ITP001 Axioms: ITP128_5.ax
%------------------------------------------------------------------------------
% File : ITP128_5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : lim_2.ax [Gau20]
% : HL4128_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 132 ( 12 unt; 31 typ; 0 def)
% Number of atoms : 3133 ( 66 equ)
% Maximal formula atoms : 15 ( 23 avg)
% Number of connectives : 384 ( 13 ~; 0 |; 137 &)
% ( 11 <=>; 223 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2661 (2661 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 50 ( 26 >; 24 *; 0 +; 0 <<)
% Number of predicates : 43 ( 42 usr; 27 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 5 con; 0-3 aty)
% Number of variables : 389 ( 362 !; 27 ?; 389 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Elim_2Econtl,type,
c_2Elim_2Econtl: $i ).
tff(mem_c_2Elim_2Econtl,axiom,
mem(c_2Elim_2Econtl,arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))) ).
tff(tp_c_2Elim_2Edifferentiable,type,
c_2Elim_2Edifferentiable: $i ).
tff(mem_c_2Elim_2Edifferentiable,axiom,
mem(c_2Elim_2Edifferentiable,arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))) ).
tff(tp_c_2Elim_2Ediffl,type,
c_2Elim_2Ediffl: $i ).
tff(mem_c_2Elim_2Ediffl,axiom,
mem(c_2Elim_2Ediffl,arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))) ).
tff(tp_c_2Elim_2Etends__real__real,type,
c_2Elim_2Etends__real__real: $i ).
tff(mem_c_2Elim_2Etends__real__real,axiom,
mem(c_2Elim_2Etends__real__real,arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))) ).
tff(ax_thm_2Elim_2Etends__real__real,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x0: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x0)))
<=> p(ap(ap(ap(c_2Enets_2Etends(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0f),inj__ty_2Erealax_2Ereal(V1l)),ap(ap(c_2Epair_2E_2C(ty_2Etopology_2Etopology(ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))),ap(c_2Emetric_2Emtop(ty_2Erealax_2Ereal),c_2Emetric_2Emr1)),ap(c_2Enets_2Etendsto(ty_2Erealax_2Ereal),ap(ap(c_2Epair_2E_2C(ty_2Emetric_2Emetric(ty_2Erealax_2Ereal),ty_2Erealax_2Ereal),c_2Emetric_2Emr1),inj__ty_2Erealax_2Ereal(V2x0)))))) ) ) ).
tff(conj_thm_2Elim_2ELIM,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1y0: tp__ty_2Erealax_2Ereal,V2x0: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V1y0)),inj__ty_2Erealax_2Ereal(V2x0)))
<=> ! [V3e: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3e)))
=> ? [V4d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4d)))
& ! [V5x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2x0)))))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2x0)))),inj__ty_2Erealax_2Ereal(V4d))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),inj__ty_2Erealax_2Ereal(V1y0)))),inj__ty_2Erealax_2Ereal(V3e))) ) ) ) ) ) ).
tff(conj_thm_2Elim_2ELIM__CONST,axiom,
! [V0k: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Etends__real__real,k(ty_2Erealax_2Ereal,inj__ty_2Erealax_2Ereal(V0k))),inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(lamtp_f2807,type,
f2807: ( $i * $i ) > $i ).
tff(lameq_f2807,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V5x: tp__ty_2Erealax_2Ereal] : ( ap(f2807(V0f,V1g),inj__ty_2Erealax_2Ereal(V5x)) = ap(ap(c_2Erealax_2Ereal__add,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),ap(V1g,inj__ty_2Erealax_2Ereal(V5x))) ) ) ) ).
tff(conj_thm_2Elim_2ELIM__ADD,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Etends__real__real,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2807(V0f,V1g)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2808,type,
f2808: ( $i * $i ) > $i ).
tff(lameq_f2808,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V5x: tp__ty_2Erealax_2Ereal] : ( ap(f2808(V0f,V1g),inj__ty_2Erealax_2Ereal(V5x)) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),ap(V1g,inj__ty_2Erealax_2Ereal(V5x))) ) ) ) ).
tff(conj_thm_2Elim_2ELIM__MUL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Etends__real__real,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2808(V0f,V1g)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2809,type,
f2809: $i > $i ).
