ITP001 Axioms: ITP130_7.ax
%------------------------------------------------------------------------------
% File : ITP130_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : poly.ax [Gau19]
% : HL4130_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 284 ( 82 unt; 122 typ; 0 def)
% Number of atoms : 334 ( 218 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 208 ( 36 ~; 10 |; 63 &)
% ( 39 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 94 ( 59 >; 35 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 118 ( 118 usr; 41 con; 0-4 aty)
% Number of variables : 474 ( 405 !; 24 ?; 474 :)
% ( 45 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epoly_2E_23_23_2E0,type,
c_2Epoly_2E_23_23_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal))) ).
tff(c_2Epoly_2E_23_23_2E1,type,
c_2Epoly_2E_23_23_2E1: tyop_2Erealax_2Ereal > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)) ).
tff(c_2Epoly_2E_23_23_2E2,type,
c_2Epoly_2E_23_23_2E2: ( tyop_2Erealax_2Ereal * tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).
tff(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Elist_2ETL_2E0,type,
c_2Elist_2ETL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2ETL_2E1,type,
c_2Elist_2ETL_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Eabs_2E0,type,
c_2Ereal_2Eabs_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Eabs_2E1,type,
c_2Ereal_2Eabs_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Elim_2Econtl_2E0,type,
c_2Elim_2Econtl_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Elim_2Econtl_2E2,type,
c_2Elim_2Econtl_2E2: ( tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Epoly_2Edegree_2E0,type,
c_2Epoly_2Edegree_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Enum_2Enum) ).
tff(c_2Epoly_2Edegree_2E1,type,
c_2Epoly_2Edegree_2E1: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) > tyop_2Enum_2Enum ).
tff(c_2Epoly_2Ediff_2E0,type,
c_2Epoly_2Ediff_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)) ).
tff(c_2Epoly_2Ediff_2E1,type,
c_2Epoly_2Ediff_2E1: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Elim_2Edifferentiable_2E0,type,
c_2Elim_2Edifferentiable_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Elim_2Edifferentiable_2E2,type,
c_2Elim_2Edifferentiable_2E2: ( tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Elim_2Ediffl_2E0,type,
c_2Elim_2Ediffl_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))) ).
tff(c_2Elim_2Ediffl_2E3,type,
c_2Elim_2Ediffl_2E3: ( tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) * tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Epoly_2Enormalize_2E0,type,
c_2Epoly_2Enormalize_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)) ).
tff(c_2Epoly_2Enormalize_2E1,type,
c_2Epoly_2Enormalize_2E1: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly_2E0,type,
c_2Epoly_2Epoly_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Epoly_2Epoly_2E1,type,
c_2Epoly_2Epoly_2E1: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) > tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly_2E2,type,
c_2Epoly_2Epoly_2E2: ( tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Epoly_2Epoly__add_2E0,type,
c_2Epoly_2Epoly__add_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal))) ).
tff(c_2Epoly_2Epoly__add_2E2,type,
c_2Epoly_2Epoly__add_2E2: ( tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) * tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly__diff__aux_2E0,type,
c_2Epoly_2Epoly__diff__aux_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal))) ).
tff(c_2Epoly_2Epoly__diff__aux_2E2,type,
c_2Epoly_2Epoly__diff__aux_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly__divides_2E0,type,
c_2Epoly_2Epoly__divides_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)) ).
tff(c_2Epoly_2Epoly__divides_2E2,type,
c_2Epoly_2Epoly__divides_2E2: ( tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) * tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ) > tyop_2Emin_2Ebool ).
tff(c_2Epoly_2Epoly__exp_2E0,type,
c_2Epoly_2Epoly__exp_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Erealax_2Ereal))) ).
tff(c_2Epoly_2Epoly__exp_2E2,type,
c_2Epoly_2Epoly__exp_2E2: ( tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly__mul_2E0,type,
c_2Epoly_2Epoly__mul_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal))) ).
tff(c_2Epoly_2Epoly__mul_2E2,type,
c_2Epoly_2Epoly__mul_2E2: ( tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) * tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly__neg_2E0,type,
c_2Epoly_2Epoly__neg_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)) ).
tff(c_2Epoly_2Epoly__neg_2E1,type,
c_2Epoly_2Epoly__neg_2E1: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) > tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ).
tff(c_2Epoly_2Epoly__order_2E0,type,
c_2Epoly_2Epoly__order_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Enum_2Enum)) ).
tff(c_2Epoly_2Epoly__order_2E2,type,
c_2Epoly_2Epoly__order_2E2: ( tyop_2Erealax_2Ereal * tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) ) > tyop_2Enum_2Enum ).
