ITP001 Axioms: ITP132+5.ax
%------------------------------------------------------------------------------
% File : ITP132+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : transc+2.ax [Gau20]
% : HL4132+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 299 ( 49 unt; 0 def)
% Number of atoms : 1104 ( 228 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 827 ( 22 ~; 2 |; 181 &)
% ( 21 <=>; 601 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 111 ( 111 usr; 65 con; 0-3 aty)
% Number of variables : 522 ( 496 !; 26 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Etransc_2EDint,axiom,
mem(c_2Etransc_2EDint,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))) ).
fof(mem_c_2Etransc_2Eacs,axiom,
mem(c_2Etransc_2Eacs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Easn,axiom,
mem(c_2Etransc_2Easn,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Eatn,axiom,
mem(c_2Etransc_2Eatn,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Ecos,axiom,
mem(c_2Etransc_2Ecos,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Edivision,axiom,
mem(c_2Etransc_2Edivision,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),bool))) ).
fof(mem_c_2Etransc_2Edsize,axiom,
mem(c_2Etransc_2Edsize,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Enum_2Enum)) ).
fof(mem_c_2Etransc_2Eexp,axiom,
mem(c_2Etransc_2Eexp,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Efine,axiom,
mem(c_2Etransc_2Efine,arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),bool))) ).
fof(mem_c_2Etransc_2Egauge,axiom,
mem(c_2Etransc_2Egauge,arr(arr(ty_2Erealax_2Ereal,bool),arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),bool))) ).
fof(mem_c_2Etransc_2Eln,axiom,
mem(c_2Etransc_2Eln,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Epi,axiom,
mem(c_2Etransc_2Epi,ty_2Erealax_2Ereal) ).
fof(mem_c_2Etransc_2Eroot,axiom,
mem(c_2Etransc_2Eroot,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
fof(mem_c_2Etransc_2Erpow,axiom,
mem(c_2Etransc_2Erpow,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
fof(mem_c_2Etransc_2Ersum,axiom,
mem(c_2Etransc_2Ersum,arr(ty_2Epair_2Eprod(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) ).
fof(mem_c_2Etransc_2Esin,axiom,
mem(c_2Etransc_2Esin,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Esqrt,axiom,
mem(c_2Etransc_2Esqrt,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Etan,axiom,
mem(c_2Etransc_2Etan,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Etransc_2Etdiv,axiom,
mem(c_2Etransc_2Etdiv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),bool))) ).
fof(lameq_f2870,axiom,
! [V2n] : ap(f2870,V2n) = ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V2n))) ).
fof(lameq_f2871,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] : ap(f2871(V0x),V1n) = ap(ap(c_2Erealax_2Ereal__mul,ap(f2870,V1n)),ap(ap(c_2Ereal_2Epow,V0x),V1n)) ) ).
fof(ax_thm_2Etransc_2Eexp,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eexp,V0x) = ap(c_2Eseq_2Esuminf,f2871(V0x)) ) ).
fof(lameq_f2872,axiom,
! [V2n] : ap(f2872,V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(c_2Earithmetic_2EEVEN,V2n)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EDIV,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V2n)))),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ).
fof(lameq_f2873,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] : ap(f2873(V0x),V1n) = ap(ap(c_2Erealax_2Ereal__mul,ap(f2872,V1n)),ap(ap(c_2Ereal_2Epow,V0x),V1n)) ) ).
fof(ax_thm_2Etransc_2Ecos,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,V0x) = ap(c_2Eseq_2Esuminf,f2873(V0x)) ) ).
fof(lameq_f2874,axiom,
! [V2n] : ap(f2874,V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(c_2Earithmetic_2EEVEN,V2n)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V2n)))) ).
fof(lameq_f2875,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] : ap(f2875(V0x),V1n) = ap(ap(c_2Erealax_2Ereal__mul,ap(f2874,V1n)),ap(ap(c_2Ereal_2Epow,V0x),V1n)) ) ).
fof(ax_thm_2Etransc_2Esin,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,V0x) = ap(c_2Eseq_2Esuminf,f2875(V0x)) ) ).
fof(conj_thm_2Etransc_2EEXP__CONVERGES,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eseq_2Esums,f2871(V0x)),ap(c_2Etransc_2Eexp,V0x))) ) ).
fof(conj_thm_2Etransc_2ESIN__CONVERGES,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eseq_2Esums,f2875(V0x)),ap(c_2Etransc_2Esin,V0x))) ) ).
fof(conj_thm_2Etransc_2ECOS__CONVERGES,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eseq_2Esums,f2873(V0x)),ap(c_2Etransc_2Ecos,V0x))) ) ).
fof(lameq_f2876,axiom,
! [V0n] : ap(f2876,V0n) = ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V0n))) ).
fof(lameq_f2877,axiom,
! [V1n] : ap(f2877,V1n) = ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V1n))) ).
fof(conj_thm_2Etransc_2EEXP__FDIFF,axiom,
ap(c_2Epowser_2Ediffs,f2876) = f2877 ).
fof(lameq_f2878,axiom,
! [V0n] : ap(f2878,V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(c_2Earithmetic_2EEVEN,V0n)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V0n)))) ).
fof(lameq_f2879,axiom,
! [V1n] : ap(f2879,V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(c_2Earithmetic_2EEVEN,V1n)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V1n)))),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ).
fof(conj_thm_2Etransc_2ESIN__FDIFF,axiom,
ap(c_2Epowser_2Ediffs,f2878) = f2879 ).
fof(lameq_f2880,axiom,
! [V0n] : ap(f2880,V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(c_2Earithmetic_2EEVEN,V0n)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V0n)))),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ).
fof(lameq_f2881,axiom,
! [V1n] : ap(f2881,V1n) = ap(c_2Erealax_2Ereal__neg,ap(f2874,V1n)) ).
fof(conj_thm_2Etransc_2ECOS__FDIFF,axiom,
ap(c_2Epowser_2Ediffs,f2880) = f2881 ).
fof(lameq_f2882,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] : ap(f2882(V0x),V1n) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,ap(f2874,V1n)),ap(ap(c_2Ereal_2Epow,V0x),V1n))) ) ).
fof(conj_thm_2Etransc_2ESIN__NEGLEMMA,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Esin,V0x)) = ap(c_2Eseq_2Esuminf,f2882(V0x)) ) ).
fof(conj_thm_2Etransc_2EDIFF__EXP,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Eexp),ap(c_2Etransc_2Eexp,V0x)),V0x)) ) ).
fof(conj_thm_2Etransc_2EDIFF__SIN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Esin),ap(c_2Etransc_2Ecos,V0x)),V0x)) ) ).
fof(conj_thm_2Etransc_2EDIFF__COS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Ecos),ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Esin,V0x))),V0x)) ) ).
fof(lameq_f2883,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V6x] : ap(f2883(V0f),V6x) = ap(c_2Erealax_2Einv,ap(V0f,V6x)) ) ).
fof(lameq_f2884,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V7x] : ap(f2884(V0f,V3g),V7x) = ap(ap(c_2Ereal_2E_2F,ap(V0f,V7x)),ap(V3g,V7x)) ) ) ).
