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 : 150 ( 61 unt; 29 typ; 0 def)
% Number of atoms : 2649 ( 157 equ)
% Maximal formula atoms : 7 ( 17 avg)
% Number of connectives : 158 ( 31 ~; 7 |; 63 &)
% ( 15 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2401 (2401 fml; 0 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 55 ( 54 usr; 30 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 16 con; 0-2 aty)
% Number of variables : 282 ( 259 !; 23 ?; 282 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(stp_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,type,
tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal: $tType ).
tff(stp_inj_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,type,
inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal > $i ).
tff(stp_surj_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,type,
surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal: $i > tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal ).
tff(stp_inj_surj_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,axiom,
! [X: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,axiom,
! [X: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : mem(inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X),ty_2Elist_2Elist(ty_2Erealax_2Ereal)) ).
tff(stp_iso_mem_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,axiom,
! [X: $i] :
( mem(X,ty_2Elist_2Elist(ty_2Erealax_2Ereal))
=> ( X = inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X)) ) ) ).
tff(tp_c_2Epoly_2E_23_23,type,
c_2Epoly_2E_23_23: $i ).
tff(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)))) ).
tff(tp_c_2Epoly_2Edegree,type,
c_2Epoly_2Edegree: $i ).
tff(mem_c_2Epoly_2Edegree,axiom,
mem(c_2Epoly_2Edegree,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Epoly_2Edegree,type,
fo__c_2Epoly_2Edegree: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Epoly_2Edegree,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( inj__ty_2Enum_2Enum(fo__c_2Epoly_2Edegree(X0)) = ap(c_2Epoly_2Edegree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X0)) ) ).
tff(tp_c_2Epoly_2Ediff,type,
c_2Epoly_2Ediff: $i ).
tff(mem_c_2Epoly_2Ediff,axiom,
mem(c_2Epoly_2Ediff,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal))) ).
tff(tp_c_2Epoly_2Enormalize,type,
c_2Epoly_2Enormalize: $i ).
tff(mem_c_2Epoly_2Enormalize,axiom,
mem(c_2Epoly_2Enormalize,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal))) ).
tff(tp_c_2Epoly_2Epoly,type,
c_2Epoly_2Epoly: $i ).
tff(mem_c_2Epoly_2Epoly,axiom,
mem(c_2Epoly_2Epoly,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Epoly_2Epoly,type,
fo__c_2Epoly_2Epoly: ( tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Epoly_2Epoly,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : ( inj__ty_2Erealax_2Ereal(fo__c_2Epoly_2Epoly(X0,X1)) = ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ) ).
tff(tp_c_2Epoly_2Epoly__add,type,
c_2Epoly_2Epoly__add: $i ).
tff(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)))) ).
tff(tp_c_2Epoly_2Epoly__diff__aux,type,
c_2Epoly_2Epoly__diff__aux: $i ).
tff(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)))) ).
tff(tp_c_2Epoly_2Epoly__divides,type,
c_2Epoly_2Epoly__divides: $i ).
tff(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))) ).
tff(stp_fo_c_2Epoly_2Epoly__divides,type,
fo__c_2Epoly_2Epoly__divides: ( tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal * tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal ) > tp__o ).
tff(stp_eq_fo_c_2Epoly_2Epoly__divides,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,X1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( inj__o(fo__c_2Epoly_2Epoly__divides(X0,X1)) = ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X0)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X1)) ) ).
tff(tp_c_2Epoly_2Epoly__exp,type,
c_2Epoly_2Epoly__exp: $i ).
tff(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)))) ).
tff(tp_c_2Epoly_2Epoly__mul,type,
c_2Epoly_2Epoly__mul: $i ).
tff(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)))) ).
tff(tp_c_2Epoly_2Epoly__neg,type,
c_2Epoly_2Epoly__neg: $i ).
tff(mem_c_2Epoly_2Epoly__neg,axiom,
mem(c_2Epoly_2Epoly__neg,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),ty_2Elist_2Elist(ty_2Erealax_2Ereal))) ).
tff(tp_c_2Epoly_2Epoly__order,type,
c_2Epoly_2Epoly__order: $i ).
tff(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))) ).
