%------------------------------------------------------------------------------
% File     : ITP102_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    : sptree.ax [Gau19]
%          : HL4102_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    : 1080 ( 434 unt; 521 typ;   0 def)
%            Number of atoms       : 1051 ( 832 equ)
%            Maximal formula atoms :   29 (   0 avg)
%            Number of connectives :  526 (  34   ~;  15   |; 239   &)
%                                         (  73 <=>; 165  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (   5 avg)
%            Maximal term depth    :   23 (   3 avg)
%            Number of types       :   52 (  51 usr)
%            Number of type conns  :  455 ( 296   >; 159   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  469 ( 469 usr; 174 con; 0-5 aty)
%            Number of variables   : 2083 (2060   !;  23   ?;2083   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(u,type,
    u: $tType ).

tff(d,type,
    d: $tType ).

tff(du,type,
    du: $tType ).

tff(mono_2Etyop_2Emin_2Ebool,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

tff(mono_2Etyop_2Eone_2Eone,type,
    mono_2Etyop_2Eone_2Eone: $tType ).

tff(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $tType ).

tff(mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: $tType ).

tff(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: d > d ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( d * d ) > d ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

tff(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( d * d ) > d ).

tff(tyop_2Esptree_2Espt,type,
    tyop_2Esptree_2Espt: d > d ).

tff(s,type,
    s: ( d * u ) > du ).

tff(app_2E2,type,
    app_2E2: ( du * du ) > u ).

tff(p,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

tff(c_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: u ).

tff(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( du * du ) > u ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: du > u ).

tff(c_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: u ).

tff(c_2Elist_2EALL__DISTINCT_2E1,type,
    c_2Elist_2EALL__DISTINCT_2E1: du > u ).

tff(c_2Ealist_2EALOOKUP_2E0,type,
    c_2Ealist_2EALOOKUP_2E0: u ).

tff(c_2Ealist_2EALOOKUP_2E2,type,
    c_2Ealist_2EALOOKUP_2E2: ( du * du ) > u ).

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: u ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

tff(c_2Esptree_2EBN_2E0,type,
    c_2Esptree_2EBN_2E0: u ).

tff(c_2Esptree_2EBN_2E2,type,
    c_2Esptree_2EBN_2E2: ( du * du ) > u ).

tff(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: u ).

tff(c_2Esptree_2EBS_2E0,type,
    c_2Esptree_2EBS_2E0: u ).

tff(c_2Esptree_2EBS_2E3,type,
    c_2Esptree_2EBS_2E3: ( du * du * du ) > u ).

tff(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: u ).

tff(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: du > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: ( du * du ) > u ).

tff(c_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: u ).

tff(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

tff(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

tff(c_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: u ).

tff(c_2Epred__set_2EDELETE_2E2,type,
    c_2Epred__set_2EDELETE_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: u ).

tff(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EDISJOINT_2E0,type,
    c_2Epred__set_2EDISJOINT_2E0: u ).

tff(c_2Epred__set_2EDISJOINT_2E2,type,
    c_2Epred__set_2EDISJOINT_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2EDIV_2E0,type,
    c_2Earithmetic_2EDIV_2E0: u ).

tff(c_2Earithmetic_2EDIV_2E2,type,
    c_2Earithmetic_2EDIV_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

tff(c_2Earithmetic_2EEVEN_2E0,type,
    c_2Earithmetic_2EEVEN_2E0: u ).

tff(c_2Earithmetic_2EEVEN_2E1,type,
    c_2Earithmetic_2EEVEN_2E1: du > u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Eind__type_2EFCONS_2E0,type,
    c_2Eind__type_2EFCONS_2E0: u ).

tff(c_2Eind__type_2EFCONS_2E2,type,
    c_2Eind__type_2EFCONS_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: u ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: du > u ).

tff(c_2Elist_2EFOLDL_2E0,type,
    c_2Elist_2EFOLDL_2E0: u ).

tff(c_2Elist_2EFOLDL_2E3,type,
    c_2Elist_2EFOLDL_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: u ).

tff(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: ( du * du * du ) > u ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

tff(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: du > u ).

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

tff(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: du > u ).

tff(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: u ).

tff(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: u ).

tff(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: u ).

tff(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: ( du * du ) > u ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

tff(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_2E1: du > u ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

tff(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: du > u ).

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: du > u ).

tff(c_2Esptree_2ELN_2E0,type,
    c_2Esptree_2ELN_2E0: u ).

tff(c_2Esptree_2ELS_2E0,type,
    c_2Esptree_2ELS_2E0: u ).

tff(c_2Esptree_2ELS_2E1,type,
    c_2Esptree_2ELS_2E1: du > u ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: ( du * du ) > u ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

tff(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

tff(c_2Eoption_2EOPTION__MAP_2E2,type,
    c_2Eoption_2EOPTION__MAP_2E2: ( du * du ) > u ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

tff(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: du > u ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: du > u ).

tff(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

tff(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: ( du * du ) > u ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: du > u ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: ( du * du ) > u ).

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

tff(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: du > u ).

tff(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: u ).

tff(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: ( du * du ) > u ).

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: u ).

tff(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: du > u ).

tff(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: u ).

tff(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: u ).

tff(c_2Epred__set_2Ecount_2E1,type,
    c_2Epred__set_2Ecount_2E1: du > u ).

tff(c_2Esptree_2Edelete_2E0,type,
    c_2Esptree_2Edelete_2E0: u ).

tff(c_2Esptree_2Edelete_2E2,type,
    c_2Esptree_2Edelete_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Edifference_2E0,type,
    c_2Esptree_2Edifference_2E0: u ).

tff(c_2Esptree_2Edifference_2E2,type,
    c_2Esptree_2Edifference_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Edomain_2E0,type,
    c_2Esptree_2Edomain_2E0: u ).

tff(c_2Esptree_2Edomain_2E1,type,
    c_2Esptree_2Edomain_2E1: du > u ).

tff(c_2Esptree_2Efilter__v_2E0,type,
    c_2Esptree_2Efilter__v_2E0: u ).

tff(c_2Esptree_2Efilter__v_2E2,type,
    c_2Esptree_2Efilter__v_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Efoldi_2E0,type,
    c_2Esptree_2Efoldi_2E0: u ).

tff(c_2Esptree_2Efoldi_2E3,type,
    c_2Esptree_2Efoldi_2E3: ( du * du * du ) > u ).

