ITP001 Axioms: ITP083^4.ax
%------------------------------------------------------------------------------
% File : ITP083^4 : 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 : fmaptree.ax [Gau19]
% : HL4083^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 210 ( 77 unt; 107 typ; 0 def)
% Number of atoms : 200 ( 109 equ; 1 cnn)
% Maximal formula atoms : 8 ( 0 avg)
% Number of connectives : 6583 ( 1 ~; 1 |; 19 &;6507 @)
% ( 15 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 8 avg;6507 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 106 ( 104 usr; 47 con; 0-3 aty)
% Number of variables : 449 ( 0 ^ 433 !; 16 ?; 449 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(tyop_2Efinite__map_2Efmap,type,
tyop_2Efinite__map_2Efmap: d > d > d ).
thf(tyop_2Efmaptree_2Efmaptree,type,
tyop_2Efmaptree_2Efmaptree: d > d > d ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: d > d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(s,type,
s: d > u > du ).
thf(app_2E2,type,
app_2E2: du > du > u ).
thf(combin_i_2E0,type,
combin_i_2E0: u ).
thf(combin_k_2E0,type,
combin_k_2E0: u ).
thf(combin_s_2E0,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0: u ).
thf(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1: du > u ).
thf(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0: u ).
thf(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2: du > du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0: u ).
thf(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2: du > du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Efinite__map_2EFAPPLY_2E0,type,
c_2Efinite__map_2EFAPPLY_2E0: u ).
thf(c_2Efinite__map_2EFAPPLY_2E2,type,
c_2Efinite__map_2EFAPPLY_2E2: du > du > u ).
thf(c_2Efinite__map_2EFDOM_2E0,type,
c_2Efinite__map_2EFDOM_2E0: u ).
thf(c_2Efinite__map_2EFDOM_2E1,type,
c_2Efinite__map_2EFDOM_2E1: du > u ).
thf(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1: du > u ).
thf(c_2Efinite__map_2EFLOOKUP_2E0,type,
c_2Efinite__map_2EFLOOKUP_2E0: u ).
thf(c_2Efinite__map_2EFLOOKUP_2E2,type,
c_2Efinite__map_2EFLOOKUP_2E2: du > du > u ).
thf(c_2Efmaptree_2EFTNode_2E0,type,
c_2Efmaptree_2EFTNode_2E0: u ).
thf(c_2Efmaptree_2EFTNode_2E2,type,
c_2Efmaptree_2EFTNode_2E2: du > du > u ).
thf(c_2Efinite__map_2EFUPDATE_2E0,type,
c_2Efinite__map_2EFUPDATE_2E0: u ).
thf(c_2Efinite__map_2EFUPDATE_2E2,type,
c_2Efinite__map_2EFUPDATE_2E2: du > du > u ).
thf(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0: u ).
thf(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1: du > u ).
thf(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
thf(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0: u ).
thf(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0: u ).
thf(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0: u ).
thf(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Efmaptree_2Eapply__path_2E0,type,
c_2Efmaptree_2Eapply__path_2E0: u ).
thf(c_2Efmaptree_2Eapply__path_2E2,type,
c_2Efmaptree_2Eapply__path_2E2: du > du > u ).
thf(c_2Efmaptree_2Econstruct_2E0,type,
c_2Efmaptree_2Econstruct_2E0: u ).
thf(c_2Efmaptree_2Econstruct_2E2,type,
c_2Efmaptree_2Econstruct_2E2: du > du > u ).
thf(c_2Efmaptree_2Econstruct_2E3,type,
c_2Efmaptree_2Econstruct_2E3: du > du > du > u ).
thf(c_2Efmaptree_2Efmtreerec_2E0,type,
c_2Efmaptree_2Efmtreerec_2E0: u ).
thf(c_2Efmaptree_2Efmtreerec_2E1,type,
c_2Efmaptree_2Efmtreerec_2E1: du > u ).
thf(c_2Efmaptree_2Efmtreerec_2E2,type,
c_2Efmaptree_2Efmtreerec_2E2: du > du > u ).
thf(c_2Efmaptree_2EfromF_2E0,type,
c_2Efmaptree_2EfromF_2E0: u ).
thf(c_2Efmaptree_2EfromF_2E1,type,
c_2Efmaptree_2EfromF_2E1: du > u ).
thf(c_2Efmaptree_2Efupd__at__path_2E0,type,
c_2Efmaptree_2Efupd__at__path_2E0: u ).
thf(c_2Efmaptree_2Efupd__at__path_2E3,type,
c_2Efmaptree_2Efupd__at__path_2E3: du > du > du > u ).