fof(lameq_f2885,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V8x] : ap(f2885(V0f,V3g),V8x) = ap(ap(c_2Erealax_2Ereal__add,ap(V0f,V8x)),ap(V3g,V8x)) ) ) ).
fof(lameq_f2886,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V9x] : ap(f2886(V0f,V3g),V9x) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0f,V9x)),ap(V3g,V9x)) ) ) ).
fof(lameq_f2887,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V10x] : ap(f2887(V0f,V3g),V10x) = ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,V10x)),ap(V3g,V10x)) ) ) ).
fof(lameq_f2888,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V11x] : ap(f2888(V0f),V11x) = ap(c_2Erealax_2Ereal__neg,ap(V0f,V11x)) ) ).
fof(lameq_f2889,axiom,
! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ! [V12x] : ap(f2889(V3g,V5n),V12x) = ap(ap(c_2Ereal_2Epow,ap(V3g,V12x)),V5n) ) ) ).
fof(lameq_f2890,axiom,
! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V13x] : ap(f2890(V3g),V13x) = ap(c_2Etransc_2Eexp,ap(V3g,V13x)) ) ).
fof(lameq_f2891,axiom,
! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V14x] : ap(f2891(V3g),V14x) = ap(c_2Etransc_2Esin,ap(V3g,V14x)) ) ).
fof(lameq_f2892,axiom,
! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V15x] : ap(f2892(V3g),V15x) = ap(c_2Etransc_2Ecos,ap(V3g,V15x)) ) ).
fof(conj_thm_2Etransc_2EDIFF__COMPOSITE,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1l] :
( mem(V1l,ty_2Erealax_2Ereal)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ! [V3g] :
( mem(V3g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V4m] :
( mem(V4m,ty_2Erealax_2Ereal)
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ( ( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),V1l),V2x))
& ap(V0f,V2x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2883(V0f)),ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,V1l),ap(ap(c_2Ereal_2Epow,ap(V0f,V2x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V2x)) )
& ( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),V1l),V2x))
& p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x))
& ap(V3g,V2x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2884(V0f,V3g)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,V1l),ap(V3g,V2x))),ap(ap(c_2Erealax_2Ereal__mul,V4m),ap(V0f,V2x)))),ap(ap(c_2Ereal_2Epow,ap(V3g,V2x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V2x)) )
& ( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),V1l),V2x))
& p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x)) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2885(V0f,V3g)),ap(ap(c_2Erealax_2Ereal__add,V1l),V4m)),V2x)) )
& ( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),V1l),V2x))
& p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x)) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2886(V0f,V3g)),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V1l),ap(V3g,V2x))),ap(ap(c_2Erealax_2Ereal__mul,V4m),ap(V0f,V2x)))),V2x)) )
& ( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),V1l),V2x))
& p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x)) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2887(V0f,V3g)),ap(ap(c_2Ereal_2Ereal__sub,V1l),V4m)),V2x)) )
& ( p(ap(ap(ap(c_2Elim_2Ediffl,V0f),V1l),V2x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2888(V0f)),ap(c_2Erealax_2Ereal__neg,V1l)),V2x)) )
& ( p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2889(V3g,V5n)),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V5n)),ap(ap(c_2Ereal_2Epow,ap(V3g,V2x)),ap(ap(c_2Earithmetic_2E_2D,V5n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),V4m)),V2x)) )
& ( p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2890(V3g)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Eexp,ap(V3g,V2x))),V4m)),V2x)) )
& ( p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2891(V3g)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Ecos,ap(V3g,V2x))),V4m)),V2x)) )
& ( p(ap(ap(ap(c_2Elim_2Ediffl,V3g),V4m),V2x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2892(V3g)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Esin,ap(V3g,V2x)))),V4m)),V2x)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EEXP__0,axiom,
ap(c_2Etransc_2Eexp,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).
fof(conj_thm_2Etransc_2EEXP__LE__X,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> 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,c_2Earithmetic_2EZERO)))),V0x)),ap(c_2Etransc_2Eexp,V0x))) ) ) ).
fof(conj_thm_2Etransc_2EEXP__LT__1,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Etransc_2Eexp,V0x))) ) ) ).
fof(conj_thm_2Etransc_2EEXP__ADD__MUL,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Eexp,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))),ap(c_2Etransc_2Eexp,ap(c_2Erealax_2Ereal__neg,V0x))) = ap(c_2Etransc_2Eexp,V1y) ) ) ).
fof(conj_thm_2Etransc_2EEXP__NEG__MUL,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Eexp,V0x)),ap(c_2Etransc_2Eexp,ap(c_2Erealax_2Ereal__neg,V0x))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Etransc_2EEXP__NEG__MUL2,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Eexp,ap(c_2Erealax_2Ereal__neg,V0x))),ap(c_2Etransc_2Eexp,V0x)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Etransc_2EEXP__NEG,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eexp,ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Erealax_2Einv,ap(c_2Etransc_2Eexp,V0x)) ) ).
fof(conj_thm_2Etransc_2EEXP__ADD,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eexp,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Eexp,V0x)),ap(c_2Etransc_2Eexp,V1y)) ) ) ).
fof(conj_thm_2Etransc_2EEXP__POS__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Eexp,V0x))) ) ).
fof(conj_thm_2Etransc_2EEXP__NZ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eexp,V0x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ).
fof(conj_thm_2Etransc_2EEXP__POS__LT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Eexp,V0x))) ) ).
fof(conj_thm_2Etransc_2EEXP__N,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eexp,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),V1x)) = ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Eexp,V1x)),V0n) ) ) ).
fof(conj_thm_2Etransc_2EEXP__SUB,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eexp,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Eexp,V0x)),ap(c_2Etransc_2Eexp,V1y)) ) ) ).
fof(conj_thm_2Etransc_2EEXP__MONO__IMP,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eexp,V0x)),ap(c_2Etransc_2Eexp,V1y))) ) ) ) ).
fof(conj_thm_2Etransc_2EEXP__MONO__LT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eexp,V0x)),ap(c_2Etransc_2Eexp,V1y)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) ) ) ).
fof(conj_thm_2Etransc_2EEXP__MONO__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Eexp,V0x)),ap(c_2Etransc_2Eexp,V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ).
fof(conj_thm_2Etransc_2EEXP__INJ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ap(c_2Etransc_2Eexp,V0x) = ap(c_2Etransc_2Eexp,V1y)
<=> V0x = V1y ) ) ) ).
fof(conj_thm_2Etransc_2EEXP__TOTAL__LEMMA,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0y))
=> ? [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V1x),ap(ap(c_2Ereal_2Ereal__sub,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))
& ap(c_2Etransc_2Eexp,V1x) = V0y ) ) ) ).
fof(conj_thm_2Etransc_2EEXP__TOTAL,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0y))
=> ? [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
& ap(c_2Etransc_2Eexp,V1x) = V0y ) ) ) ).
fof(lameq_f2893,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1u] : ap(f2893(V0x),V1u) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Etransc_2Eexp,V1u)),V0x) ) ).
fof(ax_thm_2Etransc_2Eln,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eln,V0x) = ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2893(V0x)) ) ).
fof(conj_thm_2Etransc_2ELN__EXP,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eln,ap(c_2Etransc_2Eexp,V0x)) = V0x ) ).
fof(conj_thm_2Etransc_2EEXP__LN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ap(c_2Etransc_2Eexp,ap(c_2Etransc_2Eln,V0x)) = V0x
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ).