tff(c_2Esptree_2Efoldi_2E4,type,
    c_2Esptree_2Efoldi_2E4: ( du * du * du * du ) > u ).

tff(c_2Esptree_2EfromAList_2E0,type,
    c_2Esptree_2EfromAList_2E0: u ).

tff(c_2Esptree_2EfromAList_2E1,type,
    c_2Esptree_2EfromAList_2E1: du > u ).

tff(c_2Esptree_2EfromList_2E0,type,
    c_2Esptree_2EfromList_2E0: u ).

tff(c_2Esptree_2EfromList_2E1,type,
    c_2Esptree_2EfromList_2E1: du > u ).

tff(c_2Esptree_2Einsert_2E0,type,
    c_2Esptree_2Einsert_2E0: u ).

tff(c_2Esptree_2Einsert_2E3,type,
    c_2Esptree_2Einsert_2E3: ( du * du * du ) > u ).

tff(c_2Esptree_2Einter_2E0,type,
    c_2Esptree_2Einter_2E0: u ).

tff(c_2Esptree_2Einter_2E2,type,
    c_2Esptree_2Einter_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Einter__eq_2E0,type,
    c_2Esptree_2Einter__eq_2E0: u ).

tff(c_2Esptree_2Einter__eq_2E2,type,
    c_2Esptree_2Einter__eq_2E2: ( du * du ) > u ).

tff(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: u ).

tff(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Esptree_2Elist__insert_2E0,type,
    c_2Esptree_2Elist__insert_2E0: u ).

tff(c_2Esptree_2Elist__insert_2E2,type,
    c_2Esptree_2Elist__insert_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Elist__to__num__set_2E0,type,
    c_2Esptree_2Elist__to__num__set_2E0: u ).

tff(c_2Esptree_2Elist__to__num__set_2E1,type,
    c_2Esptree_2Elist__to__num__set_2E1: du > u ).

tff(c_2Esptree_2Elookup_2E0,type,
    c_2Esptree_2Elookup_2E0: u ).

tff(c_2Esptree_2Elookup_2E2,type,
    c_2Esptree_2Elookup_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Elrnext_2E0,type,
    c_2Esptree_2Elrnext_2E0: u ).

tff(c_2Esptree_2Elrnext_2E1,type,
    c_2Esptree_2Elrnext_2E1: du > u ).

tff(c_2Esptree_2Emap_2E0,type,
    c_2Esptree_2Emap_2E0: u ).

tff(c_2Esptree_2Emap_2E2,type,
    c_2Esptree_2Emap_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Emapi_2E0,type,
    c_2Esptree_2Emapi_2E0: u ).

tff(c_2Esptree_2Emapi_2E2,type,
    c_2Esptree_2Emapi_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Emapi0_2E0,type,
    c_2Esptree_2Emapi0_2E0: u ).

tff(c_2Esptree_2Emapi0_2E3,type,
    c_2Esptree_2Emapi0_2E3: ( du * du * du ) > u ).

tff(c_2Esptree_2Emk__BN_2E0,type,
    c_2Esptree_2Emk__BN_2E0: u ).

tff(c_2Esptree_2Emk__BN_2E2,type,
    c_2Esptree_2Emk__BN_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Emk__BS_2E0,type,
    c_2Esptree_2Emk__BS_2E0: u ).

tff(c_2Esptree_2Emk__BS_2E3,type,
    c_2Esptree_2Emk__BS_2E3: ( du * du * du ) > u ).

tff(c_2Esptree_2Emk__wf_2E0,type,
    c_2Esptree_2Emk__wf_2E0: u ).

tff(c_2Esptree_2Emk__wf_2E1,type,
    c_2Esptree_2Emk__wf_2E1: du > u ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: ( du * du ) > u ).

tff(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: u ).

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: u ).

tff(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Esize_2E0,type,
    c_2Esptree_2Esize_2E0: u ).

tff(c_2Esptree_2Esize_2E1,type,
    c_2Esptree_2Esize_2E1: du > u ).

tff(c_2Esptree_2Espt__CASE_2E0,type,
    c_2Esptree_2Espt__CASE_2E0: u ).

tff(c_2Esptree_2Espt__CASE_2E5,type,
    c_2Esptree_2Espt__CASE_2E5: ( du * du * du * du * du ) > u ).

tff(c_2Esptree_2Espt__acc_2E0,type,
    c_2Esptree_2Espt__acc_2E0: u ).

tff(c_2Esptree_2Espt__acc_2E2,type,
    c_2Esptree_2Espt__acc_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Espt__center_2E0,type,
    c_2Esptree_2Espt__center_2E0: u ).

tff(c_2Esptree_2Espt__center_2E1,type,
    c_2Esptree_2Espt__center_2E1: du > u ).

tff(c_2Esptree_2Espt__fold_2E0,type,
    c_2Esptree_2Espt__fold_2E0: u ).

tff(c_2Esptree_2Espt__fold_2E3,type,
    c_2Esptree_2Espt__fold_2E3: ( du * du * du ) > u ).

tff(c_2Esptree_2Espt__left_2E0,type,
    c_2Esptree_2Espt__left_2E0: u ).

tff(c_2Esptree_2Espt__left_2E1,type,
    c_2Esptree_2Espt__left_2E1: du > u ).

tff(c_2Esptree_2Espt__right_2E0,type,
    c_2Esptree_2Espt__right_2E0: u ).

tff(c_2Esptree_2Espt__right_2E1,type,
    c_2Esptree_2Espt__right_2E1: du > u ).

tff(c_2Esptree_2Espt__size_2E0,type,
    c_2Esptree_2Espt__size_2E0: u ).

tff(c_2Esptree_2Espt__size_2E2,type,
    c_2Esptree_2Espt__size_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Esubspt_2E0,type,
    c_2Esptree_2Esubspt_2E0: u ).

tff(c_2Esptree_2Esubspt_2E2,type,
    c_2Esptree_2Esubspt_2E2: ( du * du ) > u ).

tff(c_2Esptree_2EtoAList_2E0,type,
    c_2Esptree_2EtoAList_2E0: u ).

tff(c_2Esptree_2EtoAList_2E1,type,
    c_2Esptree_2EtoAList_2E1: du > u ).

tff(c_2Esptree_2EtoList_2E0,type,
    c_2Esptree_2EtoList_2E0: u ).

tff(c_2Esptree_2EtoList_2E1,type,
    c_2Esptree_2EtoList_2E1: du > u ).