tff(stp_fo_c_2Epoly_2Epoly__order,type,
fo__c_2Epoly_2Epoly__order: ( tp__ty_2Erealax_2Ereal * tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal ) > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Epoly_2Epoly__order,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( inj__ty_2Enum_2Enum(fo__c_2Epoly_2Epoly__order(X0,X1)) = ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(X0)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X1)) ) ).
tff(tp_c_2Epoly_2Ersquarefree,type,
c_2Epoly_2Ersquarefree: $i ).
tff(mem_c_2Epoly_2Ersquarefree,axiom,
mem(c_2Epoly_2Ersquarefree,arr(ty_2Elist_2Elist(ty_2Erealax_2Ereal),bool)) ).
tff(stp_fo_c_2Epoly_2Ersquarefree,type,
fo__c_2Epoly_2Ersquarefree: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal > tp__o ).
tff(stp_eq_fo_c_2Epoly_2Ersquarefree,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( inj__o(fo__c_2Epoly_2Ersquarefree(X0)) = ap(c_2Epoly_2Ersquarefree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(X0)) ) ).
tff(ax_thm_2Epoly_2Epoly__def,axiom,
( ! [V0x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ! [V1h: tp__ty_2Erealax_2Ereal,V2t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t))),inj__ty_2Erealax_2Ereal(V3x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1h)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V3x)),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)),inj__ty_2Erealax_2Ereal(V3x))))) ) ) ).
tff(ax_thm_2Epoly_2Epoly__add__def,axiom,
( ! [V0l2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l2))) = V0l2 )
& ! [V1h: tp__ty_2Erealax_2Ereal,V2t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V3l2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1h)),ap(c_2Elist_2EHD(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2)))),ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)),ap(c_2Elist_2ETL(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2)))))) ) ) ).
tff(ax_thm_2Epoly_2Epoly__cmul__def,axiom,
( ! [V0c: tp__ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V0c)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ! [V1c: tp__ty_2Erealax_2Ereal,V2h: tp__ty_2Erealax_2Ereal,V3t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),inj__ty_2Erealax_2Ereal(V2h))),ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t)))) ) ) ).
tff(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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ).
tff(ax_thm_2Epoly_2Epoly__mul__def,axiom,
( ! [V0l2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l2))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ! [V1h: tp__ty_2Erealax_2Ereal,V2t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V3l2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2))),ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3l2)))))) ) ) ).
tff(ax_thm_2Epoly_2Epoly__exp__def,axiom,
( ! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) )
& ! [V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),inj__ty_2Enum_2Enum(V2n)))) ) ) ).
tff(ax_thm_2Epoly_2Epoly__diff__aux__def,axiom,
( ! [V0n: tp__ty_2Enum_2Enum] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V0n)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ! [V1n: tp__ty_2Enum_2Enum,V2h: tp__ty_2Erealax_2Ereal,V3t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V1n)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))),inj__ty_2Erealax_2Ereal(V2h))),ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t)))) ) ) ).
tff(ax_thm_2Epoly_2Epoly__diff__def,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Erealax_2Ereal)),inj__c_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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ETL(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l))))) ) ).
tff(conj_thm_2Epoly_2EPOLY__ADD__CLAUSES,axiom,
! [V0p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2h1: tp__ty_2Erealax_2Ereal,V3t1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V4h2: tp__ty_2Erealax_2Ereal,V5t2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))) = V0p2 )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p1)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = V1p1 )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2h1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t1))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V4h2)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V5t2)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V2h1)),inj__ty_2Erealax_2Ereal(V4h2))),ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V5t2)))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__CMUL__CLAUSES,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1h: tp__ty_2Erealax_2Ereal,V2t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V0c)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V0c)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Erealax_2Ereal(V1h))),ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V0c)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__NEG__CLAUSES,axiom,
! [V0h: tp__ty_2Erealax_2Ereal,V1t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Epoly__neg,c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Epoly__neg,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0h))),ap(c_2Epoly_2Epoly__neg,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t)))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__MUL__CLAUSES,axiom,
! [V0p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1h1: tp__ty_2Erealax_2Ereal,V2k1: tp__ty_2Erealax_2Ereal,V3t1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,c_2Elist_2ENIL(ty_2Erealax_2Ereal)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h1)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1h1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))) )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h1)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2k1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t1)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1h1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2k1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3t1))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p2))))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__CLAUSES,axiom,
! [V0c: tp__ty_2Erealax_2Ereal,V1h: tp__ty_2Erealax_2Ereal,V2t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Ediff,c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Ediff,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0c)),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Ediff,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2t))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ADD,axiom,
! [V0p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2))),inj__ty_2Erealax_2Ereal(V2x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__ty_2Erealax_2Ereal(V2x))),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)),inj__ty_2Erealax_2Ereal(V2x)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__CMUL,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1c: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),inj__ty_2Erealax_2Ereal(V2x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V2x)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__NEG,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Epoly__neg,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),inj__ty_2Erealax_2Ereal(V1x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1x)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__MUL,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p2))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p1)),inj__ty_2Erealax_2Ereal(V0x))),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p2)),inj__ty_2Erealax_2Ereal(V0x)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__EXP,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V1n))),inj__ty_2Erealax_2Ereal(V2x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V2x))),inj__ty_2Enum_2Enum(V1n))) ) ).
