ITP001 Axioms: ITP130+5.ax
%------------------------------------------------------------------------------
% File : ITP130+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 : poly+2.ax [Gau20]
% : HL4130+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 113 ( 17 unt; 0 def)
% Number of atoms : 496 ( 150 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 414 ( 31 ~; 7 |; 82 &)
% ( 15 <=>; 279 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 65 ( 65 usr; 43 con; 0-2 aty)
% Number of variables : 271 ( 248 !; 23 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Epoly_2E_23_23,axiom,
mem(c_2Epoly_2E_23_23,arr(ty_2Erealax_2Ereal,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal)))) ).
fof(mem_c_2Epoly_2Edegree,axiom,
mem(c_2Epoly_2Edegree,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Enum_2Enum)) ).
fof(mem_c_2Epoly_2Ediff,axiom,
mem(c_2Epoly_2Ediff,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal))) ).
fof(mem_c_2Epoly_2Enormalize,axiom,
mem(c_2Epoly_2Enormalize,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal))) ).
fof(mem_c_2Epoly_2Epoly,axiom,
mem(c_2Epoly_2Epoly,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
fof(mem_c_2Epoly_2Epoly__add,axiom,
mem(c_2Epoly_2Epoly__add,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal)))) ).
fof(mem_c_2Epoly_2Epoly__diff__aux,axiom,
mem(c_2Epoly_2Epoly__diff__aux,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal)))) ).
fof(mem_c_2Epoly_2Epoly__divides,axiom,
mem(c_2Epoly_2Epoly__divides,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),bool))) ).
fof(mem_c_2Epoly_2Epoly__exp,axiom,
mem(c_2Epoly_2Epoly__exp,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Erealax_2Ereal)))) ).
fof(mem_c_2Epoly_2Epoly__mul,axiom,
mem(c_2Epoly_2Epoly__mul,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal)))) ).
fof(mem_c_2Epoly_2Epoly__neg,axiom,
mem(c_2Epoly_2Epoly__neg,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal))) ).
fof(mem_c_2Epoly_2Epoly__order,axiom,
mem(c_2Epoly_2Epoly__order,arr(ty_2Erealax_2Ereal,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Enum_2Enum))) ).
fof(mem_c_2Epoly_2Ersquarefree,axiom,
mem(c_2Epoly_2Ersquarefree,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),bool)) ).
fof(ax_thm_2Epoly_2Epoly__def,axiom,
( ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
& ! [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V2t)),V3x) = ap(ap(c_2Erealax_2Ereal__add,V1h),ap(ap(c_2Erealax_2Ereal__mul,V3x),ap(ap(c_2Epoly_2Epoly,V2t),V3x))) ) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__add__def,axiom,
( ! [V0l2] :
( mem(V0l2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__add,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),V0l2) = V0l2 )
& ! [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V2t)),V3l2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),V3l2),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V2t)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__add,V1h),ap(c_2Elist_2EHD(ty_2Erealax_2Ereal),V3l2))),ap(ap(c_2Epoly_2Epoly__add,V2t),ap(c_2Elist_2ETL(ty_2Erealax_2Ereal),V3l2)))) ) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__cmul__def,axiom,
( ! [V0c] :
( mem(V0c,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2E_23_23,V0c),c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = c_2Elist_2ENIL(ty_2Erealax_2Ereal) )
& ! [V1c] :
( mem(V1c,ty_2Erealax_2Ereal)
=> ! [V2h] :
( mem(V2h,ty_2Erealax_2Ereal)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2E_23_23,V1c),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V2h),V3t)) = ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,V1c),V2h)),ap(ap(c_2Epoly_2E_23_23,V1c),V3t)) ) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__neg__def,axiom,
c_2Epoly_2Epoly__neg = ap(c_2Epoly_2E_23_23,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ).
