ V2rt ) @ V0r ) ) ) ) ).
thf(thm_2Elogroot_2EROOT__UNIQUE,axiom,
! [V0r: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V2p @ V0r ) @ V1n )
& ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2EEXP @ ( c_2Enum_2ESUC @ V2p ) @ V0r ) ) )
=> ( ( c_2Elogroot_2EROOT @ V0r @ V1n )
= V2p ) ) ).
thf(thm_2Elogroot_2ELOG__exists,axiom,
? [V0f: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
! [V1a: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V1a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2n ) )
=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V1a @ ( V0f @ V1a @ V2n ) ) @ V2n )
& ( c_2Eprim__rec_2E_3C @ V2n @ ( c_2Earithmetic_2EEXP @ V1a @ ( c_2Enum_2ESUC @ ( V0f @ V1a @ V2n ) ) ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__UNIQUE,axiom,
! [V0a: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EEXP @ V0a @ V2p ) @ V1n )
& ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2EEXP @ V0a @ ( c_2Enum_2ESUC @ V2p ) ) ) )
=> ( ( c_2Elogroot_2ELOG @ V0a @ V1n )
= V2p ) ) ).
thf(thm_2Elogroot_2ELOG__ADD1,axiom,
! [V0n: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum,V2b: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
& ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V1a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2b ) )
=> ( ( c_2Elogroot_2ELOG @ V1a @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EEXP @ V1a @ ( c_2Enum_2ESUC @ V0n ) ) @ V2b ) )
= ( c_2Enum_2ESUC @ ( c_2Elogroot_2ELOG @ V1a @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EEXP @ V1a @ V0n ) @ V2b ) ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__BASE,axiom,
! [V0a: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
=> ( ( c_2Elogroot_2ELOG @ V0a @ V0a )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__EXP,axiom,
! [V0n: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum,V2b: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V1a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2b ) )
=> ( ( c_2Elogroot_2ELOG @ V1a @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EEXP @ V1a @ V0n ) @ V2b ) )
= ( c_2Earithmetic_2E_2B @ V0n @ ( c_2Elogroot_2ELOG @ V1a @ V2b ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__1,axiom,
! [V0a: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
=> ( ( c_2Elogroot_2ELOG @ V0a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ) ) ).
thf(thm_2Elogroot_2ELOG__DIV,axiom,
! [V0a: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
& ( c_2Earithmetic_2E_3C_3D @ V0a @ V1x ) )
=> ( ( c_2Elogroot_2ELOG @ V0a @ V1x )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elogroot_2ELOG @ V0a @ ( c_2Earithmetic_2EDIV @ V1x @ V0a ) ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__ADD,axiom,
! [V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum,V2c: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
& ( c_2Eprim__rec_2E_3C @ V1b @ ( c_2Earithmetic_2EEXP @ V0a @ V2c ) ) )
=> ( ( c_2Elogroot_2ELOG @ V0a @ ( c_2Earithmetic_2E_2B @ V1b @ ( c_2Earithmetic_2EEXP @ V0a @ V2c ) ) )
= V2c ) ) ).
thf(thm_2Elogroot_2ELOG__LE__MONO,axiom,
! [V0a: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum,V2y: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1x ) )
=> ( ( c_2Earithmetic_2E_3C_3D @ V1x @ V2y )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Elogroot_2ELOG @ V0a @ V1x ) @ ( c_2Elogroot_2ELOG @ V0a @ V2y ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__RWT,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0m )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1n ) )
=> ( ( c_2Elogroot_2ELOG @ V0m @ V1n )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Eprim__rec_2E_3C @ V1n @ V0m ) @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ ( c_2Elogroot_2ELOG @ V0m @ ( c_2Earithmetic_2EDIV @ V1n @ V0m ) ) ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__EQ__0,axiom,
! [V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1b ) )
=> ( ( ( c_2Elogroot_2ELOG @ V0a @ V1b )
= c_2Enum_2E0 )
<=> ( c_2Eprim__rec_2E_3C @ V1b @ V0a ) ) ) ).
thf(thm_2Elogroot_2ELOG__MULT,axiom,
! [V0b: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0b )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1x ) )
=> ( ( c_2Elogroot_2ELOG @ V0b @ ( c_2Earithmetic_2E_2A @ V0b @ V1x ) )
= ( c_2Enum_2ESUC @ ( c_2Elogroot_2ELOG @ V0b @ V1x ) ) ) ) ).
