TPTP Problem File: ITP016_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP016_5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ereal_2ESUP__EPSILON.p, 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 : thm_2Ereal_2ESUP__EPSILON.p [Gau20]
% : HL407501_5.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 20146 (4172 unt;5127 typ; 0 def)
% Number of atoms : 334394 (16530 equ)
% Maximal formula atoms : 5763 ( 16 avg)
% Number of connectives : 61175 (1612 ~; 795 |;22931 &)
% (5115 <=>;30722 =>; 0 <=; 0 <~>)
% Maximal formula depth : 361 ( 7 avg)
% Maximal term depth : 132 ( 2 avg)
% Number of FOOLs : 259812 (259812 fml; 0 var)
% Number of types : 99 ( 97 usr)
% Number of type conns : 10252 (4369 >;5883 *; 0 +; 0 <<)
% Number of predicates : 45 ( 42 usr; 27 prp; 0-2 aty)
% Number of functors : 5028 (5028 usr; 661 con; 0-11 aty)
% Number of variables : 66559 (53075 !;13484 ?;66559 :)
% SPC : TF0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001_2.ax').
include('Axioms/ITP001/ITP002_5.ax').
include('Axioms/ITP001/ITP003_5.ax').
include('Axioms/ITP001/ITP004_5.ax').
include('Axioms/ITP001/ITP007_5.ax').
include('Axioms/ITP001/ITP006_5.ax').
include('Axioms/ITP001/ITP005_5.ax').
include('Axioms/ITP001/ITP008_5.ax').
include('Axioms/ITP001/ITP009_5.ax').
include('Axioms/ITP001/ITP010_5.ax').
include('Axioms/ITP001/ITP012_5.ax').
include('Axioms/ITP001/ITP011_5.ax').
include('Axioms/ITP001/ITP013_5.ax').
include('Axioms/ITP001/ITP014_5.ax').
include('Axioms/ITP001/ITP015_5.ax').
include('Axioms/ITP001/ITP017_5.ax').
include('Axioms/ITP001/ITP016_5.ax').
include('Axioms/ITP001/ITP019_5.ax').
include('Axioms/ITP001/ITP018_5.ax').
include('Axioms/ITP001/ITP021_5.ax').
include('Axioms/ITP001/ITP022_5.ax').
include('Axioms/ITP001/ITP020_5.ax').
include('Axioms/ITP001/ITP024_5.ax').
include('Axioms/ITP001/ITP023_5.ax').
include('Axioms/ITP001/ITP025_5.ax').
include('Axioms/ITP001/ITP026_5.ax').
include('Axioms/ITP001/ITP027_5.ax').
include('Axioms/ITP001/ITP028_5.ax').
include('Axioms/ITP001/ITP031_5.ax').
include('Axioms/ITP001/ITP029_5.ax').
include('Axioms/ITP001/ITP033_5.ax').
include('Axioms/ITP001/ITP030_5.ax').
include('Axioms/ITP001/ITP032_5.ax').
include('Axioms/ITP001/ITP038_5.ax').
include('Axioms/ITP001/ITP035_5.ax').
include('Axioms/ITP001/ITP034_5.ax').
include('Axioms/ITP001/ITP036_5.ax').
include('Axioms/ITP001/ITP037_5.ax').
include('Axioms/ITP001/ITP039_5.ax').
include('Axioms/ITP001/ITP041_5.ax').
include('Axioms/ITP001/ITP042_5.ax').
include('Axioms/ITP001/ITP040_5.ax').
include('Axioms/ITP001/ITP044_5.ax').
include('Axioms/ITP001/ITP051_5.ax').
include('Axioms/ITP001/ITP045_5.ax').
include('Axioms/ITP001/ITP056_5.ax').
include('Axioms/ITP001/ITP046_5.ax').
include('Axioms/ITP001/ITP043_5.ax').
include('Axioms/ITP001/ITP052_5.ax').
include('Axioms/ITP001/ITP057_5.ax').
include('Axioms/ITP001/ITP048_5.ax').
include('Axioms/ITP001/ITP047_5.ax').
include('Axioms/ITP001/ITP055_5.ax').
include('Axioms/ITP001/ITP053_5.ax').
include('Axioms/ITP001/ITP054_5.ax').
include('Axioms/ITP001/ITP058_5.ax').
include('Axioms/ITP001/ITP049_5.ax').
include('Axioms/ITP001/ITP050_5.ax').
include('Axioms/ITP001/ITP061_5.ax').
include('Axioms/ITP001/ITP069_5.ax').
include('Axioms/ITP001/ITP062_5.ax').
include('Axioms/ITP001/ITP068_5.ax').
include('Axioms/ITP001/ITP078_5.ax').
include('Axioms/ITP001/ITP064_5.ax').
include('Axioms/ITP001/ITP060_5.ax').
include('Axioms/ITP001/ITP067_5.ax').
include('Axioms/ITP001/ITP075_5.ax').
include('Axioms/ITP001/ITP074_5.ax').
include('Axioms/ITP001/ITP063_5.ax').
include('Axioms/ITP001/ITP059_5.ax').
include('Axioms/ITP001/ITP065_5.ax').
include('Axioms/ITP001/ITP076_5.ax').
include('Axioms/ITP001/ITP066_5.ax').
include('Axioms/ITP001/ITP077_5.ax').
include('Axioms/ITP001/ITP070_5.ax').
include('Axioms/ITP001/ITP071_5.ax').
include('Axioms/ITP001/ITP072_5.ax').
include('Axioms/ITP001/ITP073_5.ax').
include('Axioms/ITP001/ITP080_5.ax').
include('Axioms/ITP001/ITP083_5.ax').
include('Axioms/ITP001/ITP088_5.ax').
include('Axioms/ITP001/ITP082_5.ax').
include('Axioms/ITP001/ITP081_5.ax').
include('Axioms/ITP001/ITP079_5.ax').
include('Axioms/ITP001/ITP087_5.ax').
include('Axioms/ITP001/ITP085_5.ax').
include('Axioms/ITP001/ITP086_5.ax').
include('Axioms/ITP001/ITP090_5.ax').
include('Axioms/ITP001/ITP089_5.ax').
include('Axioms/ITP001/ITP084_5.ax').
include('Axioms/ITP001/ITP104_5.ax').
include('Axioms/ITP001/ITP097_5.ax').
include('Axioms/ITP001/ITP094_5.ax').
include('Axioms/ITP001/ITP095_5.ax').
include('Axioms/ITP001/ITP093_5.ax').
include('Axioms/ITP001/ITP102_5.ax').
include('Axioms/ITP001/ITP091_5.ax').
include('Axioms/ITP001/ITP098_5.ax').
include('Axioms/ITP001/ITP096_5.ax').
include('Axioms/ITP001/ITP100_5.ax').
include('Axioms/ITP001/ITP092_5.ax').
include('Axioms/ITP001/ITP105_5.ax').
include('Axioms/ITP001/ITP101_5.ax').
include('Axioms/ITP001/ITP103_5.ax').
include('Axioms/ITP001/ITP099_5.ax').
include('Axioms/ITP001/ITP111_5.ax').
include('Axioms/ITP001/ITP108_5.ax').
include('Axioms/ITP001/ITP106_5.ax').
include('Axioms/ITP001/ITP107_5.ax').
include('Axioms/ITP001/ITP114_5.ax').
include('Axioms/ITP001/ITP110_5.ax').
include('Axioms/ITP001/ITP109_5.ax').
include('Axioms/ITP001/ITP112_5.ax').
include('Axioms/ITP001/ITP113_5.ax').
include('Axioms/ITP001/ITP117_5.ax').
include('Axioms/ITP001/ITP116_5.ax').