fof(conj_thm_2Etransc_2ELN__MUL,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ap(c_2Etransc_2Eln,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Etransc_2Eln,V0x)),ap(c_2Etransc_2Eln,V1y)) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__INJ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ( ap(c_2Etransc_2Eln,V0x) = ap(c_2Etransc_2Eln,V1y)
<=> V0x = V1y ) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__1,axiom,
ap(c_2Etransc_2Eln,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2ELN__INV,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> ap(c_2Etransc_2Eln,ap(c_2Erealax_2Einv,V0x)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Eln,V0x)) ) ) ).
fof(conj_thm_2Etransc_2ELN__DIV,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ap(c_2Etransc_2Eln,ap(ap(c_2Ereal_2E_2F,V0x),V1y)) = ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Etransc_2Eln,V0x)),ap(c_2Etransc_2Eln,V1y)) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__MONO__LT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eln,V0x)),ap(c_2Etransc_2Eln,V1y)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__MONO__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Eln,V0x)),ap(c_2Etransc_2Eln,V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__POW,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> ap(c_2Etransc_2Eln,ap(ap(c_2Ereal_2Epow,V1x),V0n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Etransc_2Eln,V1x)) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Eln,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x))),V0x)) ) ) ).
fof(conj_thm_2Etransc_2ELN__LT__X,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eln,V0x)),V0x)) ) ) ).
fof(conj_thm_2Etransc_2ELN__POS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Eln,V0x))) ) ) ).
fof(lameq_f2894,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ! [V2u] : ap(f2894(V0n,V1x),V2u) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x)),ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2u))),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Epow,V2u),V0n)),V1x)) ) ) ).
fof(ax_thm_2Etransc_2Eroot,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Etransc_2Eroot,V0n),V1x) = ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2894(V0n,V1x)) ) ) ).
fof(ax_thm_2Etransc_2Esqrt,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esqrt,V0x) = ap(ap(c_2Etransc_2Eroot,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x) ) ).
fof(conj_thm_2Etransc_2EROOT__LT__LEMMA,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Eexp,ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Eln,V1x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,V0n))))),ap(c_2Enum_2ESUC,V0n)) = V1x ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__LN,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x) = ap(c_2Etransc_2Eexp,ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Eln,V1x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,V0n)))) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ).
fof(conj_thm_2Etransc_2EROOT__1,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Etransc_2EROOT__POS__LT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x))) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__POW__POS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> ap(ap(c_2Ereal_2Epow,ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x)),ap(c_2Enum_2ESUC,V0n)) = V1x ) ) ) ).
fof(conj_thm_2Etransc_2EPOW__ROOT__POS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Ereal_2Epow,V1x),ap(c_2Enum_2ESUC,V0n))) = V1x ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__POS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x))) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__POS__UNIQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ! [V2y] :
( mem(V2y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2y))
& ap(ap(c_2Ereal_2Epow,V2y),ap(c_2Enum_2ESUC,V0n)) = V1x )
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x) = V2y ) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__MUL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ! [V2y] :
( mem(V2y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2y)) )
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Erealax_2Ereal__mul,V1x),V2y)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x)),ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V2y)) ) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__INV,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),ap(c_2Erealax_2Einv,V1x)) = ap(c_2Erealax_2Einv,ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x)) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__DIV,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ! [V2y] :
( mem(V2y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2y)) )
=> ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Ereal_2E_2F,V1x),V2y)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x)),ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V2y)) ) ) ) ) ).
fof(conj_thm_2Etransc_2EROOT__MONO__LE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ! [V2y] :
( mem(V2y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V1x),V2y)) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V1x)),ap(ap(c_2Etransc_2Eroot,ap(c_2Enum_2ESUC,V0n)),V2y))) ) ) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__0,axiom,
ap(c_2Etransc_2Esqrt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2ESQRT__1,axiom,
ap(c_2Etransc_2Esqrt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).
fof(conj_thm_2Etransc_2ESQRT__POS__LT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esqrt,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__POS__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esqrt,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__POW2,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Esqrt,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = V0x
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__POW__2,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Esqrt,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = V0x ) ) ).
fof(conj_thm_2Etransc_2EPOW__2__SQRT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = V0x ) ) ).
fof(conj_thm_2Etransc_2ESQRT__POS__UNIQ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y))
& ap(ap(c_2Ereal_2Epow,V1y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = V0x )
=> ap(c_2Etransc_2Esqrt,V0x) = V1y ) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__MUL,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ap(c_2Etransc_2Esqrt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esqrt,V0x)),ap(c_2Etransc_2Esqrt,V1y)) ) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__INV,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> ap(c_2Etransc_2Esqrt,ap(c_2Erealax_2Einv,V0x)) = ap(c_2Erealax_2Einv,ap(c_2Etransc_2Esqrt,V0x)) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__DIV,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
=> ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2E_2F,V0x),V1y)) = ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Esqrt,V0x)),ap(c_2Etransc_2Esqrt,V1y)) ) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__MONO__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Esqrt,V0x)),ap(c_2Etransc_2Esqrt,V1y))) ) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__EVEN__POW2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,V0n))
=> ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0n)) = ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) ) ) ).
fof(conj_thm_2Etransc_2EREAL__DIV__SQRT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Etransc_2Esqrt,V0x)) = ap(c_2Etransc_2Esqrt,V0x) ) ) ).
fof(conj_thm_2Etransc_2ESQRT__EQ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = V1y
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) )
=> V0x = ap(c_2Etransc_2Esqrt,V1y) ) ) ) ).
fof(conj_thm_2Etransc_2ESIN__0,axiom,
ap(c_2Etransc_2Esin,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2ECOS__0,axiom,
ap(c_2Etransc_2Ecos,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).
fof(conj_thm_2Etransc_2ESIN__CIRCLE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Esin,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Etransc_2ESIN__BOUND,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Etransc_2Esin,V0x))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(conj_thm_2Etransc_2ESIN__BOUNDS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Etransc_2Esin,V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Esin,V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__BOUND,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Etransc_2Ecos,V0x))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(conj_thm_2Etransc_2ECOS__BOUNDS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Etransc_2Ecos,V0x)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__COS__ADD,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esin,V0x)),ap(c_2Etransc_2Ecos,V1y))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Etransc_2Esin,V1y))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))),ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Etransc_2Ecos,V1y))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esin,V0x)),ap(c_2Etransc_2Esin,V1y))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ).
fof(conj_thm_2Etransc_2ESIN__COS__NEG,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Etransc_2Esin,ap(c_2Erealax_2Ereal__neg,V0x))),ap(c_2Etransc_2Esin,V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Etransc_2Ecos,ap(c_2Erealax_2Ereal__neg,V0x))),ap(c_2Etransc_2Ecos,V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ).
fof(conj_thm_2Etransc_2ESIN__ADD,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esin,V0x)),ap(c_2Etransc_2Ecos,V1y))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Etransc_2Esin,V1y))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__ADD,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Etransc_2Ecos,V1y))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esin,V0x)),ap(c_2Etransc_2Esin,V1y))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__NEG,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Esin,V0x)) ) ).
fof(conj_thm_2Etransc_2ECOS__NEG,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Etransc_2Ecos,V0x) ) ).