tff(lameq_f2809,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2809(V0f),inj__ty_2Erealax_2Ereal(V3x)) = ap(c_2Erealax_2Ereal__neg,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))) ) ) ).
tff(conj_thm_2Elim_2ELIM__NEG,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
<=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2809(V0f)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1l))),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(lamtp_f2810,type,
f2810: $i > $i ).
tff(lameq_f2810,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2810(V0f),inj__ty_2Erealax_2Ereal(V3x)) = ap(c_2Erealax_2Einv,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))) ) ) ).
tff(conj_thm_2Elim_2ELIM__INV,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
& ( V1l != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2810(V0f)),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1l))),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(lamtp_f2811,type,
f2811: ( $i * $i ) > $i ).
tff(lameq_f2811,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V5x: tp__ty_2Erealax_2Ereal] : ( ap(f2811(V0f,V1g),inj__ty_2Erealax_2Ereal(V5x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),ap(V1g,inj__ty_2Erealax_2Ereal(V5x))) ) ) ) ).
tff(conj_thm_2Elim_2ELIM__SUB,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Etends__real__real,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2811(V0f,V1g)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2812,type,
f2812: ( $i * $i ) > $i ).
tff(lameq_f2812,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V5x: tp__ty_2Erealax_2Ereal] : ( ap(f2812(V0f,V1g),inj__ty_2Erealax_2Ereal(V5x)) = ap(ap(c_2Ereal_2E_2F,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),ap(V1g,inj__ty_2Erealax_2Ereal(V5x))) ) ) ) ).
tff(conj_thm_2Elim_2ELIM__DIV,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Etends__real__real,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x)))
& ( V3m != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2812(V0f,V1g)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2813,type,
f2813: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2813,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2813(V0f,V1l),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))),inj__ty_2Erealax_2Ereal(V1l)) ) ) ).
tff(conj_thm_2Elim_2ELIM__NULL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
<=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2813(V0f,V1l)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(conj_thm_2Elim_2ELIM__X,axiom,
! [V0x0: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Etends__real__real,i(ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(V0x0)),inj__ty_2Erealax_2Ereal(V0x0))) ).
tff(conj_thm_2Elim_2ELIM__UNIQ,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2m: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V2m)),inj__ty_2Erealax_2Ereal(V3x))) )
=> ( V1l = V2m ) ) ) ).
tff(conj_thm_2Elim_2ELIM__EQUAL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3x0: tp__ty_2Erealax_2Ereal] :
( ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( V4x != V3x0 )
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V4x))) = surj__ty_2Erealax_2Ereal(ap(V1g,inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ( p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3x0)))
<=> p(ap(ap(ap(c_2Elim_2Etends__real__real,V1g),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3x0))) ) ) ) ) ).
tff(lamtp_f2814,type,
f2814: ( $i * $i ) > $i ).
tff(lameq_f2814,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V4x: tp__ty_2Erealax_2Ereal] : ( ap(f2814(V0f,V1g),inj__ty_2Erealax_2Ereal(V4x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V4x))),ap(V1g,inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(conj_thm_2Elim_2ELIM__TRANSFORM,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x0: tp__ty_2Erealax_2Ereal,V3l: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Etends__real__real,f2814(V0f,V1g)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2x0)))
& p(ap(ap(ap(c_2Elim_2Etends__real__real,V1g),inj__ty_2Erealax_2Ereal(V3l)),inj__ty_2Erealax_2Ereal(V2x0))) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),inj__ty_2Erealax_2Ereal(V3l)),inj__ty_2Erealax_2Ereal(V2x0))) ) ) ) ).
tff(lamtp_f2815,type,
f2815: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2815,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3h: tp__ty_2Erealax_2Ereal] : ( ap(f2815(V0f,V2x),inj__ty_2Erealax_2Ereal(V3h)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V3h)))),ap(V0f,inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3h)) ) ) ).
tff(ax_thm_2Elim_2Ediffl,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
<=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2815(V0f,V2x)),inj__ty_2Erealax_2Ereal(V1l)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ) ).