%------------------------------------------------------------------------------
tff(tp_c_2Ereal_2E_2F,type,
c_2Ereal_2E_2F: $i ).
tff(mem_c_2Ereal_2E_2F,axiom,
mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Ereal_2E_2F,type,
fo__c_2Ereal_2E_2F: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2E_2F,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2E_2F(X0,X1)) = ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2ENUM__CEILING,type,
c_2Ereal_2ENUM__CEILING: $i ).
tff(mem_c_2Ereal_2ENUM__CEILING,axiom,
mem(c_2Ereal_2ENUM__CEILING,arr(ty_2Erealax_2Ereal,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Ereal_2ENUM__CEILING,type,
fo__c_2Ereal_2ENUM__CEILING: tp__ty_2Erealax_2Ereal > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Ereal_2ENUM__CEILING,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : inj__ty_2Enum_2Enum(fo__c_2Ereal_2ENUM__CEILING(X0)) = ap(c_2Ereal_2ENUM__CEILING,inj__ty_2Erealax_2Ereal(X0)) ).
tff(tp_c_2Ereal_2ENUM__FLOOR,type,
c_2Ereal_2ENUM__FLOOR: $i ).
tff(mem_c_2Ereal_2ENUM__FLOOR,axiom,
mem(c_2Ereal_2ENUM__FLOOR,arr(ty_2Erealax_2Ereal,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Ereal_2ENUM__FLOOR,type,
fo__c_2Ereal_2ENUM__FLOOR: tp__ty_2Erealax_2Ereal > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Ereal_2ENUM__FLOOR,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : inj__ty_2Enum_2Enum(fo__c_2Ereal_2ENUM__FLOOR(X0)) = ap(c_2Ereal_2ENUM__FLOOR,inj__ty_2Erealax_2Ereal(X0)) ).
tff(tp_c_2Ereal_2Eabs,type,
c_2Ereal_2Eabs: $i ).
tff(mem_c_2Ereal_2Eabs,axiom,
mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
tff(stp_fo_c_2Ereal_2Eabs,type,
fo__c_2Ereal_2Eabs: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Eabs,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Eabs(X0)) = ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(X0)) ).
tff(tp_c_2Ereal_2Einf,type,
c_2Ereal_2Einf: $i ).
tff(mem_c_2Ereal_2Einf,axiom,
mem(c_2Ereal_2Einf,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal)) ).
tff(tp_c_2Ereal_2Emax,type,
c_2Ereal_2Emax: $i ).
tff(mem_c_2Ereal_2Emax,axiom,
mem(c_2Ereal_2Emax,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Ereal_2Emax,type,
fo__c_2Ereal_2Emax: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Emax,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Emax(X0,X1)) = ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2Emin,type,
c_2Ereal_2Emin: $i ).
tff(mem_c_2Ereal_2Emin,axiom,
mem(c_2Ereal_2Emin,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Ereal_2Emin,type,
fo__c_2Ereal_2Emin: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Emin,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Emin(X0,X1)) = ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2Epos,type,
c_2Ereal_2Epos: $i ).
tff(mem_c_2Ereal_2Epos,axiom,
mem(c_2Ereal_2Epos,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
tff(stp_fo_c_2Ereal_2Epos,type,
fo__c_2Ereal_2Epos: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Epos,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Epos(X0)) = ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(X0)) ).
tff(tp_c_2Ereal_2Epow,type,
c_2Ereal_2Epow: $i ).
tff(mem_c_2Ereal_2Epow,axiom,
mem(c_2Ereal_2Epow,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Ereal_2Epow,type,
fo__c_2Ereal_2Epow: ( tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Epow,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Enum_2Enum] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Epow(X0,X1)) = ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Ereal_2Ereal__ge,type,
c_2Ereal_2Ereal__ge: $i ).
tff(mem_c_2Ereal_2Ereal__ge,axiom,
mem(c_2Ereal_2Ereal__ge,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) ).
tff(stp_fo_c_2Ereal_2Ereal__ge,type,
fo__c_2Ereal_2Ereal__ge: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).
tff(stp_eq_fo_c_2Ereal_2Ereal__ge,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__o(fo__c_2Ereal_2Ereal__ge(X0,X1)) = ap(ap(c_2Ereal_2Ereal__ge,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2Ereal__gt,type,
c_2Ereal_2Ereal__gt: $i ).
tff(mem_c_2Ereal_2Ereal__gt,axiom,
mem(c_2Ereal_2Ereal__gt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) ).
tff(stp_fo_c_2Ereal_2Ereal__gt,type,
fo__c_2Ereal_2Ereal__gt: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).
tff(stp_eq_fo_c_2Ereal_2Ereal__gt,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__o(fo__c_2Ereal_2Ereal__gt(X0,X1)) = ap(ap(c_2Ereal_2Ereal__gt,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2Ereal__lte,type,
c_2Ereal_2Ereal__lte: $i ).
tff(mem_c_2Ereal_2Ereal__lte,axiom,
mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) ).
tff(stp_fo_c_2Ereal_2Ereal__lte,type,
fo__c_2Ereal_2Ereal__lte: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).
tff(stp_eq_fo_c_2Ereal_2Ereal__lte,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__o(fo__c_2Ereal_2Ereal__lte(X0,X1)) = ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2Ereal__of__num,type,
c_2Ereal_2Ereal__of__num: $i ).
tff(mem_c_2Ereal_2Ereal__of__num,axiom,
mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) ).
tff(stp_fo_c_2Ereal_2Ereal__of__num,type,
fo__c_2Ereal_2Ereal__of__num: tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__of__num(X0)) = ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Ereal_2Ereal__sub,type,
c_2Ereal_2Ereal__sub: $i ).
tff(mem_c_2Ereal_2Ereal__sub,axiom,
mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Ereal_2Ereal__sub,type,
fo__c_2Ereal_2Ereal__sub: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Ereal__sub,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__sub(X0,X1)) = ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Ereal_2Esum,type,
c_2Ereal_2Esum: $i ).
tff(mem_c_2Ereal_2Esum,axiom,
mem(c_2Ereal_2Esum,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) ).
tff(tp_c_2Ereal_2Esup,type,
c_2Ereal_2Esup: $i ).
tff(mem_c_2Ereal_2Esup,axiom,
mem(c_2Ereal_2Esup,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal)) ).
tff(ax_thm_2Ereal_2Ereal__of__num,axiom,
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Erealax_2Ereal__0 )
& ! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__1))) ) ).
tff(conj_thm_2Ereal_2EREAL__0,axiom,
fo__c_2Erealax_2Ereal__0 = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__1,axiom,
fo__c_2Erealax_2Ereal__1 = surj__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))))) ).
tff(conj_thm_2Ereal_2EREAL__10,axiom,
surj__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))))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__SYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__COMM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__ASSOC,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__LID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__ADD__LINV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__LDISTRIB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ).
