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 : 130 ( 32 unt; 19 typ; 0 def)
% Number of atoms : 2630 ( 147 equ; 0 cnn)
% Maximal formula atoms : 68 ( 20 avg)
% Number of connectives : 3676 ( 31 ~; 7 |; 63 &;3518 @)
% ( 15 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg;3518 nst)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 71 usr; 66 con; 0-2 aty)
% Number of variables : 273 ( 10 ^ 240 !; 23 ?; 273 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(stp_c_ty_2Elist_2Elist_ty_2Erealax_2Ereal,type,
tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal: $tType ).
thf(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 ).
thf(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 ).
thf(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 ) ).
thf(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 ) ) ).
thf(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 ) ) ) ) ).
thf(tp_c_2Epoly_2E_23_23,type,
c_2Epoly_2E_23_23: $i ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Edegree,type,
c_2Epoly_2Edegree: $i ).
thf(mem_c_2Epoly_2Edegree,axiom,
mem @ c_2Epoly_2Edegree @ ( arr @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Epoly_2Edegree,type,
fo__c_2Epoly_2Edegree: tp__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal > tp__ty_2Enum_2Enum ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Ediff,type,
c_2Epoly_2Ediff: $i ).
thf(mem_c_2Epoly_2Ediff,axiom,
mem @ c_2Epoly_2Ediff @ ( arr @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) ) ).
thf(tp_c_2Epoly_2Enormalize,type,
c_2Epoly_2Enormalize: $i ).
thf(mem_c_2Epoly_2Enormalize,axiom,
mem @ c_2Epoly_2Enormalize @ ( arr @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) ) ).
thf(tp_c_2Epoly_2Epoly,type,
c_2Epoly_2Epoly: $i ).
thf(mem_c_2Epoly_2Epoly,axiom,
mem @ c_2Epoly_2Epoly @ ( arr @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ).
thf(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 ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Epoly__add,type,
c_2Epoly_2Epoly__add: $i ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Epoly__diff__aux,type,
c_2Epoly_2Epoly__diff__aux: $i ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Epoly__divides,type,
c_2Epoly_2Epoly__divides: $i ).
thf(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 ) ) ).
thf(tp_c_2Epoly_2Epoly__exp,type,
c_2Epoly_2Epoly__exp: $i ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Epoly__mul,type,
c_2Epoly_2Epoly__mul: $i ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Epoly__neg,type,
c_2Epoly_2Epoly__neg: $i ).
thf(mem_c_2Epoly_2Epoly__neg,axiom,
mem @ c_2Epoly_2Epoly__neg @ ( arr @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) ) ).
thf(tp_c_2Epoly_2Epoly__order,type,
c_2Epoly_2Epoly__order: $i ).
thf(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 ) ) ).
thf(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 ).
thf(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 ) ) ) ).
thf(tp_c_2Epoly_2Ersquarefree,type,
c_2Epoly_2Ersquarefree: $i ).
thf(mem_c_2Epoly_2Ersquarefree,axiom,
mem @ c_2Epoly_2Ersquarefree @ ( arr @ ( ty_2Elist_2Elist @ ty_2Erealax_2Ereal ) @ bool ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Epow @ V3x ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ ( ap @ c_2Epoly_2Epoly @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0l ) ) @ V3x ) ) ) )
@ ( 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 ) ) ) ).
thf(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
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Epoly_2Epoly @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0l ) ) @ V2x ) ) )
@ ( 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 ) ) ) ).
thf(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
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Epoly_2Epoly @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0l ) ) @ V2x ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ).
thf(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
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Epoly_2Epoly @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0l ) ) @ V2x ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V1c: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ V1c ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0p ) ) ) ) ).
thf(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 )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V2c: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ V2c ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
@ ( 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 )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V3c: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ V3c ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0p ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( 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 ) ) ) ) @ 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 @ V2n ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0p ) ) ) ) ) ) ) ) ).
thf(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 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( 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 ) ) ) ) @ 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 @ V2n ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V1p ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ).
thf(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 )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V1x: $i] : ( 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 @ ( inj__c_ty_2Elist_2Elist_ty_2Erealax_2Ereal @ V0p ) ) @ V1x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
%------------------------------------------------------------------------------