tff(lamtp_f2816,type,
f2816: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2816,axiom,
! [V1x: tp__ty_2Erealax_2Ereal,V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2h: tp__ty_2Erealax_2Ereal] : ( ap(f2816(V1x,V0f),inj__ty_2Erealax_2Ereal(V2h)) = ap(V0f,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2h))) ) ) ).
tff(ax_thm_2Elim_2Econtl,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V1x)))
<=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2816(V1x,V0f)),ap(V0f,inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ) ).
tff(ax_thm_2Elim_2Edifferentiable,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Elim_2Edifferentiable,V0f),inj__ty_2Erealax_2Ereal(V1x)))
<=> ? [V2l: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V1x))) ) ) ).
tff(conj_thm_2Elim_2EDIFF__UNIQ,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2m: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2m)),inj__ty_2Erealax_2Ereal(V3x))) )
=> ( V1l = V2m ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__CONT,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(conj_thm_2Elim_2ECONTL__LIM,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V1x)))
<=> p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),ap(V0f,inj__ty_2Erealax_2Ereal(V1x))),inj__ty_2Erealax_2Ereal(V1x))) ) ) ).
tff(conj_thm_2Elim_2EDIFF__CARAT,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
<=> ? [V3g: $i] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
& ! [V4z: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V4z))),ap(V0f,inj__ty_2Erealax_2Ereal(V2x)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(V3g,inj__ty_2Erealax_2Ereal(V4z))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V4z)),inj__ty_2Erealax_2Ereal(V2x)))) )
& p(ap(ap(c_2Elim_2Econtl,V3g),inj__ty_2Erealax_2Ereal(V2x)))
& ( surj__ty_2Erealax_2Ereal(ap(V3g,inj__ty_2Erealax_2Ereal(V2x))) = V1l ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__CONST,axiom,
! [V0k: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Elim_2Econtl,k(ty_2Erealax_2Ereal,inj__ty_2Erealax_2Ereal(V0k))),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(lamtp_f2817,type,
f2817: ( $i * $i ) > $i ).
tff(lameq_f2817,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2817(V0f,V1g),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Erealax_2Ereal__add,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))),ap(V1g,inj__ty_2Erealax_2Ereal(V3x))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__ADD,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Elim_2Econtl,V1g),inj__ty_2Erealax_2Ereal(V2x))) )
=> p(ap(ap(c_2Elim_2Econtl,f2817(V0f,V1g)),inj__ty_2Erealax_2Ereal(V2x))) ) ) ) ).
tff(lamtp_f2818,type,
f2818: ( $i * $i ) > $i ).
tff(lameq_f2818,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2818(V0f,V1g),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))),ap(V1g,inj__ty_2Erealax_2Ereal(V3x))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__MUL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Elim_2Econtl,V1g),inj__ty_2Erealax_2Ereal(V2x))) )
=> p(ap(ap(c_2Elim_2Econtl,f2818(V0f,V1g)),inj__ty_2Erealax_2Ereal(V2x))) ) ) ) ).
tff(lamtp_f2819,type,
f2819: $i > $i ).
tff(lameq_f2819,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] : ( ap(f2819(V0f),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Erealax_2Ereal__neg,ap(V0f,inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(conj_thm_2Elim_2ECONT__NEG,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V1x)))
=> p(ap(ap(c_2Elim_2Econtl,f2819(V0f)),inj__ty_2Erealax_2Ereal(V1x))) ) ) ).
tff(lamtp_f2820,type,
f2820: $i > $i ).
tff(lameq_f2820,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] : ( ap(f2820(V0f),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Erealax_2Einv,ap(V0f,inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(conj_thm_2Elim_2ECONT__INV,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V1x)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V1x))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(c_2Elim_2Econtl,f2820(V0f)),inj__ty_2Erealax_2Ereal(V1x))) ) ) ).
tff(lamtp_f2821,type,
f2821: ( $i * $i ) > $i ).
tff(lameq_f2821,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2821(V0f,V1g),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))),ap(V1g,inj__ty_2Erealax_2Ereal(V3x))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__SUB,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Elim_2Econtl,V1g),inj__ty_2Erealax_2Ereal(V2x))) )
=> p(ap(ap(c_2Elim_2Econtl,f2821(V0f,V1g)),inj__ty_2Erealax_2Ereal(V2x))) ) ) ) ).