fof(conj_thm_2Etransc_2ESIN__DOUBLE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esin,V0x)),ap(c_2Etransc_2Ecos,V0x))) ) ).
fof(conj_thm_2Etransc_2ECOS__DOUBLE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x)) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Esin,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) ) ).
fof(lameq_f2895,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] : ap(f2895(V0x),V1n) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1n)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))),ap(ap(c_2Ereal_2Epow,V0x),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(conj_thm_2Etransc_2ESIN__PAIRED,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eseq_2Esums,f2895(V0x)),ap(c_2Etransc_2Esin,V0x))) ) ).
fof(conj_thm_2Etransc_2ESIN__POS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esin,V0x))) ) ) ).
fof(lameq_f2896,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] : ap(f2896(V0x),V1n) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1n)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n))))),ap(ap(c_2Ereal_2Epow,V0x),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n))) ) ).
fof(conj_thm_2Etransc_2ECOS__PAIRED,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eseq_2Esums,f2896(V0x)),ap(c_2Etransc_2Ecos,V0x))) ) ).
fof(conj_thm_2Etransc_2ECOS__2,axiom,
p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Ecos,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ).
fof(lameq_f2897,axiom,
! [V0x] : ap(f2897,V0x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,V0x)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))) ).
fof(conj_thm_2Etransc_2ECOS__ISZERO,axiom,
p(ap(c_2Ebool_2E_3F_21(ty_2Erealax_2Ereal),f2897)) ).
fof(ax_thm_2Etransc_2Epi,axiom,
c_2Etransc_2Epi = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2897)) ).
fof(conj_thm_2Etransc_2EPI2,axiom,
ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2897) ).
fof(conj_thm_2Etransc_2ECOS__PI2,axiom,
ap(c_2Etransc_2Ecos,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2EPI2__BOUNDS,axiom,
( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ).
fof(conj_thm_2Etransc_2EPI__POS,axiom,
p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),c_2Etransc_2Epi)) ).
fof(conj_thm_2Etransc_2ESIN__PI2,axiom,
ap(c_2Etransc_2Esin,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).
fof(conj_thm_2Etransc_2ECOS__PI,axiom,
ap(c_2Etransc_2Ecos,c_2Etransc_2Epi) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ).
fof(conj_thm_2Etransc_2ESIN__PI,axiom,
ap(c_2Etransc_2Esin,c_2Etransc_2Epi) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2ESIN__COS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,V0x) = ap(c_2Etransc_2Ecos,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V0x)) ) ).
fof(conj_thm_2Etransc_2ECOS__SIN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,V0x) = ap(c_2Etransc_2Esin,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V0x)) ) ).
fof(conj_thm_2Etransc_2ESIN__PERIODIC__PI,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__add,V0x),c_2Etransc_2Epi)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Esin,V0x)) ) ).
fof(conj_thm_2Etransc_2ECOS__PERIODIC__PI,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__add,V0x),c_2Etransc_2Epi)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Ecos,V0x)) ) ).
fof(conj_thm_2Etransc_2ESIN__PERIODIC,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),c_2Etransc_2Epi))) = ap(c_2Etransc_2Esin,V0x) ) ).
fof(conj_thm_2Etransc_2ECOS__PERIODIC,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),c_2Etransc_2Epi))) = ap(c_2Etransc_2Ecos,V0x) ) ).
fof(conj_thm_2Etransc_2ECOS__NPI,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),c_2Etransc_2Epi)) = ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0n) ) ).
fof(conj_thm_2Etransc_2ESIN__NPI,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),c_2Etransc_2Epi)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ).
fof(conj_thm_2Etransc_2ESIN__POS__PI2,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esin,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__POS__PI2,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Ecos,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__POS__PI,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Ecos,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__POS__PI,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),c_2Etransc_2Epi)) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esin,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__POS__PI2__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Ecos,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__POS__PI__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Ecos,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__POS__PI2__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esin,V0x))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__POS__PI__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),c_2Etransc_2Epi)) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esin,V0x))) ) ) ).
fof(lameq_f2898,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ! [V1x] : ap(f2898(V0y),V1x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,V1x),c_2Etransc_2Epi)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,V1x)),V0y))) ) ).
fof(conj_thm_2Etransc_2ECOS__TOTAL,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> p(ap(c_2Ebool_2E_3F_21(ty_2Erealax_2Ereal),f2898(V0y))) ) ) ).
fof(lameq_f2899,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ! [V1x] : ap(f2899(V0y),V1x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V1x)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,V1x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Etransc_2Esin,V1x)),V0y))) ) ).
fof(conj_thm_2Etransc_2ESIN__TOTAL,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> p(ap(c_2Ebool_2E_3F_21(ty_2Erealax_2Ereal),f2899(V0y))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__ZERO__LEMMA,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& ap(c_2Etransc_2Ecos,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& ~ p(ap(c_2Earithmetic_2EEVEN,V1n))
& V0x = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V1n)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ) ).
fof(conj_thm_2Etransc_2ESIN__ZERO__LEMMA,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& ap(c_2Etransc_2Esin,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& p(ap(c_2Earithmetic_2EEVEN,V1n))
& V0x = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V1n)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ) ).
fof(conj_thm_2Etransc_2ECOS__ZERO,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ap(c_2Etransc_2Ecos,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
<=> ( ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& ~ p(ap(c_2Earithmetic_2EEVEN,V1n))
& V0x = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V1n)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) )
| ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& ~ p(ap(c_2Earithmetic_2EEVEN,V2n))
& V0x = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V2n)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ) ) ).
fof(conj_thm_2Etransc_2ESIN__ZERO,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ap(c_2Etransc_2Esin,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
<=> ( ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& p(ap(c_2Earithmetic_2EEVEN,V1n))
& V0x = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V1n)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) )
| ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& p(ap(c_2Earithmetic_2EEVEN,V2n))
& V0x = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V2n)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ) ) ).
fof(ax_thm_2Etransc_2Etan,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Etan,V0x) = ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Esin,V0x)),ap(c_2Etransc_2Ecos,V0x)) ) ).
fof(conj_thm_2Etransc_2ETAN__0,axiom,
ap(c_2Etransc_2Etan,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2ETAN__PI,axiom,
ap(c_2Etransc_2Etan,c_2Etransc_2Epi) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ).
fof(conj_thm_2Etransc_2ETAN__NPI,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Etransc_2Etan,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),c_2Etransc_2Epi)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ).
fof(conj_thm_2Etransc_2ETAN__NEG,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Etan,ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Etan,V0x)) ) ).
fof(conj_thm_2Etransc_2ETAN__PERIODIC,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Etan,ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),c_2Etransc_2Epi))) = ap(c_2Etransc_2Etan,V0x) ) ).
fof(conj_thm_2Etransc_2ETAN__ADD,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( ( ap(c_2Etransc_2Ecos,V0x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& ap(c_2Etransc_2Ecos,V1y) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> ap(c_2Etransc_2Etan,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Etransc_2Etan,V0x)),ap(c_2Etransc_2Etan,V1y))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Etan,V0x)),ap(c_2Etransc_2Etan,V1y)))) ) ) ) ).