tff(conj_thm_2Ereal_2EREAL__LT__TOTAL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( V0x = V1y )
| p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
| p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__REFL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : ~ p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__LT__TRANS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__IADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__ALLPOS,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,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(V1x))) )
& ? [V2x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V2x)))
& ? [V3z: tp__ty_2Erealax_2Ereal] :
! [V4x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V4x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V3z))) ) )
=> ? [V5s: tp__ty_2Erealax_2Ereal] :
! [V6y: tp__ty_2Erealax_2Ereal] :
( ? [V7x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V7x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6y)),inj__ty_2Erealax_2Ereal(V7x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6y)),inj__ty_2Erealax_2Ereal(V5s))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MUL__SYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__COMM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__ASSOC,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__LID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,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))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__MUL__LINV,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x))) = surj__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))))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__MUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& 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(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__0,axiom,
surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(ax_thm_2Ereal_2Ereal__sub,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(ax_thm_2Ereal_2Ereal__lte,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> ~ p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(ax_thm_2Ereal_2Ereal__gt,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__gt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(ax_thm_2Ereal_2Ereal__ge,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__ge,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(ax_thm_2Ereal_2Ereal__div,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__RID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__ADD__RINV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__RID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__MUL__RINV,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) = surj__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))))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__RDISTRIB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) ).
tff(conj_thm_2Ereal_2EREAL__EQ__LADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( V1y = V2z ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__RADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD__LID__UNIQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V1y )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD__RID__UNIQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V0x )
<=> ( V1y = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LNEG__UNIQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__RNEG__UNIQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V1y = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__LZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__RZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__NEG__LMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__NEG__RMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__NEGNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__NEG__MUL2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__ENTIRE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
| ( V1y = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__LADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__NOT__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ~ p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ANTISYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
~ ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__GT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> ~ p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__NOT__LE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ~ p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__TOTAL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
| p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LET__TOTAL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
| p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LTE__TOTAL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
| p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__REFL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__LE__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
| ( V0x = V1y ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__LE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& ( V0x != V1y ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__IMP__LE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__LTE__TRANS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LET__TRANS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__TRANS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__ANTISYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) )
<=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__LET__ANTISYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
~ ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LTE__ANTISYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
~ ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LTE__ANTSYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
~ ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__LT0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))
<=> 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(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__GT0,axiom,
! [V0x: 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_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__LE0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__GE0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__NEGTOTAL,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(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
| p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__NEGTOTAL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
| p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__MUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__SQUARE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EREAL__LE__01,axiom,
p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ).
tff(conj_thm_2Ereal_2EREAL__LT__01,axiom,
p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ).
tff(conj_thm_2Ereal_2EREAL__LE__LADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__RADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADD2,axiom,
! [V0w: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V3z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V3z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__ADD2,axiom,
! [V0w: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V3z))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V3z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& 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(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADDNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V2z)))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADDNEG2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))),inj__ty_2Erealax_2Ereal(V2z)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADD1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V1y))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__SUB__ADD2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__SUB__REFL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__DOUBLE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__NEGL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__NEGR,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__EQ0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__0,axiom,
surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__NEG__SUB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__LE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD__SUB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V0x))) = V1y ).
tff(conj_thm_2Ereal_2EREAL__EQ__LMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
| ( V1y = V2z ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__RMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( ( V2z = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
| ( V0x = V1y ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__LDISTRIB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__RDISTRIB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) ).
tff(conj_thm_2Ereal_2EREAL__NEG__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))) = V1y )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__MINUS1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,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(conj_thm_2Ereal_2EREAL__INV__NZ,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INVINV,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) = V0x ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__IMP__NE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> ( V0x != V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__POS,axiom,
! [V0x: 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(V0x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__LMUL__0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> 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(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RMUL__0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V1y)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> 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(V0x))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__LMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V0x)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RMUL__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& 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(V2z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__LMUL__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))
& 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(V0x))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LINV__UNIQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__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))))) )
=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__RINV__UNIQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__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))))) )
=> ( V1y = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__INV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__INV__EQ__0,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__INV,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__1OVER,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,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(conj_thm_2Ereal_2EREAL__LT__INV__EQ,axiom,
! [V0x: 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_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))))
<=> 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(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__INV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__INV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__ADDR,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__ADDL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADDR,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> 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(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADDL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> 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(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ).
tff(conj_thm_2Ereal_2EREAL__POS,axiom,
! [V0n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))) ).
tff(conj_thm_2Ereal_2EREAL__LE,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) ) ).
tff(conj_thm_2Ereal_2EREAL__INJ,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))) )
<=> ( V0m = V1n ) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__MUL,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__INV1,axiom,
surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__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))))) ).
tff(conj_thm_2Ereal_2EREAL__OVER1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__DIV__REFL,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = surj__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))))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__DIV__LZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__LT__NZ,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))) ) ).
tff(conj_thm_2Ereal_2EREAL__NZ__IMP__LT,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( V0n != fo__c_2Enum_2E0 )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RDIV__0,axiom,
! [V0y: tp__ty_2Erealax_2Ereal,V1z: 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(V1z)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0y)),inj__ty_2Erealax_2Ereal(V1z))))
<=> 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(V0y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RDIV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__FRACTION__0,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1d: tp__ty_2Erealax_2Ereal] :
( ( V0n != fo__c_2Enum_2E0 )
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1d)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))))
<=> 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(V1d))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__MULTIPLE,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0n)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1d)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Erealax_2Ereal(V1d))))
<=> 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(V1d))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__FRACTION,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0n)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1d)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),inj__ty_2Erealax_2Ereal(V1d)))
<=> 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(V1d))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__HALF1,axiom,
! [V0d: 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(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0d)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))
<=> 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(V0d))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__HALF2,axiom,
! [V0d: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0d)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Erealax_2Ereal(V0d)))
<=> 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(V0d))) ) ).
tff(conj_thm_2Ereal_2EREAL__DOUBLE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__DIV__LMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( V1y != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = V0x ) ) ).
tff(conj_thm_2Ereal_2EREAL__DIV__RMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( V1y != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V1y))) = V0x ) ) ).
tff(conj_thm_2Ereal_2EREAL__HALF__DOUBLE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__DOWN,axiom,
! [V0x: 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(V0x)))
=> ? [V1y: 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(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__DOWN2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& 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(V1y))) )
=> ? [V2z: 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(V2z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__SUB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__LT__ADD__SUB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__SUB__RADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__SUB__LADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__SUB__LADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__SUB__RADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V1y))),inj__ty_2Erealax_2Ereal(V2z)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD2__SUB2,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal,V2c: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2c)),inj__ty_2Erealax_2Ereal(V3d)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V2c))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V3d)))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__LZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__RZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__LET__ADD2,axiom,
! [V0w: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V3z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V3z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LTE__ADD2,axiom,
! [V0w: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V3z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V3z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LET__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& 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(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LTE__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__MUL2,axiom,
! [V0x1: tp__ty_2Erealax_2Ereal,V1x2: tp__ty_2Erealax_2Ereal,V2y1: tp__ty_2Erealax_2Ereal,V3y2: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x1)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2y1)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V1x2)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2y1)),inj__ty_2Erealax_2Ereal(V3y2))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V2y1))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1x2)),inj__ty_2Erealax_2Ereal(V3y2)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__INV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__LNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__RNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__NEG2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__SUB__TRIANGLE,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal,V2c: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V2c)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V2c))) ).