tff(c_2Ereal_2Epow_2E0,type,
c_2Ereal_2Epow_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Epow_2E2,type,
c_2Ereal_2Epow_2E2: ( tyop_2Erealax_2Ereal * tyop_2Enum_2Enum ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__gt_2E0,type,
c_2Ereal_2Ereal__gt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__gt_2E2,type,
c_2Ereal_2Ereal__gt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__sub_2E0,type,
c_2Ereal_2Ereal__sub_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Ereal__sub_2E2,type,
c_2Ereal_2Ereal__sub_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Epoly_2Ersquarefree_2E0,type,
c_2Epoly_2Ersquarefree_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool) ).
tff(c_2Epoly_2Ersquarefree_2E1,type,
c_2Epoly_2Ersquarefree_2E1: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2E_23_23_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2E_23_23_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Epoly_2E_23_23_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2E_23_23_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2E_23_23_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Epoly_2E_23_23_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Emin_2E_40_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Erealax_2Ereal_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Elist_2ECONS_2E0(tyop_2Erealax_2Ereal),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2EEVERY_2E2(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Erealax_2Ereal),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2EHD_2E1(tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,c_2Elist_2EHD_2E0(tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2EMAP_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Elist_2EMAP_2E0(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2ETL_2E1(tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),c_2Elist_2ETL_2E0(tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Eabs_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Elim_2Econtl_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Elim_2Econtl_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Elim_2Econtl_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2Edegree_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Edegree_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Enum_2Enum,c_2Epoly_2Edegree_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2Ediff_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Ediff_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),c_2Epoly_2Ediff_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Elim_2Edifferentiable_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Elim_2Edifferentiable_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Elim_2Edifferentiable_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elim_2Ediffl_2E3,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal,X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Elim_2Ediffl_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Elim_2Ediffl_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2Enormalize_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Enormalize_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),c_2Epoly_2Enormalize_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2Epoly_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epoly_2Epoly_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epoly_2Epoly_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly__add_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Epoly_2Epoly__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly__diff__aux_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__diff__aux_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Epoly_2Epoly__diff__aux_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly__divides_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__divides_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),c_2Epoly_2Epoly__divides_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly__exp_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly__exp_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Epoly_2Epoly__exp_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly__mul_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)),c_2Epoly_2Epoly__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2Epoly__neg_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__neg_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),c_2Epoly_2Epoly__neg_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epoly_2Epoly__order_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__order_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Enum_2Enum,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Enum_2Enum),c_2Epoly_2Epoly__order_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Epow_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Epow_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__gt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Ereal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__sub_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epoly_2Ersquarefree_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Ersquarefree_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,c_2Epoly_2Ersquarefree_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Epoly_2Epoly__def,axiom,
( ! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),V0x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
& ! [V1h_2E0: tyop_2Erealax_2Ereal,V2t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3x_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V2t_2E0),V3x_2E0) = c_2Erealax_2Ereal__add_2E2(V1h_2E0,c_2Erealax_2Ereal__mul_2E2(V3x_2E0,c_2Epoly_2Epoly_2E2(V2t_2E0,V3x_2E0))) ) ) ).
tff(thm_2Epoly_2Epoly__add__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)] :
( ! [V3l2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V3l2_2E0))
<=> ( V3l2_2E0 = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) ) )
=> ( ! [V0l2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__add_2E2(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),V0l2_2E0) = V0l2_2E0 )
& ! [V1h_2E0: tyop_2Erealax_2Ereal,V2t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3l2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__add_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V2t_2E0),V3l2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V3l2_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V2t_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(V1h_2E0,c_2Elist_2EHD_2E1(tyop_2Erealax_2Ereal,V3l2_2E0)),c_2Epoly_2Epoly__add_2E2(V2t_2E0,c_2Elist_2ETL_2E1(tyop_2Erealax_2Ereal,V3l2_2E0)))) ) ) ) ).
tff(thm_2Epoly_2Epoly__cmul__def,axiom,
( ! [V0c_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2E_23_23_2E2(V0c_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ! [V1c_2E0: tyop_2Erealax_2Ereal,V2h_2E0: tyop_2Erealax_2Ereal,V3t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2E_23_23_2E2(V1c_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V2h_2E0,V3t_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(V1c_2E0,V2h_2E0),c_2Epoly_2E_23_23_2E2(V1c_2E0,V3t_2E0)) ) ) ).
tff(thm_2Epoly_2Epoly__neg__def,axiom,
c_2Epoly_2Epoly__neg_2E0 = c_2Epoly_2E_23_23_2E1(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ).
