ITP001 Axioms: ITP048^4.ax
%------------------------------------------------------------------------------
% File : ITP048^4 : TPTP v9.0.0. 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 : inftree.ax [Gau19]
% : HL4048^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 152 ( 48 unt; 77 typ; 0 def)
% Number of atoms : 182 ( 94 equ; 2 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 5956 ( 2 ~; 6 |; 23 &;5864 @)
% ( 22 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 10 avg;5864 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 74 usr; 33 con; 0-4 aty)
% Number of variables : 436 ( 0 ^ 416 !; 20 ?; 436 :)
% 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_2Einftree_2Einftree,type,
tyop_2Einftree_2Einftree: d > 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_2Esum_2Esum,type,
tyop_2Esum_2Esum: 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_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_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_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0: u ).
thf(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1: du > u ).
thf(c_2Esum_2EINL_2E0,type,
c_2Esum_2EINL_2E0: u ).
thf(c_2Esum_2EINL_2E1,type,
c_2Esum_2EINL_2E1: du > u ).
thf(c_2Esum_2EINR_2E0,type,
c_2Esum_2EINR_2E0: u ).
thf(c_2Esum_2EINR_2E1,type,
c_2Esum_2EINR_2E1: du > u ).
thf(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0: u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Elist_2ETL_2E0,type,
c_2Elist_2ETL_2E0: u ).
thf(c_2Elist_2ETL_2E1,type,
c_2Elist_2ETL_2E1: du > 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_2Einftree_2Efrom__inftree_2E0,type,
c_2Einftree_2Efrom__inftree_2E0: u ).
thf(c_2Einftree_2Efrom__inftree_2E1,type,
c_2Einftree_2Efrom__inftree_2E1: du > u ).
thf(c_2Einftree_2Efrom__inftree_2E2,type,
c_2Einftree_2Efrom__inftree_2E2: du > du > u ).
thf(c_2Einftree_2EiLf_2E0,type,
c_2Einftree_2EiLf_2E0: u ).
thf(c_2Einftree_2EiLf_2E1,type,
c_2Einftree_2EiLf_2E1: du > u ).
thf(c_2Einftree_2EiNd_2E0,type,
c_2Einftree_2EiNd_2E0: u ).
thf(c_2Einftree_2EiNd_2E2,type,
c_2Einftree_2EiNd_2E2: du > du > u ).
thf(c_2Einftree_2Einftree__CASE_2E0,type,
c_2Einftree_2Einftree__CASE_2E0: u ).
thf(c_2Einftree_2Einftree__CASE_2E3,type,
c_2Einftree_2Einftree__CASE_2E3: du > du > du > u ).
thf(c_2Einftree_2Einftree__rec_2E0,type,
c_2Einftree_2Einftree__rec_2E0: u ).
thf(c_2Einftree_2Einftree__rec_2E3,type,
c_2Einftree_2Einftree__rec_2E3: du > du > du > u ).
thf(c_2Einftree_2Eis__tree_2E0,type,
c_2Einftree_2Eis__tree_2E0: u ).
thf(c_2Einftree_2Eis__tree_2E1,type,
c_2Einftree_2Eis__tree_2E1: du > u ).
thf(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0: u ).
thf(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2: du > du > u ).
thf(c_2Einftree_2Erelrec_2E0,type,
c_2Einftree_2Erelrec_2E0: u ).
thf(c_2Einftree_2Erelrec_2E4,type,
c_2Einftree_2Erelrec_2E4: du > du > du > du > u ).
thf(c_2Einftree_2Eto__inftree_2E0,type,
c_2Einftree_2Eto__inftree_2E0: u ).
