ITP001 Axioms: ITP107+4.ax
%------------------------------------------------------------------------------
% File : ITP107+4 : 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 : fmapal.ax [Gau19]
% : HL4107+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 241 ( 149 unt; 0 def)
% Number of atoms : 568 ( 321 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 342 ( 15 ~; 4 |; 124 &)
% ( 46 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 32 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 209 ( 209 usr; 108 con; 0-5 aty)
% Number of variables : 1640 (1639 !; 1 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(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))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Efinite__map_2EFDOM_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))) ).
fof(arityeq1_2Ec_2Efmapal_2Efmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efmapal_2Efmap_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2EFMAPAL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efmapal_2EFMAPAL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27z,axiom,
! [A_27z,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27z),X0_2E0),s(tyop_2Elist_2Elist(A_27z),X1_2E0))) = s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27z),X0_2E0))),s(tyop_2Elist_2Elist(A_27z),X1_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
! [A_27z,X0_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27z),X0_2E0))) = s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27z),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2E_2C_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Etoto_2Etoto_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),c_2Epair_2E_2C_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X1_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Efmapal_2EOPTION__FLAT_2E1_2Emono_2EA_27z,axiom,
! [A_27z,X0_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X0_2E0))) = s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),c_2Efmapal_2EOPTION__FLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29,axiom,
! [A_27z,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))))),c_2Elist_2ECONS_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X1_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
! [A_27z,X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27z),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(A_27z),X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27z,axiom,
! [A_27z,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27z),app_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27z)),c_2Eoption_2ESOME_2E0),s(A_27z,X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29,axiom,
! [A_27z,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Ediff__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ediff__merge_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Einter__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Einter__merge_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Emerge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Emerge_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq1_2Ec_2Efmapal_2EAP__SND_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2EAP__SND_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Efmapal_2EAP__SND_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Efmapal_2Efmap_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efmapal_2Efmap_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0))) ).
fof(arityeq1_2Ec_2Efmapal_2Eunlookup_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Eunlookup_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efmapal_2Eunlookup_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Eenumeral_2Enode_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq1_2Ec_2Eenumeral_2Ezerbl_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ezerbl_2E1(s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eenumeral_2Ezerbl_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2Eonebl_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Eonebl_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Eenumeral_2Eonebl_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27z_29,axiom,
! [A_27z,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)))),c_2Elist_2ECONS_2E0),s(tyop_2Eoption_2Eoption(A_27z),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Elist_2ECONS_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq5_2Ec_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(A_27a,X3_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X4_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(A_27a,X3_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X4_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2ELESS__ALL_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eenumeral_2ELESS__ALL_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Eenumeral_2ELESS__ALL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__orl__lb_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__orl__ub_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2EAP__SND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Efmapal_2EAP__SND_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Efmapal_2EAP__SND_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Eincr__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),c_2Efmapal_2Eincr__merge_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X2_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EDRESTRICT_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2Eenumeral_2EENUMERAL_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eenumeral_2EENUMERAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eenumeral_2EENUMERAL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eenumeral_2Ebt(A_27a),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eenumeral_2Ebt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(A_27a))),c_2Efmapal_2Ebt__map_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Efinite__map_2EFAPPLY_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Elist__to__bt_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eenumeral_2Elist__to__bt_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eincr__sort_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__sort_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__sort_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2EFMAPAL_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c))),c_2Efmapal_2EFMAPAL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)))),c_2Efmapal_2Ebt__map_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFUNION_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFUPDATE_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFUN__FMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFUPDATE__LIST_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq4_2Ec_2Efmapal_2Ebt__rplacv__cn_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__rplacv__cn_2E4(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),X3_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Ebt__rplacv__cn_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),X3_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Elist__rplacv__cn_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Elist__rplacv__cn_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Elist__rplacv__cn_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X2_2E0))) ).
fof(arityeq2_2Ec_2Eenumeral_2EOL_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eenumeral_2EOL_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Eenumeral_2EOL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2EORL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Efmapal_2EORL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2EORL__bt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Efmapal_2EORL__bt_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2EORL__sublists_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__sublists_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),c_2Efmapal_2EORL__sublists_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27z,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
! [A_27z,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),X1_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Etoto_2Etoto_28A_27a_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eassocv_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eassocv_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Efmapal_2Eassocv_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Ebl__to__fmap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebl__to__fmap_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efmapal_2Ebl__to__fmap_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eenumeral_2Ebt(A_27b),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),X1_2E0))) = s(tyop_2Eenumeral_2Ebt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27b))),c_2Efmapal_2Ebt__map_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eenumeral_2Ebt(A_27a),X1_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eenumeral_2Ebt(A_27a),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),X2_2E0))) = s(tyop_2Eenumeral_2Ebt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)))),c_2Eenumeral_2Enode_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(A_27a),X2_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Ebt__to__orl_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eincr__build_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__build_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Eincr__build_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eincr__flat_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__flat_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__flat_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Eo__f_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))),c_2Efinite__map_2Eo__f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Efmapal_2Eoptry_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27g,axiom,
! [A_27g,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27g),X0_2E0),s(tyop_2Eoption_2Eoption(A_27g),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Eoption_2Eoption(A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Eoption_2Eoption(A_27g))),c_2Efmapal_2Eoptry_2E0),s(tyop_2Eoption_2Eoption(A_27g),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27g),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eoptry__list_2E2_2Emono_2EA_27g_20mono_2EA_27z,axiom,
! [A_27g,A_27z,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g))),c_2Efmapal_2Eoptry__list_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27z,axiom,
! [A_27z,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27z),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27z),X0_2E0),s(tyop_2Eoption_2Eoption(A_27z),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Eoption_2Eoption(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Eoption_2Eoption(A_27z))),c_2Efmapal_2Eoptry_2E0),s(tyop_2Eoption_2Eoption(A_27z),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27z),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Etoto_2Etoto_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Efmapal_2Evcossa_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Evcossa_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Efmapal_2Evcossa_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) ).
fof(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Ebt__to__orl__lb__ub_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__ub__ac_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Ebt__to__orl__ub__ac_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) ).
fof(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__lb__ac_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Ebt__to__orl__lb__ac_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) ).
fof(arityeq2_2Ec_2Eenumeral_2Ebt__to__list__ac_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ebt__to__list__ac_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Eenumeral_2Ebt__to__list__ac_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__ac_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ac_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__orl__ac_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2EOFU_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EOFU_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),c_2Efmapal_2EOFU_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2EOPTION__UPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2EOPTION__UPDATE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Efmapal_2EOPTION__UPDATE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2EORL__bt__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Efmapal_2EORL__bt__lb_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2EORL__bt__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Efmapal_2EORL__bt__ub_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2EORWL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Efmapal_2EORWL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2EOWL_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eenumeral_2EOWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Eenumeral_2EOWL_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2EUFO_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EUFO_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),c_2Efmapal_2EUFO_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) ).