tff(c_2Esptree_2EtoListA_2E0,type,
    c_2Esptree_2EtoListA_2E0: u ).

tff(c_2Esptree_2EtoListA_2E2,type,
    c_2Esptree_2EtoListA_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Eunion_2E0,type,
    c_2Esptree_2Eunion_2E0: u ).

tff(c_2Esptree_2Eunion_2E2,type,
    c_2Esptree_2Eunion_2E2: ( du * du ) > u ).

tff(c_2Esptree_2Ewf_2E0,type,
    c_2Esptree_2Ewf_2E0: u ).

tff(c_2Esptree_2Ewf_2E1,type,
    c_2Esptree_2Ewf_2E1: du > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Eone_2Eone ) > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Eone_2Eone ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Earithmetic_2E_2A_2E0,type,
    mono_2Ec_2Earithmetic_2E_2A_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2A_2E2,type,
    mono_2Ec_2Earithmetic_2E_2A_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E0,type,
    mono_2Ec_2Earithmetic_2E_2B_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E2,type,
    mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E0,type,
    mono_2Ec_2Earithmetic_2E_2D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E2,type,
    mono_2Ec_2Earithmetic_2E_2D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Enum_2E0_2E0,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E0,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E2,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E2,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Epred__set_2EDIFF_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDIFF_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EDIV_2E0,type,
    mono_2Ec_2Earithmetic_2EDIV_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2EDIV_2E2,type,
    mono_2Ec_2Earithmetic_2EDIV_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Earithmetic_2EEVEN_2E0,type,
    mono_2Ec_2Earithmetic_2EEVEN_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Earithmetic_2EEVEN_2E1,type,
    mono_2Ec_2Earithmetic_2EEVEN_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Epred__set_2EIMAGE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EIMAGE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Epred__set_2EINTER_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EINTER_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Esptree_2ELN_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2ELN_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E1,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Enum_2ESUC_2E0,type,
    mono_2Ec_2Enum_2ESUC_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Enum_2ESUC_2E1,type,
    mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Erelation_2EWF_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Erelation_2EWF_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Erelation_2EWFREC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Erelation_2EWFREC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EZERO_2E0,type,
    mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2Ecount_2E0,type,
    mono_2Ec_2Epred__set_2Ecount_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Epred__set_2Ecount_2E1,type,
    mono_2Ec_2Epred__set_2Ecount_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Esptree_2Edomain_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Edomain_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Esptree_2Einsert_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Einsert_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(mono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Eone_2Eone * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Esptree_2Elist__insert_2E0,type,
    mono_2Ec_2Esptree_2Elist__insert_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Ec_2Esptree_2Elist__insert_2E2,type,
    mono_2Ec_2Esptree_2Elist__insert_2E2: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Esptree_2Elist__to__num__set_2E0,type,
    mono_2Ec_2Esptree_2Elist__to__num__set_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Esptree_2Elist__to__num__set_2E1,type,
    mono_2Ec_2Esptree_2Elist__to__num__set_2E1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Esptree_2Elookup_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Elookup_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Esptree_2Elrnext_2E0,type,
    mono_2Ec_2Esptree_2Elrnext_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Esptree_2Elrnext_2E1,type,
    mono_2Ec_2Esptree_2Elrnext_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eone_2Eone_2E0,type,
    mono_2Ec_2Eone_2Eone_2E0: mono_2Etyop_2Eone_2Eone ).

tff(mono_2Ec_2Esptree_2Espt__acc_2E0,type,
    mono_2Ec_2Esptree_2Espt__acc_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Esptree_2Espt__acc_2E2,type,
    mono_2Ec_2Esptree_2Espt__acc_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Esptree_2Esubspt_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Esubspt_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Esptree_2Eunion_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Eunion_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 * mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Esptree_2Ewf_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Ewf_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

tff(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: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

tff(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: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

tff(i_mono_2Etyop_2Eone_2Eone,type,
    i_mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > u ).

tff(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > u ).

tff(i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > u ).

tff(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

tff(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 > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(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 > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

tff(j_mono_2Etyop_2Eone_2Eone,type,
    j_mono_2Etyop_2Eone_2Eone: du > mono_2Etyop_2Eone_2Eone ).

tff(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

tff(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) ) ) ).

tff(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(reserved_2Eho_2Etruth,axiom,
    p(mono_2Ec_2Ebool_2ET_2E0) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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))))) ) ).

tff(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( p(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) ) ) ).

tff(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(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] : p(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))))) ) ).

tff(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(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] : p(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))))) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,V0_2E0)))) = s(tyop_2Enum_2Enum,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(j_mono_2Etyop_2Eone_2Eone(s(tyop_2Eone_2Eone,V0_2E0)))) = s(tyop_2Eone_2Eone,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),V0_2E0)))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),V0_2E0)))) = s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),V0_2E0) ) ).

tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Eone_2Eone] : ( j_mono_2Etyop_2Eone_2Eone(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0))) = V0_2E0 ) ).

tff(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)))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(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) )
    <=> p(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))))) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27a_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ealist_2EALOOKUP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ealist_2EALOOKUP_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),c_2Ealist_2EALOOKUP_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT2_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Esptree_2EBN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2EBN_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2EBN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27b),X0_2E0),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2EBN_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2EBS_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),c_2Esptree_2EBS_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2EBS_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27b),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)))),c_2Esptree_2EBS_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,X2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Esptree_2Espt(A_27a),X1_2E0),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EDIFF_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2EDIV_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2EFCONS_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(X2_2E0)))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(A_27a)))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27b))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EI_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Ecombin_2EI_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EIMAGE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EINTER_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EK_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EK_2E0),s(A_27b,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2EK_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2EK_2E0),s(A_27b,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2ELS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2ELS_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2ELS_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELS_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2ELS_2E0),s(A_27b,X0_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) = j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Esptree_2Espt(A_27a)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Eone_2Eone] : ( mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: 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_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27a_29_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( mono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Erelation_2EWF_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( mono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Ec_2Erelation_2EWFREC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Epred__set_2Ecount_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2Ecount_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Esptree_2Edelete_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Edelete_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Edifference_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Edifference_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Edifference_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Edifference_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Esptree_2Edomain_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),X0_2E0)))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Esptree_2Edomain_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27c),X0_2E0)))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Esptree_2Edomain_2E0),s(tyop_2Esptree_2Espt(A_27c),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Esptree_2Edomain_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0) ) ).