tff(thm_2Epoly_2Epoly__mul__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)] :
( ! [V2t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V2t_2E0))
<=> ( V2t_2E0 = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) ) )
=> ( ! [V0l2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),V0l2_2E0) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ! [V1h_2E0: tyop_2Erealax_2Ereal,V2t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3l2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V2t_2E0),V3l2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V2t_2E0),c_2Epoly_2E_23_23_2E2(V1h_2E0,V3l2_2E0),c_2Epoly_2Epoly__add_2E2(c_2Epoly_2E_23_23_2E2(V1h_2E0,V3l2_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Epoly_2Epoly__mul_2E2(V2t_2E0,V3l2_2E0)))) ) ) ) ).
tff(thm_2Epoly_2Epoly__exp__def,axiom,
( ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__exp_2E2(V0p_2E0,c_2Enum_2E0_2E0) = c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ! [V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly__exp_2E2(V1p_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)) = c_2Epoly_2Epoly__mul_2E2(V1p_2E0,c_2Epoly_2Epoly__exp_2E2(V1p_2E0,V2n_2E0)) ) ) ).
tff(thm_2Epoly_2Epoly__diff__aux__def,axiom,
( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly__diff__aux_2E2(V0n_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2h_2E0: tyop_2Erealax_2Ereal,V3t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__diff__aux_2E2(V1n_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V2h_2E0,V3t_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(V1n_2E0),V2h_2E0),c_2Epoly_2Epoly__diff__aux_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V3t_2E0)) ) ) ).
tff(thm_2Epoly_2Epoly__diff__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)] :
( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V0l_2E0))
<=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) ) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Ediff_2E1(V0l_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V0l_2E0),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),c_2Epoly_2Epoly__diff__aux_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Elist_2ETL_2E1(tyop_2Erealax_2Ereal,V0l_2E0))) ) ) ).
tff(thm_2Epoly_2Epoly__divides,axiom,
! [V0p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(c_2Epoly_2Epoly__divides_2E2(V0p1_2E0,V1p2_2E0))
<=> ? [V2q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(V1p2_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V0p1_2E0,V2q_2E0)) ) ) ).
tff(thm_2Epoly_2Epoly__order,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0a_2E0: tyop_2Erealax_2Ereal,V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0a_2E0),V1p_2E0),V2n_2E0))
<=> ( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2n_2E0),V1p_2E0))
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(V2n_2E0)),V1p_2E0)) ) )
=> ! [V0a_2E0: tyop_2Erealax_2Ereal,V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly__order_2E2(V0a_2E0,V1p_2E0) = c_2Emin_2E_40_2E1(tyop_2Enum_2Enum,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0a_2E0),V1p_2E0)) ) ) ).
tff(thm_2Epoly_2Ersquarefree,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(c_2Epoly_2Ersquarefree_2E1(V0p_2E0))
<=> ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ! [V1a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) = c_2Enum_2E0_2E0 )
| ( c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ) ) ).
tff(thm_2Epoly_2Enormalize,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)] :
( ! [V0h_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F1_2E0,V0h_2E0))
<=> ( V0h_2E0 = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ( ! [V1t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V1t_2E0))
<=> ( c_2Epoly_2Enormalize_2E1(V1t_2E0) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) ) )
=> ( ( c_2Epoly_2Enormalize_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ! [V0h_2E0: tyop_2Erealax_2Ereal,V1t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Enormalize_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0h_2E0,V1t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,F0_2E0,V1t_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F1_2E0,V0h_2E0),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0h_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0h_2E0,c_2Epoly_2Enormalize_2E1(V1t_2E0))) ) ) ) ) ).
tff(thm_2Epoly_2Edegree,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Edegree_2E1(V0p_2E0) = c_2Eprim__rec_2EPRE_2E1(c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,c_2Epoly_2Enormalize_2E1(V0p_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__ADD__CLAUSES,axiom,
! [V0t2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1t1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V4h2_2E0: tyop_2Erealax_2Ereal,V5h1_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly__add_2E2(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),V2p2_2E0) = V2p2_2E0 )
& ( c_2Epoly_2Epoly__add_2E2(V3p1_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = V3p1_2E0 )
& ( c_2Epoly_2Epoly__add_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V5h1_2E0,V1t1_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V4h2_2E0,V0t2_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(V5h1_2E0,V4h2_2E0),c_2Epoly_2Epoly__add_2E2(V1t1_2E0,V0t2_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__CMUL__CLAUSES,axiom,
! [V0t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1h_2E0: tyop_2Erealax_2Ereal,V2c_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2E_23_23_2E2(V2c_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ( c_2Epoly_2E_23_23_2E2(V2c_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V0t_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(V2c_2E0,V1h_2E0),c_2Epoly_2E_23_23_2E2(V2c_2E0,V0t_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__NEG__CLAUSES,axiom,
! [V0t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1h_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly__neg_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ( c_2Epoly_2Epoly__neg_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V0t_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1h_2E0),c_2Epoly_2Epoly__neg_2E1(V0t_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__MUL__CLAUSES,axiom,
! [V0t1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2k1_2E0: tyop_2Erealax_2Ereal,V3h1_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal),V1p2_2E0) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ( c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V3h1_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)),V1p2_2E0) = c_2Epoly_2E_23_23_2E2(V3h1_2E0,V1p2_2E0) )
& ( c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V3h1_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V2k1_2E0,V0t1_2E0)),V1p2_2E0) = c_2Epoly_2Epoly__add_2E2(c_2Epoly_2E_23_23_2E2(V3h1_2E0,V1p2_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V2k1_2E0,V0t1_2E0),V1p2_2E0))) ) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__CLAUSES,axiom,
! [V0t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1h_2E0: tyop_2Erealax_2Ereal,V2c_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Ediff_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ( c_2Epoly_2Ediff_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V2c_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))) = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
& ( c_2Epoly_2Ediff_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V0t_2E0)) = c_2Epoly_2Epoly__diff__aux_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t_2E0) ) ) ).