tff(lamtp_f2834,type,
f2834: ( tp__ty_2Enum_2Enum * tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2834,axiom,
! [V1n: tp__ty_2Enum_2Enum,V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V3x: tp__ty_2Erealax_2Ereal] : ( ap(f2834(V1n,V0l),inj__ty_2Erealax_2Ereal(V3x)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V3x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n)))),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l)),inj__ty_2Erealax_2Ereal(V3x))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__LEMMA,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,f2834(V1n,V0l)),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V1n))),ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l))),inj__ty_2Erealax_2Ereal(V2x)))),inj__ty_2Erealax_2Ereal(V2x))) ).
tff(lamtp_f2835,type,
f2835: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal > $i ).
tff(lameq_f2835,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] : ( ap(f2835(V0l),inj__ty_2Erealax_2Ereal(V2x)) = ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l)),inj__ty_2Erealax_2Ereal(V2x)) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(ap(c_2Elim_2Ediffl,f2835(V0l)),ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0l))),inj__ty_2Erealax_2Ereal(V1x))),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(conj_thm_2Epoly_2EPOLY__DIFFERENTIABLE,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Elim_2Edifferentiable,f2835(V0l)),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(conj_thm_2Epoly_2EPOLY__CONT,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Elim_2Econtl,f2835(V0l)),inj__ty_2Erealax_2Ereal(V1x))) ).
tff(conj_thm_2Epoly_2EPOLY__IVT__POS,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1a))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))
& p(ap(ap(c_2Ereal_2Ereal__gt,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V2b))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) )
=> ? [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V3x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__IVT__NEG,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
& p(ap(ap(c_2Ereal_2Ereal__gt,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1a))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V2b))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) )
=> ? [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V3x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__MVT,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V2b)))
=> ? [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1a)),inj__ty_2Erealax_2Ereal(V3x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V3x)),inj__ty_2Erealax_2Ereal(V2b)))
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V2b))),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1a)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2b)),inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),inj__ty_2Erealax_2Ereal(V3x)))) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ADD__RZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) ) ).
tff(conj_thm_2Epoly_2EPOLY__MUL__ASSOC,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r))) ) ).