tff(lamtp_f2822,type,
f2822: ( $i * $i ) > $i ).
tff(lameq_f2822,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2822(V0f,V1g),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Ereal_2E_2F,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))),ap(V1g,inj__ty_2Erealax_2Ereal(V3x))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__DIV,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Elim_2Econtl,V1g),inj__ty_2Erealax_2Ereal(V2x)))
& ( surj__ty_2Erealax_2Ereal(ap(V1g,inj__ty_2Erealax_2Ereal(V2x))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(c_2Elim_2Econtl,f2822(V0f,V1g)),inj__ty_2Erealax_2Ereal(V2x))) ) ) ) ).
tff(lamtp_f2823,type,
f2823: ( $i * $i ) > $i ).
tff(lameq_f2823,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2823(V0f,V1g),inj__ty_2Erealax_2Ereal(V3x)) = ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__COMPOSE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Elim_2Econtl,V1g),ap(V0f,inj__ty_2Erealax_2Ereal(V2x)))) )
=> p(ap(ap(c_2Elim_2Econtl,f2823(V0f,V1g)),inj__ty_2Erealax_2Ereal(V2x))) ) ) ) ).
tff(conj_thm_2Elim_2EIVT,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V1a))),inj__ty_2Erealax_2Ereal(V3y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3y)),ap(V0f,inj__ty_2Erealax_2Ereal(V2b))))
& ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ? [V5x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V5x))) = V3y ) ) ) ) ).
tff(conj_thm_2Elim_2EIVT2,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V2b))),inj__ty_2Erealax_2Ereal(V3y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3y)),ap(V0f,inj__ty_2Erealax_2Ereal(V1a))))
& ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ? [V5x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V5x))) = V3y ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__CONST,axiom,
! [V0k: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,k(ty_2Erealax_2Ereal,inj__ty_2Erealax_2Ereal(V0k))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(conj_thm_2Elim_2EDIFF__ADD,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2807(V0f,V1g)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__MUL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2808(V0f,V1g)),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2l)),ap(V1g,inj__ty_2Erealax_2Ereal(V4x)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V3m)),ap(V0f,inj__ty_2Erealax_2Ereal(V4x))))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2824,type,
f2824: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2824,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1c: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] : ( ap(f2824(V0f,V1c),inj__ty_2Erealax_2Ereal(V4x)) = ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),ap(V0f,inj__ty_2Erealax_2Ereal(V4x))) ) ) ).
tff(conj_thm_2Elim_2EDIFF__CMUL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1c: tp__ty_2Erealax_2Ereal,V2l: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2824(V0f,V1c)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),inj__ty_2Erealax_2Ereal(V2l))),inj__ty_2Erealax_2Ereal(V3x))) ) ) ).
tff(conj_thm_2Elim_2EDIFF__NEG,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2809(V0f)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1l))),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(conj_thm_2Elim_2EDIFF__SUB,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2811(V0f,V1g)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2825,type,
f2825: ( $i * $i ) > $i ).
tff(lameq_f2825,axiom,
! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V5x: tp__ty_2Erealax_2Ereal] : ( ap(f2825(V1g,V0f),inj__ty_2Erealax_2Ereal(V5x)) = ap(V0f,ap(V1g,inj__ty_2Erealax_2Ereal(V5x))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__CHAIN,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),ap(V1g,inj__ty_2Erealax_2Ereal(V4x))))
& p(ap(ap(ap(c_2Elim_2Ediffl,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2825(V1g,V0f)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3m))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__X,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,i(ty_2Erealax_2Ereal)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(lamtp_f2826,type,
f2826: tp__ty_2Enum_2Enum > $i ).
tff(lameq_f2826,axiom,
! [V0n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Erealax_2Ereal] : ( ap(f2826(V0n),inj__ty_2Erealax_2Ereal(V2x)) = ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V0n)) ) ).
tff(conj_thm_2Elim_2EDIFF__POW,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,f2826(V0n)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(lamtp_f2827,type,
f2827: $i ).
tff(lameq_f2827,axiom,
! [V1x: tp__ty_2Erealax_2Ereal] : ( ap(f2827,inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1x)) ) ).