tff(arityeq2_2Ec_2Esptree_2Efilter__v_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Efilter__v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(A_27b,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(A_27b,X2_2E0),s(tyop_2Esptree_2Espt(A_27a),X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))),c_2Esptree_2Efoldi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(A_27b,X2_2E0))),s(tyop_2Esptree_2Espt(A_27a),X3_2E0))) ) ).

tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X2_2E0)),s(tyop_2Esptree_2Espt(A_27a),X3_2E0)))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))),c_2Esptree_2Efoldi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(X2_2E0)))),s(tyop_2Esptree_2Espt(A_27a),X3_2E0)))) ) ).

tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27b),X2_2E0),s(tyop_2Esptree_2Espt(A_27a),X3_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b))))),c_2Esptree_2Efoldi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))),s(tyop_2Esptree_2Espt(A_27a),X3_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Efoldi_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Esptree_2Efoldi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))))),c_2Esptree_2Efoldi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) ) ).

tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0),s(tyop_2Esptree_2Espt(A_27a),X3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))))),c_2Esptree_2Efoldi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))),s(tyop_2Esptree_2Espt(A_27a),X3_2E0))) ) ).

tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(A_27a,X2_2E0),s(tyop_2Esptree_2Espt(A_27b),X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a)))),c_2Esptree_2Efoldi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(A_27a,X2_2E0))),s(tyop_2Esptree_2Espt(A_27b),X3_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2EfromAList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2EfromAList_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2EfromAList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2EfromAList_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2EfromList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2EfromList_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),c_2Esptree_2Einsert_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27b,X1_2E0),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)))),c_2Esptree_2Einsert_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27b,X1_2E0))),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Eone_2Eone,X2_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Esptree_2Einsert_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Einter_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Einter_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27b),X0_2E0),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2Einter_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27c),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c))),c_2Esptree_2Einter_2E0),s(tyop_2Esptree_2Espt(A_27c),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Einter__eq_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Einter__eq_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a)))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Elist__insert_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Elist__insert_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(mono_2Ec_2Esptree_2Elist__insert_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Esptree_2Elist__to__num__set_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Esptree_2Elist__to__num__set_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Ec_2Esptree_2Elist__to__num__set_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Esptree_2Elookup_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Esptree_2Elookup_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Ec_2Esptree_2Elookup_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Esptree_2Elrnext_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Elrnext_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Elrnext_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c))),c_2Esptree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27c))),c_2Esptree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Esptree_2Espt(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Emapi_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Emapi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Esptree_2Espt(A_27b),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Emapi0_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b)))),c_2Esptree_2Emapi0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Emapi0_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),c_2Esptree_2Emapi0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Emk__BN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Emk__BN_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Emk__BS_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),c_2Esptree_2Emk__BS_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Esptree_2Espt(A_27a),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2Emk__wf_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Emk__wf_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2Emk__wf_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27b),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2Emk__wf_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = 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_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2Esize_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum),c_2Esptree_2Esize_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0)))) ) ).

tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] : ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),X4_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b))))),c_2Esptree_2Espt__CASE_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),X4_2E0))) ) ).

tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),X4_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a)))))),c_2Esptree_2Espt__CASE_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),X4_2E0))) ) ).

tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),X4_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)))))),c_2Esptree_2Espt__CASE_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),X4_2E0))) ) ).

tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27b_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),X4_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)))))),c_2Esptree_2Espt__CASE_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),X4_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Espt__acc_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Esptree_2Espt__acc_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Esptree_2Espt__center_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Esptree_2Espt__center_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq3_2Ec_2Esptree_2Espt__fold_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a))),c_2Esptree_2Espt__fold_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Esptree_2Espt(A_27b),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2Espt__left_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Espt__left_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2Espt__right_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Espt__right_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Espt__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum)),c_2Esptree_2Espt__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Esptree_2Esubspt_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),c_2Esptree_2Esubspt_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,X1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Esptree_2Esubspt_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Esptree_2EtoAList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Esptree_2EtoAList_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2EtoAList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b))),c_2Esptree_2EtoAList_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2EtoList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Esptree_2EtoList_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Esptree_2EtoList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Esptree_2EtoList_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2EtoListA_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Esptree_2EtoListA_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Eunion_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),X0_2E0),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Eunion_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0))),s(tyop_2Esptree_2Espt(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,X1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(mono_2Ec_2Esptree_2Eunion_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),c_2Esptree_2Ewf_2E0),s(tyop_2Esptree_2Espt(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27b),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool),c_2Esptree_2Ewf_2E0),s(tyop_2Esptree_2Espt(A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Esptree_2Ewf_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( 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(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Eone_2Eone] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Eone_2Eone] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0) ).

tff(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EAPPEND_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool,V2_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Enum_2Enum,V2_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V1_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ECONS_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDIFF_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epred__set_2EDIFF_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ecombin_2EI_2E0) ).

tff(monoeq_2Emono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Enum_2Enum,c_2Ecombin_2EI_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EIMAGE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epred__set_2EIMAGE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EINTER_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epred__set_2EINTER_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2ELN_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Ec_2Esptree_2ELN_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),c_2Esptree_2ELN_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ENONE_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Eoption_2ESOME_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Eone_2Eone] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Erelation_2EWF_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Erelation_2EWF_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0) ).

tff(monoeq_2Emono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Erelation_2EWFREC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(mono_2Ec_2Erelation_2EWFREC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Erelation_2EWFREC_2E0) ).

tff(monoeq_2Emono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Edomain_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Esptree_2Edomain_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Esptree_2Edomain_2E0) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Einsert_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29(mono_2Ec_2Esptree_2Einsert_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)))),c_2Esptree_2Einsert_2E0) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Eone_2Eone,V2_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V1_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Elookup_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Esptree_2Elookup_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),c_2Esptree_2Elookup_2E0) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Esubspt_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Esptree_2Esubspt_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),c_2Esptree_2Esubspt_2E0) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Eunion_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Esptree_2Eunion_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),c_2Esptree_2Eunion_2E0) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone(V0_2E0,V1_2E0))) = s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0)),s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Ewf_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Esptree_2Ewf_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Esptree_2Ewf_2E0) ).

tff(monoeq_2Emono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29(V0_2E0)))) ) ).