fof(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2Eapto_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2Ebt__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ebt__CASE_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Eenumeral_2Ebt__CASE_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Ebt__to__fmap__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebt__to__fmap__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__fmap__lb_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Ebt__to__fmap__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebt__to__fmap__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__fmap__ub_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
! [A_27z,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X0_2E0),s(tyop_2Elist_2Elist(A_27z),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),X2_2E0))) = s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X0_2E0))),s(tyop_2Elist_2Elist(A_27z),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),X2_2E0))) ).
fof(arityeq3_2Ec_2Efmapal_2Emerge__out_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Emerge__out_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X2_2E0))) ).
fof(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eenumeral_2Ebt(A_27b),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(A_27b),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Eenumeral_2Ebt(A_27b),X2_2E0))) = s(tyop_2Eenumeral_2Ebt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Eenumeral_2Ebt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Eenumeral_2Ebt(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Eenumeral_2Ebt(A_27b)))),c_2Eenumeral_2Enode_2E0),s(tyop_2Eenumeral_2Ebt(A_27b),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Eenumeral_2Ebt(A_27b),X2_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27z_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
! [A_27z,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X0_2E0),s(tyop_2Elist_2Elist(A_27z),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),X2_2E0))) = s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X0_2E0))),s(tyop_2Elist_2Elist(A_27z),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),X2_2E0))) ).
fof(arityeq4_2Ec_2Efmapal_2EORL__bt__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Efmapal_2EORL__bt__lb__ub_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2Efmapal_2Ebt__to__fmap__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27b,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0),s(A_27b,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0),s(tyop_2Emin_2Ebool,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))),s(tyop_2Emin_2Ebool,X3_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0))) ).
fof(thm_2Efmapal_2Eoptry,axiom,
! [A_27z] :
( ! [V0p_2E0,V1q_2E0] : s(tyop_2Eoption_2Eoption(A_27z),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,V0p_2E0))),s(tyop_2Eoption_2Eoption(A_27z),V1q_2E0))) = s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,V0p_2E0)))
& ! [V2q_2E0] : s(tyop_2Eoption_2Eoption(A_27z),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27z),V2q_2E0))) = s(tyop_2Eoption_2Eoption(A_27z),V2q_2E0) ) ).
fof(thm_2Efmapal_2Evcossa,axiom,
! [A_27a,A_27b,V0a_2E0,V1l_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Evcossa_2E2(s(A_27a,V0a_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eassocv_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(A_27a,V0a_2E0))) ).
fof(thm_2Efmapal_2EOPTION__UPDATE,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2x_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2EOPTION__UPDATE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(thm_2Efmapal_2Eincr__build,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__build_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0)
& ! [V1cmp_2E0,V2ab_2E0,V3l_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__build_2E2(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2ab_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2ab_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__build_2E2(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))))) ) ).
fof(thm_2Efmapal_2Eincr__flat,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1lol_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__flat_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V1lol_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V1lol_2E0))) ).
fof(thm_2Efmapal_2Eincr__sort,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__sort_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__build_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) ).
fof(thm_2Efmapal_2EOPTION__FLAT__primitive,axiom,
! [A_27z,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
( ! [V4OPTION__FLAT_2E0,V7l_2E0,V8a_2E0] : s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V7l_2E0))),s(tyop_2Elist_2Elist(A_27z),V8a_2E0))) = s(tyop_2Elist_2Elist(A_27z),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27z),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27z),V8a_2E0),s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V7l_2E0)))))))
=> ( ! [V4OPTION__FLAT_2E0,V6v_2E0,V7l_2E0] : s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),V6v_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V7l_2E0))) = s(tyop_2Elist_2Elist(A_27z),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),V6v_2E0),s(tyop_2Elist_2Elist(A_27z),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V7l_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V7l_2E0)))))
=> ( ! [V4OPTION__FLAT_2E0,V5a_27_2E0] : s(tyop_2Elist_2Elist(A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V5a_27_2E0))) = s(tyop_2Elist_2Elist(A_27z),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V5a_27_2E0),s(tyop_2Elist_2Elist(A_27z),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27z),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V4OPTION__FLAT_2E0)))))
=> ( ! [V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),V0R_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),V0R_2E0))))
& ! [V1l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V1l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V1l_2E0))))))
& ! [V2a_2E0,V3l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V3l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27z),V2a_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V3l_2E0)))))) ) )
=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),c_2Efmapal_2EOPTION__FLAT_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),F1_2E0))) ) ) ) ) ).
fof(thm_2Efmapal_2Eunlookup,axiom,
! [A_27a,A_27b,V0f_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Eunlookup_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),c_2Eoption_2ETHE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f_2E0))))) ).
fof(thm_2Efmapal_2Ebt__to__fmap__lb,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V0cmp_2E0,V1lb_2E0,V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V3x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V1lb_2E0),s(A_27a,V3x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0cmp_2E0,V1lb_2E0,V3x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V3x_2E0)))))
=> ! [V0cmp_2E0,V1lb_2E0,V2t_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebt__to__fmap__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V1lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__fmap__ub,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V0cmp_2E0,V3x_2E0,V2ub_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V3x_2E0))),s(A_27a,V2ub_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V3x_2E0),s(A_27a,V2ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0cmp_2E0,V2ub_2E0,V3x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V2ub_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V3x_2E0))),s(A_27a,V2ub_2E0)))))
=> ! [V0cmp_2E0,V1t_2E0,V2ub_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebt__to__fmap__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0),s(A_27a,V2ub_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V2ub_2E0))))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V0cmp_2E0,V1lb_2E0,V4x_2E0,V3ub_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V3ub_2E0))))
<=> ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V1lb_2E0),s(A_27a,V4x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V4x_2E0),s(A_27a,V3ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) )
=> ( ! [V0cmp_2E0,V1lb_2E0,V3ub_2E0,V4x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V3ub_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V3ub_2E0)))))
=> ! [V0cmp_2E0,V1lb_2E0,V2t_2E0,V3ub_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V1lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0),s(A_27a,V3ub_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V1lb_2E0))),s(A_27a,V3ub_2E0))))))) ) ) ).
fof(thm_2Efmapal_2Ebt__map,axiom,
! [A_27a,A_27b] :
( ! [V0f_2E0] : s(tyop_2Eenumeral_2Ebt(A_27b),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),c_2Eenumeral_2Ent_2E0))) = s(tyop_2Eenumeral_2Ebt(A_27b),c_2Eenumeral_2Ent_2E0)
& ! [V1f_2E0,V2l_2E0,V3x_2E0,V4r_2E0] : s(tyop_2Eenumeral_2Ebt(A_27b),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(A_27a),V2l_2E0),s(A_27a,V3x_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),V4r_2E0))))) = s(tyop_2Eenumeral_2Ebt(A_27b),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(A_27b),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),V2l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Eenumeral_2Ebt(A_27b),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),V4r_2E0))))) ) ).