fof(ax_thm_2Epoly_2Epoly__mul__def,axiom,
( ! [V0l2] :
( mem(V0l2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__mul,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),V0l2) = c_2Elist_2ENIL(ty_2Erealax_2Ereal) )
& ! [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V2t)),V3l2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),V2t),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),ap(ap(c_2Epoly_2E_23_23,V1h),V3l2)),ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2E_23_23,V1h),V3l2)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Epoly_2Epoly__mul,V2t),V3l2)))) ) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__exp__def,axiom,
( ! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__exp,V0p),c_2Enum_2E0) = ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Epoly_2Epoly__exp,V1p),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Epoly_2Epoly__mul,V1p),ap(ap(c_2Epoly_2Epoly__exp,V1p),V2n)) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__diff__aux__def,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Epoly_2Epoly__diff__aux,V0n),c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = c_2Elist_2ENIL(ty_2Erealax_2Ereal) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2h] :
( mem(V2h,ty_2Erealax_2Ereal)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__diff__aux,V1n),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V2h),V3t)) = ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V1n)),V2h)),ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,V1n)),V3t)) ) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__diff__def,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Ediff,V0l) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),V0l),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)),ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ETL(ty_2Erealax_2Ereal),V0l))) ) ).
fof(conj_thm_2Epoly_2EPOLY__ADD__CLAUSES,axiom,
! [V0p2] :
( mem(V0p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1p1] :
( mem(V1p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2h1] :
( mem(V2h1,ty_2Erealax_2Ereal)
=> ! [V3t1] :
( mem(V3t1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V4h2] :
( mem(V4h2,ty_2Erealax_2Ereal)
=> ! [V5t2] :
( mem(V5t2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(ap(c_2Epoly_2Epoly__add,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),V0p2) = V0p2
& ap(ap(c_2Epoly_2Epoly__add,V1p1),c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = V1p1
& ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V2h1),V3t1)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V4h2),V5t2)) = ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__add,V2h1),V4h2)),ap(ap(c_2Epoly_2Epoly__add,V3t1),V5t2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__CMUL__CLAUSES,axiom,
! [V0c] :
( mem(V0c,ty_2Erealax_2Ereal)
=> ! [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(ap(c_2Epoly_2E_23_23,V0c),c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
& ap(ap(c_2Epoly_2E_23_23,V0c),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V2t)) = ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,V0c),V1h)),ap(ap(c_2Epoly_2E_23_23,V0c),V2t)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__NEG__CLAUSES,axiom,
! [V0h] :
( mem(V0h,ty_2Erealax_2Ereal)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly__neg,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
& ap(c_2Epoly_2Epoly__neg,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0h),V1t)) = ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0h)),ap(c_2Epoly_2Epoly__neg,V1t)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__MUL__CLAUSES,axiom,
! [V0p2] :
( mem(V0p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1h1] :
( mem(V1h1,ty_2Erealax_2Ereal)
=> ! [V2k1] :
( mem(V2k1,ty_2Erealax_2Ereal)
=> ! [V3t1] :
( mem(V3t1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(ap(c_2Epoly_2Epoly__mul,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),V0p2) = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
& ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h1),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),V0p2) = ap(ap(c_2Epoly_2E_23_23,V1h1),V0p2)
& ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h1),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V2k1),V3t1))),V0p2) = ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2E_23_23,V1h1),V0p2)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V2k1),V3t1)),V0p2))) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__CLAUSES,axiom,
! [V0c] :
( mem(V0c,ty_2Erealax_2Ereal)
=> ! [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Ediff,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
& ap(c_2Epoly_2Ediff,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0c),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
& ap(c_2Epoly_2Ediff,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V2t)) = ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V2t) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ADD,axiom,
! [V0p1] :
( mem(V0p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1p2] :
( mem(V1p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,V0p1),V1p2)),V2x) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Epoly_2Epoly,V0p1),V2x)),ap(ap(c_2Epoly_2Epoly,V1p2),V2x)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__CMUL,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1c] :
( mem(V1c,ty_2Erealax_2Ereal)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,V1c),V0p)),V2x) = ap(ap(c_2Erealax_2Ereal__mul,V1c),ap(ap(c_2Epoly_2Epoly,V0p),V2x)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__NEG,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Epoly__neg,V0p)),V1x) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Epoly_2Epoly,V0p),V1x)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__MUL,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1p1] :
( mem(V1p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2p2] :
( mem(V2p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V1p1),V2p2)),V0x) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epoly_2Epoly,V1p1),V0x)),ap(ap(c_2Epoly_2Epoly,V2p2),V0x)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__EXP,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,V0p),V1n)),V2x) = ap(ap(c_2Ereal_2Epow,ap(ap(c_2Epoly_2Epoly,V0p),V2x)),V1n) ) ) ) ).