thf(c_2Einftree_2Eto__inftree_2E1,type,
c_2Einftree_2Eto__inftree_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_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27c_2CA_27a_29,axiom,
! [A_27a: d,A_27c: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ A_27b @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) @ c_2Elist_2EHD_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( s @ A_27c @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ A_27c ) @ c_2Elist_2EHD_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27d,axiom,
! [A_27d: d,X0_2E0: u] :
( ( s @ A_27d @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27d ) @ c_2Elist_2EHD_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ c_2Elist_2ETL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ c_2Elist_2ETL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27d,axiom,
! [A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ c_2Elist_2ETL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27d_29_2Ctyop_2Esum_2Esum_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Einftree_2Einftree_28A_27a_2CA_27b_2CA_27d_29,axiom,
! [A_27a: d,A_27b: d,A_27d: 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_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Einftree_2Efrom__inftree_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 @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Einftree_2Efrom__inftree_2E2 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ c_2Einftree_2Efrom__inftree_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2Efrom__inftree_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Einftree_2Efrom__inftree_2E1 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ c_2Einftree_2Efrom__inftree_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Einftree_2Efrom__inftree_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( c_2Einftree_2Efrom__inftree_2E2 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) @ c_2Einftree_2Efrom__inftree_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2EiLf_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_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ c_2Einftree_2EiLf_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2EiLf_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ c_2Einftree_2EiLf_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Einftree_2EiNd_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 @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) ) @ c_2Einftree_2EiNd_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Einftree_2EiNd_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) ) @ c_2Einftree_2EiNd_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Einftree_2Einftree__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27d @ ( c_2Einftree_2Einftree__CASE_2E3 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ X2_2E0 ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ A_27d ) ) ) @ c_2Einftree_2Einftree__CASE_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Einftree_2Einftree__rec_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Einftree_2Einftree__rec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ X2_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ A_27a ) ) ) @ c_2Einftree_2Einftree__rec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2Eis__tree_2E1_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ 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_2Esum_2Esum @ A_27c @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Einftree_2Eis__tree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2Eis__tree_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Einftree_2Eis__tree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2Etyop_2Einftree_2Einftree_28A_27a_2CA_27b_2CA_27c_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Einftree_2Erelrec_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ X2_2E0 ) @ ( s @ A_27b @ X3_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Einftree_2Erelrec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ X2_2E0 ) ) ) @ ( s @ A_27b @ X3_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2Einftree_2Erelrec_2E4_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ X2_2E0 ) @ ( s @ A_27a @ X3_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_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Einftree_2Erelrec_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2Eto__inftree_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_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2Eto__inftree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ c_2Einftree_2Eto__inftree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Einftree_2Eto__inftree_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( c_2Einftree_2Eto__inftree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) ) @ c_2Einftree_2Eto__inftree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ 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_2Einftree_2Eis__tree__def,axiom,
! [A_27a: d,A_27b: d,A_27d: d,F0_2E0: u] :
( ! [V7x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V7x_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V7x_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0x_2E0 ) ) ) )
<=> ! [V1is__tree_27_2E0: u] :
( ! [V2a0_2E0: u] :
( ( ? [V3a_2E0: u] :
! [V4x_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V2a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V4x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) )
| ? [V5f_2E0: u,V6b_2E0: u] :
( ! [V7x_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V2a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V7x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V7x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V6b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V5f_2E0 ) @ ( s @ A_27d @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V7x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V7x_2E0 ) ) ) ) ) ) ) )
& ! [V8d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V1is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V5f_2E0 ) @ ( s @ A_27d @ V8d_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V1is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V2a0_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V1is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0x_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__TY__DEF,axiom,
! [A_27a: d,A_27b: d,A_27d: 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_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Einftree_2Eis__tree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V0rep_2E0 ) ) ) ) ).
thf(thm_2Einftree_2Einftree__bijections,axiom,
! [A_27a: d,A_27b: d,A_27d: d] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( c_2Einftree_2Eto__inftree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Einftree_2Efrom__inftree_2E1 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ V0a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ V0a_2E0 ) )
& ! [V1r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V1r_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Einftree_2Efrom__inftree_2E1 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27d ) @ ( c_2Einftree_2Eto__inftree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V1r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V1r_2E0 ) ) ) ) ).