fof(thm_2Efmapal_2Efmap,axiom,
! [A_27a,A_27b,V0l_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))))) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__AUX,axiom,
! [A_27a,A_27b,F7_2E0,F6_2E0,F5_2E0,F4_2E0,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
( ! [V3cmp_2E0,V5lb_2E0,V14x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F7_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V14x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V14x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V3cmp_2E0,V5lb_2E0,V9ub_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0,V11l_2E0,V13r_2E0,V10m_2E0,V14x_2E0,V15y_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))))),F6_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11l_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))),s(A_27a,V14x_2E0))),s(A_27b,V15y_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F7_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V14x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F7_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V14x_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0),s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E2(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E2(s(A_27a,V5lb_2E0),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2E_2C_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11l_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E2(s(A_27a,V14x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V14x_2E0),s(A_27b,V15y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0),s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E2(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E2(s(A_27a,V14x_2E0),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2E_2C_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13r_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E2(s(A_27a,V9ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))))))))))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0),s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E2(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E2(s(A_27a,V5lb_2E0),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2E_2C_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11l_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E2(s(A_27a,V9ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))))))))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0),s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E2(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E2(s(A_27a,V5lb_2E0),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2E_2C_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13r_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E2(s(A_27a,V9ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))))))))))))))
=> ( ! [V3cmp_2E0,V5lb_2E0,V9ub_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0,V10m_2E0,V11l_2E0,V12v9_2E0,V13r_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),F5_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11l_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V12v9_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13r_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V12v9_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))))),F6_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11l_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))))
=> ( ! [V7v4_2E0,V3cmp_2E0,V5lb_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0,V9ub_2E0,V10m_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),F4_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v4_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ebt__CASE_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v4_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),F5_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))))
=> ( ! [V3cmp_2E0,V5lb_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0,V7v4_2E0,V8v5_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F3_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v4_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8v5_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8v5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),F4_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v4_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0)))))
=> ( ! [V3cmp_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0,V5lb_2E0,V6v3_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F2_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6v3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6v3_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F3_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0)))))
=> ( ! [V1bt__to__orl__lb__ub__ac__tupled_2E0,V3cmp_2E0,V4v1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V4v1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V4v1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F2_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0)))))
=> ( ! [V1bt__to__orl__lb__ub__ac__tupled_2E0,V2a_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0))),s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),V2a_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1bt__to__orl__lb__ub__ac__tupled_2E0)))))
=> ! [V0R_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),F0_2E0))) ) ) ) ) ) ) ) ) ).
fof(thm_2Efmapal_2EORWL,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1f_2E0,V2l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))
<=> ( s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))) ) ) ).
fof(thm_2Efmapal_2EOFU,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0cmp_2E0,V2g_2E0,V3x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,c_2Eenumeral_2ELESS__ALL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0)))))))
=> ! [V0cmp_2E0,V1f_2E0,V2g_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EOFU_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))) ) ).
fof(thm_2Efmapal_2EUFO,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V1f_2E0,V0cmp_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V3y_2E0))))
<=> ! [V4z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0))))))
=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V4z_2E0),s(A_27a,V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) )
=> ( ! [V1f_2E0,V0cmp_2E0,V3y_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(A_27a,V3y_2E0)))))
=> ! [V0cmp_2E0,V1f_2E0,V2g_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EUFO_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))))))))) ) ) ).
fof(thm_2Efmapal_2EAP__SND,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1a_2E0,V2b_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Efmapal_2EAP__SND_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(A_27b,V2b_2E0))))) ).
fof(thm_2Efmapal_2EORL__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))
& ! [V2cmp_2E0,V3a_2E0,V4b_2E0,V5l_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V4b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0)))))) ) )
=> ! [V6v_2E0,V7v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v1_2E0)))) ) ).
fof(thm_2Efmapal_2EORL,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V1l_2E0,V2cmp_2E0,V3b_2E0,V4a_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4a_2E0),s(A_27b,V3b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))
& ! [V5p_2E0,V6q_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5p_2E0),s(A_27b,V6q_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))))
=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(A_27a,V4a_2E0),s(A_27a,V5p_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) ) ) ) ).
fof(thm_2Efmapal_2Eoptry__list__ind,axiom,
! [A_27g,A_27z,V0P_2E0] :
( ( ! [V1f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V1f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ENIL_2E0))))
& ! [V2f_2E0,V3l_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V3l_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V3l_2E0)))))) )
& ! [V4f_2E0,V5z_2E0,V6l_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V4f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V6l_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V4f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,V5z_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V6l_2E0)))))) ) )
=> ! [V7v_2E0,V8v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V7v_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V8v1_2E0)))) ) ).
fof(thm_2Efmapal_2Eoptry__list,axiom,
! [A_27g,A_27z] :
( ! [V0f_2E0] : s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V0f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27g),c_2Eoption_2ENONE_2E0)
& ! [V1l_2E0,V2f_2E0] : s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V1l_2E0)))
& ! [V3z_2E0,V4l_2E0,V5f_2E0] : s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,V3z_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V4l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27g),app_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5f_2E0),s(A_27z,V3z_2E0))),s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V4l_2E0))))) ) ).
fof(thm_2Efmapal_2Eassocv__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1a_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(A_27a,V1a_2E0))))
& ! [V2x_2E0,V3y_2E0,V4l_2E0,V5a_2E0] :
( ( s(A_27a,V5a_2E0) != s(A_27a,V2x_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(A_27a,V5a_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))))),s(A_27a,V5a_2E0)))) ) )
=> ! [V6v_2E0,V7v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6v_2E0))),s(A_27a,V7v1_2E0)))) ) ).
fof(thm_2Efmapal_2Eassocv,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V4a_2E0,V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V4a_2E0))),s(A_27a,V2x_2E0))))
<=> s(A_27a,V4a_2E0) = s(A_27a,V2x_2E0) )
=> ( ! [V0a_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eassocv_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(A_27a,V0a_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)
& ! [V1y_2E0,V2x_2E0,V3l_2E0,V4a_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eassocv_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))),s(A_27a,V4a_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V4a_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1y_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Efmapal_2Eassocv_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(A_27a,V4a_2E0))))) ) ) ).
fof(thm_2Efmapal_2Emerge__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))
& ! [V3cmp_2E0,V4v4_2E0,V5v5_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4v4_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5v5_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))
& ! [V6cmp_2E0,V7a1_2E0,V8b1_2E0,V9l1_2E0,V10a2_2E0,V11b2_2E0,V12l2_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(A_27a,V7a1_2E0),s(A_27a,V10a2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l2_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(A_27a,V7a1_2E0),s(A_27a,V10a2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7a1_2E0),s(A_27b,V8b1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l1_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l2_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(A_27a,V7a1_2E0),s(A_27a,V10a2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a2_2E0),s(A_27b,V11b2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l2_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7a1_2E0),s(A_27b,V8b1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l1_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a2_2E0),s(A_27b,V11b2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l2_2E0)))))) ) )
=> ! [V13v_2E0,V14v1_2E0,V15v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V13v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V15v2_2E0)))) ) ).