tff(thm_2Epoly_2EPOLY__ADD,axiom,
! [V0p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(c_2Epoly_2Epoly__add_2E2(V0p1_2E0,V1p2_2E0),V2x_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Epoly_2Epoly_2E2(V0p1_2E0,V2x_2E0),c_2Epoly_2Epoly_2E2(V1p2_2E0,V2x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__CMUL,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1c_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(c_2Epoly_2E_23_23_2E2(V1c_2E0,V0p_2E0),V2x_2E0) = c_2Erealax_2Ereal__mul_2E2(V1c_2E0,c_2Epoly_2Epoly_2E2(V0p_2E0,V2x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__NEG,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(c_2Epoly_2Epoly__neg_2E1(V0p_2E0),V1x_2E0) = c_2Erealax_2Ereal__neg_2E1(c_2Epoly_2Epoly_2E2(V0p_2E0,V1x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__MUL,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E2(c_2Epoly_2Epoly__mul_2E2(V1p1_2E0,V2p2_2E0),V0x_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Epoly_2Epoly_2E2(V1p1_2E0,V0x_2E0),c_2Epoly_2Epoly_2E2(V2p2_2E0,V0x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__EXP,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E2(c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V1n_2E0),V2x_2E0) = c_2Ereal_2Epow_2E2(c_2Epoly_2Epoly_2E2(V0p_2E0,V2x_2E0),V1n_2E0) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__LEMMA,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)))] :
( ! [V1n_2E0: tyop_2Enum_2Enum,V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3x_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0,V1n_2E0),V0l_2E0),V3x_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(V3x_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)),c_2Epoly_2Epoly_2E2(V0l_2E0,V3x_2E0)) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Erealax_2Ereal] : p(c_2Elim_2Ediffl_2E3(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0,V1n_2E0),V0l_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(V2x_2E0,V1n_2E0),c_2Epoly_2Epoly_2E2(c_2Epoly_2Epoly__diff__aux_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V0l_2E0),V2x_2E0)),V2x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIFF,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))] :
( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2x_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0,V0l_2E0),V2x_2E0) = c_2Epoly_2Epoly_2E2(V0l_2E0,V2x_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal] : p(c_2Elim_2Ediffl_2E3(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0,V0l_2E0),c_2Epoly_2Epoly_2E2(c_2Epoly_2Ediff_2E1(V0l_2E0),V1x_2E0),V1x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIFFERENTIABLE,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))] :
( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2x_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0,V0l_2E0),V2x_2E0) = c_2Epoly_2Epoly_2E2(V0l_2E0,V2x_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal] : p(c_2Elim_2Edifferentiable_2E2(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0,V0l_2E0),V1x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__CONT,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))] :
( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2x_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0,V0l_2E0),V2x_2E0) = c_2Epoly_2Epoly_2E2(V0l_2E0,V2x_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal] : p(c_2Elim_2Econtl_2E2(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0,V0l_2E0),V1x_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__IVT__POS,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal,V2b_2E0: tyop_2Erealax_2Ereal] :
( ( p(c_2Erealax_2Ereal__lt_2E2(V1a_2E0,V2b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Epoly_2Epoly_2E2(V0p_2E0,V1a_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
& p(c_2Ereal_2Ereal__gt_2E2(c_2Epoly_2Epoly_2E2(V0p_2E0,V2b_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) )
=> ? [V3x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(V1a_2E0,V3x_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(V3x_2E0,V2b_2E0))
& ( c_2Epoly_2Epoly_2E2(V0p_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Epoly_2EPOLY__IVT__NEG,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal,V2b_2E0: tyop_2Erealax_2Ereal] :
( ( p(c_2Erealax_2Ereal__lt_2E2(V1a_2E0,V2b_2E0))
& p(c_2Ereal_2Ereal__gt_2E2(c_2Epoly_2Epoly_2E2(V0p_2E0,V1a_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Epoly_2Epoly_2E2(V0p_2E0,V2b_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) )
=> ? [V3x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(V1a_2E0,V3x_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(V3x_2E0,V2b_2E0))
& ( c_2Epoly_2Epoly_2E2(V0p_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Epoly_2EPOLY__MVT,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal,V2b_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(V1a_2E0,V2b_2E0))
=> ? [V3x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(V1a_2E0,V3x_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(V3x_2E0,V2b_2E0))
& ( c_2Ereal_2Ereal__sub_2E2(c_2Epoly_2Epoly_2E2(V0p_2E0,V2b_2E0),c_2Epoly_2Epoly_2E2(V0p_2E0,V1a_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__sub_2E2(V2b_2E0,V1a_2E0),c_2Epoly_2Epoly_2E2(c_2Epoly_2Ediff_2E1(V0p_2E0),V3x_2E0)) ) ) ) ).