thf(thm_2Einftree_2EiLf__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
( ! [V0a_2E0: u,V1p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) )
=> ! [V0a_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2Eto__inftree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2EiNd__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
( ! [V2p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ tyop_2Emin_2Ebool ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V2p_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V2p_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ( ! [V0b_2E0: u,V1f_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ tyop_2Emin_2Ebool ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V2p_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Einftree_2Efrom__inftree_2E2 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V1f_2E0 ) @ ( s @ A_27c @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V2p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V2p_2E0 ) ) ) ) ) ) ) )
=> ! [V0b_2E0: u,V1f_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V0b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V1f_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2Eto__inftree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V1f_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Erelrec__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: u,V3x_27_27_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V1x_27_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V2x_27_27_2E0 ) @ ( s @ A_27b @ V3x_27_27_27_2E0 ) ) ) )
<=> ! [V4relrec_27_2E0: u] :
( ! [V5a0_2E0: u,V6a1_2E0: u,V7a2_2E0: u,V8a3_2E0: u] :
( ( ? [V9a_2E0: u] :
( ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V7a2_2E0 )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V9a_2E0 ) ) ) )
& ( ( s @ A_27b @ V8a3_2E0 )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5a0_2E0 ) @ ( s @ A_27a @ V9a_2E0 ) ) ) ) )
| ? [V10b_2E0: u,V11df_2E0: u,V12g_2E0: u] :
( ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V7a2_2E0 )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27c @ V10b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V11df_2E0 ) ) ) )
& ( ( s @ A_27b @ V8a3_2E0 )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V6a1_2E0 ) @ ( s @ A_27c @ V10b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V12g_2E0 ) ) ) )
& ! [V13d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V4relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V6a1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V11df_2E0 ) @ ( s @ A_27d @ V13d_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V12g_2E0 ) @ ( s @ A_27d @ V13d_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V4relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V6a1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V7a2_2E0 ) ) ) @ ( s @ A_27b @ V8a3_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V4relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V1x_27_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V2x_27_27_2E0 ) ) ) @ ( s @ A_27b @ V3x_27_27_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__rec__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
( ! [V0lf_2E0: u,V1nd_2E0: u,V2t_2E0: u,V3r_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_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ V1nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V3r_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0lf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ V1nd_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ V2t_2E0 ) @ ( s @ A_27a @ V3r_2E0 ) ) ) ) )
=> ! [V0lf_2E0: u,V1nd_2E0: u,V2t_2E0: u] :
( ( s @ A_27a @ ( c_2Einftree_2Einftree__rec_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0lf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ V1nd_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ V2t_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_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27a ) @ A_27a ) ) @ V1nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27b @ A_27c @ A_27d ) @ V2t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__case__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0a_2E0: u,V1f_2E0: u,V2f1_2E0: u] :
( ( s @ A_27d @ ( c_2Einftree_2Einftree__CASE_2E3 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ V2f1_2E0 ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ V1f_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) ) )
& ! [V3b_2E0: u,V4d_2E0: u,V5f_2E0: u,V6f1_2E0: u] :
( ( s @ A_27d @ ( c_2Einftree_2Einftree__CASE_2E3 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V3b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V4d_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ V5f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ V6f1_2E0 ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ A_27d ) ) @ V6f1_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V4d_2E0 ) ) ) ) ) ).