fof(conj_thm_2Etransc_2ETAN__DOUBLE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( ap(c_2Etransc_2Ecos,V0x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& ap(c_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x)) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> ap(c_2Etransc_2Etan,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Etransc_2Etan,V0x))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Etan,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2ETAN__POS__PI2,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Etan,V0x))) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__TAN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ap(c_2Etransc_2Ecos,V0x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Etan),ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V0x)) ) ) ).
fof(conj_thm_2Etransc_2ETAN__TOTAL__LEMMA,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0y))
=> ? [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V1x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0y),ap(c_2Etransc_2Etan,V1x))) ) ) ) ).
fof(conj_thm_2Etransc_2ETAN__TOTAL__POS,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0y))
=> ? [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V1x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
& ap(c_2Etransc_2Etan,V1x) = V0y ) ) ) ).
fof(lameq_f2900,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ! [V1x] : ap(f2900(V0y),V1x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V1x)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Erealax_2Ereal__lt,V1x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Etransc_2Etan,V1x)),V0y))) ) ).
fof(conj_thm_2Etransc_2ETAN__TOTAL,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> p(ap(c_2Ebool_2E_3F_21(ty_2Erealax_2Ereal),f2900(V0y))) ) ).
fof(ax_thm_2Etransc_2Easn,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Easn,V0y) = ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2899(V0y)) ) ).
fof(ax_thm_2Etransc_2Eacs,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eacs,V0y) = ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2898(V0y)) ) ).
fof(ax_thm_2Etransc_2Eatn,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Eatn,V0y) = ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f2900(V0y)) ) ).
fof(conj_thm_2Etransc_2EASN,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(c_2Etransc_2Easn,V0y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Easn,V0y)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
& ap(c_2Etransc_2Esin,ap(c_2Etransc_2Easn,V0y)) = V0y ) ) ) ).
fof(conj_thm_2Etransc_2EASN__SIN,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ap(c_2Etransc_2Esin,ap(c_2Etransc_2Easn,V0y)) = V0y ) ) ).
fof(conj_thm_2Etransc_2EASN__BOUNDS,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(c_2Etransc_2Easn,V0y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Easn,V0y)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ) ).
fof(conj_thm_2Etransc_2EASN__BOUNDS__LT,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(c_2Etransc_2Easn,V0y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Easn,V0y)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ) ).
fof(conj_thm_2Etransc_2ESIN__ASN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> ap(c_2Etransc_2Easn,ap(c_2Etransc_2Esin,V0x)) = V0x ) ) ).
fof(conj_thm_2Etransc_2EACS,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Eacs,V0y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Eacs,V0y)),c_2Etransc_2Epi))
& ap(c_2Etransc_2Ecos,ap(c_2Etransc_2Eacs,V0y)) = V0y ) ) ) ).
fof(conj_thm_2Etransc_2EACS__COS,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ap(c_2Etransc_2Ecos,ap(c_2Etransc_2Eacs,V0y)) = V0y ) ) ).
fof(conj_thm_2Etransc_2EACS__BOUNDS,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Eacs,V0y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Eacs,V0y)),c_2Etransc_2Epi)) ) ) ) ).
fof(conj_thm_2Etransc_2EACS__BOUNDS__LT,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0y))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Eacs,V0y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eacs,V0y)),c_2Etransc_2Epi)) ) ) ) ).
fof(conj_thm_2Etransc_2ECOS__ACS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),c_2Etransc_2Epi)) )
=> ap(c_2Etransc_2Eacs,ap(c_2Etransc_2Ecos,V0x)) = V0x ) ) ).
fof(conj_thm_2Etransc_2EATN,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(c_2Etransc_2Eatn,V0y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eatn,V0y)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
& ap(c_2Etransc_2Etan,ap(c_2Etransc_2Eatn,V0y)) = V0y ) ) ).
fof(conj_thm_2Etransc_2EATN__TAN,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Etan,ap(c_2Etransc_2Eatn,V0y)) = V0y ) ).
fof(conj_thm_2Etransc_2EATN__BOUNDS,axiom,
! [V0y] :
( mem(V0y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(c_2Etransc_2Eatn,V0y)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Etransc_2Eatn,V0y)),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ).
fof(conj_thm_2Etransc_2ETAN__ATN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> ap(c_2Etransc_2Eatn,ap(c_2Etransc_2Etan,V0x)) = V0x ) ) ).
fof(conj_thm_2Etransc_2ETAN__SEC,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ap(c_2Etransc_2Ecos,V0x) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
=> ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Etan,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Einv,ap(c_2Etransc_2Ecos,V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__COS__SQ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),c_2Etransc_2Epi)) )
=> ap(c_2Etransc_2Esin,V0x) = ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__SIN__SQ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V0x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2E_2F,c_2Etransc_2Epi),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) )
=> ap(c_2Etransc_2Ecos,V0x) = ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Esin,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2ECOS__ATN__NZ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Etransc_2Ecos,ap(c_2Etransc_2Eatn,V0x)) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ).
fof(conj_thm_2Etransc_2ECOS__ASN__NZ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ap(c_2Etransc_2Ecos,ap(c_2Etransc_2Easn,V0x)) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ).
fof(conj_thm_2Etransc_2ESIN__ACS__NZ,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> ap(c_2Etransc_2Esin,ap(c_2Etransc_2Eacs,V0x)) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ).
fof(conj_thm_2Etransc_2ECOS__SIN__SQRT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Ecos,V0x)))
=> ap(c_2Etransc_2Ecos,V0x) = ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Esin,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2ESIN__COS__SQRT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Etransc_2Esin,V0x)))
=> ap(c_2Etransc_2Esin,V0x) = ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Etransc_2Ecos,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__LN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Eln),ap(c_2Erealax_2Einv,V0x)),V0x)) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__ASN__LEMMA,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Easn),ap(c_2Erealax_2Einv,ap(c_2Etransc_2Ecos,ap(c_2Etransc_2Easn,V0x)))),V0x)) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__ASN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Easn),ap(c_2Erealax_2Einv,ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))),V0x)) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__ACS__LEMMA,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Eacs),ap(c_2Erealax_2Einv,ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Esin,ap(c_2Etransc_2Eacs,V0x))))),V0x)) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__ACS,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Eacs),ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Einv,ap(c_2Etransc_2Esqrt,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))),V0x)) ) ) ).
fof(conj_thm_2Etransc_2EDIFF__ATN,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,c_2Etransc_2Eatn),ap(c_2Erealax_2Einv,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),V0x)) ) ).
fof(ax_thm_2Etransc_2Edivision,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2D] :
( mem(V2D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2D))
<=> ( ap(V2D,c_2Enum_2E0) = V0a
& ? [V3N] :
( mem(V3N,ty_2Enum_2Enum)
& ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V4n),V3N))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V2D,V4n)),ap(V2D,ap(c_2Enum_2ESUC,V4n)))) ) )
& ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V5n),V3N))
=> ap(V2D,V5n) = V1b ) ) ) ) ) ) ) ) ).
fof(lameq_f2901,axiom,
! [V1N] :
( mem(V1N,ty_2Enum_2Enum)
=> ! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2n] : ap(f2901(V1N,V0D),V2n) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Eprim__rec_2E_3C,V2n),V1N)),ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,V2n)),ap(V0D,ap(c_2Enum_2ESUC,V2n)))) ) ) ).