tff(thm_2Esptree_2Efilter__v__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V1f_2E0: u,V2x_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2x_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
      & ! [V3f_2E0: u,V4l_2E0: u,V5r_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4l_2E0),s(tyop_2Esptree_2Espt(A_27a),V5r_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0),s(tyop_2Esptree_2Espt(A_27a),V4l_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0),s(tyop_2Esptree_2Espt(A_27a),V5r_2E0))))) )
      & ! [V6f_2E0: u,V7l_2E0: u,V8x_2E0: u,V9r_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7l_2E0),s(A_27a,V8x_2E0),s(tyop_2Esptree_2Espt(A_27a),V9r_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0),s(A_27a,V8x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),V7l_2E0))),s(A_27a,V8x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),V9r_2E0))))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),V7l_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),V9r_2E0))))))) ) ) ).

tff(thm_2Esptree_2Espt__center__primitive__def,axiom,
    ! [A_27a: d,F3_2E0: u,F4_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V4v7_2E0: u,V5v8_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F3_2E0),s(tyop_2Esptree_2Espt(A_27a),V4v7_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5v8_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) )
     => ( ! [V6t1_2E0: u,V7x_27_2E0: u,V8t2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0))),s(A_27a,V7x_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8t2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_27_2E0))))) )
       => ( ! [V3x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F2_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))))) )
         => ( ! [V1spt__center_2E0: u,V2a_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),V1spt__center_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2a_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V2a_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),F4_2E0))) )
           => ( ! [V0R_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0R_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0R_2E0)))) )
             => ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Esptree_2Espt__center_2E0) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F1_2E0))) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Espt__right__def,axiom,
    ! [A_27a: d] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V0x_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0) )
      & ! [V3t1_2E0: u,V4x_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(A_27a,V4x_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0) ) ) ).

tff(thm_2Esptree_2Espt__left__def,axiom,
    ! [A_27a: d] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V0x_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0) )
      & ! [V3t1_2E0: u,V4x_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(A_27a,V4x_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0) ) ) ).

tff(thm_2Esptree_2Emap__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V1f_2E0: u,V2a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELS_2E1(s(A_27b,V2a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V2a_2E0))))) )
      & ! [V3f_2E0: u,V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27b),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V5t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(tyop_2Esptree_2Espt(A_27b),V4t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(tyop_2Esptree_2Espt(A_27b),V5t2_2E0))))) )
      & ! [V6f_2E0: u,V7t1_2E0: u,V8a_2E0: u,V9t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V6f_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0),s(A_27b,V8a_2E0),s(tyop_2Esptree_2Espt(A_27b),V9t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V6f_2E0),s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V6f_2E0),s(A_27b,V8a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V6f_2E0),s(tyop_2Esptree_2Espt(A_27b),V9t2_2E0))))) ) ) ).

tff(thm_2Esptree_2EfromAList__primitive__def,axiom,
    ! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V4fromAList_2E0: u,V7xs_2E0: u,V8x_2E0: mono_2Etyop_2Enum_2Enum,V9y_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V4fromAList_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V7xs_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8x_2E0)))),s(A_27a,V9y_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8x_2E0)),s(A_27a,V9y_2E0),s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V4fromAList_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V7xs_2E0))))))) )
     => ( ! [V4fromAList_2E0: u,V6v_2E0: u,V7xs_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V4fromAList_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),V6v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V7xs_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),V6v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V4fromAList_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V7xs_2E0))))) )
       => ( ! [V4fromAList_2E0: u,V5a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V4fromAList_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V5a_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V4fromAList_2E0))))) )
         => ( ! [V0R_2E0: u] :
                ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),V0R_2E0)))))
              <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),V0R_2E0)))))
                  & ! [V1y_2E0: u,V2x_2E0: mono_2Etyop_2Enum_2Enum,V3xs_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V3xs_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(A_27a,V1y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V3xs_2E0))))))) ) )
           => ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2EfromAList_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),F1_2E0))) ) ) ) ) ) ).

tff(thm_2Esptree_2Emk__wf__def,axiom,
    ! [A_27a: d] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V0x_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0x_2E0))) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))))) )
      & ! [V3t1_2E0: u,V4x_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(A_27a,V4x_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0))),s(A_27a,V4x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) ) ) ).

tff(thm_2Esptree_2EtoList__def,axiom,
    ! [A_27a: d,V0m_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0m_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Esptree_2Espt(A_27a),V0m_2E0))) ) ).

tff(thm_2Esptree_2EtoListA__def,axiom,
    ! [A_27a: d] :
      ( ! [V0acc_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V0acc_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0acc_2E0) )
      & ! [V1acc_2E0: u,V2a_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V1acc_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2a_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V1acc_2E0))) )
      & ! [V3acc_2E0: u,V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V3acc_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V3acc_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0))) )
      & ! [V6acc_2E0: u,V7t1_2E0: u,V8a_2E0: u,V9t2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V6acc_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V8a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V6acc_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0))) ) ) ).

tff(thm_2Esptree_2EtoAList__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0k_2E0: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2a_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)))),s(A_27a,V1v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V2a_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V2a_2E0))) )
     => ( s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Esptree_2EtoAList_2E0) = s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Esptree_2Efoldi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ENIL_2E0))) ) ) ).

tff(thm_2Esptree_2Emapi__def,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1pt_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Esptree_2Espt(A_27b),V1pt_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27b),V1pt_2E0))) ) ).

tff(thm_2Esptree_2Emapi0__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V5f_2E0: u,V6i_2E0: mono_2Etyop_2Enum_2Enum,V7t1_2E0: u,V8t2_2E0: u,V9inc_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V5f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6i_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V8t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9inc_2E0)))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V5f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V6i_2E0,mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V9inc_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V5f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V6i_2E0,V9inc_2E0))),s(tyop_2Esptree_2Espt(A_27b),V8t2_2E0))))) )
     => ( ! [V10f_2E0: u,V11i_2E0: mono_2Etyop_2Enum_2Enum,V12t1_2E0: u,V13a_2E0: u,V14t2_2E0: u,V15inc_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V10f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V11i_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V12t1_2E0))),s(A_27b,V13a_2E0))),s(tyop_2Esptree_2Espt(A_27b),V14t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V15inc_2E0)))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V10f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V11i_2E0,mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V15inc_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V12t1_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V10f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V11i_2E0)))),s(A_27b,V13a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V10f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V11i_2E0,V15inc_2E0))),s(tyop_2Esptree_2Espt(A_27b),V14t2_2E0))))) )
       => ( ! [V0f_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
          & ! [V2f_2E0: u,V3i_2E0: mono_2Etyop_2Enum_2Enum,V4a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELS_2E1(s(A_27b,V4a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)))),s(A_27b,V4a_2E0))))) )
          & ! [V5f_2E0: u,V6i_2E0: mono_2Etyop_2Enum_2Enum,V7t1_2E0: u,V8t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V5f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6i_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V8t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V5f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6i_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V8t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Elrnext_2E1(V6i_2E0))))) )
          & ! [V10f_2E0: u,V11i_2E0: mono_2Etyop_2Enum_2Enum,V12t1_2E0: u,V13a_2E0: u,V14t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V10f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V11i_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27b),V12t1_2E0),s(A_27b,V13a_2E0),s(tyop_2Esptree_2Espt(A_27b),V14t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V10f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V11i_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V12t1_2E0))),s(A_27b,V13a_2E0))),s(tyop_2Esptree_2Espt(A_27b),V14t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Elrnext_2E1(V11i_2E0))))) ) ) ) ) ).