tff(conj_thm_2Ereal_2EREAL__EQ__SUB__LADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( V0x = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__SUB__RADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V2z )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__MUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( V1y != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V0x)))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__RMUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__INV2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( V1y != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__SUB2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = V1y ).
tff(conj_thm_2Ereal_2EREAL__ADD__SUB2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__MEAN,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> ? [V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__LMUL2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( ( V1y = V2z )
<=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__MUL2,axiom,
! [V0x1: tp__ty_2Erealax_2Ereal,V1x2: tp__ty_2Erealax_2Ereal,V2y1: tp__ty_2Erealax_2Ereal,V3y2: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x1)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2y1)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V1x2)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2y1)),inj__ty_2Erealax_2Ereal(V3y2))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V2y1))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1x2)),inj__ty_2Erealax_2Ereal(V3y2)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LDIV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__RDIV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__DIV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& 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(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__DIV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LMUL__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__RMUL__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__IMP__LE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( V0x = V1y )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__LT1,axiom,
! [V0x: 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(V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__POS__NZ,axiom,
! [V0x: 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(V0x)))
=> ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__RMUL__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( ( V2z != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__LMUL__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ( V1y = V2z ) ) ).
tff(conj_thm_2Ereal_2EREAL__FACT__NZ,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,inj__ty_2Enum_2Enum(V0n)))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__DIFFSQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__POASQ,axiom,
! [V0x: 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(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))))
<=> ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUMSQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( V1y = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))) )
<=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__DIV__MUL2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1z: tp__ty_2Erealax_2Ereal] :
( ( ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( V1z != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ! [V2y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V1z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__MIDDLE1,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0a)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ).
tff(conj_thm_2Ereal_2EREAL__MIDDLE2,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Erealax_2Ereal(V1b))) ) ).
tff(ax_thm_2Ereal_2Eabs,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EABS__ZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EABS__0,axiom,
surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EABS__1,axiom,
surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__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))))) ).
tff(conj_thm_2Ereal_2EABS__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EABS__TRIANGLE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EABS__TRIANGLE__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EABS__TRIANGLE__SUB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))))) ).
tff(conj_thm_2Ereal_2EABS__TRIANGLE__LT,axiom,
! [V0e: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2y)))),inj__ty_2Erealax_2Ereal(V0e)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y)))),inj__ty_2Erealax_2Ereal(V0e))) ) ).
tff(conj_thm_2Ereal_2EABS__POS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EABS__MUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EABS__LT__MUL2,axiom,
! [V0w: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0w))),inj__ty_2Erealax_2Ereal(V2y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))),inj__ty_2Erealax_2Ereal(V3z))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0w)),inj__ty_2Erealax_2Ereal(V1x)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V3z)))) ) ).
tff(conj_thm_2Ereal_2EABS__SUB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EABS__NZ,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(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EABS__INV,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))) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) ) ) ).
tff(conj_thm_2Ereal_2EABS__ABS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EABS__LE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EABS__REFL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) = V0x )
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EABS__N,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))) ).
tff(conj_thm_2Ereal_2EABS__BETWEEN,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2d: 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(V2d)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2d))),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2d)))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))),inj__ty_2Erealax_2Ereal(V2d))) ) ).
tff(conj_thm_2Ereal_2EABS__BOUND,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2d: 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(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),inj__ty_2Erealax_2Ereal(V2d)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2d)))) ) ).
tff(conj_thm_2Ereal_2EABS__STILLNZ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))))
=> ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EABS__CASES,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(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EABS__BETWEEN1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ).
tff(conj_thm_2Ereal_2EABS__SIGN,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),inj__ty_2Erealax_2Ereal(V1y)))
=> 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(V0x))) ) ).
tff(conj_thm_2Ereal_2EABS__SIGN2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EABS__DIV,axiom,
! [V0y: tp__ty_2Erealax_2Ereal] :
( ( V0y != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ! [V1x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0y)))) ) ).
tff(conj_thm_2Ereal_2EABS__CIRCLE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2h: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2h))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2h)))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__ABS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y)))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EABS__SUB__ABS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EABS__BETWEEN2,axiom,
! [V0x0: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y0: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x0)),inj__ty_2Erealax_2Ereal(V2y0)))
& 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(V0x0)))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2y0)),inj__ty_2Erealax_2Ereal(V0x0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V3y)),inj__ty_2Erealax_2Ereal(V2y0)))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2y0)),inj__ty_2Erealax_2Ereal(V0x0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V3y))) ) ).
tff(conj_thm_2Ereal_2EABS__BOUNDS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1k: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1k)))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1k))),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1k))) ) ) ).
tff(ax_thm_2Ereal_2Epow,axiom,
( ! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__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)))))
& ! [V1x: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V2n)))) ) ).
tff(conj_thm_2Ereal_2EPOW__0,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EPOW__NZ,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] :
( ( V0c != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Enum_2Enum(V1n))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EPOW__INV,axiom,
! [V0c: tp__ty_2Erealax_2Ereal] :
( ( V0c != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ! [V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0c))),inj__ty_2Enum_2Enum(V1n))) ) ).
tff(conj_thm_2Ereal_2EPOW__ABS,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0c))),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EPOW__PLUS1,axiom,
! [V0e: 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(V0e)))
=> ! [V1n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))),inj__ty_2Erealax_2Ereal(V0e)))),ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,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(V0e))),inj__ty_2Enum_2Enum(V1n)))) ) ).
tff(conj_thm_2Ereal_2EPOW__ADD,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Enum_2Enum(V1m))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Enum_2Enum(V2n)))) ).
tff(conj_thm_2Ereal_2EPOW__1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = V0x ).
tff(conj_thm_2Ereal_2EPOW__2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EPOW__ONE,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V0n))) = surj__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))))) ).
tff(conj_thm_2Ereal_2EPOW__POS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
=> ! [V1n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1n)))) ) ).
tff(conj_thm_2Ereal_2EPOW__LE,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Enum_2Enum(V0n)))) ) ).
tff(conj_thm_2Ereal_2EPOW__M1,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Enum_2Enum(V0n)))) = surj__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))))) ).
tff(conj_thm_2Ereal_2EPOW__MUL,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Enum_2Enum(V0n)))) ).
tff(conj_thm_2Ereal_2EREAL__LE__POW2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ).
tff(conj_thm_2Ereal_2EABS__POW2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ).
tff(conj_thm_2Ereal_2EREAL__POW2__ABS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ).
tff(conj_thm_2Ereal_2EREAL__LE1__POW2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,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)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ).
tff(conj_thm_2Ereal_2EREAL__LT1__POW2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,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)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ).
tff(conj_thm_2Ereal_2EPOW__POS__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] :
( 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(V0x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))))) ) ).
tff(conj_thm_2Ereal_2EPOW__2__LE1,axiom,
! [V0n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V0n)))) ).
tff(conj_thm_2Ereal_2EPOW__2__LT,axiom,
! [V0n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V0n)))) ).
tff(conj_thm_2Ereal_2EPOW__MINUS1,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0n)))) = surj__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))))) ).
tff(conj_thm_2Ereal_2EPOW__LT,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))))) ) ).
tff(conj_thm_2Ereal_2EREAL__POW__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] :
( 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(V0x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1n)))) ) ).