thf(thm_2Einftree_2Eis__tree__rules,axiom,
! [A_27a: d,A_27b: d,A_27d: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V5p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5p_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5p_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ( ! [V3b_2E0: u,V2f_2E0: u,V5p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5p_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V2f_2E0 ) @ ( s @ A_27d @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5p_2E0 ) ) ) ) ) ) ) )
=> ( ! [V0a_2E0: u,V1p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) )
=> ( ! [V0a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) ) ) ) )
& ! [V2f_2E0: u,V3b_2E0: u] :
( ! [V4d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V2f_2E0 ) @ ( s @ A_27d @ V4d_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V2f_2E0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Eis__tree__ind,axiom,
! [A_27a: d,A_27b: d,A_27d: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V6p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ( ! [V4b_2E0: u,V3f_2E0: u,V6p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) ) ) ) ) )
=> ( ! [V1a_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
=> ! [V0is__tree_27_2E0: u] :
( ( ! [V1a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
& ! [V3f_2E0: u,V4b_2E0: u] :
( ! [V5d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ V5d_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) ) ) ) ) ) ) )
=> ! [V7a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V7a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V7a0_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Eis__tree__strongind,axiom,
! [A_27a: d,A_27b: d,A_27d: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V6p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ( ! [V4b_2E0: u,V3f_2E0: u,V6p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V6p_2E0 ) ) ) ) ) ) ) )
=> ( ! [V1a_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
=> ! [V0is__tree_27_2E0: u] :
( ( ! [V1a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
& ! [V3f_2E0: u,V4b_2E0: u] :
( ! [V5d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ V5d_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ V5d_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) ) ) ) ) ) ) )
=> ! [V7a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V7a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V0is__tree_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V7a0_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Eis__tree__cases,axiom,
! [A_27a: d,A_27b: d,A_27d: d,F0_2E0: u] :
( ! [V5x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5x_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5x_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ! [V0a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0a0_2E0 ) ) ) )
<=> ( ? [V1a_2E0: u] :
! [V2x_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
| ? [V3f_2E0: u,V4b_2E0: u] :
( ! [V5x_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V5x_2E0 ) ) ) ) ) ) ) )
& ! [V6d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ A_27d @ V6d_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2EiNd__is__tree,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
( ! [V2p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2p_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2p_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ c_2Elist_2ENIL_2E0 ) ) )
=> ( ! [V0b_2E0: u,V1f_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27a @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) @ ( c_2Einftree_2Efrom__inftree_2E2 @ ( s @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ V1f_2E0 ) @ ( s @ A_27b @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) )
=> ! [V0b_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Eis__tree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Einftree_2Einftree @ A_27c @ A_27a @ A_27b ) ) @ V1f_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__11,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f2_2E0: u,V1f1_2E0: u,V2b2_2E0: u,V3b1_2E0: u,V4a2_2E0: u,V5a1_2E0: u] :
( ( ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V5a1_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V4a2_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V5a1_2E0 )
= ( s @ A_27a @ V4a2_2E0 ) ) )
& ( ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V3b1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V1f1_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V2b2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V0f2_2E0 ) ) ) )
<=> ( ( ( s @ A_27b @ V3b1_2E0 )
= ( s @ A_27b @ V2b2_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V1f1_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V0f2_2E0 ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__distinct,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1b_2E0: u,V2a_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V1b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__ind,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
( ( ! [V1a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
& ! [V2b_2E0: u,V3f_2E0: u] :
( ! [V4d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V3f_2E0 ) @ ( s @ A_27c @ V4d_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V2b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V3f_2E0 ) ) ) ) ) ) ) )
=> ! [V5t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ V5t_2E0 ) ) ) ) ) ).
thf(thm_2Einftree_2Erelrec__rules,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0lf_2E0: u,V1nd_2E0: u,V2a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0lf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V1nd_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0lf_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
& ! [V3lf_2E0: u,V4nd_2E0: u,V5b_2E0: u,V6df_2E0: u,V7g_2E0: u] :
( ! [V8d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V3lf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V4nd_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V6df_2E0 ) @ ( s @ A_27d @ V8d_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V7g_2E0 ) @ ( s @ A_27d @ V8d_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V3lf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V4nd_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27c @ V5b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V6df_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V4nd_2E0 ) @ ( s @ A_27c @ V5b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V7g_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Erelrec__ind,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0relrec_27_2E0: u] :
( ( ! [V1lf_2E0: u,V2nd_2E0: u,V3a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V2nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1lf_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) )
& ! [V4lf_2E0: u,V5nd_2E0: u,V6b_2E0: u,V7df_2E0: u,V8g_2E0: u] :
( ! [V9d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V7df_2E0 ) @ ( s @ A_27d @ V9d_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V8g_2E0 ) @ ( s @ A_27d @ V9d_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27c @ V6b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V7df_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) @ ( s @ A_27c @ V6b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V8g_2E0 ) ) ) ) ) ) ) )
=> ! [V10a0_2E0: u,V11a1_2E0: u,V12a2_2E0: u,V13a3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V10a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V11a1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V12a2_2E0 ) @ ( s @ A_27b @ V13a3_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V10a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V11a1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V12a2_2E0 ) ) ) @ ( s @ A_27b @ V13a3_2E0 ) ) ) ) ) ) ).