tff(thm_2Esptree_2Efoldi__def,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V13f_2E0: u,V14i_2E0: mono_2Etyop_2Enum_2Enum,V17a_2E0: u,V15acc_2E0: u,V16t1_2E0: u,V18t2_2E0: u,V19inc_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V14i_2E0)))),s(A_27b,V17a_2E0))),s(A_27a,V15acc_2E0))),s(tyop_2Esptree_2Espt(A_27b),V16t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V18t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V19inc_2E0)))) = s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V14i_2E0,V19inc_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V14i_2E0)))),s(A_27b,V17a_2E0))),s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V14i_2E0,mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V19inc_2E0)))),s(A_27a,V15acc_2E0),s(tyop_2Esptree_2Espt(A_27b),V16t1_2E0))))),s(tyop_2Esptree_2Espt(A_27b),V18t2_2E0))) )
     => ( ! [V7f_2E0: u,V8i_2E0: mono_2Etyop_2Enum_2Enum,V9acc_2E0: u,V10t1_2E0: u,V11t2_2E0: u,V12inc_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V7f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8i_2E0)))),s(A_27a,V9acc_2E0))),s(tyop_2Esptree_2Espt(A_27b),V10t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V11t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V12inc_2E0)))) = s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V7f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V8i_2E0,V12inc_2E0))),s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V7f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V8i_2E0,mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V12inc_2E0)))),s(A_27a,V9acc_2E0),s(tyop_2Esptree_2Espt(A_27b),V10t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V11t2_2E0))) )
       => ( ! [V0f_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2acc_2E0: u] : ( s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(A_27a,V2acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0))) = s(A_27a,V2acc_2E0) )
          & ! [V3f_2E0: u,V4i_2E0: mono_2Etyop_2Enum_2Enum,V5acc_2E0: u,V6a_2E0: u] : ( s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(A_27a,V5acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELS_2E1(s(A_27b,V6a_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)))),s(A_27b,V6a_2E0))),s(A_27a,V5acc_2E0))) )
          & ! [V7f_2E0: u,V8i_2E0: mono_2Etyop_2Enum_2Enum,V9acc_2E0: u,V10t1_2E0: u,V11t2_2E0: u] : ( s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V7f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8i_2E0)),s(A_27a,V9acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27b),V10t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V11t2_2E0))))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V7f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8i_2E0)))),s(A_27a,V9acc_2E0))),s(tyop_2Esptree_2Espt(A_27b),V10t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V11t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Elrnext_2E1(V8i_2E0))))) )
          & ! [V13f_2E0: u,V14i_2E0: mono_2Etyop_2Enum_2Enum,V15acc_2E0: u,V16t1_2E0: u,V17a_2E0: u,V18t2_2E0: u] : ( s(A_27a,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V14i_2E0)),s(A_27a,V15acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27b),V16t1_2E0),s(A_27b,V17a_2E0),s(tyop_2Esptree_2Espt(A_27b),V18t2_2E0))))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V14i_2E0)))),s(A_27b,V17a_2E0))),s(A_27a,V15acc_2E0))),s(tyop_2Esptree_2Espt(A_27b),V16t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V18t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Elrnext_2E1(V14i_2E0))))) ) ) ) ) ).

tff(thm_2Esptree_2Espt__TY__DEF,axiom,
    ! [A_27a: d,F4_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V13n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F4_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V13n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
     => ( ! [V9n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F3_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
       => ( ! [V6n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
         => ( ! [V4n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
           => ( ! [V1a0_27_2E0: u] :
                  ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0)))))
                <=> ! [V2_27spt_27_2E0: u] :
                      ( ! [V3a0_27_2E0: u] :
                          ( ( ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0))) )
                            | ? [V5a_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))),s(A_27a,V5a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0))) )
                            | ? [V7a0_2E0: u,V8a1_2E0: u] :
                                ( ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)))),s(A_27a,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V7a0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V8a1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F3_2E0))))))) )
                                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27spt_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V7a0_2E0)))))
                                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27spt_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V8a1_2E0))))) )
                            | ? [V10a0_2E0: u,V11a1_2E0: u,V12a2_2E0: u] :
                                ( ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))))),s(A_27a,V11a1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V10a0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V12a2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F4_2E0))))))) )
                                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27spt_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V10a0_2E0)))))
                                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27spt_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V12a2_2E0))))) ) )
                         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27spt_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0))))) )
                     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27spt_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0))))) ) )
             => ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),V0rep_2E0))))) ) ) ) ) ) ).

tff(thm_2Esptree_2Espt__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0v_2E0: u,V1f_2E0: u,V2f1_2E0: u,V3f2_2E0: u] : ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V2f1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V3f2_2E0))) = s(A_27b,V0v_2E0) )
      & ! [V4a_2E0: u,V5v_2E0: u,V6f_2E0: u,V7f1_2E0: u,V8f2_2E0: u] : ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V7f1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V8f2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V4a_2E0))) )
      & ! [V9a0_2E0: u,V10a1_2E0: u,V11v_2E0: u,V12f_2E0: u,V13f1_2E0: u,V14f2_2E0: u] : ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V10a1_2E0))),s(A_27b,V11v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V12f_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V13f1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V14f2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V13f1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9a0_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10a1_2E0))) )
      & ! [V15a0_2E0: u,V16a1_2E0: u,V17a2_2E0: u,V18v_2E0: u,V19f_2E0: u,V20f1_2E0: u,V21f2_2E0: u] : ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V15a0_2E0),s(A_27a,V16a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V17a2_2E0))),s(A_27b,V18v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V19f_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V20f1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V21f2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V21f2_2E0),s(tyop_2Esptree_2Espt(A_27a),V15a0_2E0))),s(A_27a,V16a1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V17a2_2E0))) ) ) ).