tff(thm_2Epoly_2EPOLY__ADD__RZERO,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(V0p_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))) = c_2Epoly_2Epoly_2E1(V0p_2E0) ) ).
tff(thm_2Epoly_2EPOLY__MUL__ASSOC,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V0p_2E0,c_2Epoly_2Epoly__mul_2E2(V1q_2E0,V2r_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(c_2Epoly_2Epoly__mul_2E2(V0p_2E0,V1q_2E0),V2r_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__EXP__ADD,axiom,
! [V0d_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__exp_2E2(V2p_2E0,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0d_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(c_2Epoly_2Epoly__exp_2E2(V2p_2E0,V1n_2E0),c_2Epoly_2Epoly__exp_2E2(V2p_2E0,V0d_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__AUX__ADD,axiom,
! [V0p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__diff__aux_2E2(V2n_2E0,c_2Epoly_2Epoly__add_2E2(V0p1_2E0,V1p2_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Epoly_2Epoly__diff__aux_2E2(V2n_2E0,V0p1_2E0),c_2Epoly_2Epoly__diff__aux_2E2(V2n_2E0,V1p2_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__AUX__CMUL,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1c_2E0: tyop_2Erealax_2Ereal,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__diff__aux_2E2(V2n_2E0,c_2Epoly_2E_23_23_2E2(V1c_2E0,V0p_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2E_23_23_2E2(V1c_2E0,c_2Epoly_2Epoly__diff__aux_2E2(V2n_2E0,V0p_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__AUX__NEG,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__diff__aux_2E2(V1n_2E0,c_2Epoly_2Epoly__neg_2E1(V0p_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__neg_2E1(c_2Epoly_2Epoly__diff__aux_2E2(V1n_2E0,V0p_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__AUX__MUL__LEMMA,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__diff__aux_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V0p_2E0)) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Epoly_2Epoly__diff__aux_2E2(V1n_2E0,V0p_2E0),V0p_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__ADD,axiom,
! [V0p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Epoly_2Epoly__add_2E2(V0p1_2E0,V1p2_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Epoly_2Ediff_2E1(V0p1_2E0),c_2Epoly_2Ediff_2E1(V1p2_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__CMUL,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1c_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Epoly_2E_23_23_2E2(V1c_2E0,V0p_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2E_23_23_2E2(V1c_2E0,c_2Epoly_2Ediff_2E1(V0p_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__NEG,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Epoly_2Epoly__neg_2E1(V0p_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__neg_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__MUL__LEMMA,axiom,
! [V0t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1h_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,V0t_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Epoly_2Ediff_2E1(V0t_2E0)),V0t_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__MUL,axiom,
! [V0p1_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1p2_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Epoly_2Epoly__mul_2E2(V0p1_2E0,V1p2_2E0))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Epoly_2Epoly__mul_2E2(V0p1_2E0,c_2Epoly_2Ediff_2E1(V1p2_2E0)),c_2Epoly_2Epoly__mul_2E2(c_2Epoly_2Ediff_2E1(V0p1_2E0),V1p2_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__EXP,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Epoly_2Epoly__exp_2E2(V0p_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(c_2Epoly_2E_23_23_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2ESUC_2E1(V1n_2E0)),c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V1n_2E0)),c_2Epoly_2Ediff_2E1(V0p_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__EXP__PRIME,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(V0n_2E0)))) = c_2Epoly_2Epoly_2E1(c_2Epoly_2E_23_23_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)),c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V0n_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__LINEAR__REM,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2h_2E0: tyop_2Erealax_2Ereal] :
? [V3q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V4r_2E0: tyop_2Erealax_2Ereal] : ( c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V2h_2E0,V1t_2E0) = c_2Epoly_2Epoly__add_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V4r_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)),c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V3q_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__LINEAR__DIVIDES,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E2(V1p_2E0,V0a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( ( V1p_2E0 = c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal) )
| ? [V2q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( V1p_2E0 = c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2q_2E0) ) ) ) ).