thf(thm_2Elogroot_2ELOG__add__digit,axiom,
! [V0b: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum,V2y: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0b )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2y )
& ( c_2Eprim__rec_2E_3C @ V1x @ V0b ) )
=> ( ( c_2Elogroot_2ELOG @ V0b @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ V0b @ V2y ) @ V1x ) )
= ( c_2Enum_2ESUC @ ( c_2Elogroot_2ELOG @ V0b @ V2y ) ) ) ) ).
thf(thm_2Elogroot_2EROOT__DIV,axiom,
! [V0r: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum,V2y: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0r )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2y ) )
=> ( ( c_2Earithmetic_2EDIV @ ( c_2Elogroot_2EROOT @ V0r @ V1x ) @ V2y )
= ( c_2Elogroot_2EROOT @ V0r @ ( c_2Earithmetic_2EDIV @ V1x @ ( c_2Earithmetic_2EEXP @ V2y @ V0r ) ) ) ) ) ).
thf(thm_2Elogroot_2EROOT__LE__MONO,axiom,
! [V0r: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum,V2y: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0r )
=> ( ( c_2Earithmetic_2E_3C_3D @ V1x @ V2y )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Elogroot_2EROOT @ V0r @ V1x ) @ ( c_2Elogroot_2EROOT @ V0r @ V2y ) ) ) ) ).
thf(thm_2Elogroot_2EEXP__MUL,axiom,
! [V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum,V2c: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2EEXP @ V0a @ V1b ) @ V2c )
= ( c_2Earithmetic_2EEXP @ V0a @ ( c_2Earithmetic_2E_2A @ V1b @ V2c ) ) ) ).
thf(thm_2Elogroot_2ELOG__ROOT,axiom,
! [V0a: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum,V2r: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0a )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1x )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2r ) )
=> ( ( c_2Elogroot_2ELOG @ V0a @ ( c_2Elogroot_2EROOT @ V2r @ V1x ) )
= ( c_2Earithmetic_2EDIV @ ( c_2Elogroot_2ELOG @ V0a @ V1x ) @ V2r ) ) ) ).
thf(thm_2Elogroot_2ELOG__MOD,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
=> ( V0n
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elogroot_2ELOG @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elogroot_2ELOG @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ) ) ) ).
thf(thm_2Elogroot_2EROOT__COMPUTE,axiom,
! [V0r: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0r )
=> ( ( ( c_2Elogroot_2EROOT @ V0r @ c_2Enum_2E0 )
= c_2Enum_2E0 )
& ( ( c_2Elogroot_2EROOT @ V0r @ V1n )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum
@ ^ [V2x: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2EEXP @ ( c_2Enum_2ESUC @ V2x ) @ V0r ) ) @ V2x @ ( c_2Enum_2ESUC @ V2x ) )
@ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elogroot_2EROOT @ V0r @ ( c_2Earithmetic_2EDIV @ V1n @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0r ) ) ) ) ) ) ) ) ).
thf(thm_2Elogroot_2Enumeral__sqrt,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( ( c_2Elogroot_2ESQRTd @ c_2Earithmetic_2EZERO )
= ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ V0n ) ) )
= ( c_2Elogroot_2EiSQRT3 @ V0n ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ V0n ) ) )
= ( c_2Elogroot_2EiSQRT0 @ ( c_2Enum_2ESUC @ V0n ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ V0n ) ) )
= ( c_2Elogroot_2EiSQRT1 @ ( c_2Enum_2ESUC @ V0n ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ V0n ) ) )
= ( c_2Elogroot_2EiSQRT2 @ ( c_2Enum_2ESUC @ V0n ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= ( c_2Elogroot_2EiSQRT0 @ ( c_2Enum_2ESUC @ V0n ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= ( c_2Elogroot_2EiSQRT1 @ ( c_2Enum_2ESUC @ V0n ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= ( c_2Elogroot_2EiSQRT2 @ ( c_2Enum_2ESUC @ V0n ) ) )
& ( ( c_2Elogroot_2ESQRTd @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= ( c_2Elogroot_2EiSQRT3 @ ( c_2Enum_2ESUC @ V0n ) ) ) ) ).
thf(thm_2Elogroot_2Enumeral__root2,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elogroot_2EROOT @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ V0n ) )
= ( c_2Epair_2EFST @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Elogroot_2ESQRTd @ V0n ) ) ) ).
%------------------------------------------------------------------------------