tff(thm_2Esptree_2Espt__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
      & ! [V1f_2E0: u,V2a_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2a_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2a_2E0))))) )
      & ! [V3f_2E0: u,V4a0_2E0: u,V5a1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V5a1_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Esptree_2Espt(A_27a),V4a0_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Esptree_2Espt(A_27a),V5a1_2E0)))))) )
      & ! [V6f_2E0: u,V7a0_2E0: u,V8a1_2E0: u,V9a2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7a0_2E0),s(A_27a,V8a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9a2_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),V7a0_2E0)))),mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6f_2E0),s(A_27a,V8a1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Espt__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6f_2E0),s(tyop_2Esptree_2Espt(A_27a),V9a2_2E0))))))) ) ) ).

tff(thm_2Esptree_2Ewf__def,axiom,
    ! [A_27a: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V0a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0a_2E0)))))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V1t1_2E0: u,V2t2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0)))))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0)))))
            & ~ ( ( s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
                & ( s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) ) ) ) )
      & ! [V3t1_2E0: u,V4a_2E0: u,V5t2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0)))))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0)))))
            & ~ ( ( s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
                & ( s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) ) ) ) ) ) ).

tff(thm_2Esptree_2Edelete__def,axiom,
    ! [A_27a: d,F2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V6k_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V6k_2E0))
        <=> ( V6k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V3k_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V3k_2E0))
          <=> ( V3k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ! [V1k_2E0: mono_2Etyop_2Enum_2Enum] :
              ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1k_2E0))
            <=> ( V1k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
         => ( ! [V0k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
            & ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2a_2E0))))) )
            & ! [V3k_2E0: mono_2Etyop_2Enum_2Enum,V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V3k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V3k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V3k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V3k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))))))) )
            & ! [V6k_2E0: mono_2Etyop_2Enum_2Enum,V7t1_2E0: u,V8a_2E0: u,V9t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V6k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V6k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V6k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0))),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V6k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))))))) ) ) ) ) ) ).

tff(thm_2Esptree_2EfromList__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1i_2E0: mono_2Etyop_2Enum_2Enum,V2t_2E0: u,V3a_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))),s(A_27a,V3a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V1i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(A_27a,V3a_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) )
     => ! [V0l_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),F0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Esptree_2Esize__def,axiom,
    ! [A_27a: d] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
      & ! [V0a_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0a_2E0)))))) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))))) )
      & ! [V3t1_2E0: u,V4a_2E0: u,V5t2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ) ).