fof(lameq_f2834,axiom,
! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V3x] : ap(f2834(V1n,V0l),V3x) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,V3x),ap(c_2Enum_2ESUC,V1n))),ap(ap(c_2Epoly_2Epoly,V0l),V3x)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__LEMMA,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2834(V1n,V0l)),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,V2x),V1n)),ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,V1n)),V0l)),V2x))),V2x)) ) ) ) ).
fof(lameq_f2835,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2x] : ap(f2835(V0l),V2x) = ap(ap(c_2Epoly_2Epoly,V0l),V2x) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2835(V0l)),ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0l)),V1x)),V1x)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFFERENTIABLE,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Elim_2Edifferentiable,f2835(V0l)),V1x)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__CONT,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Elim_2Econtl,f2835(V0l)),V1x)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__IVT__POS,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V1a),V2b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Epoly_2Epoly,V0p),V1a)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
& p(ap(ap(c_2Ereal_2Ereal__gt,ap(ap(c_2Epoly_2Epoly,V0p),V2b)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
=> ? [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,V1a),V3x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V3x),V2b))
& ap(ap(c_2Epoly_2Epoly,V0p),V3x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__IVT__NEG,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V1a),V2b))
& p(ap(ap(c_2Ereal_2Ereal__gt,ap(ap(c_2Epoly_2Epoly,V0p),V1a)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Epoly_2Epoly,V0p),V2b)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
=> ? [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,V1a),V3x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V3x),V2b))
& ap(ap(c_2Epoly_2Epoly,V0p),V3x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__MVT,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2b] :
( mem(V2b,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,V1a),V2b))
=> ? [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Erealax_2Ereal__lt,V1a),V3x))
& p(ap(ap(c_2Erealax_2Ereal__lt,V3x),V2b))
& ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Epoly_2Epoly,V0p),V2b)),ap(ap(c_2Epoly_2Epoly,V0p),V1a)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,V2b),V1a)),ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)),V3x)) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ADD__RZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,V0p),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = ap(c_2Epoly_2Epoly,V0p) ) ).