thf(c_2Efmaptree_2Eitem_2E0,type,
c_2Efmaptree_2Eitem_2E0: u ).
thf(c_2Efmaptree_2Eitem_2E1,type,
c_2Efmaptree_2Eitem_2E1: du > u ).
thf(c_2Elist_2Elist__CASE_2E0,type,
c_2Elist_2Elist__CASE_2E0: u ).
thf(c_2Elist_2Elist__CASE_2E3,type,
c_2Elist_2Elist__CASE_2E3: du > du > du > u ).
thf(c_2Efmaptree_2Emap_2E0,type,
c_2Efmaptree_2Emap_2E0: u ).
thf(c_2Efmaptree_2Emap_2E1,type,
c_2Efmaptree_2Emap_2E1: du > u ).
thf(c_2Efinite__map_2Eo__f_2E0,type,
c_2Efinite__map_2Eo__f_2E0: u ).
thf(c_2Efinite__map_2Eo__f_2E2,type,
c_2Efinite__map_2Eo__f_2E2: du > du > u ).
thf(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0: u ).
thf(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
thf(c_2Efmaptree_2Erelrec_2E0,type,
c_2Efmaptree_2Erelrec_2E0: u ).
thf(c_2Efmaptree_2Erelrec_2E3,type,
c_2Efmaptree_2Erelrec_2E3: du > du > du > u ).
thf(c_2Efmaptree_2EtoF_2E0,type,
c_2Efmaptree_2EtoF_2E0: u ).
thf(c_2Efmaptree_2EtoF_2E1,type,
c_2Efmaptree_2EtoF_2E1: du > u ).
thf(c_2Efmaptree_2Eupdate__at__path_2E0,type,
c_2Efmaptree_2Eupdate__at__path_2E0: u ).
thf(c_2Efmaptree_2Eupdate__at__path_2E3,type,
c_2Efmaptree_2Eupdate__at__path_2E3: du > du > du > u ).
thf(c_2Efmaptree_2Ewf_2E0,type,
c_2Efmaptree_2Ewf_2E0: u ).
thf(c_2Efmaptree_2Ewf_2E1,type,
c_2Efmaptree_2Ewf_2E1: du > u ).
thf(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( 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 ) ) ) ).
thf(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( 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 ) ) ).
thf(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( 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 ) ) ).
thf(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( ( 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 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0_2E0: u,X1: $o] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ 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 @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29_29,axiom,
! [A_27a: d,A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( 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 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ 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 @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2EFTNode_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) ) @ c_2Efmaptree_2EFTNode_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2EFTNode_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ c_2Efmaptree_2EFTNode_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2EFTNode_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) ) @ c_2Efmaptree_2EFTNode_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27key_29_2Ctyop_2Eoption_2Eoption_28A_27value_29_29_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27key_2CA_27value_29,axiom,
! [A_27key: d,A_27value: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2Eapply__path_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ c_2Efmaptree_2Eapply__path_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2Econstruct_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Efmaptree_2Econstruct_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Efmaptree_2Econstruct_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efmaptree_2Econstruct_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Efmaptree_2Econstruct_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2Econstruct_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Efmaptree_2Econstruct_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Efmtreerec_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ ( c_2Efmaptree_2Efmtreerec_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) ) @ c_2Efmaptree_2Efmtreerec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efmaptree_2Efmtreerec_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ A_27a @ ( c_2Efmaptree_2Efmtreerec_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ X1_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) ) @ c_2Efmaptree_2Efmtreerec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2EfromF_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EfromF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Efmaptree_2EfromF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2EfromF_2E1_2Emono_2EA_27key_20mono_2EA_27value,axiom,
! [A_27key: d,A_27value: d,X0_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( c_2Efmaptree_2EfromF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) ) @ c_2Efmaptree_2EfromF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Efmaptree_2Efupd__at__path_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Efupd__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ c_2Efmaptree_2Efupd__at__path_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Eitem_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27b @ ( c_2Efmaptree_2Eitem_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ A_27b ) @ c_2Efmaptree_2Eitem_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Eitem_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Efmaptree_2Eitem_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ A_27a ) @ c_2Efmaptree_2Eitem_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Elist_2Elist__CASE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Emap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ c_2Efmaptree_2Emap_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Emap_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) ) @ c_2Efmaptree_2Emap_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27b_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27b_2CA_27a_29_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27c_20mono_2Etyop_2Efmaptree_2Efmaptree_28A_27c_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Efmaptree_2Efmaptree_28A_27a_2CA_27b_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Efmaptree_2Erelrec_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ X1_2E0 ) @ ( s @ A_27c @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ c_2Efmaptree_2Erelrec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27c @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Efmaptree_2Erelrec_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Efmaptree_2Erelrec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2EtoF_2E1_2Emono_2EA_27key_20mono_2EA_27value,axiom,