tff(conj_thm_2Epoly_2EPOLY__EXP__ADD,axiom,
! [V0d: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0d)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p)),inj__ty_2Enum_2Enum(V1n))),ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p)),inj__ty_2Enum_2Enum(V0d)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__AUX__ADD,axiom,
! [V0p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V2n)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1))),ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V2n)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__AUX__CMUL,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1c: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V2n)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__AUX__NEG,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V1n)),ap(c_2Epoly_2Epoly__neg,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) = ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Epoly__neg,ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V1n)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__AUX__MUL__LEMMA,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__diff__aux,inj__ty_2Enum_2Enum(V1n)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__ADD,axiom,
! [V0p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1))),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__CMUL,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1c: tp__ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,inj__ty_2Erealax_2Ereal(V1c)),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__NEG,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(c_2Epoly_2Epoly__neg,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) = ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Epoly__neg,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__MUL__LEMMA,axiom,
! [V0t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1h: tp__ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0t)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0t))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__MUL,axiom,
! [V0p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))),ap(ap(c_2Epoly_2Epoly__mul,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__EXP,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(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,inj__ty_2Enum_2Enum(V1n)))),ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V1n)))),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__EXP__PRIME,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1a: tp__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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2E_23_23,ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V0n)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__LINEAR__REM,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2h: tp__ty_2Erealax_2Ereal] :
? [V3q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V4r: tp__ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__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,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3q)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__LINEAR__DIVIDES,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),inj__ty_2Erealax_2Ereal(V0a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( ( V1p = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
| ? [V2q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( V1p = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__LENGTH__MUL,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__ty_2Enum_2Enum(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,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__ROOTS__INDEX__LEMMA,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p))) = V0n ) )
=> ? [V2i: $i] :
( mem(V2i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),inj__ty_2Erealax_2Ereal(V3x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ? [V4m: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V4m)),inj__ty_2Enum_2Enum(V0n)))
& ( V3x = surj__ty_2Erealax_2Ereal(ap(V2i,inj__ty_2Enum_2Enum(V4m))) ) ) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ROOTS__INDEX__LENGTH,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ? [V1i: $i] :
( mem(V1i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V2x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V2x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ? [V3n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V3n)),ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))
& ( V2x = surj__ty_2Erealax_2Ereal(ap(V1i,inj__ty_2Enum_2Enum(V3n))) ) ) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ROOTS__FINITE__LEMMA,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ? [V1N: tp__ty_2Enum_2Enum,V2i: $i] :
( mem(V2i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V3x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ? [V4n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),inj__ty_2Enum_2Enum(V1N)))
& ( V3x = surj__ty_2Erealax_2Ereal(ap(V2i,inj__ty_2Enum_2Enum(V4n))) ) ) ) ) ) ).
tff(conj_thm_2Epoly_2EFINITE__LEMMA,axiom,
! [V0i: $i] :
( mem(V0i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1N: tp__ty_2Enum_2Enum,V2P: $i] :
( mem(V2P,arr(ty_2Erealax_2Ereal,bool))
=> ( ! [V3x: tp__ty_2Erealax_2Ereal] :
( p(ap(V2P,inj__ty_2Erealax_2Ereal(V3x)))
=> ? [V4n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),inj__ty_2Enum_2Enum(V1N)))
& ( V3x = surj__ty_2Erealax_2Ereal(ap(V0i,inj__ty_2Enum_2Enum(V4n))) ) ) )
=> ? [V5a: tp__ty_2Erealax_2Ereal] :
! [V6x: tp__ty_2Erealax_2Ereal] :
( p(ap(V2P,inj__ty_2Erealax_2Ereal(V6x)))
=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Erealax_2Ereal(V5a))) ) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ROOTS__FINITE,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
<=> ? [V1N: tp__ty_2Enum_2Enum,V2i: $i] :
( mem(V2i,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
& ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V3x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ? [V4n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),inj__ty_2Enum_2Enum(V1N)))
& ( V3x = surj__ty_2Erealax_2Ereal(ap(V2i,inj__ty_2Enum_2Enum(V4n))) ) ) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ENTIRE__LEMMA,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) )
=> ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__ENTIRE,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
<=> ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
| ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__MUL__LCANCEL,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r))) )
<=> ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
| ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)) = ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r)) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__EXP__EQ__0,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] :
( ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V1n))) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
<=> ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( V1n != fo__c_2Enum_2E0 ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__PRIME__EQ__0,axiom,
! [V0a: tp__ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ).
tff(conj_thm_2Epoly_2EPOLY__EXP__PRIME__EQ__0,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] : ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__exp,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V1n))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ).
tff(conj_thm_2Epoly_2EPOLY__ZERO__LEMMA,axiom,
! [V0h: tp__ty_2Erealax_2Ereal,V1t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t))) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ( ( V0h = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ).
tff(lamtp_f2836,type,
f2836: $i ).
tff(lameq_f2836,axiom,
! [V1c: tp__ty_2Erealax_2Ereal] : ( ap(f2836,inj__ty_2Erealax_2Ereal(V1c)) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1c)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ).
tff(conj_thm_2Epoly_2EPOLY__ZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
<=> p(ap(ap(c_2Elist_2EEVERY(ty_2Erealax_2Ereal),f2836),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ) ).
tff(lamtp_f2837,type,
f2837: $i ).