fof(thm_2Efmapal_2Emerge,axiom,
! [A_27a,A_27b] :
( ! [V0l_2E0,V1cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0)
& ! [V2v5_2E0,V3v4_2E0,V4cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v4_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2v5_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v4_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2v5_2E0)))
& ! [V5l2_2E0,V6l1_2E0,V7cmp_2E0,V8b2_2E0,V9b1_2E0,V10a2_2E0,V11a1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V11a1_2E0),s(A_27b,V9b1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a2_2E0),s(A_27b,V8b2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V11a1_2E0),s(A_27a,V10a2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V11a1_2E0),s(A_27b,V9b1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a2_2E0),s(A_27b,V8b2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l2_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V11a1_2E0),s(A_27b,V9b1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a2_2E0),s(A_27b,V8b2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V11a1_2E0),s(A_27b,V9b1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l2_2E0))))))) ) ).
fof(thm_2Efmapal_2Eincr__merge__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0))))
& ! [V3cmp_2E0,V4l_2E0,V5lol_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5lol_2E0))))))
& ! [V6cmp_2E0,V7l_2E0,V8m_2E0,V9lol_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V9lol_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V9lol_2E0)))))) ) )
=> ! [V10v_2E0,V11v1_2E0,V12v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V10v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V12v2_2E0)))) ) ).
fof(thm_2Efmapal_2Eincr__merge,axiom,
! [A_27a,A_27b] :
( ! [V0l_2E0,V1cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0)))
& ! [V2lol_2E0,V3l_2E0,V4cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V2lol_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V2lol_2E0)))
& ! [V5m_2E0,V6lol_2E0,V7l_2E0,V8cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V8cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6lol_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V8cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V8cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6lol_2E0))))) ) ).
fof(thm_2Efmapal_2EORL__sublists__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0))))
& ! [V2cmp_2E0,V3lol_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V3lol_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V3lol_2E0)))))) )
& ! [V4cmp_2E0,V5m_2E0,V6lol_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6lol_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6lol_2E0)))))) ) )
=> ! [V7v_2E0,V8v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7v_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V8v1_2E0)))) ) ).
fof(thm_2Efmapal_2EORL__sublists,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__sublists_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V1lol_2E0,V2cmp_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__sublists_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V1lol_2E0))))) = s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__sublists_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V1lol_2E0)))
& ! [V3m_2E0,V4lol_2E0,V5cmp_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__sublists_2E2(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V4lol_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__sublists_2E2(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V4lol_2E0)))) ) ) ) ).
fof(thm_2Efmapal_2Emerge__out__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0))))
& ! [V3cmp_2E0,V4l_2E0,V5lol_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5lol_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5lol_2E0)))))) )
& ! [V6cmp_2E0,V7l_2E0,V8m_2E0,V9lol_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V9lol_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V9lol_2E0)))))) ) )
=> ! [V10v_2E0,V11v1_2E0,V12v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V10v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V12v2_2E0)))) ) ).
fof(thm_2Efmapal_2Emerge__out,axiom,
! [A_27a,A_27b] :
( ! [V0l_2E0,V1cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0)
& ! [V2lol_2E0,V3l_2E0,V4cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V2lol_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V2lol_2E0)))
& ! [V5m_2E0,V6lol_2E0,V7l_2E0,V8cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V8cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6lol_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge__out_2E3(s(tyop_2Etoto_2Etoto(A_27a),V8cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V8cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V6lol_2E0))) ) ).
fof(thm_2Efmapal_2EOPTION__FLAT__ind,axiom,
! [A_27z,V0P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ENIL_2E0))))
& ! [V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V1l_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V1l_2E0)))))) )
& ! [V2a_2E0,V3l_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V3l_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27z),V2a_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V3l_2E0)))))) ) )
=> ! [V4v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V4v_2E0)))) ) ).
fof(thm_2Efmapal_2EOPTION__FLAT,axiom,
! [A_27z] :
( s(tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27z),c_2Elist_2ENIL_2E0)
& ! [V0l_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V0l_2E0)))
& ! [V1l_2E0,V2a_2E0] : s(tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27z),V2a_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27z),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27z),V2a_2E0),s(tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V1l_2E0))))) ) ).
fof(thm_2Efmapal_2Ebt__to__fmap__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))))
& ! [V2cmp_2E0,V3l_2E0,V4x_2E0,V5v_2E0,V6r_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0)))))) ) )
=> ! [V7v_2E0,V8v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8v1_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__fmap,axiom,
! [A_27a,A_27b,F3_2E0,F1_2E0,F2_2E0,F0_2E0] :
( ! [V5cmp_2E0,V1x_2E0,V7z_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V1x_2E0))),s(A_27a,V7z_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V1x_2E0),s(A_27a,V7z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V5cmp_2E0,V1x_2E0,V7z_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V1x_2E0))),s(A_27a,V7z_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V7z_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V1x_2E0))),s(A_27a,V7z_2E0)))))
=> ( ! [V5cmp_2E0,V6y_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V6y_2E0))),s(A_27a,V1x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6y_2E0),s(A_27a,V1x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V5cmp_2E0,V1x_2E0,V6y_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V1x_2E0))),s(A_27a,V6y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V6y_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V6y_2E0))),s(A_27a,V1x_2E0)))))
=> ( ! [V0cmp_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0)
& ! [V1x_2E0,V2v_2E0,V3r_2E0,V4l_2E0,V5cmp_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3r_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V1x_2E0))))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2v_2E0))))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V1x_2E0))))))))) ) ) ) ) ) ).
fof(thm_2Efmapal_2EFAPPLY__nt,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1x_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V1x_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(A_27a,V1x_2E0))) ).
fof(thm_2Efmapal_2EFAPPLY__node,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1x_2E0,V2l_2E0,V3a_2E0,V4b_2E0,V5r_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V4b_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0))))),s(A_27a,V1x_2E0))) = s(A_27b,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(A_27a,V1x_2E0),s(A_27a,V3a_2E0))),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(A_27a,V1x_2E0))),s(A_27b,V4b_2E0),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0))),s(A_27a,V1x_2E0))))) ).