! [A_27key: d,A_27value: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ ( c_2Efmaptree_2EtoF_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) ) @ c_2Efmaptree_2EtoF_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Efmaptree_2Eupdate__at__path_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eupdate__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ c_2Efmaptree_2Eupdate__at__path_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Ewf_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Efmaptree_2Ewf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Efmaptree_2Ewf_2E1_2Emono_2EA_27value_20mono_2EA_27key,axiom,
! [A_27key: d,A_27value: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ tyop_2Emin_2Ebool ) @ c_2Efmaptree_2Ewf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ X0_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Efmaptree_2Econstruct__def,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V1kfm_2E0: u,V3h_2E0: u,V4t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1kfm_2E0 ) ) ) @ ( s @ A_27b @ V3h_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V4t_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1kfm_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1kfm_2E0 ) @ ( s @ A_27b @ V3h_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V4t_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
=> ! [V0a_2E0: u,V1kfm_2E0: u,V2kl_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efmaptree_2Econstruct_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1kfm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2kl_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2kl_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1kfm_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Ewf__def,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0x_2E0 ) ) ) )
<=> ! [V1wf_27_2E0: u] :
( ! [V2a0_2E0: u] :
( ? [V3a_2E0: u,V4fm_2E0: u] :
( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2a0_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V4fm_2E0 ) ) ) )
& ! [V5k_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V5k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V4fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V4fm_2E0 ) @ ( s @ A_27b @ V5k_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2a0_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Efmaptree__TY__DEF,axiom,
! [A_27key: d,A_27value: d] :
? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ tyop_2Emin_2Ebool ) @ c_2Efmaptree_2Ewf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) ) @ V0rep_2E0 ) ) ) ) ).
thf(thm_2Efmaptree_2Efmap__bij__thm,axiom,
! [A_27key: d,A_27value: d] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( c_2Efmaptree_2EfromF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ ( c_2Efmaptree_2EtoF_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ V0a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ V0a_2E0 ) )
& ! [V1r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ V1r_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ ( c_2Efmaptree_2EtoF_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27key @ A_27value ) @ ( c_2Efmaptree_2EfromF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ V1r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27key ) @ ( tyop_2Eoption_2Eoption @ A_27value ) ) @ V1r_2E0 ) ) ) ) ).
thf(thm_2Efmaptree_2EFTNode__def,axiom,
! [A_27a: d,A_27b: d,V0i_2E0: u,V1fm_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V0i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V1fm_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EfromF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27b @ V0i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efmaptree_2EtoF_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V1fm_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Eitem__map__def,axiom,
! [A_27a: d,A_27b: d,V0ft_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ ( c_2Efmaptree_2Eitem_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Eapply__path__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0ft_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) )
& ! [V1h_2E0: u,V2t_2E0: u,V3ft_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V3ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V3ft_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2t_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V3ft_2E0 ) ) ) @ ( s @ A_27a @ V1h_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).
thf(thm_2Efmaptree_2Eupdate__at__path__def,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V5ft_2E0: u,V2h_2E0: u,V6ft_27_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ A_27a @ V2h_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V6ft_27_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ ( c_2Efmaptree_2Eitem_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V6ft_27_2E0 ) ) ) ) ) ) ) ) ) )
=> ( ! [V0a_2E0: u,V1ft_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eupdate__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ A_27b @ V0a_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V1ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V0a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V1ft_2E0 ) ) ) ) ) ) ) )
& ! [V2h_2E0: u,V3t_2E0: u,V4a_2E0: u,V5ft_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eupdate__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3t_2E0 ) ) ) @ ( s @ A_27b @ V4a_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eupdate__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3t_2E0 ) @ ( s @ A_27b @ V4a_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Efupd__at__path__def,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V5ft_2E0: u,V2h_2E0: u,V6ft_27_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ A_27a @ V2h_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V6ft_27_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ ( c_2Efmaptree_2Eitem_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V6ft_27_2E0 ) ) ) ) ) ) ) ) ) )