tff(lameq_f2837,axiom,
! [V2c: tp__ty_2Erealax_2Ereal] : ( ap(f2837,inj__ty_2Erealax_2Ereal(V2c)) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2c)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ).
tff(lamtp_f2838,type,
f2838: $i ).
tff(lameq_f2838,axiom,
! [V3c: tp__ty_2Erealax_2Ereal] : ( ap(f2838,inj__ty_2Erealax_2Ereal(V3c)) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V3c)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__AUX__ISZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Elist_2EEVERY(ty_2Erealax_2Ereal),f2837),ap(ap(c_2Epoly_2Epoly__diff__aux,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))
<=> p(ap(ap(c_2Elist_2EEVERY(ty_2Erealax_2Ereal),f2838),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__ISZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ? [V1h: tp__ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1h)),c_2Elist_2ENIL(ty_2Erealax_2Ereal))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__ZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIFF__WELLDEF,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)) )
=> ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) ) ) ).
tff(ax_thm_2Epoly_2Epoly__divides,axiom,
! [V0p1: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1p2: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)))
<=> ? [V2q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p2)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p1)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__PRIMES,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))))
<=> ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)))
| p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__REFL,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__TRANS,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))
& p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__EXP,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))
=> p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V1m))),ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V2n)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__EXP__DIVIDES,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V3n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Epoly_2Epoly__exp,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Enum_2Enum(V2m))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__ADD,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))
& p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__SUB,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))
& p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r)))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__SUB2,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r)))
& p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),ap(ap(c_2Epoly_2Epoly__add,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2r)))) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) ) ).
tff(conj_thm_2Epoly_2EPOLY__DIVIDES__ZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> p(ap(ap(c_2Epoly_2Epoly__divides,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ) ).
tff(conj_thm_2Epoly_2EPOLY__ORDER__EXISTS,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1d: tp__ty_2Enum_2Enum,V2p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ( surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p))) = V1d )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) )
=> ? [V3n: tp__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,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V3n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V3n)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p))) ) ) ).
tff(lamtp_f2839,type,
f2839: ( tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2839,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : ( ap(f2839(V0p,V1a),inj__ty_2Enum_2Enum(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V2n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__ORDER,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> p(ap(c_2Ebool_2E_3F_21(ty_2Enum_2Enum),f2839(V0p,V1a))) ) ).
tff(lamtp_f2840,type,
f2840: ( tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2840,axiom,
! [V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V0a: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : ( ap(f2840(V1p,V0a),inj__ty_2Enum_2Enum(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,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V2n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__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,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)))) ) ).
tff(ax_thm_2Epoly_2Epoly__order,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V0a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p))) = surj__ty_2Enum_2Enum(ap(c_2Emin_2E_40(ty_2Enum_2Enum),f2840(V1p,V0a))) ) ).
tff(conj_thm_2Epoly_2EORDER,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2n: tp__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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V2n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) )
<=> ( ( V2n = surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) ) ) ) ).
tff(conj_thm_2Epoly_2EORDER__THM,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ) ) ).
tff(conj_thm_2Epoly_2EORDER__UNIQUE,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] :
( ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V2n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) )
=> ( V2n = surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) ) ) ).
tff(conj_thm_2Epoly_2EORDER__POLY,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2a: tp__ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)) )
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V2a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V2a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) ) ) ).
tff(conj_thm_2Epoly_2EORDER__ROOT,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
| ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) != fo__c_2Enum_2E0 ) ) ) ).
tff(conj_thm_2Epoly_2EORDER__DIVIDES,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal,V2n: tp__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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__ty_2Enum_2Enum(V2n))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))
<=> ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
| p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))) ) ) ).
tff(conj_thm_2Epoly_2EORDER__DECOMP,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ? [V2q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) )
& ~ p(ap(ap(c_2Epoly_2Epoly__divides,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) ) ) ).
tff(conj_thm_2Epoly_2EORDER__MUL,axiom,
! [V0a: tp__ty_2Erealax_2Ereal,V1p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V0a)),ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V0a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1p))),ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V0a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q)))) ) ) ).
tff(conj_thm_2Epoly_2EORDER__DIFF,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal] :
( ( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) != fo__c_2Enum_2E0 ) )
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__SQUAREFREE__DECOMP__ORDER,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2d: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V3e: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V4r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V5s: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2d))) )
& ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3e)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2d))) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2d)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V4r)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V5s)),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))) ) )
=> ! [V6a: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V6a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V6a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) ) ).