fof(thm_2Efmapal_2Ebt__FST__FDOM,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1t_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eenumeral_2EENUMERAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ub__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2lb_2E0,V3ub_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(A_27a,V2lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V3ub_2E0))))
& ! [V4cmp_2E0,V5lb_2E0,V6l_2E0,V7x_2E0,V8y_2E0,V9r_2E0,V10ub_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V7x_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))),s(A_27a,V10ub_2E0)))) )
& ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V7x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V7x_2E0),s(A_27a,V10ub_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0))),s(A_27a,V10ub_2E0)))) )
& ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V7x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V7x_2E0),s(A_27a,V10ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0))),s(A_27a,V7x_2E0)))) )
& ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V7x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V7x_2E0),s(A_27a,V10ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V7x_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))),s(A_27a,V10ub_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27b,V8y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))))),s(A_27a,V10ub_2E0)))) ) )
=> ! [V11v_2E0,V12v1_2E0,V13v2_2E0,V14v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11v_2E0))),s(A_27a,V12v1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13v2_2E0))),s(A_27a,V14v3_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V9cmp_2E0,V7lb_2E0,V4x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V7lb_2E0))),s(A_27a,V4x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(A_27a,V4x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0ub_2E0,V1lb_2E0,V2cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(A_27a,V1lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(A_27a,V0ub_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V3y_2E0,V4x_2E0,V5ub_2E0,V6r_2E0,V7lb_2E0,V8l_2E0,V9cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0))),s(A_27a,V5ub_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V7lb_2E0))),s(A_27a,V4x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V5ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(A_27a,V4x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V4x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0),s(A_27a,V5ub_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(A_27a,V5ub_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0),s(A_27a,V5ub_2E0))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2lb_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(A_27a,V2lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))))
& ! [V3cmp_2E0,V4lb_2E0,V5l_2E0,V6x_2E0,V7y_2E0,V8r_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(A_27a,V4lb_2E0),s(A_27a,V6x_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V4lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(A_27a,V4lb_2E0),s(A_27a,V6x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V6x_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V4lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0)))))) ) )
=> ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9v_2E0))),s(A_27a,V10v1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v2_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V7cmp_2E0,V5lb_2E0,V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V3x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V3x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0lb_2E0,V1cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(A_27a,V0lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V2y_2E0,V3x_2E0,V4r_2E0,V5lb_2E0,V6l_2E0,V7cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V5lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4r_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0))),s(A_27a,V5lb_2E0))),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V5lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V3x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4r_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V5lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4r_2E0))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ub__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2ub_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V2ub_2E0))))
& ! [V3cmp_2E0,V4l_2E0,V5x_2E0,V6y_2E0,V7r_2E0,V8ub_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(A_27a,V5x_2E0),s(A_27a,V8ub_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(A_27a,V8ub_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(A_27a,V5x_2E0),s(A_27a,V8ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(A_27a,V5x_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0))))),s(A_27a,V8ub_2E0)))) ) )
=> ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10v1_2E0))),s(A_27a,V11v2_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ub,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V7cmp_2E0,V3x_2E0,V4ub_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0))),s(A_27a,V3x_2E0))),s(A_27a,V4ub_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V3x_2E0),s(A_27a,V4ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0ub_2E0,V1cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(A_27a,V0ub_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V2y_2E0,V3x_2E0,V4ub_2E0,V5r_2E0,V6l_2E0,V7cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0))),s(A_27a,V4ub_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0))),s(A_27a,V3x_2E0))),s(A_27a,V4ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V3x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0),s(A_27a,V4ub_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(A_27a,V4ub_2E0))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))))
& ! [V2cmp_2E0,V3l_2E0,V4x_2E0,V5y_2E0,V6r_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0)))))) )
=> ! [V7v_2E0,V8v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8v1_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl,axiom,
! [A_27a,A_27b,V0y_2E0,V1x_2E0,V2r_2E0,V3l_2E0,V4cmp_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl_2E2(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl_2E2(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2r_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V1x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2r_2E0))))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2lb_2E0,V3ub_2E0,V4m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(A_27a,V2lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V3ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4m_2E0))))
& ! [V5cmp_2E0,V6lb_2E0,V7l_2E0,V8x_2E0,V9y_2E0,V10r_2E0,V11ub_2E0,V12m_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6lb_2E0),s(A_27a,V8x_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V6lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10r_2E0))),s(A_27a,V11ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0)))) )
& ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6lb_2E0),s(A_27a,V8x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V8x_2E0),s(A_27a,V11ub_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V6lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0))),s(A_27a,V11ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0)))) )
& ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6lb_2E0),s(A_27a,V8x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V8x_2E0),s(A_27a,V11ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V6lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0))),s(A_27a,V8x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8x_2E0),s(A_27b,V9y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V8x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10r_2E0),s(A_27a,V11ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0)))))))) )
& ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6lb_2E0),s(A_27a,V8x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V8x_2E0),s(A_27a,V11ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V8x_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10r_2E0))),s(A_27a,V11ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(A_27a,V6lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8x_2E0),s(A_27b,V9y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10r_2E0))))),s(A_27a,V11ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0)))) ) )
=> ! [V13v_2E0,V14v1_2E0,V15v2_2E0,V16v3_2E0,V17v4_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V13v_2E0))),s(A_27a,V14v1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V15v2_2E0))),s(A_27a,V16v3_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V17v4_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V11cmp_2E0,V9lb_2E0,V5x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0))),s(A_27a,V9lb_2E0))),s(A_27a,V5x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V9lb_2E0),s(A_27a,V5x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0ub_2E0,V1m_2E0,V2lb_2E0,V3cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(A_27a,V2lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(A_27a,V0ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1m_2E0)
& ! [V4y_2E0,V5x_2E0,V6ub_2E0,V7r_2E0,V8m_2E0,V9lb_2E0,V10l_2E0,V11cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V9lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0))),s(A_27a,V6ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0))),s(A_27a,V9lb_2E0))),s(A_27a,V5x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V9lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(A_27a,V5x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V5x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0),s(A_27a,V6ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V9lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(A_27a,V6ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V9lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0),s(A_27a,V6ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ac__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2lb_2E0,V3m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(A_27a,V2lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))))
& ! [V4cmp_2E0,V5lb_2E0,V6l_2E0,V7x_2E0,V8y_2E0,V9r_2E0,V10m_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V7x_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V5lb_2E0),s(A_27a,V7x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V7x_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27b,V8y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))) ) )
=> ! [V11v_2E0,V12v1_2E0,V13v2_2E0,V14v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11v_2E0))),s(A_27a,V12v1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13v2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v3_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V9cmp_2E0,V7lb_2E0,V4x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V7lb_2E0))),s(A_27a,V4x_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(A_27a,V4x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0m_2E0,V1lb_2E0,V2cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(A_27a,V1lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0m_2E0)
& ! [V3y_2E0,V4x_2E0,V5r_2E0,V6m_2E0,V7lb_2E0,V8l_2E0,V9cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V7lb_2E0))),s(A_27a,V4x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V4x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6m_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6m_2E0))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ub__ac__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2ub_2E0,V3m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V2ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))))
& ! [V4cmp_2E0,V5l_2E0,V6x_2E0,V7y_2E0,V8r_2E0,V9ub_2E0,V10m_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V6x_2E0),s(A_27a,V9ub_2E0))) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0))),s(A_27a,V9ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V6x_2E0),s(A_27a,V9ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0))),s(A_27a,V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V6x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0),s(A_27a,V9ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0))))),s(A_27a,V9ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))) ) )
=> ! [V11v_2E0,V12v1_2E0,V13v2_2E0,V14v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12v1_2E0))),s(A_27a,V13v2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v3_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V9cmp_2E0,V4x_2E0,V5ub_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V5ub_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V4x_2E0),s(A_27a,V5ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V0ub_2E0,V1m_2E0,V2cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(A_27a,V0ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1m_2E0)
& ! [V3y_2E0,V4x_2E0,V5ub_2E0,V6r_2E0,V7m_2E0,V8l_2E0,V9cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0))),s(A_27a,V5ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V5ub_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V4x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0),s(A_27a,V5ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7m_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(A_27a,V5ub_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7m_2E0))))) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ac__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2m_2E0))))
& ! [V3cmp_2E0,V4l_2E0,V5x_2E0,V6y_2E0,V7r_2E0,V8m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0)))) )
=> ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10v1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v2_2E0)))) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ac,axiom,
! [A_27a,A_27b,V0y_2E0,V1x_2E0,V2r_2E0,V3m_2E0,V4l_2E0,V5cmp_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ac_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0)
& s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ac_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0),s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V1x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2r_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0))))))) ) ).