tff(conj_thm_2Ereal_2EPOW__EQ,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2y)))
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) ) )
=> ( V1x = V2y ) ) ).
tff(conj_thm_2Ereal_2EPOW__ZERO,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( V1x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EPOW__ZERO__EQ,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V1x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__POW__LT2,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( ( ( V0n != fo__c_2Enum_2E0 )
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Enum_2Enum(V0n)))) ) ).
tff(conj_thm_2Ereal_2EREAL__POW__MONO__LT,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,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(V2x)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V0m))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V1n)))) ) ).
tff(conj_thm_2Ereal_2EREAL__POW__POW,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1m))),inj__ty_2Enum_2Enum(V2n))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))) ).
tff(conj_thm_2Ereal_2EREAL__SUP__SOMEPOS,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,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(V1x))) )
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ? [V4s: tp__ty_2Erealax_2Ereal] :
! [V5y: tp__ty_2Erealax_2Ereal] :
( ? [V6x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V6x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5y)),inj__ty_2Erealax_2Ereal(V6x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5y)),inj__ty_2Erealax_2Ereal(V4s))) ) ) ) ).
tff(lamtp_f2713,type,
f2713: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2713,axiom,
! [V2d: tp__ty_2Erealax_2Ereal,V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V5x: tp__ty_2Erealax_2Ereal] : ap(f2713(V2d,V0P),inj__ty_2Erealax_2Ereal(V5x)) = ap(V0P,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V2d))) ) ).
tff(conj_thm_2Ereal_2ESUP__LEMMA1,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1s: tp__ty_2Erealax_2Ereal,V2d: tp__ty_2Erealax_2Ereal] :
( ! [V3y: tp__ty_2Erealax_2Ereal] :
( ? [V4x: tp__ty_2Erealax_2Ereal] :
( p(ap(f2713(V2d,V0P),inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3y)),inj__ty_2Erealax_2Ereal(V4x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3y)),inj__ty_2Erealax_2Ereal(V1s))) )
=> ! [V6y: tp__ty_2Erealax_2Ereal] :
( ? [V7x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V7x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6y)),inj__ty_2Erealax_2Ereal(V7x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6y)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1s)),inj__ty_2Erealax_2Ereal(V2d)))) ) ) ) ).
tff(lamtp_f2714,type,
f2714: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2714,axiom,
! [V2d: tp__ty_2Erealax_2Ereal,V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V4x: tp__ty_2Erealax_2Ereal] : ap(f2714(V2d,V0P),inj__ty_2Erealax_2Ereal(V4x)) = ap(V0P,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V2d))) ) ).
tff(conj_thm_2Ereal_2ESUP__LEMMA2,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
=> ? [V2d: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(f2714(V2d,V0P),inj__ty_2Erealax_2Ereal(V3x)))
& 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(V3x))) ) ) ) ).
tff(lamtp_f2715,type,
f2715: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2715,axiom,
! [V1d: tp__ty_2Erealax_2Ereal,V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V6x: tp__ty_2Erealax_2Ereal] : ap(f2715(V1d,V0P),inj__ty_2Erealax_2Ereal(V6x)) = ap(V0P,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Erealax_2Ereal(V1d))) ) ).
tff(conj_thm_2Ereal_2ESUP__LEMMA3,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1d: tp__ty_2Erealax_2Ereal] :
( ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) )
=> ? [V4z: tp__ty_2Erealax_2Ereal] :
! [V5x: tp__ty_2Erealax_2Ereal] :
( p(ap(f2715(V1d,V0P),inj__ty_2Erealax_2Ereal(V5x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V4z))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__EXISTS,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ? [V4s: tp__ty_2Erealax_2Ereal] :
! [V5y: tp__ty_2Erealax_2Ereal] :
( ? [V6x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V6x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5y)),inj__ty_2Erealax_2Ereal(V6x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5y)),inj__ty_2Erealax_2Ereal(V4s))) ) ) ) ).
tff(lamtp_f2716,type,
f2716: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2716,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V2y: tp__ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] : ap(f2716(V0P,V2y),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,inj__ty_2Erealax_2Ereal(V3x))),ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V3x))) ) ).
tff(lamtp_f2717,type,
f2717: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2717,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1s: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : ap(f2717(V0P,V1s),inj__ty_2Erealax_2Ereal(V2y)) = ap(ap(c_2Emin_2E_3D(bool),ap(c_2Ebool_2E_3F(ty_2Erealax_2Ereal),f2716(V0P,V2y))),ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V1s))) ) ).
tff(lamtp_f2718,type,
f2718: $i > $i ).
tff(lameq_f2718,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1s: tp__ty_2Erealax_2Ereal] : ap(f2718(V0P),inj__ty_2Erealax_2Ereal(V1s)) = ap(c_2Ebool_2E_21(ty_2Erealax_2Ereal),f2717(V0P,V1s)) ) ).
tff(ax_thm_2Ereal_2Esup,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Esup,V0P)) = surj__ty_2Erealax_2Ereal(ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2718(V0P))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ! [V4y: tp__ty_2Erealax_2Ereal] :
( ? [V5x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4y)),inj__ty_2Erealax_2Ereal(V5x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4y)),ap(c_2Ereal_2Esup,V0P))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__UBOUND,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V4y)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4y)),ap(c_2Ereal_2Esup,V0P))) ) ) ) ).
tff(conj_thm_2Ereal_2ESETOK__LE__LT,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
<=> ( ? [V4x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V4x)))
& ? [V5z: tp__ty_2Erealax_2Ereal] :
! [V6x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V6x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Erealax_2Ereal(V5z))) ) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__LE,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ! [V4y: tp__ty_2Erealax_2Ereal] :
( ? [V5x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4y)),inj__ty_2Erealax_2Ereal(V5x))) )
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4y)),ap(c_2Ereal_2Esup,V0P))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__UBOUND__LE,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> ! [V4y: tp__ty_2Erealax_2Ereal] :
( p(ap(V0P,inj__ty_2Erealax_2Ereal(V4y)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4y)),ap(c_2Ereal_2Esup,V0P))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__ARCH,axiom,
! [V0x: 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(V0x)))
=> ! [V1y: tp__ty_2Erealax_2Ereal] :
? [V2n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2n))),inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Ereal_2EREAL__ARCH__LEAST,axiom,
! [V0y: 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(V0y)))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1x)))
=> ? [V2n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2n))),inj__ty_2Erealax_2Ereal(V0y))),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))),inj__ty_2Erealax_2Ereal(V0y)))) ) ) ) ).
tff(conj_thm_2Ereal_2Esum__ind,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),bool)))
=> ( ( ! [V1n: tp__ty_2Enum_2Enum,V2f: $i] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),V2f)) )
& ! [V3n: tp__ty_2Enum_2Enum,V4m: tp__ty_2Enum_2Enum,V5f: $i] :
( mem(V5f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3n)),inj__ty_2Enum_2Enum(V4m))),V5f))
=> p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3n)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V4m)))),V5f)) ) ) )
=> ! [V6v: tp__ty_2Enum_2Enum,V7v1: tp__ty_2Enum_2Enum,V8v2: $i] :
( mem(V8v2,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V6v)),inj__ty_2Enum_2Enum(V7v1))),V8v2)) ) ) ) ).