=> ( ! [V0f_2E0: u,V1ft_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Efupd__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V1ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V1ft_2E0 ) ) ) )
& ! [V2h_2E0: u,V3t_2E0: u,V4f_2E0: u,V5ft_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Efupd__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ V4f_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Efupd__at__path_2E3 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3t_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ V4f_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V5ft_2E0 ) ) ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Erelrec__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0x_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V1x_27_2E0 ) @ ( s @ A_27c @ V2x_27_27_2E0 ) ) ) )
<=> ! [V3relrec_27_2E0: u] :
( ! [V4a0_2E0: u,V5a1_2E0: u] :
( ? [V6i_2E0: u,V7fm_2E0: u,V8rfm_2E0: u] :
( ( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V4a0_2E0 )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V6i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V7fm_2E0 ) ) ) )
& ( ( s @ A_27c @ V5a1_2E0 )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0x_2E0 ) @ ( s @ A_27a @ V6i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V8rfm_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V7fm_2E0 ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V8rfm_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V7fm_2E0 ) ) ) )
& ! [V9d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V9d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V7fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V3relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V7fm_2E0 ) @ ( s @ A_27b @ V9d_2E0 ) ) ) ) ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V8rfm_2E0 ) @ ( s @ A_27b @ V9d_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V3relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V4a0_2E0 ) ) ) @ ( s @ A_27c @ V5a1_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V3relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V1x_27_2E0 ) ) ) @ ( s @ A_27c @ V2x_27_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Efmtreerec__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
( ! [V0h_2E0: u,V1ft_2E0: u,V2r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V0h_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ V1ft_2E0 ) ) ) @ ( s @ A_27a @ V2r_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ V1ft_2E0 ) @ ( s @ A_27a @ V2r_2E0 ) ) ) ) )
=> ! [V0h_2E0: u,V1ft_2E0: u] :
( ( s @ A_27a @ ( c_2Efmaptree_2Efmtreerec_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ V1ft_2E0 ) ) )
= ( s @ A_27a @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V0h_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ V1ft_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Ewf__rules,axiom,
! [A_27a: d,A_27b: d,V0a_2E0: u,V1fm_2E0: u] :
( ! [V2k_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1fm_2E0 ) @ ( s @ A_27b @ V2k_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V1fm_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Ewf__ind,axiom,
! [A_27a: d,A_27b: d,V0wf_27_2E0: u] :
( ! [V1a_2E0: u,V2fm_2E0: u] :
( ! [V3k_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) ) ) ) ) ) )
=> ! [V4a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Ewf__strongind,axiom,
! [A_27a: d,A_27b: d,V0wf_27_2E0: u] :
( ! [V1a_2E0: u,V2fm_2E0: u] :
( ! [V3k_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) ) ) ) ) ) )
=> ! [V4a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0wf_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Ewf__cases,axiom,
! [A_27a: d,A_27b: d,V0a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0a0_2E0 ) ) ) )
<=> ? [V1a_2E0: u,V2fm_2E0: u] :
( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0a0_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efmaptree_2Econstruct_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) ) ) )
& ! [V3k_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Ewf_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V2fm_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2EFTNode__11,axiom,
! [A_27a: d,A_27b: d,V0i2_2E0: u,V1i1_2E0: u,V2f2_2E0: u,V3f1_2E0: u] :
( ( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V1i1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V3f1_2E0 ) ) )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V0i2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V2f2_2E0 ) ) ) )
<=> ( ( ( s @ A_27b @ V1i1_2E0 )
= ( s @ A_27b @ V0i2_2E0 ) )
& ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V3f1_2E0 )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V2f2_2E0 ) ) ) ) ).
thf(thm_2Efmaptree_2Efmaptree__nchotomy,axiom,
! [A_27a: d,A_27b: d,V0ft_2E0: u] :
? [V1i_2E0: u,V2fm_2E0: u] :
( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V1i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V2fm_2E0 ) ) ) ) ).
thf(thm_2Efmaptree_2Eitem__thm,axiom,
! [A_27a: d,A_27b: d,V0i_2E0: u,V1fm_2E0: u] :
( ( s @ A_27a @ ( c_2Efmaptree_2Eitem_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V0i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V1fm_2E0 ) ) ) ) )
= ( s @ A_27a @ V0i_2E0 ) ) ).
thf(thm_2Efmaptree_2Emap__thm,axiom,
! [A_27a: d,A_27b: d,V0i_2E0: u,V1fm_2E0: u] :
( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V0i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V1fm_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V1fm_2E0 ) ) ).
thf(thm_2Efmaptree_2Eft__ind,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ! [V1a_2E0: u,V2fm_2E0: u] :
( ! [V3k_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V2fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V2fm_2E0 ) @ ( s @ A_27a @ V3k_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V1a_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ V2fm_2E0 ) ) ) ) ) ) )
=> ! [V4ft_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V4ft_2E0 ) ) ) ) ) ).