tff(thm_2Epoly_2EPOLY__LENGTH__MUL,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V1q_2E0)) = c_2Enum_2ESUC_2E1(c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,V1q_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__ROOTS__INDEX__LEMMA,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( ( c_2Epoly_2Epoly_2E1(V1p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ( c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,V1p_2E0) = V0n_2E0 ) )
=> ? [V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] :
! [V3x_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E2(V1p_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
=> ? [V4m_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V4m_2E0,V0n_2E0))
& ( V3x_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V2i_2E0,V4m_2E0) ) ) ) ) ).
tff(thm_2Epoly_2EPOLY__ROOTS__INDEX__LENGTH,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ? [V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] :
! [V2x_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E2(V0p_2E0,V2x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
=> ? [V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,V0p_2E0)))
& ( V2x_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1i_2E0,V3n_2E0) ) ) ) ) ).
tff(thm_2Epoly_2EPOLY__ROOTS__FINITE__LEMMA,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ? [V1N_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] :
! [V3x_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E2(V0p_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
=> ? [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V1N_2E0))
& ( V3x_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V2i_2E0,V4n_2E0) ) ) ) ) ).
tff(thm_2Epoly_2EFINITE__LEMMA,axiom,
! [V0i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1N_2E0: tyop_2Enum_2Enum,V2P_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0))
=> ? [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V1N_2E0))
& ( V3x_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0i_2E0,V4n_2E0) ) ) )
=> ? [V5a_2E0: tyop_2Erealax_2Ereal] :
! [V6x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V2P_2E0,V6x_2E0))
=> p(c_2Erealax_2Ereal__lt_2E2(V6x_2E0,V5a_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__ROOTS__FINITE,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
<=> ? [V1N_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] :
! [V3x_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E2(V0p_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
=> ? [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V1N_2E0))
& ( V3x_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V2i_2E0,V4n_2E0) ) ) ) ) ).
tff(thm_2Epoly_2EPOLY__ENTIRE__LEMMA,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ( c_2Epoly_2Epoly_2E1(V1q_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) )
=> ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V0p_2E0,V1q_2E0)) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ) ).
tff(thm_2Epoly_2EPOLY__ENTIRE,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V0p_2E0,V1q_2E0)) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
<=> ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
| ( c_2Epoly_2Epoly_2E1(V1q_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ) ) ).
tff(thm_2Epoly_2EPOLY__MUL__LCANCEL,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V0p_2E0,V1q_2E0)) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V0p_2E0,V2r_2E0)) )
<=> ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
| ( c_2Epoly_2Epoly_2E1(V1q_2E0) = c_2Epoly_2Epoly_2E1(V2r_2E0) ) ) ) ).
tff(thm_2Epoly_2EPOLY__EXP__EQ__0,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] :
( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V1n_2E0)) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
<=> ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ( V1n_2E0 != c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Epoly_2EPOLY__PRIME__EQ__0,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0a_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)))) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ).
tff(thm_2Epoly_2EPOLY__EXP__PRIME__EQ__0,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0a_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V1n_2E0)) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ).
tff(thm_2Epoly_2EPOLY__ZERO__LEMMA,axiom,
! [V0h_2E0: tyop_2Erealax_2Ereal,V1t_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0h_2E0,V1t_2E0)) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ( ( V0h_2E0 = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
& ( c_2Epoly_2Epoly_2E1(V1t_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ) ) ).
tff(thm_2Epoly_2EPOLY__ZERO,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ! [V1c_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F0_2E0,V1c_2E0))
<=> ( V1c_2E0 = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
<=> p(c_2Elist_2EEVERY_2E2(tyop_2Erealax_2Ereal,F0_2E0,V0p_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__AUX__ISZERO,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ! [V3c_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F1_2E0,V3c_2E0))
<=> ( V3c_2E0 = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ( ! [V2c_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F0_2E0,V2c_2E0))
<=> ( V2c_2E0 = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EEVERY_2E2(tyop_2Erealax_2Ereal,F0_2E0,c_2Epoly_2Epoly__diff__aux_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V0p_2E0)) = c_2Elist_2EEVERY_2E2(tyop_2Erealax_2Ereal,F1_2E0,V0p_2E0) ) ) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__ISZERO,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ? [V1h_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V1h_2E0,c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))) ) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__ZERO,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ) ).