fof(lameq_f2902,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1N] :
( mem(V1N,ty_2Enum_2Enum)
=> ! [V3n] : ap(f2902(V0D,V1N),V3n) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Earithmetic_2E_3E_3D,V3n),V1N)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(V0D,V3n)),ap(V0D,V1N))) ) ) ).
fof(lameq_f2903,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1N] : ap(f2903(V0D),V1N) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2901(V1N,V0D))),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2902(V0D,V1N))) ) ).
fof(ax_thm_2Etransc_2Edsize,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ap(c_2Etransc_2Edsize,V0D) = ap(c_2Emin_2E_40(ty_2Enum_2Enum),f2903(V0D)) ) ).
fof(ax_thm_2Etransc_2Etdiv,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2D] :
( mem(V2D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3p] :
( mem(V3p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V2D),V3p)))
<=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2D))
& ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(V2D,V4n)),ap(V3p,V4n)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(V3p,V4n)),ap(V2D,ap(c_2Enum_2ESUC,V4n)))) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Etransc_2Egauge,axiom,
! [V0E] :
( mem(V0E,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1g] :
( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Etransc_2Egauge,V0E),V1g))
<=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( p(ap(V0E,V2x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(V1g,V2x))) ) ) ) ) ) ).
fof(ax_thm_2Etransc_2Efine,axiom,
! [V0g] :
( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1D] :
( mem(V1D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2p] :
( mem(V2p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Etransc_2Efine,V0g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V1D),V2p)))
<=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V1D)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Ereal__sub,ap(V1D,ap(c_2Enum_2ESUC,V3n))),ap(V1D,V3n))),ap(V0g,ap(V2p,V3n)))) ) ) ) ) ) ) ).
fof(lameq_f2904,axiom,
! [V1p] :
( mem(V1p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2f] :
( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3n] : ap(f2904(V1p,V2f,V0D),V3n) = ap(ap(c_2Erealax_2Ereal__mul,ap(V2f,ap(V1p,V3n))),ap(ap(c_2Ereal_2Ereal__sub,ap(V0D,ap(c_2Enum_2ESUC,V3n))),ap(V0D,V3n))) ) ) ) ).
fof(ax_thm_2Etransc_2Ersum,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1p] :
( mem(V1p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2f] :
( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ap(ap(c_2Etransc_2Ersum,ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V0D),V1p)),V2f) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),ap(c_2Etransc_2Edsize,V0D))),f2904(V1p,V2f,V0D)) ) ) ) ).
fof(lameq_f2905,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V6x] : ap(f2905(V0a,V1b),V6x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,V0a),V6x)),ap(ap(c_2Ereal_2Ereal__lte,V6x),V1b)) ) ) ).
fof(ax_thm_2Etransc_2EDint,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2f] :
( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3k] :
( mem(V3k,ty_2Erealax_2Ereal)
=> ( p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2f),V3k))
<=> ! [V4e] :
( mem(V4e,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V4e))
=> ? [V5g] :
( mem(V5g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
& p(ap(ap(c_2Etransc_2Egauge,f2905(V0a,V1b)),V5g))
& ! [V7D] :
( mem(V7D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V8p] :
( mem(V8p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V7D),V8p)))
& p(ap(ap(c_2Etransc_2Efine,V5g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V7D),V8p))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Etransc_2Ersum,ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V7D),V8p)),V2f)),V3k))),V4e)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f2906,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2n] : ap(f2906(V0a,V1b),V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0a),V1b) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__0,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( V0a = V1b
=> ap(c_2Etransc_2Edsize,f2906(V0a,V1b)) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__1,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,V0a),V1b))
=> ap(c_2Etransc_2Edsize,f2906(V0a,V1b)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__SINGLE,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V1b))
=> p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),f2906(V0a,V1b))) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__LHS,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ap(V0D,c_2Enum_2E0) = V1a ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__THM,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
<=> ( ap(V0D,c_2Enum_2E0) = V1a
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V0D)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,V3n)),ap(V0D,ap(c_2Enum_2ESUC,V3n)))) ) )
& ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V4n),ap(c_2Etransc_2Edsize,V0D)))
=> ap(V0D,V4n) = V2b ) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__RHS,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ap(V0D,ap(c_2Etransc_2Edsize,V0D)) = V2b ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__LT__GEN,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V4n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V4n),ap(c_2Etransc_2Edsize,V0D))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,V3m)),ap(V0D,V4n))) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__LT,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V0D)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,c_2Enum_2E0)),ap(V0D,ap(c_2Enum_2ESUC,V3n)))) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__LE,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> p(ap(ap(c_2Ereal_2Ereal__lte,V1a),V2b)) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__GT,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V0D)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,V3n)),ap(V0D,ap(c_2Etransc_2Edsize,V0D)))) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__EQ,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ( V1a = V2b
<=> ap(c_2Etransc_2Edsize,V0D) = c_2Enum_2E0 ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__LBOUND,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ! [V3r] :
( mem(V3r,ty_2Enum_2Enum)
=> p(ap(ap(c_2Ereal_2Ereal__lte,V1a),ap(V0D,V3r))) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__LBOUND__LT,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
& ap(c_2Etransc_2Edsize,V0D) != c_2Enum_2E0 )
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Erealax_2Ereal__lt,V1a),ap(V0D,ap(c_2Enum_2ESUC,V3n)))) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__UBOUND,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
=> ! [V3r] :
( mem(V3r,ty_2Enum_2Enum)
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0D,V3r)),V2b)) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__UBOUND__LT,axiom,
! [V0D] :
( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V0D))) )
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,V3n)),V2b)) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__APPEND,axiom,
! [V0g] :
( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ! [V3c] :
( mem(V3c,ty_2Erealax_2Ereal)
=> ( ( ? [V4D1] :
( mem(V4D1,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ? [V5p1] :
( mem(V5p1,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V4D1),V5p1)))
& p(ap(ap(c_2Etransc_2Efine,V0g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V4D1),V5p1))) ) )
& ? [V6D2] :
( mem(V6D2,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ? [V7p2] :
( mem(V7p2,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V2b),V3c)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V6D2),V7p2)))
& p(ap(ap(c_2Etransc_2Efine,V0g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V6D2),V7p2))) ) ) )
=> ? [V8D] :
( mem(V8D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ? [V9p] :
( mem(V9p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V3c)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V8D),V9p)))
& p(ap(ap(c_2Etransc_2Efine,V0g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V8D),V9p))) ) ) ) ) ) ) ) ).
fof(lameq_f2907,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V3x] : ap(f2907(V0a,V1b),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ereal_2Ereal__lte,V0a),V3x)),ap(ap(c_2Ereal_2Ereal__lte,V3x),V1b)) ) ) ).
fof(conj_thm_2Etransc_2EDIVISION__EXISTS,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2g] :
( mem(V2g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V1b))
& p(ap(ap(c_2Etransc_2Egauge,f2907(V0a,V1b)),V2g)) )
=> ? [V4D] :
( mem(V4D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ? [V5p] :
( mem(V5p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V4D),V5p)))
& p(ap(ap(c_2Etransc_2Efine,V2g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V4D),V5p))) ) ) ) ) ) ) ).
fof(lameq_f2908,axiom,
! [V1g1] :
( mem(V1g1,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2g2] :
( mem(V2g2,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x] : ap(f2908(V1g1,V2g2),V3x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__lt,ap(V1g1,V3x)),ap(V2g2,V3x))),ap(V1g1,V3x)),ap(V2g2,V3x)) ) ) ).