fof(conj_thm_2Epoly_2EPOLY__MUL__ASSOC,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2r] :
( mem(V2r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V0p),ap(ap(c_2Epoly_2Epoly__mul,V1q),V2r))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Epoly_2Epoly__mul,V0p),V1q)),V2r)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__EXP__ADD,axiom,
! [V0d] :
( mem(V0d,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,V2p),ap(ap(c_2Earithmetic_2E_2B,V1n),V0d))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Epoly_2Epoly__exp,V2p),V1n)),ap(ap(c_2Epoly_2Epoly__exp,V2p),V0d))) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__AUX__ADD,axiom,
! [V0p1] :
( mem(V0p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1p2] :
( mem(V1p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,V2n),ap(ap(c_2Epoly_2Epoly__add,V0p1),V1p2))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__diff__aux,V2n),V0p1)),ap(ap(c_2Epoly_2Epoly__diff__aux,V2n),V1p2))) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__AUX__CMUL,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1c] :
( mem(V1c,ty_2Erealax_2Ereal)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,V2n),ap(ap(c_2Epoly_2E_23_23,V1c),V0p))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,V1c),ap(ap(c_2Epoly_2Epoly__diff__aux,V2n),V0p))) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__AUX__NEG,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,V1n),ap(c_2Epoly_2Epoly__neg,V0p))) = ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Epoly__neg,ap(ap(c_2Epoly_2Epoly__diff__aux,V1n),V0p))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__AUX__MUL__LEMMA,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,V1n)),V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__diff__aux,V1n),V0p)),V0p)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__ADD,axiom,
! [V0p1] :
( mem(V0p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1p2] :
( mem(V1p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__add,V0p1),V1p2))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(c_2Epoly_2Ediff,V0p1)),ap(c_2Epoly_2Ediff,V1p2))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__CMUL,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1c] :
( mem(V1c,ty_2Erealax_2Ereal)
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2E_23_23,V1c),V0p))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,V1c),ap(c_2Epoly_2Ediff,V0p))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__NEG,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(c_2Epoly_2Epoly__neg,V0p))) = ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Epoly__neg,ap(c_2Epoly_2Ediff,V0p))) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__MUL__LEMMA,axiom,
! [V0t] :
( mem(V0t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),V0t))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Epoly_2Ediff,V0t))),V0t)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__MUL,axiom,
! [V0p1] :
( mem(V0p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1p2] :
( mem(V1p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__mul,V0p1),V1p2))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__mul,V0p1),ap(c_2Epoly_2Ediff,V1p2))),ap(ap(c_2Epoly_2Epoly__mul,ap(c_2Epoly_2Ediff,V0p1)),V1p2))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__EXP,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__exp,V0p),ap(c_2Enum_2ESUC,V1n)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Epoly_2E_23_23,ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,V1n))),ap(ap(c_2Epoly_2Epoly__exp,V0p),V1n))),ap(c_2Epoly_2Ediff,V0p))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__EXP__PRIME,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,V0n)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,V0n))),ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V0n))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__LINEAR__REM,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2h] :
( mem(V2h,ty_2Erealax_2Ereal)
=> ? [V3q] :
( mem(V3q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
& ? [V4r] :
( mem(V4r,ty_2Erealax_2Ereal)
& ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V2h),V1t) = ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V4r),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V3q)) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__LINEAR__DIVIDES,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(ap(c_2Epoly_2Epoly,V1p),V0a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
<=> ( V1p = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
| ? [V2q] :
( mem(V2q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
& V1p = ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2q) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__LENGTH__MUL,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V1q)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),V1q)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ROOTS__INDEX__LEMMA,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( ap(c_2Epoly_2Epoly,V1p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),V1p) = V0n )
=> ? [V2i] :
( mem(V2i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly,V1p),V3x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
=> ? [V4m] :
( mem(V4m,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V4m),V0n))
& V3x = ap(V2i,V4m) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ROOTS__INDEX__LENGTH,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ? [V1i] :
( mem(V1i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly,V0p),V2x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V3n),ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),V0p)))
& V2x = ap(V1i,V3n) ) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ROOTS__FINITE__LEMMA,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ? [V1N] :
( mem(V1N,ty_2Enum_2Enum)
& ? [V2i] :
( mem(V2i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly,V0p),V3x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
=> ? [V4n] :
( mem(V4n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4n),V1N))
& V3x = ap(V2i,V4n) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EFINITE__LEMMA,axiom,
! [V0i] :
( mem(V0i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1N] :
( mem(V1N,ty_2Enum_2Enum)
=> ! [V2P] :
( mem(V2P,arr(ty_2Erealax_2Ereal,bool))
=> ( ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ( p(ap(V2P,V3x))
=> ? [V4n] :
( mem(V4n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4n),V1N))
& V3x = ap(V0i,V4n) ) ) )
=> ? [V5a] :
( mem(V5a,ty_2Erealax_2Ereal)
& ! [V6x] :
( mem(V6x,ty_2Erealax_2Ereal)
=> ( p(ap(V2P,V6x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,V6x),V5a)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ROOTS__FINITE,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
<=> ? [V1N] :
( mem(V1N,ty_2Enum_2Enum)
& ? [V2i] :
( mem(V2i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly,V0p),V3x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
=> ? [V4n] :
( mem(V4n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4n),V1N))
& V3x = ap(V2i,V4n) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ENTIRE__LEMMA,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& ap(c_2Epoly_2Epoly,V1q) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V0p),V1q)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ENTIRE,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V0p),V1q)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
<=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
| ap(c_2Epoly_2Epoly,V1q) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__MUL__LCANCEL,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2r] :
( mem(V2r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V0p),V1q)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V0p),V2r))
<=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
| ap(c_2Epoly_2Epoly,V1q) = ap(c_2Epoly_2Epoly,V2r) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__EXP__EQ__0,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,V0p),V1n)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
<=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& V1n != c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__PRIME__EQ__0,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0a),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ).