tff(thm_2Epoly_2EPOLY__DIFF__WELLDEF,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(V1q_2E0) )
=> ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V1q_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__PRIMES,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(c_2Epoly_2Epoly__divides_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0a_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Epoly_2Epoly__mul_2E2(V1p_2E0,V2q_2E0)))
<=> ( p(c_2Epoly_2Epoly__divides_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0a_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V1p_2E0))
| p(c_2Epoly_2Epoly__divides_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,V0a_2E0,c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2q_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__REFL,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V0p_2E0)) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__TRANS,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V1q_2E0))
& p(c_2Epoly_2Epoly__divides_2E2(V1q_2E0,V2r_2E0)) )
=> p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V2r_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__EXP,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V2n_2E0))
=> p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V1m_2E0),c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V2n_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__EXP__DIVIDES,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V3n_2E0),V1q_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,V3n_2E0)) )
=> p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(V0p_2E0,V2m_2E0),V1q_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__ADD,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V1q_2E0))
& p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V2r_2E0)) )
=> p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,c_2Epoly_2Epoly__add_2E2(V1q_2E0,V2r_2E0))) ) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__SUB,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V1q_2E0))
& p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,c_2Epoly_2Epoly__add_2E2(V1q_2E0,V2r_2E0))) )
=> p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V2r_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__SUB2,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V2r_2E0))
& p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,c_2Epoly_2Epoly__add_2E2(V1q_2E0,V2r_2E0))) )
=> p(c_2Epoly_2Epoly__divides_2E2(V0p_2E0,V1q_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__DIVIDES__ZERO,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> p(c_2Epoly_2Epoly__divides_2E2(V1q_2E0,V0p_2E0)) ) ).
tff(thm_2Epoly_2EPOLY__ORDER__EXISTS,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1d_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( ( c_2Elist_2ELENGTH_2E1(tyop_2Erealax_2Ereal,V2p_2E0) = V1d_2E0 )
& ( c_2Epoly_2Epoly_2E1(V2p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) )
=> ? [V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V3n_2E0),V2p_2E0))
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V0a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(V3n_2E0)),V2p_2E0)) ) ) ).
tff(thm_2Epoly_2EPOLY__ORDER,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V1a_2E0: tyop_2Erealax_2Ereal,V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0p_2E0),V2n_2E0))
<=> ( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2n_2E0),V0p_2E0))
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(V2n_2E0)),V0p_2E0)) ) )
=> ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> p(c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0p_2E0))) ) ) ).
tff(thm_2Epoly_2EORDER,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal,V2n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2n_2E0),V0p_2E0))
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(V2n_2E0)),V0p_2E0)) )
<=> ( ( V2n_2E0 = c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) )
& ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) ) ) ) ).
tff(thm_2Epoly_2EORDER__THM,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0)),V0p_2E0))
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0))),V0p_2E0)) ) ) ).
tff(thm_2Epoly_2EORDER__UNIQUE,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal,V2n_2E0: tyop_2Enum_2Enum] :
( ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2n_2E0),V0p_2E0))
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Enum_2ESUC_2E1(V2n_2E0)),V0p_2E0)) )
=> ( V2n_2E0 = c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) ) ) ).
tff(thm_2Epoly_2EORDER__POLY,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(V1q_2E0) )
=> ( c_2Epoly_2Epoly__order_2E2(V2a_2E0,V0p_2E0) = c_2Epoly_2Epoly__order_2E2(V2a_2E0,V1q_2E0) ) ) ).
tff(thm_2Epoly_2EORDER__ROOT,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E2(V0p_2E0,V1a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
| ( c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) != c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Epoly_2EORDER__DIVIDES,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Epoly_2Epoly__divides_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2n_2E0),V0p_2E0))
<=> ( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
| p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0))) ) ) ).
tff(thm_2Epoly_2EORDER__DECOMP,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ? [V2q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(c_2Epoly_2Epoly__exp_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0)),V2q_2E0)) )
& ~ p(c_2Epoly_2Epoly__divides_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2q_2E0)) ) ) ).
tff(thm_2Epoly_2EORDER__MUL,axiom,
! [V0a_2E0: tyop_2Erealax_2Ereal,V1p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V1p_2E0,V2q_2E0)) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ( c_2Epoly_2Epoly__order_2E2(V0a_2E0,c_2Epoly_2Epoly__mul_2E2(V1p_2E0,V2q_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Epoly_2Epoly__order_2E2(V0a_2E0,V1p_2E0),c_2Epoly_2Epoly__order_2E2(V0a_2E0,V2q_2E0)) ) ) ).
tff(thm_2Epoly_2EORDER__DIFF,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal] :
( ( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ( c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) != c_2Enum_2E0_2E0 ) )
=> ( c_2Epoly_2Epoly__order_2E2(V1a_2E0,V0p_2E0) = c_2Enum_2ESUC_2E1(c_2Epoly_2Epoly__order_2E2(V1a_2E0,c_2Epoly_2Ediff_2E1(V0p_2E0))) ) ) ).