tff(conj_thm_2Ereal_2Esum,axiom,
( ! [V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),V1f)) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum,V4f: $i] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2n)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V3m)))),V4f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(V3m))),V4f)),ap(V4f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(V3m))))) ) ) ) ).
tff(conj_thm_2Ereal_2Esum__compute,axiom,
( ! [V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),V1f)) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum,V4f: $i] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3m))))),V4f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3m)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),V4f)),ap(V4f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3m)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))) ) )
& ! [V5n: tp__ty_2Enum_2Enum,V6m: tp__ty_2Enum_2Enum,V7f: $i] :
( mem(V7f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V5n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V6m))))),V7f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V5n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V6m))))),V7f)),ap(V7f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V5n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V6m))))))) ) ) ) ).
tff(conj_thm_2Ereal_2ESUM__TWO,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V1n))),V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2p))),V0f))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2p)))),V0f)) ) ).
tff(conj_thm_2Ereal_2ESUM__DIFF,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),V0f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))),V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V1m))),V0f))) ) ).
tff(lamtp_f2719,type,
f2719: $i > $i ).
tff(lameq_f2719,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3n: tp__ty_2Enum_2Enum] : ap(f2719(V0f),inj__ty_2Enum_2Enum(V3n)) = ap(c_2Ereal_2Eabs,ap(V0f,inj__ty_2Enum_2Enum(V3n))) ) ).
tff(conj_thm_2Ereal_2EABS__SUM,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),V0f))),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),f2719(V0f)))) ) ).
tff(conj_thm_2Ereal_2ESUM__LE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ! [V4r: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V4r)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4r)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V3n)),inj__ty_2Enum_2Enum(V2m)))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Enum_2Enum(V4r))),ap(V1g,inj__ty_2Enum_2Enum(V4r)))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,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))),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))),V1g))) ) ) ) ).
tff(conj_thm_2Ereal_2ESUM__EQ,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ! [V4r: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V4r)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4r)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V3n)),inj__ty_2Enum_2Enum(V2m)))) )
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Enum_2Enum(V4r))) = surj__ty_2Erealax_2Ereal(ap(V1g,inj__ty_2Enum_2Enum(V4r))) ) )
=> ( surj__ty_2Erealax_2Ereal(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))),V0f)) = surj__ty_2Erealax_2Ereal(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))),V1g)) ) ) ) ) ).
tff(conj_thm_2Ereal_2ESUM__POS,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( ! [V1n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(V0f,inj__ty_2Enum_2Enum(V1n))))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),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))),V0f))) ) ) ).
tff(conj_thm_2Ereal_2ESUM__POS__GEN,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1m: tp__ty_2Enum_2Enum] :
( ! [V2n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(V0f,inj__ty_2Enum_2Enum(V2n)))) )
=> ! [V3n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V3n))),V0f))) ) ) ).
tff(lamtp_f2720,type,
f2720: $i > $i ).
tff(lameq_f2720,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3m: tp__ty_2Enum_2Enum] : ap(f2720(V0f),inj__ty_2Enum_2Enum(V3m)) = ap(c_2Ereal_2Eabs,ap(V0f,inj__ty_2Enum_2Enum(V3m))) ) ).
tff(lamtp_f2721,type,
f2721: $i > $i ).
tff(lameq_f2721,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V4m: tp__ty_2Enum_2Enum] : ap(f2721(V0f),inj__ty_2Enum_2Enum(V4m)) = ap(c_2Ereal_2Eabs,ap(V0f,inj__ty_2Enum_2Enum(V4m))) ) ).
tff(conj_thm_2Ereal_2ESUM__ABS,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),f2720(V0f)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),f2721(V0f))) ) ).
tff(conj_thm_2Ereal_2ESUM__ABS__LE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),V0f))),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),f2719(V0f)))) ) ).
tff(conj_thm_2Ereal_2ESUM__ZERO,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1N: tp__ty_2Enum_2Enum] :
( ! [V2n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(V1N)))
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Enum_2Enum(V2n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ! [V3m: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(V3m)),inj__ty_2Enum_2Enum(V1N)))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3m)),inj__ty_2Enum_2Enum(V4n))),V0f)) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ) ).
tff(lamtp_f2722,type,
f2722: ( $i * $i ) > $i ).
tff(lameq_f2722,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V4n: tp__ty_2Enum_2Enum] : ap(f2722(V0f,V1g),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__add,ap(V0f,inj__ty_2Enum_2Enum(V4n))),ap(V1g,inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(conj_thm_2Ereal_2ESUM__ADD,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(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))),f2722(V0f,V1g))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,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))),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))),V1g))) ) ) ).
tff(lamtp_f2723,type,
f2723: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2723,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1c: tp__ty_2Erealax_2Ereal,V4n: tp__ty_2Enum_2Enum] : ap(f2723(V0f,V1c),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),ap(V0f,inj__ty_2Enum_2Enum(V4n))) ) ).
tff(conj_thm_2Ereal_2ESUM__CMUL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1c: tp__ty_2Erealax_2Ereal,V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(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))),f2723(V0f,V1c))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),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))),V0f))) ) ).
tff(lamtp_f2724,type,
f2724: $i > $i ).
tff(lameq_f2724,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3n: tp__ty_2Enum_2Enum] : ap(f2724(V0f),inj__ty_2Enum_2Enum(V3n)) = ap(c_2Erealax_2Ereal__neg,ap(V0f,inj__ty_2Enum_2Enum(V3n))) ) ).
tff(conj_thm_2Ereal_2ESUM__NEG,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum,V2d: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2d))),f2724(V0f))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2d))),V0f))) ) ).
tff(lamtp_f2725,type,
f2725: ( $i * $i ) > $i ).
tff(lameq_f2725,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V4n: tp__ty_2Enum_2Enum] : ap(f2725(V0f,V1g),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,inj__ty_2Enum_2Enum(V4n))),ap(V1g,inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(conj_thm_2Ereal_2ESUM__SUB,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(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))),f2725(V0f,V1g))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,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))),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))),V1g))) ) ) ).
tff(conj_thm_2Ereal_2ESUM__SUBST,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ! [V4p: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V4p)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4p)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n)))) )
=> ( surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Enum_2Enum(V4p))) = surj__ty_2Erealax_2Ereal(ap(V1g,inj__ty_2Enum_2Enum(V4p))) ) )
=> ( surj__ty_2Erealax_2Ereal(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))),V0f)) = surj__ty_2Erealax_2Ereal(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))),V1g)) ) ) ) ) ).
tff(lamtp_f2726,type,
f2726: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2726,axiom,
! [V1f: $i] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2c: tp__ty_2Erealax_2Ereal,V3p: tp__ty_2Enum_2Enum] : ap(f2726(V1f,V2c),inj__ty_2Enum_2Enum(V3p)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V1f,inj__ty_2Enum_2Enum(V3p))),inj__ty_2Erealax_2Ereal(V2c)) ) ).
tff(conj_thm_2Ereal_2ESUM__NSUB,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2c: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),V1f)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Erealax_2Ereal(V2c)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2726(V1f,V2c))) ) ).
tff(conj_thm_2Ereal_2ESUM__BOUND,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1k: tp__ty_2Erealax_2Ereal,V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ! [V4p: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V4p)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4p)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n)))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,inj__ty_2Enum_2Enum(V4p))),inj__ty_2Erealax_2Ereal(V1k))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,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))),V0f)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V3n))),inj__ty_2Erealax_2Ereal(V1k)))) ) ) ).