fof(conj_thm_2Epoly_2EPOLY__EXP__PRIME__EQ__0,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0a),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V1n)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ZERO__LEMMA,axiom,
! [V0h] :
( mem(V0h,ty_2Erealax_2Ereal)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0h),V1t)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ( V0h = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& ap(c_2Epoly_2Epoly,V1t) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ) ).
fof(lameq_f2836,axiom,
! [V1c] : ap(f2836,V1c) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V1c),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ).
fof(conj_thm_2Epoly_2EPOLY__ZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
<=> p(ap(ap(c_2Elist_2EEVERY(ty_2Erealax_2Ereal),f2836),V0p)) ) ) ).
fof(lameq_f2837,axiom,
! [V2c] : ap(f2837,V2c) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V2c),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ).
fof(lameq_f2838,axiom,
! [V3c] : ap(f2838,V3c) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V3c),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__AUX__ISZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Elist_2EEVERY(ty_2Erealax_2Ereal),f2837),ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,V1n)),V0p)))
<=> p(ap(ap(c_2Elist_2EEVERY(ty_2Erealax_2Ereal),f2838),V0p)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__ISZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ? [V1h] :
( mem(V1h,ty_2Erealax_2Ereal)
& ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V1h),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__ZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIFF__WELLDEF,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,V1q)
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) = ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V1q)) ) ) ) ).
fof(ax_thm_2Epoly_2Epoly__divides,axiom,
! [V0p1] :
( mem(V0p1,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1p2] :
( mem(V1p2,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Epoly_2Epoly__divides,V0p1),V1p2))
<=> ? [V2q] :
( mem(V2q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
& ap(c_2Epoly_2Epoly,V1p2) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V0p1),V2q)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__PRIMES,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2q] :
( mem(V2q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0a),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Epoly_2Epoly__mul,V1p),V2q)))
<=> ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0a),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V1p))
| p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0a),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2q)) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__REFL,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V0p)) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__TRANS,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2r] :
( mem(V2r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V1q))
& p(ap(ap(c_2Epoly_2Epoly__divides,V1q),V2r)) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V2r)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__EXP,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
=> p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,V0p),V1m)),ap(ap(c_2Epoly_2Epoly__exp,V0p),V2n))) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__EXP__DIVIDES,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,V0p),V3n)),V1q))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V3n)) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,V0p),V2m)),V1q)) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__ADD,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2r] :
( mem(V2r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V1q))
& p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V2r)) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,V0p),ap(ap(c_2Epoly_2Epoly__add,V1q),V2r))) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__SUB,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2r] :
( mem(V2r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V1q))
& p(ap(ap(c_2Epoly_2Epoly__divides,V0p),ap(ap(c_2Epoly_2Epoly__add,V1q),V2r))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V2r)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__SUB2,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2r] :
( mem(V2r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V2r))
& p(ap(ap(c_2Epoly_2Epoly__divides,V0p),ap(ap(c_2Epoly_2Epoly__add,V1q),V2r))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,V0p),V1q)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__DIVIDES__ZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> p(ap(ap(c_2Epoly_2Epoly__divides,V1q),V0p)) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ORDER__EXISTS,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1d] :
( mem(V1d,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),V2p) = V1d
& ap(c_2Epoly_2Epoly,V2p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V3n)),V2p))
& ~ p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,V3n))),V2p)) ) ) ) ) ) ).