tff(conj_thm_2Elim_2EDIFF__XM1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2827),ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Elim_2EDIFF__INV,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V1l)),inj__ty_2Erealax_2Ereal(V2x)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V2x))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2810(V0f)),ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1l)),ap(ap(c_2Ereal_2Epow,ap(V0f,inj__ty_2Erealax_2Ereal(V2x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
tff(conj_thm_2Elim_2EDIFF__DIV,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3m: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V1g),inj__ty_2Erealax_2Ereal(V3m)),inj__ty_2Erealax_2Ereal(V4x)))
& ( surj__ty_2Erealax_2Ereal(ap(V1g,inj__ty_2Erealax_2Ereal(V4x))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2812(V0f,V1g)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2l)),ap(V1g,inj__ty_2Erealax_2Ereal(V4x)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V3m)),ap(V0f,inj__ty_2Erealax_2Ereal(V4x))))),ap(ap(c_2Ereal_2Epow,ap(V1g,inj__ty_2Erealax_2Ereal(V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(lamtp_f2828,type,
f2828: ( tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2828,axiom,
! [V5r: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V6x: tp__ty_2Erealax_2Ereal] : ( ap(f2828(V5r,V0f),inj__ty_2Erealax_2Ereal(V6x)) = ap(ap(V0f,inj__ty_2Enum_2Enum(V5r)),inj__ty_2Erealax_2Ereal(V6x)) ) ) ).
tff(lamtp_f2829,type,
f2829: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2829,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V7x: tp__ty_2Erealax_2Ereal,V8n: tp__ty_2Enum_2Enum] : ( ap(f2829(V0f,V7x),inj__ty_2Enum_2Enum(V8n)) = ap(ap(V0f,inj__ty_2Enum_2Enum(V8n)),inj__ty_2Erealax_2Ereal(V7x)) ) ) ).
tff(lamtp_f2830,type,
f2830: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2830,axiom,
! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V7x: tp__ty_2Erealax_2Ereal] : ( ap(f2830(V2m,V3n,V0f),inj__ty_2Erealax_2Ereal(V7x)) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n))),f2829(V0f,V7x)) ) ) ).
tff(lamtp_f2831,type,
f2831: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2831,axiom,
! [V1f_27: $i] :
( mem(V1f_27,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V4x: tp__ty_2Erealax_2Ereal,V9r: tp__ty_2Enum_2Enum] : ( ap(f2831(V1f_27,V4x),inj__ty_2Enum_2Enum(V9r)) = ap(ap(V1f_27,inj__ty_2Enum_2Enum(V9r)),inj__ty_2Erealax_2Ereal(V4x)) ) ) ).
tff(conj_thm_2Elim_2EDIFF__SUM,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V1f_27: $i] :
( mem(V1f_27,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum,V4x: tp__ty_2Erealax_2Ereal] :
( ! [V5r: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V5r)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V5r)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n)))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2828(V5r,V0f)),ap(ap(V1f_27,inj__ty_2Enum_2Enum(V5r)),inj__ty_2Erealax_2Ereal(V4x))),inj__ty_2Erealax_2Ereal(V4x))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2830(V2m,V3n,V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n))),f2831(V1f_27,V4x))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__BOUNDED,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) ) )
=> ? [V4M: tp__ty_2Erealax_2Ereal] :
! [V5x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),inj__ty_2Erealax_2Ereal(V4M))) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__HASSUP,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) ) )
=> ? [V4M: tp__ty_2Erealax_2Ereal] :
( ! [V5x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),inj__ty_2Erealax_2Ereal(V4M))) )
& ! [V6N: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6N)),inj__ty_2Erealax_2Ereal(V4M)))
=> ? [V7x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V7x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V7x)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6N)),ap(V0f,inj__ty_2Erealax_2Ereal(V7x)))) ) ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__ATTAINS,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) ) )
=> ? [V4M: tp__ty_2Erealax_2Ereal] :
( ! [V5x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V5x))),inj__ty_2Erealax_2Ereal(V4M))) )
& ? [V6x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V6x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V6x))) = V4M ) ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__ATTAINS2,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) ) )
=> ? [V4M: tp__ty_2Erealax_2Ereal] :
( ! [V5x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4M)),ap(V0f,inj__ty_2Erealax_2Ereal(V5x)))) )
& ? [V6x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V6x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V6x))) = V4M ) ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__ATTAINS__ALL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) ) )
=> ? [V4L: tp__ty_2Erealax_2Ereal,V5M: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4L)),inj__ty_2Erealax_2Ereal(V5M)))
& ! [V6y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4L)),inj__ty_2Erealax_2Ereal(V6y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V6y)),inj__ty_2Erealax_2Ereal(V5M))) )
=> ? [V7x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V7x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V7x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V7x))) = V6y ) ) )
& ! [V8x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V8x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V8x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4L)),ap(V0f,inj__ty_2Erealax_2Ereal(V8x))))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V8x))),inj__ty_2Erealax_2Ereal(V5M))) ) ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__LINC,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2l: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2l))) )
=> ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4h: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4h)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4h)),inj__ty_2Erealax_2Ereal(V3d))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0f,inj__ty_2Erealax_2Ereal(V1x))),ap(V0f,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V4h))))) ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__LDEC,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2l: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2l)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) )
=> ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4h: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4h)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4h)),inj__ty_2Erealax_2Ereal(V3d))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0f,inj__ty_2Erealax_2Ereal(V1x))),ap(V0f,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V4h))))) ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__LMAX,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2l: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V1x)))
& ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V4y)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V4y))),ap(V0f,inj__ty_2Erealax_2Ereal(V1x)))) ) ) )
=> ( V2l = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__LMIN,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2l: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V1x)))
& ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V4y)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V1x))),ap(V0f,inj__ty_2Erealax_2Ereal(V4y)))) ) ) )
=> ( V2l = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__LCONST,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2l: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V1x)))
& ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V4y)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V4y))) = surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V1x))) ) ) ) )
=> ( V2l = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Elim_2EINTERVAL__LEMMA,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V1b))) )
=> ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V4y)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V4y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4y)),inj__ty_2Erealax_2Ereal(V1b))) ) ) ) ) ).
tff(conj_thm_2Elim_2EROLLE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V1a))) = surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V2b))) )
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) )
& ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Edifferentiable,V0f),inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ? [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V0f),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V5z))) ) ) ) ).
tff(lamtp_f2832,type,
f2832: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2832,axiom,
! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal,V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2832(V1a,V2b,V0f),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V3x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V2b))),ap(V0f,inj__ty_2Erealax_2Ereal(V1a)))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2b)),inj__ty_2Erealax_2Ereal(V1a)))),inj__ty_2Erealax_2Ereal(V3x))) ) ) ).
tff(lamtp_f2833,type,
f2833: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2833,axiom,
! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal,V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V4x: tp__ty_2Erealax_2Ereal] : ( ap(f2833(V1a,V2b,V0f),inj__ty_2Erealax_2Ereal(V4x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V4x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V2b))),ap(V0f,inj__ty_2Erealax_2Ereal(V1a)))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2b)),inj__ty_2Erealax_2Ereal(V1a)))),inj__ty_2Erealax_2Ereal(V4x))) ) ) ).
tff(conj_thm_2Elim_2EMVT__LEMMA,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(f2832(V1a,V2b,V0f),inj__ty_2Erealax_2Ereal(V1a))) = surj__ty_2Erealax_2Ereal(ap(f2833(V1a,V2b,V0f),inj__ty_2Erealax_2Ereal(V2b))) ) ) ).
tff(conj_thm_2Elim_2EMVT,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) )
& ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Edifferentiable,V0f),inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ? [V5l: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V6z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6z)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V5l)),inj__ty_2Erealax_2Ereal(V6z)))
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Erealax_2Ereal(V2b))),ap(V0f,inj__ty_2Erealax_2Ereal(V1a)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2b)),inj__ty_2Erealax_2Ereal(V1a))),inj__ty_2Erealax_2Ereal(V5l))) ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__ISCONST__END,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) )
& ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,V0f),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V2b))) = surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V1a))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__ISCONST,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V3x))) )
& ! [V4x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,V0f),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4x))) ) )
=> ! [V5x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2b))) )
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V5x))) = surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V1a))) ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__ISCONST__ALL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( ! [V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,V0f),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x)))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V2x))) = surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V3y))) ) ) ) ).