tff(lamtp_f2727,type,
f2727: ( tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2727,axiom,
! [V1k: tp__ty_2Enum_2Enum,V2f: $i] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3m: tp__ty_2Enum_2Enum] : ap(f2727(V1k,V2f),inj__ty_2Enum_2Enum(V3m)) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V3m)),inj__ty_2Enum_2Enum(V1k))),inj__ty_2Enum_2Enum(V1k))),V2f) ) ).
tff(conj_thm_2Ereal_2ESUM__GROUP,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum,V2f: $i] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2727(V1k,V2f))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1k)))),V2f)) ) ) ).
tff(conj_thm_2Ereal_2ESUM__1,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V0f)) = surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Enum_2Enum(V1n))) ) ).
tff(conj_thm_2Ereal_2ESUM__2,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V0f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(V0f,inj__ty_2Enum_2Enum(V1n))),ap(V0f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ).
tff(lamtp_f2728,type,
f2728: ( tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2728,axiom,
! [V2k: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3m: tp__ty_2Enum_2Enum] : ap(f2728(V2k,V0f),inj__ty_2Enum_2Enum(V3m)) = ap(V0f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V3m)),inj__ty_2Enum_2Enum(V2k))) ) ).
tff(conj_thm_2Ereal_2ESUM__OFFSET,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V1n))),f2728(V2k,V0f))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2k)))),V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V2k))),V0f))) ) ).
tff(lamtp_f2729,type,
f2729: ( tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2729,axiom,
! [V2k: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V4r: tp__ty_2Enum_2Enum] : ap(f2729(V2k,V0f),inj__ty_2Enum_2Enum(V4r)) = ap(V0f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V4r)),inj__ty_2Enum_2Enum(V2k))) ) ).
tff(conj_thm_2Ereal_2ESUM__REINDEX,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1m: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2k))),inj__ty_2Enum_2Enum(V3n))),V0f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V3n))),f2729(V2k,V0f))) ) ).
tff(conj_thm_2Ereal_2ESUM__0,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))),k(ty_2Enum_2Enum,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(lamtp_f2730,type,
f2730: ( tp__ty_2Enum_2Enum * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2730,axiom,
! [V2y: tp__ty_2Enum_2Enum,V1p: $i] :
( mem(V1p,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V0n: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum] : ap(f2730(V2y,V1p,V0n),inj__ty_2Enum_2Enum(V3x)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V3x)),inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(V1p,inj__ty_2Enum_2Enum(V3x))),inj__ty_2Enum_2Enum(V2y))) ) ).
tff(lamtp_f2731,type,
f2731: ( $i * $i ) > $i ).
tff(lameq_f2731,axiom,
! [V1p: $i] :
( mem(V1p,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V4f: $i] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V5n: tp__ty_2Enum_2Enum] : ap(f2731(V1p,V4f),inj__ty_2Enum_2Enum(V5n)) = ap(V4f,ap(V1p,inj__ty_2Enum_2Enum(V5n))) ) ) ).
tff(conj_thm_2Ereal_2ESUM__PERMUTE__0,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1p: $i] :
( mem(V1p,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V2y: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2y)),inj__ty_2Enum_2Enum(V0n)))
=> p(ap(c_2Ebool_2E_3F_21(ty_2Enum_2Enum),f2730(V2y,V1p,V0n))) )
=> ! [V4f: $i] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2731(V1p,V4f))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),V4f)) ) ) ) ) ).
tff(lamtp_f2732,type,
f2732: $i > $i ).
tff(lameq_f2732,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3n: tp__ty_2Enum_2Enum] : ap(f2732(V0f),inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V3n)))),ap(V0f,inj__ty_2Enum_2Enum(V3n))) ) ).
tff(conj_thm_2Ereal_2ESUM__CANCEL,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum,V2d: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2d))),f2732(V0f))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2d)))),ap(V0f,inj__ty_2Enum_2Enum(V1n)))) ) ).
tff(conj_thm_2Ereal_2EREAL__MUL__RNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__LNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2Ereal__lt,axiom,
! [V0y: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0y)))
<=> ~ p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0y)),inj__ty_2Erealax_2Ereal(V1x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LADD__IMP,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__NEG2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__LE__RNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EREAL__POW__INV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__POW__DIV,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Enum_2Enum(V2n))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Enum_2Enum(V2n)))) ).
tff(conj_thm_2Ereal_2EREAL__POW__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1m))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V2n)))) ).
tff(conj_thm_2Ereal_2EREAL__LE__RDIV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LDIV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__RDIV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__LDIV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__RDIV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( ( V0x = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) = V1y ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__LDIV__EQ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: 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(V2z)))
=> ( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) = V1y )
<=> ( V0x = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__POW,axiom,
! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0x))),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__LDISTRIB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__RDISTRIB,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__ADD,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__LE,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) ) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__MUL,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__SUC,axiom,
! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__EQ,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))) )
<=> ( V0m = V1n ) ) ).
tff(conj_thm_2Ereal_2EREAL__EQ__MUL__LCANCEL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))) )
<=> ( ( V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
| ( V1y = V2z ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__ABS__0,axiom,
surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ).
tff(conj_thm_2Ereal_2EREAL__ABS__TRIANGLE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EREAL__ABS__MUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__ABS__POS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EREAL__LE__EPSILON,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ! [V2e: 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(V2e)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2e)))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ).
tff(conj_thm_2Ereal_2EREAL__BIGNUM,axiom,
! [V0r: tp__ty_2Erealax_2Ereal] :
? [V1n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0r)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__INV__LT__ANTIMONO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: 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(V0x)))
& 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(V1y))) )
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INV__INJ,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y))) )
<=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__DIV__RMUL__CANCEL,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( V0c != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V0c))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2b)),inj__ty_2Erealax_2Ereal(V0c)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__DIV__LMUL__CANCEL,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( V0c != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Erealax_2Ereal(V2b)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__DIV__ADD,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__ADD__RAT,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal,V2c: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] :
( ( ( V1b != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( V3d != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2c)),inj__ty_2Erealax_2Ereal(V3d)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V3d))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V2c)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V3d)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB__RAT,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal,V2c: tp__ty_2Erealax_2Ereal,V3d: tp__ty_2Erealax_2Ereal] :
( ( ( V1b != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( V3d != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2c)),inj__ty_2Erealax_2Ereal(V3d)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V3d))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V2c)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V3d)))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUB,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m))))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))) ).
tff(ax_thm_2Ereal_2Epos__def,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ).
tff(conj_thm_2Ereal_2EREAL__POS__POS,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EREAL__POS__ID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x)))
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V0x))) = V0x ) ) ).
tff(conj_thm_2Ereal_2EREAL__POS__INFLATE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V0x)))) ).
tff(conj_thm_2Ereal_2EREAL__POS__MONO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__POS__EQ__ZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Epos,inj__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(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EREAL__POS__LE__ZERO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Epos,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(ax_thm_2Ereal_2Emin__def,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__MIN__REFL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__LE__MIN,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V2y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__LE,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Erealax_2Ereal(V0z)))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0z)))
| p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V0z))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__LE1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__MIN__LE2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V1y))) ).