fof(conj_thm_2Etransc_2EGAUGE__MIN,axiom,
! [V0E] :
( mem(V0E,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1g1] :
( mem(V1g1,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2g2] :
( mem(V2g2,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Etransc_2Egauge,V0E),V1g1))
& p(ap(ap(c_2Etransc_2Egauge,V0E),V2g2)) )
=> p(ap(ap(c_2Etransc_2Egauge,V0E),f2908(V1g1,V2g2))) ) ) ) ) ).
fof(lameq_f2909,axiom,
! [V0g1] :
( mem(V0g1,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g2] :
( mem(V1g2,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V4x] : ap(f2909(V0g1,V1g2),V4x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__lt,ap(V0g1,V4x)),ap(V1g2,V4x))),ap(V0g1,V4x)),ap(V1g2,V4x)) ) ) ).
fof(conj_thm_2Etransc_2EFINE__MIN,axiom,
! [V0g1] :
( mem(V0g1,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1g2] :
( mem(V1g2,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2D] :
( mem(V2D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3p] :
( mem(V3p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Etransc_2Efine,f2909(V0g1,V1g2)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V2D),V3p)))
=> ( p(ap(ap(c_2Etransc_2Efine,V0g1),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V2D),V3p)))
& p(ap(ap(c_2Etransc_2Efine,V1g2),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V2D),V3p))) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EDINT__UNIQ,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2f] :
( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3k1] :
( mem(V3k1,ty_2Erealax_2Ereal)
=> ! [V4k2] :
( mem(V4k2,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V1b))
& p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2f),V3k1))
& p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2f),V4k2)) )
=> V3k1 = V4k2 ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EINTEGRAL__NULL,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V1a)),V0f),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ).
fof(conj_thm_2Etransc_2EFTC1,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1f_27] :
( mem(V1f_27,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V2a] :
( mem(V2a,ty_2Erealax_2Ereal)
=> ! [V3b] :
( mem(V3b,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V2a),V3b))
& ! [V4x] :
( mem(V4x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V2a),V4x))
& p(ap(ap(c_2Ereal_2Ereal__lte,V4x),V3b)) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,V0f),ap(V1f_27,V4x)),V4x)) ) ) )
=> p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V2a),V3b)),V1f_27),ap(ap(c_2Ereal_2Ereal__sub,ap(V0f,V3b)),ap(V0f,V2a)))) ) ) ) ) ) ).
fof(lameq_f2910,axiom,
! [V1diff] :
( mem(V1diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V2h] :
( mem(V2h,ty_2Erealax_2Ereal)
=> ! [V7m] : ap(f2910(V1diff,V2h),V7m) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V1diff,V7m),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V7m)))),ap(ap(c_2Ereal_2Epow,V2h),V7m)) ) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1diff] :
( mem(V1diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V2h] :
( mem(V2h,ty_2Erealax_2Ereal)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2h))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3n))
& ap(V1diff,c_2Enum_2E0) = V0f
& ! [V4m] :
( mem(V4m,ty_2Enum_2Enum)
=> ! [V5t] :
( mem(V5t,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V5t))
& p(ap(ap(c_2Ereal_2Ereal__lte,V5t),V2h)) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,ap(V1diff,V4m)),ap(ap(V1diff,ap(c_2Enum_2ESUC,V4m)),V5t)),V5t)) ) ) ) )
=> ? [V6t] :
( mem(V6t,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V6t))
& p(ap(ap(c_2Erealax_2Ereal__lt,V6t),V2h))
& ap(V0f,V2h) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V3n)),f2910(V1diff,V2h))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V1diff,V3n),V6t)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V3n)))),ap(ap(c_2Ereal_2Epow,V2h),V3n))) ) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN__NEG,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1diff] :
( mem(V1diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V2h] :
( mem(V2h,ty_2Erealax_2Ereal)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V2h),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3n))
& ap(V1diff,c_2Enum_2E0) = V0f
& ! [V4m] :
( mem(V4m,ty_2Enum_2Enum)
=> ! [V5t] :
( mem(V5t,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n))
& p(ap(ap(c_2Ereal_2Ereal__lte,V2h),V5t))
& p(ap(ap(c_2Ereal_2Ereal__lte,V5t),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,ap(V1diff,V4m)),ap(ap(V1diff,ap(c_2Enum_2ESUC,V4m)),V5t)),V5t)) ) ) ) )
=> ? [V6t] :
( mem(V6t,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,V2h),V6t))
& p(ap(ap(c_2Erealax_2Ereal__lt,V6t),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
& ap(V0f,V2h) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V3n)),f2910(V1diff,V2h))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V1diff,V3n),V6t)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V3n)))),ap(ap(c_2Ereal_2Epow,V2h),V3n))) ) ) ) ) ) ) ).
fof(lameq_f2911,axiom,
! [V1diff] :
( mem(V1diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V4x] :
( mem(V4x,ty_2Erealax_2Ereal)
=> ! [V7m] : ap(f2911(V1diff,V4x),V7m) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V1diff,V7m),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V7m)))),ap(ap(c_2Ereal_2Epow,V4x),V7m)) ) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN__ALL__LT,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1diff] :
( mem(V1diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ( ( ap(V1diff,c_2Enum_2E0) = V0f
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,ap(V1diff,V2m)),ap(ap(V1diff,ap(c_2Enum_2ESUC,V2m)),V3x)),V3x)) ) ) )
=> ! [V4x] :
( mem(V4x,ty_2Erealax_2Ereal)
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ( ( V4x != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V5n)) )
=> ? [V6t] :
( mem(V6t,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Eabs,V6t)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V6t)),ap(c_2Ereal_2Eabs,V4x)))
& ap(V0f,V4x) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V5n)),f2911(V1diff,V4x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V1diff,V5n),V6t)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V5n)))),ap(ap(c_2Ereal_2Epow,V4x),V5n))) ) ) ) ) ) ) ) ).
fof(lameq_f2912,axiom,
! [V0diff] :
( mem(V0diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ! [V3m] : ap(f2912(V0diff,V2x),V3m) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V0diff,V3m),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V3m)))),ap(ap(c_2Ereal_2Epow,V2x),V3m)) ) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN__ZERO,axiom,
! [V0diff] :
( mem(V0diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( ( V2x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) )
=> ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V1n)),f2912(V0diff,V2x)) = ap(ap(V0diff,c_2Enum_2E0),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ) ) ) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN__ALL__LE,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1diff] :
( mem(V1diff,arr(ty_2Enum_2Enum,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))
=> ( ( ap(V1diff,c_2Enum_2E0) = V0f
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,ap(V1diff,V2m)),ap(ap(V1diff,ap(c_2Enum_2ESUC,V2m)),V3x)),V3x)) ) ) )
=> ! [V4x] :
( mem(V4x,ty_2Erealax_2Ereal)
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ? [V6t] :
( mem(V6t,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V6t)),ap(c_2Ereal_2Eabs,V4x)))
& ap(V0f,V4x) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V5n)),f2911(V1diff,V4x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(V1diff,V5n),V6t)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V5n)))),ap(ap(c_2Ereal_2Epow,V4x),V5n))) ) ) ) ) ) ) ).