fof(lameq_f2839,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2n] : ap(f2839(V0p,V1a),V2n) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2n)),V0p)),ap(c_2Ebool_2E_7E,ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,V2n))),V0p))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__ORDER,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> p(ap(c_2Ebool_2E_3F_21(ty_2Enum_2Enum),f2839(V0p,V1a))) ) ) ) ).
fof(lameq_f2840,axiom,
! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V2n] : ap(f2840(V1p,V0a),V2n) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2n)),V1p)),ap(c_2Ebool_2E_7E,ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V0a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,V2n))),V1p))) ) ) ).
fof(ax_thm_2Epoly_2Epoly__order,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__order,V0a),V1p) = ap(c_2Emin_2E_40(ty_2Enum_2Enum),f2840(V1p,V0a)) ) ) ).
fof(conj_thm_2Epoly_2EORDER,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2n)),V0p))
& ~ p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,V2n))),V0p)) )
<=> ( V2n = ap(ap(c_2Epoly_2Epoly__order,V1a),V0p)
& ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__THM,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Epoly_2Epoly__order,V1a),V0p))),V0p))
& ~ p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,ap(ap(c_2Epoly_2Epoly__order,V1a),V0p)))),V0p)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__UNIQUE,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2n)),V0p))
& ~ p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,V2n))),V0p)) )
=> V2n = ap(ap(c_2Epoly_2Epoly__order,V1a),V0p) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__POLY,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2a] :
( mem(V2a,ty_2Erealax_2Ereal)
=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,V1q)
=> ap(ap(c_2Epoly_2Epoly__order,V2a),V0p) = ap(ap(c_2Epoly_2Epoly__order,V2a),V1q) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__ROOT,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly,V0p),V1a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
<=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
| ap(ap(c_2Epoly_2Epoly__order,V1a),V0p) != c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__DIVIDES,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2n)),V0p))
<=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),ap(ap(c_2Epoly_2Epoly__order,V1a),V0p))) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__DECOMP,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ? [V2q] :
( mem(V2q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
& ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Epoly_2Epoly__order,V1a),V0p))),V2q))
& ~ p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2q)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__MUL,axiom,
! [V0a] :
( mem(V0a,ty_2Erealax_2Ereal)
=> ! [V1p] :
( mem(V1p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2q] :
( mem(V2q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V1p),V2q)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ap(ap(c_2Epoly_2Epoly__order,V0a),ap(ap(c_2Epoly_2Epoly__mul,V1p),V2q)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Epoly_2Epoly__order,V0a),V1p)),ap(ap(c_2Epoly_2Epoly__order,V0a),V2q)) ) ) ) ) ).
fof(conj_thm_2Epoly_2EORDER__DIFF,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& ap(ap(c_2Epoly_2Epoly__order,V1a),V0p) != c_2Enum_2E0 )
=> ap(ap(c_2Epoly_2Epoly__order,V1a),V0p) = ap(c_2Enum_2ESUC,ap(ap(c_2Epoly_2Epoly__order,V1a),ap(c_2Epoly_2Ediff,V0p))) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__SQUAREFREE__DECOMP__ORDER,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2d] :
( mem(V2d,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V3e] :
( mem(V3e,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V4r] :
( mem(V4r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V5s] :
( mem(V5s,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V1q),V2d))
& ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V3e),V2d))
& ap(c_2Epoly_2Epoly,V2d) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__mul,V4r),V0p)),ap(ap(c_2Epoly_2Epoly__mul,V5s),ap(c_2Epoly_2Ediff,V0p)))) )
=> ! [V6a] :
( mem(V6a,ty_2Erealax_2Ereal)
=> ap(ap(c_2Epoly_2Epoly__order,V6a),V1q) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Epoly_2Epoly__order,V6a),V0p)),c_2Enum_2E0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Epoly_2Ersquarefree,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( p(ap(c_2Epoly_2Ersquarefree,V0p))
<=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly__order,V1a),V0p) = c_2Enum_2E0
| ap(ap(c_2Epoly_2Epoly__order,V1a),V0p) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ) ) ).