fof(thm_2Efmapal_2EORWL__bt__to__orl,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1t_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0)))))) ).
fof(thm_2Efmapal_2Ebl__to__fmap__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enbl_2E0))))
& ! [V2cmp_2E0,V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V3b_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ezerbl_2E1(s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V3b_2E0)))))) )
& ! [V4cmp_2E0,V5x_2E0,V6y_2E0,V7t_2E0,V8b_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V8b_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Eonebl_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7t_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V8b_2E0)))))) ) )
=> ! [V9v_2E0,V10v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9v_2E0))),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V10v1_2E0)))) ) ).
fof(thm_2Efmapal_2Ebl__to__fmap,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V6cmp_2E0,V4x_2E0,V8z_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V8z_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(A_27a,V4x_2E0),s(A_27a,V8z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
=> ( ! [V6cmp_2E0,V4x_2E0,V8z_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V8z_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V8z_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(A_27a,V4x_2E0))),s(A_27a,V8z_2E0)))))
=> ( ! [V0cmp_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebl__to__fmap_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enbl_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0)
& ! [V1cmp_2E0,V2b_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebl__to__fmap_2E2(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ezerbl_2E1(s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V2b_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebl__to__fmap_2E2(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V2b_2E0)))
& ! [V3y_2E0,V4x_2E0,V5t_2E0,V6cmp_2E0,V7b_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebl__to__fmap_2E2(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Eonebl_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5t_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V7b_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EOFU_2E3(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(A_27a,V4x_2E0))))))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Ebl__to__fmap_2E2(s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0),s(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),V7b_2E0))))) ) ) ) ).
fof(thm_2Efmapal_2Ebt__to__orl__ID__IMP,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))
=> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Elist__to__bt_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0) ) ).
fof(thm_2Efmapal_2Efmap__FDOM,axiom,
! [A_27a,A_27b,V0l_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))))) ).
fof(thm_2Efmapal_2EORL__FUNION__IMP,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))
=> ! [V2m_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2m_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2m_2E0))))))
& s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2m_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2m_2E0))))) ) ) ) ).
fof(thm_2Efmapal_2EFMAPAL__FDOM__THM,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0,V1x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [V2cmp_2E0,V3x_2E0,V4a_2E0,V5b_2E0,V6l_2E0,V7r_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4a_2E0),s(A_27b,V5b_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(A_27a,V3x_2E0),s(A_27a,V4a_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0))))))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0))))))))) ) ).
fof(thm_2Efmapal_2Einter__merge__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))
& ! [V2cmp_2E0,V3a_2E0,V4b_2E0,V5l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V4b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))
& ! [V6cmp_2E0,V7y_2E0,V8m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7y_2E0),s(tyop_2Elist_2Elist(A_27a),V8m_2E0))))))
& ! [V9cmp_2E0,V10a_2E0,V11b_2E0,V12l_2E0,V13y_2E0,V14m_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V10a_2E0),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V10a_2E0),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a_2E0),s(A_27b,V11b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))))),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V10a_2E0),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V13y_2E0),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a_2E0),s(A_27b,V11b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V13y_2E0),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))))) ) )
=> ! [V15v_2E0,V16v1_2E0,V17v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V15v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V16v1_2E0))),s(tyop_2Elist_2Elist(A_27a),V17v2_2E0)))) ) ).
fof(thm_2Efmapal_2Einter__merge,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V1l_2E0,V2cmp_2E0,V3b_2E0,V4a_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4a_2E0),s(A_27b,V3b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V5y_2E0,V6m_2E0,V7cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V6m_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V8y_2E0,V9m_2E0,V10l_2E0,V11cmp_2E0,V12b_2E0,V13a_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V13a_2E0),s(A_27b,V12b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V8y_2E0),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V13a_2E0),s(A_27a,V8y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V8y_2E0),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V13a_2E0),s(A_27b,V12b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V13a_2E0),s(A_27b,V12b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0))),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))) ) ).
fof(thm_2Efmapal_2EORL__DRESTRICT__IMP,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))
=> ! [V2m_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eenumeral_2EOL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))))
& s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))) ) ) ) ).
fof(thm_2Efmapal_2Ediff__merge__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))
& ! [V2cmp_2E0,V3a_2E0,V4b_2E0,V5l_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V4b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))
& ! [V6cmp_2E0,V7y_2E0,V8m_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V6cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7y_2E0),s(tyop_2Elist_2Elist(A_27a),V8m_2E0))))))
& ! [V9cmp_2E0,V10a_2E0,V11b_2E0,V12l_2E0,V13y_2E0,V14m_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V10a_2E0),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V10a_2E0),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a_2E0),s(A_27b,V11b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))))),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V10a_2E0),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V13y_2E0),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10a_2E0),s(A_27b,V11b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V13y_2E0),s(tyop_2Elist_2Elist(A_27a),V14m_2E0)))))) ) )
=> ! [V15v_2E0,V16v1_2E0,V17v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V15v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V16v1_2E0))),s(tyop_2Elist_2Elist(A_27a),V17v2_2E0)))) ) ).
fof(thm_2Efmapal_2Ediff__merge,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V1l_2E0,V2cmp_2E0,V3b_2E0,V4a_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4a_2E0),s(A_27b,V3b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4a_2E0),s(A_27b,V3b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0)))
& ! [V5y_2E0,V6m_2E0,V7cmp_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V6m_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V8y_2E0,V9m_2E0,V10l_2E0,V11cmp_2E0,V12b_2E0,V13a_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V13a_2E0),s(A_27b,V12b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V8y_2E0),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V13a_2E0),s(A_27a,V8y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V13a_2E0),s(A_27b,V12b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V8y_2E0),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V13a_2E0),s(A_27b,V12b_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10l_2E0))),s(tyop_2Elist_2Elist(A_27a),V9m_2E0))))) ) ).
fof(thm_2Efmapal_2EORL__DRESTRICT__COMPL__IMP,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))
=> ! [V2m_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eenumeral_2EOL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))))
& s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0),s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2m_2E0))))))) ) ) ) ).
fof(thm_2Efmapal_2EFMAPAL__fmap,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Elist__to__bt_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__sort_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))))) ).
fof(thm_2Efmapal_2EORL__FMAPAL,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))
=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Elist__to__bt_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) ) ).
fof(thm_2Efmapal_2EORWL__FUNION__THM,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1s_2E0,V2l_2E0,V3t_2E0,V4m_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3t_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4m_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3t_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Emerge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4m_2E0)))))) ) ).