fof(lameq_f2913,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V3m] : ap(f2913(V0x),V3m) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,V0x),V3m)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V3m))) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN__EXP__LT,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( V0x != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) )
=> ? [V2t] :
( mem(V2t,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Eabs,V2t)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V2t)),ap(c_2Ereal_2Eabs,V0x)))
& ap(c_2Etransc_2Eexp,V0x) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V1n)),f2913(V0x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Eexp,V2t)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V1n)))),ap(ap(c_2Ereal_2Epow,V0x),V1n))) ) ) ) ) ).
fof(conj_thm_2Etransc_2EMCLAURIN__EXP__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ? [V2t] :
( mem(V2t,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2t)),ap(c_2Ereal_2Eabs,V0x)))
& ap(c_2Etransc_2Eexp,V0x) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V1n)),f2913(V0x))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(c_2Etransc_2Eexp,V2t)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V1n)))),ap(ap(c_2Ereal_2Epow,V0x),V1n))) ) ) ) ).
fof(lameq_f2914,axiom,
! [V0g] :
( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x] : ap(f2914(V0g),V3x) = ap(c_2Etransc_2Eln,ap(V0g,V3x)) ) ).
fof(conj_thm_2Etransc_2EDIFF__LN__COMPOSITE,axiom,
! [V0g] :
( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1m] :
( mem(V1m,ty_2Erealax_2Ereal)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(ap(c_2Elim_2Ediffl,V0g),V1m),V2x))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(V0g,V2x))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2914(V0g)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,ap(V0g,V2x))),V1m)),V2x)) ) ) ) ) ).
fof(ax_thm_2Etransc_2Erpow__def,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ap(ap(c_2Etransc_2Erpow,V0a),V1b) = ap(c_2Etransc_2Eexp,ap(ap(c_2Erealax_2Ereal__mul,V1b),ap(c_2Etransc_2Eln,V0a))) ) ) ).
fof(conj_thm_2Etransc_2EGEN__RPOW,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Ereal_2Epow,V0a),V1n) = ap(ap(c_2Etransc_2Erpow,V0a),ap(c_2Ereal_2Ereal__of__num,V1n)) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__SUC__N,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Etransc_2Erpow,V0a),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V1n)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Ereal_2Epow,V0a),ap(c_2Enum_2ESUC,V1n)) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__0,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Etransc_2Erpow,V0a),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__1,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Etransc_2Erpow,V0a),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0a ) ) ).
fof(conj_thm_2Etransc_2EONE__RPOW,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Etransc_2Erpow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0a) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__POS__LT,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Etransc_2Erpow,V0a),V1b))) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__NZ,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) != V0a
=> ap(ap(c_2Etransc_2Erpow,V0a),V1b) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Etransc_2ELN__RPOW,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(c_2Etransc_2Eln,ap(ap(c_2Etransc_2Erpow,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,V1b),ap(c_2Etransc_2Eln,V0a)) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__ADD,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ap(ap(c_2Etransc_2Erpow,V0a),ap(ap(c_2Erealax_2Ereal__add,V1b),V2c)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),ap(ap(c_2Etransc_2Erpow,V0a),V2c)) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__ADD__MUL,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Etransc_2Erpow,V0a),ap(ap(c_2Erealax_2Ereal__add,V1b),V2c))),ap(ap(c_2Etransc_2Erpow,V0a),ap(c_2Erealax_2Ereal__neg,V1b))) = ap(ap(c_2Etransc_2Erpow,V0a),V2c) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__SUB,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ap(ap(c_2Etransc_2Erpow,V0a),ap(ap(c_2Ereal_2Ereal__sub,V1b),V2c)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),ap(ap(c_2Etransc_2Erpow,V0a),V2c)) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__DIV,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1b)) )
=> ap(ap(c_2Etransc_2Erpow,ap(ap(c_2Ereal_2E_2F,V0a),V1b)),V2c) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Etransc_2Erpow,V0a),V2c)),ap(ap(c_2Etransc_2Erpow,V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__INV,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Etransc_2Erpow,ap(c_2Erealax_2Einv,V0a)),V1b) = ap(c_2Erealax_2Einv,ap(ap(c_2Etransc_2Erpow,V0a),V1b)) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__MUL,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1b)) )
=> ap(ap(c_2Etransc_2Erpow,ap(ap(c_2Erealax_2Ereal__mul,V0a),V1b)),V2c) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Etransc_2Erpow,V0a),V2c)),ap(ap(c_2Etransc_2Erpow,V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__RPOW,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
=> ap(ap(c_2Etransc_2Erpow,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),V2c) = ap(ap(c_2Etransc_2Erpow,V0a),ap(ap(c_2Erealax_2Ereal__mul,V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__LT,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0a))
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),ap(ap(c_2Etransc_2Erpow,V0a),V2c)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,V1b),V2c)) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__LE,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0a))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),ap(ap(c_2Etransc_2Erpow,V0a),V2c)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,V1b),V2c)) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EBASE__RPOW__LE,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1b)) )
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),ap(ap(c_2Etransc_2Erpow,V2c),V1b)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V2c)) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2EBASE__RPOW__LT,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1b)) )
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Etransc_2Erpow,V0a),V1b)),ap(ap(c_2Etransc_2Erpow,V2c),V1b)))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,V0a),V2c)) ) ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__UNIQ__BASE,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0a))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c))
& ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) != V1b
& ap(ap(c_2Etransc_2Erpow,V0a),V1b) = ap(ap(c_2Etransc_2Erpow,V2c),V1b) )
=> V0a = V2c ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__UNIQ__EXP,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Erealax_2Ereal)
=> ! [V2c] :
( mem(V2c,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0a))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1b))
& ap(ap(c_2Etransc_2Erpow,V0a),V1b) = ap(ap(c_2Etransc_2Erpow,V0a),V2c) )
=> V1b = V2c ) ) ) ) ).
fof(conj_thm_2Etransc_2ERPOW__DIV__BASE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1t] :
( mem(V1t,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Etransc_2Erpow,V0x),V1t)),V0x) = ap(ap(c_2Etransc_2Erpow,V0x),ap(ap(c_2Ereal_2Ereal__sub,V1t),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ).
fof(lameq_f2915,axiom,
! [V0g] :
( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V3x] : ap(f2915(V0g),V3x) = ap(c_2Etransc_2Eexp,ap(V0g,V3x)) ) ).
fof(conj_thm_2Etransc_2EDIFF__COMPOSITE__EXP,axiom,
! [V0g] :
( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1m] :
( mem(V1m,ty_2Erealax_2Ereal)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(ap(c_2Elim_2Ediffl,V0g),V1m),V2x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2915(V0g)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Eexp,ap(V0g,V2x))),V1m)),V2x)) ) ) ) ) ).
fof(lameq_f2916,axiom,
! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ! [V2x] : ap(f2916(V1y),V2x) = ap(ap(c_2Etransc_2Erpow,V2x),V1y) ) ).
fof(conj_thm_2Etransc_2EDIFF__RPOW,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2916(V1y)),ap(ap(c_2Erealax_2Ereal__mul,V1y),ap(ap(c_2Etransc_2Erpow,V0x),ap(ap(c_2Ereal_2Ereal__sub,V1y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))),V0x)) ) ) ) ).
%------------------------------------------------------------------------------