fof(conj_thm_2Epoly_2ERSQUAREFREE__ROOTS,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( p(ap(c_2Epoly_2Ersquarefree,V0p))
<=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ~ ( ap(ap(c_2Epoly_2Epoly,V0p),V1a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
& ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)),V1a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Epoly_2ERSQUAREFREE__DECOMP,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1a] :
( mem(V1a,ty_2Erealax_2Ereal)
=> ( ( p(ap(c_2Epoly_2Ersquarefree,V0p))
& ap(ap(c_2Epoly_2Epoly,V0p),V1a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) )
=> ? [V2q] :
( mem(V2q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
& ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,V1a)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),V2q))
& ap(ap(c_2Epoly_2Epoly,V2q),V1a) != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__SQUAREFREE__DECOMP,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1q] :
( mem(V1q,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V2d] :
( mem(V2d,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V3e] :
( mem(V3e,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V4r] :
( mem(V4r,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V5s] :
( mem(V5s,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
& ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V1q),V2d))
& ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,V3e),V2d))
& ap(c_2Epoly_2Epoly,V2d) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__mul,V4r),V0p)),ap(ap(c_2Epoly_2Epoly__mul,V5s),ap(c_2Epoly_2Ediff,V0p)))) )
=> ( p(ap(c_2Epoly_2Ersquarefree,V1q))
& ! [V6a] :
( mem(V6a,ty_2Erealax_2Ereal)
=> ( ap(ap(c_2Epoly_2Epoly,V1q),V6a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)
<=> ap(ap(c_2Epoly_2Epoly,V0p),V6a) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Epoly_2Enormalize,axiom,
( ap(c_2Epoly_2Enormalize,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) = c_2Elist_2ENIL(ty_2Erealax_2Ereal)
& ! [V0h] :
( mem(V0h,ty_2Erealax_2Ereal)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Enormalize,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(c_2Epoly_2Enormalize,V1t)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V0h),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0h),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),V0h),ap(c_2Epoly_2Enormalize,V1t))) ) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__NORMALIZE,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Enormalize,V0p)) = ap(c_2Epoly_2Epoly,V0p) ) ).
fof(ax_thm_2Epoly_2Edegree,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Edegree,V0p) = ap(c_2Eprim__rec_2EPRE,ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),ap(c_2Epoly_2Enormalize,V0p))) ) ).
fof(conj_thm_2Epoly_2EDEGREE__ZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> ap(c_2Epoly_2Edegree,V0p) = c_2Enum_2E0 ) ) ).
fof(lameq_f2841,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ! [V1x] : ap(f2841(V0p),V1x) = ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,bool),V1x),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(ap(c_2Epoly_2Epoly,V0p),V1x)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ).
fof(conj_thm_2Epoly_2EPOLY__ROOTS__FINITE__SET,axiom,
! [V0p] :
( mem(V0p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( ap(c_2Epoly_2Epoly,V0p) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal))
=> p(ap(c_2Epred__set_2EFINITE(ty_2Erealax_2Ereal),ap(c_2Epred__set_2EGSPEC(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),f2841(V0p)))) ) ) ).
fof(conj_thm_2Epoly_2EPOLY__MONO,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1k] :
( mem(V1k,ty_2Erealax_2Ereal)
=> ! [V2p] :
( mem(V2p,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V0x)),V1k))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Epoly_2Epoly,V2p),V0x))),ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2EMAP(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),c_2Ereal_2Eabs),V2p)),V1k))) ) ) ) ) ).
%------------------------------------------------------------------------------