tff(thm_2Epoly_2EPOLY__SQUAREFREE__DECOMP__ORDER,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool))] :
( ! [V6a_2E0: tyop_2Erealax_2Ereal,V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),F0_2E0,V6a_2E0),V0p_2E0))
<=> ( c_2Epoly_2Epoly__order_2E2(V6a_2E0,V0p_2E0) = c_2Enum_2E0_2E0 ) )
=> ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2d_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3e_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V4r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V5s_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V1q_2E0,V2d_2E0)) )
& ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V3e_2E0,V2d_2E0)) )
& ( c_2Epoly_2Epoly_2E1(V2d_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Epoly_2Epoly__mul_2E2(V4r_2E0,V0p_2E0),c_2Epoly_2Epoly__mul_2E2(V5s_2E0,c_2Epoly_2Ediff_2E1(V0p_2E0)))) ) )
=> ! [V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Epoly_2Epoly__order_2E2(V6a_2E0,V1q_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),F0_2E0,V6a_2E0),V0p_2E0),c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ) ).
tff(thm_2Epoly_2ERSQUAREFREE__ROOTS,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(c_2Epoly_2Ersquarefree_2E1(V0p_2E0))
<=> ! [V1a_2E0: tyop_2Erealax_2Ereal] :
~ ( ( c_2Epoly_2Epoly_2E2(V0p_2E0,V1a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
& ( c_2Epoly_2Epoly_2E2(c_2Epoly_2Ediff_2E1(V0p_2E0),V1a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Epoly_2ERSQUAREFREE__DECOMP,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1a_2E0: tyop_2Erealax_2Ereal] :
( ( p(c_2Epoly_2Ersquarefree_2E1(V0p_2E0))
& ( c_2Epoly_2Epoly_2E2(V0p_2E0,V1a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ? [V2q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(V1a_2E0),c_2Elist_2ECONS_2E2(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal))),V2q_2E0)) )
& ( c_2Epoly_2Epoly_2E2(V2q_2E0,V1a_2E0) != c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Epoly_2EPOLY__SQUAREFREE__DECOMP,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1q_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V2d_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V3e_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V4r_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V5s_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
& ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V1q_2E0,V2d_2E0)) )
& ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Ediff_2E1(V0p_2E0)) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__mul_2E2(V3e_2E0,V2d_2E0)) )
& ( c_2Epoly_2Epoly_2E1(V2d_2E0) = c_2Epoly_2Epoly_2E1(c_2Epoly_2Epoly__add_2E2(c_2Epoly_2Epoly__mul_2E2(V4r_2E0,V0p_2E0),c_2Epoly_2Epoly__mul_2E2(V5s_2E0,c_2Epoly_2Ediff_2E1(V0p_2E0)))) ) )
=> ( p(c_2Epoly_2Ersquarefree_2E1(V1q_2E0))
& ! [V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Epoly_2Epoly_2E2(V1q_2E0,V6a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( c_2Epoly_2Epoly_2E2(V0p_2E0,V6a_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ) ).
tff(thm_2Epoly_2EPOLY__NORMALIZE,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] : ( c_2Epoly_2Epoly_2E1(c_2Epoly_2Enormalize_2E1(V0p_2E0)) = c_2Epoly_2Epoly_2E1(V0p_2E0) ) ).
tff(thm_2Epoly_2EDEGREE__ZERO,axiom,
! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) = c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> ( c_2Epoly_2Edegree_2E1(V0p_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Epoly_2EPOLY__ROOTS__FINITE__SET,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)))] :
( ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F1_2E0,V0p_2E0),V1x_2E0))
<=> ( c_2Epoly_2Epoly_2E2(V0p_2E0,V1x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ( ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F0_2E0,V0p_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F1_2E0,V0p_2E0),V1x_2E0)) )
=> ! [V0p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( ( c_2Epoly_2Epoly_2E1(V0p_2E0) != c_2Epoly_2Epoly_2E1(c_2Elist_2ENIL_2E0(tyop_2Erealax_2Ereal)) )
=> p(c_2Epred__set_2EFINITE_2E1(tyop_2Erealax_2Ereal,c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Elist_2Elist(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F0_2E0,V0p_2E0)))) ) ) ) ).
tff(thm_2Epoly_2EPOLY__MONO,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1k_2E0: tyop_2Erealax_2Ereal,V2p_2E0: tyop_2Elist_2Elist(tyop_2Erealax_2Ereal)] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),V1k_2E0))
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Epoly_2Epoly_2E2(V2p_2E0,V0x_2E0)),c_2Epoly_2Epoly_2E2(c_2Elist_2EMAP_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E0,V2p_2E0),V1k_2E0))) ) ).
%------------------------------------------------------------------------------