tff(ax_thm_2Epoly_2Ersquarefree,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( p(ap(c_2Epoly_2Ersquarefree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))
<=> ( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ! [V1a: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = fo__c_2Enum_2E0 )
| ( surj__ty_2Enum_2Enum(ap(ap(c_2Epoly_2Epoly__order,inj__ty_2Erealax_2Ereal(V1a)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) ) ) ) ).
tff(conj_thm_2Epoly_2ERSQUAREFREE__ROOTS,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( p(ap(c_2Epoly_2Ersquarefree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))
<=> ! [V1a: tp__ty_2Erealax_2Ereal] :
~ ( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),inj__ty_2Erealax_2Ereal(V1a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Epoly_2ERSQUAREFREE__DECOMP,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1a: tp__ty_2Erealax_2Ereal] :
( ( p(ap(c_2Epoly_2Ersquarefree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)))
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) )
=> ? [V2q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1a))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q))) )
& ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2q)),inj__ty_2Erealax_2Ereal(V1a))) != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__SQUAREFREE__DECOMP,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1q: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V2d: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V3e: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V4r: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V5s: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) != ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2d))) )
& ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V3e)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2d))) )
& ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2d)) = ap(c_2Epoly_2Epoly,ap(ap(c_2Epoly_2Epoly__add,ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V4r)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))),ap(ap(c_2Epoly_2Epoly__mul,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V5s)),ap(c_2Epoly_2Ediff,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))) ) )
=> ( p(ap(c_2Epoly_2Ersquarefree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)))
& ! [V6a: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1q)),inj__ty_2Erealax_2Ereal(V6a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V6a))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ) ) ).
tff(ax_thm_2Epoly_2Enormalize,axiom,
( ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Enormalize,c_2Elist_2ENIL(ty_2Erealax_2Ereal))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
& ! [V0h: tp__ty_2Erealax_2Ereal,V1t: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(ap(c_2Epoly_2Enormalize,ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0h)),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t)))) = surj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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),inj__ty_2Erealax_2Ereal(V0h)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),c_2Elist_2ENIL(ty_2Erealax_2Ereal)),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0h)),c_2Elist_2ENIL(ty_2Erealax_2Ereal)))),ap(ap(c_2Elist_2ECONS(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0h)),ap(c_2Epoly_2Enormalize,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V1t))))) ) ) ).
tff(conj_thm_2Epoly_2EPOLY__NORMALIZE,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( ap(c_2Epoly_2Epoly,ap(c_2Epoly_2Enormalize,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) ) ).
tff(ax_thm_2Epoly_2Edegree,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] : ( surj__ty_2Enum_2Enum(ap(c_2Epoly_2Edegree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = surj__ty_2Enum_2Enum(ap(c_2Eprim__rec_2EPRE,ap(c_2Elist_2ELENGTH(ty_2Erealax_2Ereal),ap(c_2Epoly_2Enormalize,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))))) ) ).
tff(conj_thm_2Epoly_2EDEGREE__ZERO,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)) = ap(c_2Epoly_2Epoly,c_2Elist_2ENIL(ty_2Erealax_2Ereal)) )
=> ( surj__ty_2Enum_2Enum(ap(c_2Epoly_2Edegree,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p))) = fo__c_2Enum_2E0 ) ) ).
tff(lamtp_f2841,type,
f2841: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal > $i ).
tff(lameq_f2841,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] : ( ap(f2841(V0p),inj__ty_2Erealax_2Ereal(V1x)) = ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,bool),inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V0p)),inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__ROOTS__FINITE__SET,axiom,
! [V0p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( ( ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(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)))) ) ).
tff(conj_thm_2Epoly_2EPOLY__MONO,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1k: tp__ty_2Erealax_2Ereal,V2p: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1k)))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Epoly_2Epoly,inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p)),inj__ty_2Erealax_2Ereal(V0x)))),ap(ap(c_2Epoly_2Epoly,ap(ap(c_2Elist_2EMAP(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),c_2Ereal_2Eabs),inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal(V2p))),inj__ty_2Erealax_2Ereal(V1k)))) ) ).
%------------------------------------------------------------------------------