thf(thm_2Efmaptree_2Eapplicable__paths__FINITE,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V1p_2E0: u,V0ft_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1p_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) )
<=> ? [V2ft_27_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1p_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V2ft_27_2E0 ) ) ) ) )
=> ( ! [V0ft_2E0: u,V1p_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1p_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1p_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) ) ) )
=> ! [V0ft_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Eapply__path__SNOC,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3ft_27_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V3ft_27_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Emap_2E1 @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V3ft_27_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
=> ! [V0ft_2E0: u,V1x_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2p_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ ( c_2Efmaptree_2Eapply__path_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2p_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ V0ft_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Efmaptree_2Efmaptree @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Erelrec__rules,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0h_2E0: u,V1i_2E0: u,V2fm_2E0: u,V3rfm_2E0: u] :
( ( ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3rfm_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V2fm_2E0 ) ) ) )
& ! [V4d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V4d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V2fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V2fm_2E0 ) @ ( s @ A_27b @ V4d_2E0 ) ) ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3rfm_2E0 ) @ ( s @ A_27b @ V4d_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V1i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V2fm_2E0 ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ A_27a @ V1i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3rfm_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V2fm_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Erelrec__ind,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0h_2E0: u,V1relrec_27_2E0: u] :
( ! [V2i_2E0: u,V3fm_2E0: u,V4rfm_2E0: u] :
( ( ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) )
& ! [V5d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V5d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) @ ( s @ A_27b @ V5d_2E0 ) ) ) ) ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) @ ( s @ A_27b @ V5d_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V2i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ A_27a @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) ) )
=> ! [V6a0_2E0: u,V7a1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V6a0_2E0 ) @ ( s @ A_27c @ V7a1_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V6a0_2E0 ) ) ) @ ( s @ A_27c @ V7a1_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Erelrec__strongind,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0h_2E0: u,V1relrec_27_2E0: u] :
( ! [V2i_2E0: u,V3fm_2E0: u,V4rfm_2E0: u] :
( ( ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) )
& ! [V5d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V5d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) @ ( s @ A_27b @ V5d_2E0 ) ) ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) @ ( s @ A_27b @ V5d_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) @ ( s @ A_27b @ V5d_2E0 ) ) ) ) ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) @ ( s @ A_27b @ V5d_2E0 ) ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V2i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ A_27a @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4rfm_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) ) )
=> ! [V6a0_2E0: u,V7a1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V6a0_2E0 ) @ ( s @ A_27c @ V7a1_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1relrec_27_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V6a0_2E0 ) ) ) @ ( s @ A_27c @ V7a1_2E0 ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Erelrec__cases,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0h_2E0: u,V1a0_2E0: u,V2a1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V1a0_2E0 ) @ ( s @ A_27c @ V2a1_2E0 ) ) ) )
<=> ? [V3i_2E0: u,V4fm_2E0: u,V5rfm_2E0: u] :
( ( ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ V1a0_2E0 )
= ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V3i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V4fm_2E0 ) ) ) )
& ( ( s @ A_27c @ V2a1_2E0 )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ A_27a @ V3i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V5rfm_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V4fm_2E0 ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V5rfm_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V4fm_2E0 ) ) ) )
& ! [V6d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V6d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V4fm_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmaptree_2Erelrec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V4fm_2E0 ) @ ( s @ A_27b @ V6d_2E0 ) ) ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V5rfm_2E0 ) @ ( s @ A_27b @ V6d_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Efmaptree_2Efmtreerec__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0i_2E0: u,V1h_2E0: u,V2fm_2E0: u] :
( ( s @ A_27a @ ( c_2Efmaptree_2Efmtreerec_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V1h_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27b @ V0i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ V2fm_2E0 ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V1h_2E0 ) @ ( s @ A_27b @ V0i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) @ A_27a ) @ ( c_2Efmaptree_2Efmtreerec_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ A_27a ) ) ) @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ V2fm_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ ( tyop_2Efmaptree_2Efmaptree @ A_27c @ A_27b ) ) @ V2fm_2E0 ) ) ) ) ).
thf(thm_2Efmaptree_2Efmtree__Axiom,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0h_2E0: u] :
? [V1f_2E0: u] :
! [V2i_2E0: u,V3fm_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ ( c_2Efmaptree_2EFTNode_2E2 @ ( s @ A_27a @ V2i_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ A_27c ) ) ) @ V0h_2E0 ) @ ( s @ A_27a @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ ( tyop_2Efmaptree_2Efmaptree @ A_27b @ A_27a ) ) @ V3fm_2E0 ) ) ) ) ) ) ).
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