ITP001 Axioms: ITP130^5.ax


%------------------------------------------------------------------------------
% File     : ITP130^5 : TPTP v9.0.0. 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 ) ) ) ) ) ).

%------------------------------------------------------------------------------