fof(thm_2Efmapal_2EORWL__DRESTRICT__THM,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1s_2E0,V2l_2E0,V3t_2E0,V4m_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eenumeral_2EOWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Elist_2Elist(A_27a),V4m_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Einter__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V4m_2E0)))))) ) ).
fof(thm_2Efmapal_2EORWL__DRESTRICT__COMPL__THM,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1s_2E0,V2l_2E0,V3t_2E0,V4m_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eenumeral_2EOWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Elist_2Elist(A_27a),V4m_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ediff__merge_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V4m_2E0)))))) ) ).
fof(thm_2Efmapal_2Eo__f__bt__map,axiom,
! [A_27a,A_27b,A_27c,V0cmp_2E0,V1f_2E0,V2t_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Eo__f_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2Ebt__map_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2EAP__SND_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) ).
fof(thm_2Efmapal_2EFAPPLY__fmap__NIL,axiom,
! [A_27a,A_27b,V0x_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(A_27a,V0x_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(A_27a,V0x_2E0))) ).
fof(thm_2Efmapal_2EFAPPLY__fmap__CONS,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0x_2E0,V1y_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0))))
<=> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) )
=> ! [V0x_2E0,V1y_2E0,V2z_2E0,V3l_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1y_2E0),s(A_27b,V2z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))))),s(A_27a,V0x_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0))),s(A_27b,V2z_2E0),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0))),s(A_27a,V0x_2E0))))) ) ).
fof(thm_2Efmapal_2Eo__f__fmap,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1l_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Eo__f_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2EAP__SND_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) ).
fof(thm_2Efmapal_2EORL__bt__lb__ub__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2lb_2E0,V3ub_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(A_27a,V2lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V3ub_2E0))))
& ! [V4cmp_2E0,V5lb_2E0,V6l_2E0,V7x_2E0,V8y_2E0,V9r_2E0,V10ub_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0))),s(A_27a,V7x_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V7x_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))),s(A_27a,V10ub_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0))),s(A_27a,V5lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27b,V8y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9r_2E0))))),s(A_27a,V10ub_2E0)))) ) )
=> ! [V11v_2E0,V12v1_2E0,V13v2_2E0,V14v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V11v_2E0))),s(A_27a,V12v1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13v2_2E0))),s(A_27a,V14v3_2E0)))) ) ).
fof(thm_2Efmapal_2EORL__bt__lb__ub,axiom,
! [A_27a,A_27b] :
( ! [V0ub_2E0,V1lb_2E0,V2cmp_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(A_27a,V1lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(A_27a,V0ub_2E0))))
<=> s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0),s(A_27a,V1lb_2E0),s(A_27a,V0ub_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
& ! [V3y_2E0,V4x_2E0,V5ub_2E0,V6r_2E0,V7lb_2E0,V8l_2E0,V9cmp_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0))),s(A_27a,V5ub_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V7lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(A_27a,V4x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V9cmp_2E0),s(A_27a,V4x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0),s(A_27a,V5ub_2E0)))) ) ) ) ).
fof(thm_2Efmapal_2EORL__bt__lb__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2lb_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(A_27a,V2lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))))
& ! [V3cmp_2E0,V4lb_2E0,V5l_2E0,V6x_2E0,V7y_2E0,V8r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V6x_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(A_27a,V4lb_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0)))))) ) )
=> ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9v_2E0))),s(A_27a,V10v1_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v2_2E0)))) ) ).
fof(thm_2Efmapal_2EORL__bt__lb,axiom,
! [A_27a,A_27b] :
( ! [V0lb_2E0,V1cmp_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(A_27a,V0lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V2y_2E0,V3x_2E0,V4r_2E0,V5lb_2E0,V6l_2E0,V7cmp_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V5lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4r_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V5lb_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(A_27a,V3x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V3x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4r_2E0)))) ) ) ) ).
fof(thm_2Efmapal_2EORL__bt__ub__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0,V2ub_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(A_27a,V2ub_2E0))))
& ! [V3cmp_2E0,V4l_2E0,V5x_2E0,V6y_2E0,V7r_2E0,V8ub_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))),s(A_27a,V5x_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0))))),s(A_27a,V8ub_2E0)))) ) )
=> ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V9v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10v1_2E0))),s(A_27a,V11v2_2E0)))) ) ).
fof(thm_2Efmapal_2EORL__bt__ub,axiom,
! [A_27a,A_27b] :
( ! [V0ub_2E0,V1cmp_2E0] : s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(A_27a,V0ub_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V2y_2E0,V3x_2E0,V4ub_2E0,V5r_2E0,V6l_2E0,V7cmp_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0))),s(A_27a,V4ub_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0),s(A_27a,V3x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb__ub_2E4(s(tyop_2Etoto_2Etoto(A_27a),V7cmp_2E0),s(A_27a,V3x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5r_2E0),s(A_27a,V4ub_2E0)))) ) ) ) ).
fof(thm_2Efmapal_2EORL__bt__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))))
& ! [V2cmp_2E0,V3l_2E0,V4x_2E0,V5y_2E0,V6r_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V2cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6r_2E0)))))) )
=> ! [V7v_2E0,V8v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V7v_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8v1_2E0)))) ) ).
fof(thm_2Efmapal_2EORL__bt,axiom,
! [A_27a,A_27b,V0y_2E0,V1x_2E0,V2r_2E0,V3l_2E0,V4cmp_2E0] :
( s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt_2E2(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt_2E2(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2r_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__ub_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),s(A_27a,V1x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt__lb_2E3(s(tyop_2Etoto_2Etoto(A_27a),V4cmp_2E0),s(A_27a,V1x_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2r_2E0)))) ) ) ) ).
fof(thm_2Efmapal_2Ebetter__bt__to__orl,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1t_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORL__bt_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ebt__to__list__ac_2E2(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__to__orl__ac_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))) ).
fof(thm_2Efmapal_2Elist__rplacv__cn__ind,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V9cn_2E0,V6w_2E0,V7z_2E0,V10m_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V9cn_2E0))),s(A_27a,V6w_2E0))),s(A_27b,V7z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V9cn_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6w_2E0),s(A_27b,V7z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0)))))
=> ! [V0P_2E0] :
( ( ! [V1x_2E0,V2y_2E0,V3cn_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V3cn_2E0))))
& ! [V4x_2E0,V5y_2E0,V6w_2E0,V7z_2E0,V8l_2E0,V9cn_2E0] :
( ( s(A_27a,V4x_2E0) != s(A_27a,V6w_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V9cn_2E0))),s(A_27a,V6w_2E0))),s(A_27b,V7z_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6w_2E0),s(A_27b,V7z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V9cn_2E0)))) ) )
=> ! [V11v_2E0,V12v1_2E0,V13v2_2E0,V14v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V11v_2E0),s(A_27b,V12v1_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V13v2_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V14v3_2E0)))) ) ) ).