thf(thm_2Einftree_2Erelrec__strongind,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0relrec_27_2E0: u] :
( ( ! [V1lf_2E0: u,V2nd_2E0: u,V3a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V2nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1lf_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) )
& ! [V4lf_2E0: u,V5nd_2E0: u,V6b_2E0: u,V7df_2E0: u,V8g_2E0: u] :
( ! [V9d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4lf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V7df_2E0 ) @ ( s @ A_27d @ V9d_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V8g_2E0 ) @ ( s @ A_27d @ V9d_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V7df_2E0 ) @ ( s @ A_27d @ V9d_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V8g_2E0 ) @ ( s @ A_27d @ V9d_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4lf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27c @ V6b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V7df_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V5nd_2E0 ) @ ( s @ A_27c @ V6b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V8g_2E0 ) ) ) ) ) ) ) )
=> ! [V10a0_2E0: u,V11a1_2E0: u,V12a2_2E0: u,V13a3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V10a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V11a1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V12a2_2E0 ) @ ( s @ A_27b @ V13a3_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0relrec_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V10a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V11a1_2E0 ) ) ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V12a2_2E0 ) ) ) @ ( s @ A_27b @ V13a3_2E0 ) ) ) ) ) ) ).
thf(thm_2Einftree_2Erelrec__cases,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: u,V3a3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V1a1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V2a2_2E0 ) @ ( s @ A_27b @ V3a3_2E0 ) ) ) )
<=> ( ? [V4a_2E0: u] :
( ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V2a2_2E0 )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
& ( ( s @ A_27b @ V3a3_2E0 )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0a0_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
| ? [V5b_2E0: u,V6df_2E0: u,V7g_2E0: u] :
( ( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ V2a2_2E0 )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27c @ V5b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V6df_2E0 ) ) ) )
& ( ( s @ A_27b @ V3a3_2E0 )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V1a1_2E0 ) @ ( s @ A_27c @ V5b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V7g_2E0 ) ) ) )
& ! [V8d_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einftree_2Erelrec_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ A_27b ) ) @ V1a1_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27c @ A_27d ) ) @ V6df_2E0 ) @ ( s @ A_27d @ V8d_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V7g_2E0 ) @ ( s @ A_27d @ V8d_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__Axiom,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0lf_2E0: u,V1nd_2E0: u] :
? [V2f_2E0: u] :
( ! [V3a_2E0: u] :
( ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ A_27d ) @ V2f_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ V0lf_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) )
& ! [V4b_2E0: u,V5d_2E0: u] :
( ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ A_27d ) @ V2f_2E0 ) @ ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V4b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V5d_2E0 ) ) ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ A_27d ) ) ) @ V1nd_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V5d_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ A_27d ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V5d_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Einftree_2Einftree__nchotomy,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0t_2E0: u] :
( ? [V1a_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ V0t_2E0 )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiLf_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
| ? [V2b_2E0: u,V3d_2E0: u] :
( ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ V0t_2E0 )
= ( s @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) @ ( c_2Einftree_2EiNd_2E2 @ ( s @ A_27b @ V2b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Einftree_2Einftree @ A_27a @ A_27b @ A_27c ) ) @ V3d_2E0 ) ) ) ) ) ).
%------------------------------------------------------------------------------