tff(conj_thm_2Elim_2EINTERVAL__ABS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1z: tp__ty_2Erealax_2Ereal,V2d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2d))),inj__ty_2Erealax_2Ereal(V1z)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1z)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2d)))) )
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V0x)))),inj__ty_2Erealax_2Ereal(V2d))) ) ).
tff(conj_thm_2Elim_2ECONT__INJ__LEMMA,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V4z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V4z)))) = V4z ) )
& ! [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V5z))) ) )
=> ~ ! [V6z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V6z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V6z))),ap(V0f,inj__ty_2Erealax_2Ereal(V2x)))) ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__INJ__LEMMA2,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V4z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V4z)))) = V4z ) )
& ! [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V5z))) ) )
=> ~ ! [V6z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V6z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Erealax_2Ereal(V2x))),ap(V0f,inj__ty_2Erealax_2Ereal(V6z)))) ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__INJ__RANGE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V4z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V4z)))) = V4z ) )
& ! [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V5z))) ) )
=> ? [V6e: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V6e)))
& ! [V7y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V7y)),ap(V0f,inj__ty_2Erealax_2Ereal(V2x))))),inj__ty_2Erealax_2Ereal(V6e)))
=> ? [V8z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V8z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
& ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Erealax_2Ereal(V8z))) = V7y ) ) ) ) ) ) ) ).
tff(conj_thm_2Elim_2ECONT__INVERSE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V4z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V4z)))) = V4z ) )
& ! [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V5z))) ) )
=> p(ap(ap(c_2Elim_2Econtl,V1g),ap(V0f,inj__ty_2Erealax_2Ereal(V2x)))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__INVERSE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal,V4d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4d)))
& ! [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V3x)))),inj__ty_2Erealax_2Ereal(V4d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V5z)))) = V5z ) )
& ! [V6z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V6z)),inj__ty_2Erealax_2Ereal(V3x)))),inj__ty_2Erealax_2Ereal(V4d)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V6z))) )
& p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3x)))
& ( V2l != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,V1g),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V2l))),ap(V0f,inj__ty_2Erealax_2Ereal(V3x)))) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__INVERSE__LT,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal,V4d: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V4d)))
& ! [V5z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V5z)),inj__ty_2Erealax_2Ereal(V3x)))),inj__ty_2Erealax_2Ereal(V4d)))
=> ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V5z)))) = V5z ) )
& ! [V6z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V6z)),inj__ty_2Erealax_2Ereal(V3x)))),inj__ty_2Erealax_2Ereal(V4d)))
=> p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V6z))) )
& p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V3x)))
& ( V2l != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,V1g),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V2l))),ap(V0f,inj__ty_2Erealax_2Ereal(V3x)))) ) ) ) ).
tff(conj_thm_2Elim_2EINTERVAL__CLEMMA,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V1b))) )
=> ? [V3d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V3d)))
& ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V4y)),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V3d)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V4y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4y)),inj__ty_2Erealax_2Ereal(V1b))) ) ) ) ) ).
tff(conj_thm_2Elim_2EDIFF__INVERSE__OPEN,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2l: tp__ty_2Erealax_2Ereal,V3a: tp__ty_2Erealax_2Ereal,V4x: tp__ty_2Erealax_2Ereal,V5b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3a)),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V5b)))
& ! [V6z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3a)),inj__ty_2Erealax_2Ereal(V6z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6z)),inj__ty_2Erealax_2Ereal(V5b))) )
=> ( ( surj__ty_2Erealax_2Ereal(ap(V1g,ap(V0f,inj__ty_2Erealax_2Ereal(V6z)))) = V6z )
& p(ap(ap(c_2Elim_2Econtl,V0f),inj__ty_2Erealax_2Ereal(V6z))) ) )
& p(ap(ap(ap(c_2Elim_2Ediffl,V0f),inj__ty_2Erealax_2Ereal(V2l)),inj__ty_2Erealax_2Ereal(V4x)))
& ( V2l != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,V1g),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V2l))),ap(V0f,inj__ty_2Erealax_2Ereal(V4x)))) ) ) ) ).
%------------------------------------------------------------------------------