fof(thm_2Efmapal_2Elist__rplacv__cn,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V8cn_2E0,V6w_2E0,V3z_2E0,V9m_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8cn_2E0))),s(A_27a,V6w_2E0))),s(A_27b,V3z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8cn_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6w_2E0),s(A_27b,V3z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9m_2E0)))))
=> ( ! [V5x_2E0,V6w_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6w_2E0))))
<=> s(A_27a,V5x_2E0) = s(A_27a,V6w_2E0) )
=> ( ! [V0y_2E0,V1x_2E0,V2cn_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Elist__rplacv__cn_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V2cn_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V3z_2E0,V4y_2E0,V5x_2E0,V6w_2E0,V7l_2E0,V8cn_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Elist__rplacv__cn_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6w_2E0),s(A_27b,V3z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8cn_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6w_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8cn_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Elist__rplacv__cn_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V8cn_2E0))),s(A_27a,V6w_2E0))),s(A_27b,V3z_2E0))))))) ) ) ) ).
fof(thm_2Efmapal_2Efmap__FDOM__rec,axiom,
! [A_27a,A_27b] :
( ! [V0x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [V1x_2E0,V2w_2E0,V3z_2E0,V4l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2w_2E0),s(A_27b,V3z_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0))))))))))
<=> ( s(A_27a,V1x_2E0) = s(A_27a,V2w_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0)))))))) ) ) ) ).
fof(thm_2Efmapal_2Elist__rplacv__thm,axiom,
! [A_27a,A_27b,F1_2E0,F2_2E0,F3_2E0,F4_2E0,F0_2E0] :
( ! [V4m_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),F1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4m_2E0)
=> ( ! [V3ans_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0))))
<=> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0) )
=> ( ! [V0x_2E0,V2l_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),F3_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))))))) )
=> ( ! [V0x_2E0,V2l_2E0,V1y_2E0,V3ans_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F4_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(A_27b,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))))))))
& s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0))) ) )
=> ( ! [V0x_2E0,V2l_2E0,V1y_2E0,V3ans_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(A_27b,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),F3_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F4_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(A_27b,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ans_2E0)))))
=> ! [V0x_2E0,V1y_2E0,V2l_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0))),s(A_27b,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Elist__rplacv__cn_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),F1_2E0)))))) ) ) ) ) ) ).
fof(thm_2Efmapal_2Ebt__rplacv__cn__ind,axiom,
! [A_27a,A_27b,F0_2E0,F1_2E0] :
( ! [V12cn_2E0,V8l_2E0,V9w_2E0,V10z_2E0,V13m_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0))),s(A_27a,V9w_2E0))),s(A_27b,V10z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13m_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V9w_2E0),s(A_27b,V10z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13m_2E0)))))
=> ( ! [V12cn_2E0,V9w_2E0,V10z_2E0,V11r_2E0,V14m_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0))),s(A_27a,V9w_2E0))),s(A_27b,V10z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11r_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V14m_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V14m_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V9w_2E0),s(A_27b,V10z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11r_2E0)))))
=> ! [V0P_2E0] :
( ( ! [V1cmp_2E0,V2x_2E0,V3y_2E0,V4cn_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V1cmp_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V4cn_2E0))))
& ! [V5cmp_2E0,V6x_2E0,V7y_2E0,V8l_2E0,V9w_2E0,V10z_2E0,V11r_2E0,V12cn_2E0] :
( ( ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6x_2E0),s(A_27a,V9w_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11r_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0))),s(A_27a,V9w_2E0))),s(A_27b,V10z_2E0)))))) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0),s(A_27a,V6x_2E0),s(A_27a,V9w_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0))),s(A_27a,V9w_2E0))),s(A_27b,V10z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11r_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V5cmp_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V9w_2E0),s(A_27b,V10z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11r_2E0))))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V12cn_2E0)))) ) )
=> ! [V15v_2E0,V16v1_2E0,V17v2_2E0,V18v3_2E0,V19v4_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Etoto_2Etoto(A_27a),V15v_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V16v1_2E0),s(A_27b,V17v2_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V18v3_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V19v4_2E0)))) ) ) ) ).
fof(thm_2Efmapal_2Ebt__rplacv__cn,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V10cn_2E0,V9l_2E0,V7w_2E0,V4z_2E0,V13m_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0))),s(A_27a,V7w_2E0))),s(A_27b,V4z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13m_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7w_2E0),s(A_27b,V4z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13m_2E0)))))
=> ( ! [V10cn_2E0,V7w_2E0,V4z_2E0,V8r_2E0,V12m_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0))),s(A_27a,V7w_2E0))),s(A_27b,V4z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7w_2E0),s(A_27b,V4z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0)))))
=> ( ! [V0y_2E0,V1x_2E0,V2cn_2E0,V3cmp_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__rplacv__cn_2E4(s(tyop_2Etoto_2Etoto(A_27a),V3cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V2cn_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0)
& ! [V4z_2E0,V5y_2E0,V6x_2E0,V7w_2E0,V8r_2E0,V9l_2E0,V10cn_2E0,V11cmp_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__rplacv__cn_2E4(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V5y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V7w_2E0),s(A_27b,V4z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(A_27a,V6x_2E0),s(A_27a,V7w_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__rplacv__cn_2E4(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V5y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0))),s(A_27a,V7w_2E0))),s(A_27b,V4z_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Enode_2E3(s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V5y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0))))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__rplacv__cn_2E4(s(tyop_2Etoto_2Etoto(A_27a),V11cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V5y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8r_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V10cn_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0))),s(A_27a,V7w_2E0))),s(A_27b,V4z_2E0))))))) ) ) ) ).
fof(thm_2Efmapal_2Ebt__rplacv__thm,axiom,
! [A_27a,A_27b,F1_2E0,F2_2E0,F3_2E0,F4_2E0,F0_2E0] :
( ! [V5m_2E0] : s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),F1_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0))) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0)
=> ( ! [V4ans_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0))))
<=> s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0) = s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ent_2E0) )
=> ( ! [V1x_2E0,V0cmp_2E0,V3t_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F3_2E0),s(A_27a,V1x_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0)))))))) )
=> ( ! [V1x_2E0,V0cmp_2E0,V3t_2E0,V2y_2E0,V4ans_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),F4_2E0),s(A_27a,V1x_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))))))))
& s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2EFMAPAL_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0))) ) )
=> ( ! [V1x_2E0,V0cmp_2E0,V3t_2E0,V2y_2E0,V4ans_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),F0_2E0),s(A_27a,V1x_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F3_2E0),s(A_27a,V1x_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),F4_2E0),s(A_27a,V1x_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4ans_2E0)))))
=> ! [V0cmp_2E0,V1x_2E0,V2y_2E0,V3t_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),F0_2E0),s(A_27a,V1x_2E0))),s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0))),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Ebt__rplacv__cn_2E4(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),F1_2E0)))))) ) ) ) ) ) ).
fof(thm_2Efmapal_2EFUN__fmap__thm,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0f_2E0,V2x_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))))
=> ! [V0f_2E0,V1l_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ).
fof(thm_2Efmapal_2Efmap__ORWL__thm,axiom,
! [A_27a,A_27b,V0cmp_2E0,V1l_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efmapal_2EORWL_2E3(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__sort_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0)))))) ).
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).
%------------------------------------------------------------------------------