tff(conj_thm_2Ereal_2EREAL__LT__MIN,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z)))
<=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))
| p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__ALT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V0x ) )
& ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V1y ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__LE__LIN,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0z)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,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(V0z))),inj__ty_2Erealax_2Ereal(V2y))))) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__ADD,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Erealax_2Ereal(V0z))) ).
tff(conj_thm_2Ereal_2EREAL__MIN__SUB,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Erealax_2Ereal(V0z))) ).
tff(conj_thm_2Ereal_2EREAL__IMP__MIN__LE2,axiom,
! [V0x1: tp__ty_2Erealax_2Ereal,V1x2: tp__ty_2Erealax_2Ereal,V2y1: tp__ty_2Erealax_2Ereal,V3y2: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V2y1)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x2)),inj__ty_2Erealax_2Ereal(V3y2))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V1x2))),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V2y1)),inj__ty_2Erealax_2Ereal(V3y2)))) ) ).
tff(conj_thm_2Ereal_2EREAL__MIN__ACI,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = V0x )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(ax_thm_2Ereal_2Emax__def,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ).
tff(conj_thm_2Ereal_2EREAL__MAX__REFL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__LE__MAX,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1x)))
| p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V2y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__MAX1,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__LE__MAX2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__MAX__LE,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Erealax_2Ereal(V0z)))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0z)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V0z))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__LT__MAX,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))
<=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0x)))
| p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MAX__LT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z)))
<=> ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MAX__ALT,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V1y ) )
& ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = V0x ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__MAX__MIN,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2Emin,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EREAL__MIN__MAX,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2Emax,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))) ).
tff(conj_thm_2Ereal_2EREAL__LIN__LE__MAX,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0z)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0z)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,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(V0z))),inj__ty_2Erealax_2Ereal(V2y)))),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__MAX__ADD,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Erealax_2Ereal(V0z))) ).
tff(conj_thm_2Ereal_2EREAL__MAX__SUB,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),inj__ty_2Erealax_2Ereal(V0z))) ).
tff(conj_thm_2Ereal_2EREAL__IMP__MAX__LE2,axiom,
! [V0x1: tp__ty_2Erealax_2Ereal,V1x2: tp__ty_2Erealax_2Ereal,V2y1: tp__ty_2Erealax_2Ereal,V3y2: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V2y1)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x2)),inj__ty_2Erealax_2Ereal(V3y2))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x1)),inj__ty_2Erealax_2Ereal(V1x2))),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V2y1)),inj__ty_2Erealax_2Ereal(V3y2)))) ) ).
tff(conj_thm_2Ereal_2EREAL__MAX__ACI,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = V0x )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Emax,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) ) ) ).
tff(lamtp_f2733,type,
f2733: $i > $i ).
tff(lameq_f2733,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1r: tp__ty_2Erealax_2Ereal] : ap(f2733(V0p),inj__ty_2Erealax_2Ereal(V1r)) = ap(V0p,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1r))) ) ).
tff(ax_thm_2Ereal_2Einf__def,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Einf,V0p)) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Esup,f2733(V0p)))) ) ) ).
tff(lamtp_f2734,type,
f2734: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2734,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V5y: tp__ty_2Erealax_2Ereal,V6x: tp__ty_2Erealax_2Ereal] : ap(f2734(V0p,V5y),inj__ty_2Erealax_2Ereal(V6x)) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0p,inj__ty_2Erealax_2Ereal(V6x))),ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5y)),inj__ty_2Erealax_2Ereal(V6x))) ) ).
tff(lamtp_f2735,type,
f2735: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2735,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V4s: tp__ty_2Erealax_2Ereal,V5y: tp__ty_2Erealax_2Ereal] : ap(f2735(V0p,V4s),inj__ty_2Erealax_2Ereal(V5y)) = ap(ap(c_2Emin_2E_3D(bool),ap(c_2Ebool_2E_3F(ty_2Erealax_2Ereal),f2734(V0p,V5y))),ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V5y)),inj__ty_2Erealax_2Ereal(V4s))) ) ).
tff(lamtp_f2736,type,
f2736: $i > $i ).
tff(lameq_f2736,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V4s: tp__ty_2Erealax_2Ereal] : ap(f2736(V0p),inj__ty_2Erealax_2Ereal(V4s)) = ap(c_2Ebool_2E_21(ty_2Erealax_2Ereal),f2735(V0p,V4s)) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__EXISTS__UNIQUE,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V1x)))
& ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2z))) ) )
=> p(ap(c_2Ebool_2E_3F_21(ty_2Erealax_2Ereal),f2736(V0p))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__SUP__MAX,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(V0p,inj__ty_2Erealax_2Ereal(V1z)))
& ! [V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V2x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V1z))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Esup,V0p)) = V1z ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__IMP__SUP__LE,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( ( ? [V2r: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V2r)))
& ! [V3r: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V3r)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3r)),inj__ty_2Erealax_2Ereal(V1x))) ) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Esup,V0p)),inj__ty_2Erealax_2Ereal(V1x))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__IMP__LE__SUP,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( ( ? [V2r: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V2r)))
& ? [V3z: tp__ty_2Erealax_2Ereal] :
! [V4r: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V4r)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4r)),inj__ty_2Erealax_2Ereal(V3z))) )
& ? [V5r: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V5r)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V5r))) ) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Ereal_2Esup,V0p))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INF__MIN,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(V0p,inj__ty_2Erealax_2Ereal(V1z)))
& ! [V2x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V2x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V2x))) ) )
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Einf,V0p)) = V1z ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__IMP__LE__INF,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1r: tp__ty_2Erealax_2Ereal] :
( ( ? [V2x: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V2x)))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1r)),inj__ty_2Erealax_2Ereal(V3x))) ) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1r)),ap(c_2Ereal_2Einf,V0p))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__IMP__INF__LE,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1r: tp__ty_2Erealax_2Ereal] :
( ( ? [V2z: tp__ty_2Erealax_2Ereal] :
! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V3x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V3x))) )
& ? [V4x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V4x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V1r))) ) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Einf,V0p)),inj__ty_2Erealax_2Ereal(V1r))) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INF__LT,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1z: tp__ty_2Erealax_2Ereal] :
( ( ? [V2x: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V2x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Einf,V0p)),inj__ty_2Erealax_2Ereal(V1z))) )
=> ? [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V1z))) ) ) ) ).
tff(conj_thm_2Ereal_2EREAL__INF__CLOSE,axiom,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1e: tp__ty_2Erealax_2Ereal] :
( ( ? [V2x: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V2x)))
& 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(V1e))) )
=> ? [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Einf,V0p)),inj__ty_2Erealax_2Ereal(V1e)))) ) ) ) ).
tff(conj_thm_2Ereal_2ESUP__EPSILON,conjecture,
! [V0p: $i] :
( mem(V0p,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1e: 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(V1e)))
& ? [V2x: tp__ty_2Erealax_2Ereal] : p(ap(V0p,inj__ty_2Erealax_2Ereal(V2x)))
& ? [V3z: tp__ty_2Erealax_2Ereal] :
! [V4x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V4x)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V3z))) ) )
=> ? [V5x: tp__ty_2Erealax_2Ereal] :
( p(ap(V0p,inj__ty_2Erealax_2Ereal(V5x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Esup,V0p)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V1e)))) ) ) ) ).
%------------------------------------------------------------------------------