tff(thm_2Esptree_2Eunion__def,axiom,
    ! [A_27a: d,F4_2E0: u,F7_2E0: u,F1_2E0: u,F5_2E0: u,F8_2E0: u,F2_2E0: u,F3_2E0: u,F6_2E0: u,F0_2E0: u] :
      ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V14t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V14t2_27_2E0))))) )
     => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0))),s(A_27a,V16a_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V17t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0))),s(A_27a,V16a_27_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V17t2_27_27_2E0))))) )
       => ( ! [V9t1_2E0: u,V10t2_2E0: u,V12a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(A_27a,V12a_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(A_27a,V12a_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))) )
         => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V24t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0))),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V24t2_27_2E0))))) )
           => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))))),F8_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0))),s(A_27a,V26a_27_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V27t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0))),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V27t2_27_27_2E0))))) )
             => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V22a_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))))),F2_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(A_27a,V22a_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))) )
               => ( ! [V1a_2E0: u,V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F3_2E0),s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))) )
                 => ( ! [V1a_2E0: u,V6t1_27_2E0: u,V7v4_2E0: u,V8t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F6_2E0),s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V6t1_27_2E0))),s(A_27a,V7v4_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V6t1_27_2E0),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),V8t2_27_2E0))) )
                   => ( ! [V1a_2E0: u,V3b_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F0_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3b_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))) )
                     => ( ! [V0t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) )
                        & ! [V1a_2E0: u,V2t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V2t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F0_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F3_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F6_2E0),s(A_27a,V1a_2E0))))) )
                        & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V11t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V11t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))))) )
                        & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V21t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V21t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))))),F2_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))))),F8_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))))) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Einter__def,axiom,
    ! [A_27a: d,A_27b: d,F3_2E0: u,F5_2E0: u,F4_2E0: u,F7_2E0: u,F8_2E0: u,F1_2E0: u,F6_2E0: u,F2_2E0: u,F0_2E0: u] :
      ( ! [V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),F3_2E0),s(tyop_2Esptree_2Espt(A_27b),V4t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V5t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
     => ( ! [V18t1_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V23t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V24t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V23t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V24t2_27_2E0))))) )
       => ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V14t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V14t2_27_2E0))))) )
         => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V15t1_27_27_2E0))),s(A_27b,V16a_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V17t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V15t1_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V17t2_27_27_2E0))))) )
           => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))))),F8_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V25t1_27_27_2E0))),s(A_27b,V26a_27_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V27t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V25t1_27_27_2E0))),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V27t2_27_27_2E0))))) )
             => ( ! [V12a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F1_2E0),s(A_27b,V12a_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
               => ( ! [V1a_2E0: u,V6t1_27_2E0: u,V7v4_2E0: u,V8t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F6_2E0),s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27b),V6t1_27_2E0))),s(A_27b,V7v4_2E0))),s(tyop_2Esptree_2Espt(A_27b),V8t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))) )
                 => ( ! [V19a_2E0: u,V22a_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F2_2E0),s(A_27a,V19a_2E0))),s(A_27b,V22a_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V19a_2E0))) )
                   => ( ! [V1a_2E0: u,V3b_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F0_2E0),s(A_27a,V1a_2E0))),s(A_27b,V3b_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))) )
                     => ( ! [V0t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27b),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
                        & ! [V1a_2E0: u,V2t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27b),V2t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),V2t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F0_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F6_2E0),s(A_27a,V1a_2E0))))) )
                        & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V11t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),V11t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))))) )
                        & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V21t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),V21t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F2_2E0),s(A_27a,V19a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))))),F8_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))))) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Einter__eq__def,axiom,
    ! [A_27a: d,F3_2E0: u,F5_2E0: u,F4_2E0: u,F7_2E0: u,F1_2E0: u,F12_2E0: u,F8_2E0: u,F11_2E0: u,F6_2E0: u,F10_2E0: u,F0_2E0: u,F9_2E0: u,F2_2E0: u] :
      ( ! [V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),F3_2E0),s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
     => ( ! [V18t1_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V24t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V24t2_27_2E0))))) )
       => ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V14t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V14t2_27_2E0))))) )
         => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0))),s(A_27a,V16a_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V17t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V17t2_27_27_2E0))))) )
           => ( ! [V12a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F1_2E0),s(A_27a,V12a_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
             => ( ! [V26a_27_27_27_2E0: u,V19a_2E0: u] :
                    ( p(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)),F12_2E0),s(A_27a,V26a_27_27_27_2E0))),s(A_27a,V19a_2E0)))))
                  <=> ( s(A_27a,V26a_27_27_27_2E0) = s(A_27a,V19a_2E0) ) )
               => ( ! [V19a_2E0: u,V18t1_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))))),F8_2E0),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0))),s(A_27a,V26a_27_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V27t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F12_2E0),s(A_27a,V26a_27_27_27_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0))),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V27t2_27_27_2E0))))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V27t2_27_27_2E0))))))) )
                 => ( ! [V1a_2E0: u,V7b_27_2E0: u] :
                        ( p(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)),F11_2E0),s(A_27a,V1a_2E0))),s(A_27a,V7b_27_2E0)))))
                      <=> ( s(A_27a,V1a_2E0) = s(A_27a,V7b_27_2E0) ) )
                   => ( ! [V1a_2E0: u,V6t1_27_2E0: u,V7b_27_2E0: u,V8t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F6_2E0),s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V6t1_27_2E0))),s(A_27a,V7b_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F11_2E0),s(A_27a,V1a_2E0))),s(A_27a,V7b_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
                     => ( ! [V1a_2E0: u,V3b_2E0: u] :
                            ( p(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)),F10_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3b_2E0)))))
                          <=> ( s(A_27a,V1a_2E0) = s(A_27a,V3b_2E0) ) )
                       => ( ! [V1a_2E0: u,V3b_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F0_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3b_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F10_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3b_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
                         => ( ! [V22a_27_2E0: u,V19a_2E0: u] :
                                ( p(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)),F9_2E0),s(A_27a,V22a_27_2E0))),s(A_27a,V19a_2E0)))))
                              <=> ( s(A_27a,V22a_27_2E0) = s(A_27a,V19a_2E0) ) )
                           => ( ! [V19a_2E0: u,V22a_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F2_2E0),s(A_27a,V19a_2E0))),s(A_27a,V22a_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F9_2E0),s(A_27a,V22a_27_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
                             => ( ! [V0t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
                                & ! [V1a_2E0: u,V2t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V2t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F0_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F6_2E0),s(A_27a,V1a_2E0))))) )
                                & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V11t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V11t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))))) )
                                & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V21t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V21t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F2_2E0),s(A_27a,V19a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))))),F8_2E0),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Edifference__def,axiom,
    ! [A_27a: d,A_27b: d,F6_2E0: u,F4_2E0: u,F8_2E0: u,F7_2E0: u,F2_2E0: u,F1_2E0: u,F5_2E0: u,F0_2E0: u,F3_2E0: u] :
      ( ! [V6t1_27_2E0: u,V7b_27_2E0: u,V8t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F6_2E0),s(tyop_2Esptree_2Espt(A_27b),V6t1_27_2E0))),s(A_27b,V7b_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V8t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
     => ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V14t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V13t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V14t2_27_2E0))))) )
       => ( ! [V18t1_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V25t1_27_27_2E0))),s(A_27b,V26a_27_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V27t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V25t1_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V27t2_27_27_2E0))))) )
         => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V15t1_27_27_2E0))),s(A_27b,V16a_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V17t2_27_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V15t1_27_27_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V17t2_27_27_2E0))))) )
           => ( ! [V18t1_2E0: u,V20t2_2E0: u,V22a_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))),F2_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(A_27b,V22a_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))) )
             => ( ! [V9t1_2E0: u,V10t2_2E0: u,V12a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))),F1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(A_27b,V12a_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))) )
               => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V23t1_27_2E0))),s(tyop_2Esptree_2Espt(A_27b),V24t2_27_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V23t1_27_2E0))),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0),s(tyop_2Esptree_2Espt(A_27b),V24t2_27_2E0))))) )
                 => ( ! [V3b_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F0_2E0),s(A_27b,V3b_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
                   => ( ! [V1a_2E0: u,V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F3_2E0),s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27b),V4t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V5t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))) )
                     => ( ! [V0t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27b),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
                        & ! [V1a_2E0: u,V2t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27b),V2t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),V2t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F3_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F6_2E0))) )
                        & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V11t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),V11t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))),F1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F4_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))))) )
                        & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Esptree_2Espt(A_27b),V21t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27b),V21t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0),s(A_27a,V19a_2E0),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))),F2_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F5_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V20t2_2E0))))) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Elrnext__primitive__def,axiom,
    ! [F2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V3a_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V3a_2E0))
        <=> ( V3a_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V2lrnext_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V3a_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(F1_2E0,V2lrnext_2E0),V3a_2E0) = mono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V3a_2E0),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V2lrnext_2E0,mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V3a_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))) )
       => ( ! [V0R_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
              ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0R_2E0))
            <=> ( p(mono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum(V0R_2E0))
                & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
                    ( ( V1n_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                   => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0R_2E0,mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))),V1n_2E0)) ) ) )
         => ( mono_2Ec_2Esptree_2Elrnext_2E0 = mono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(F0_2E0),F1_2E0) ) ) ) ) ).

tff(thm_2Esptree_2Edomain__def,axiom,
    ! [A_27a: d,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,F3_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,F2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
      ( ! [V8n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F1_2E0,V8n_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V8n_2E0),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) )
     => ( ! [V3n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F0_2E0,V3n_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V3n_2E0),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) )
       => ( ! [V9n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F3_2E0,V9n_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V9n_2E0),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) )
         => ( ! [V4n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F2_2E0,V4n_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),V4n_2E0),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) )
           => ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))) = mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum )
              & ! [V0v0_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0v0_2E0)))))) = mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum) )
              & ! [V1t1_2E0: u,V2t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0)))))) = mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F0_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))))),mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F2_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0)))))) )
              & ! [V5t1_2E0: u,V6v1_2E0: u,V7t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V5t1_2E0),s(A_27a,V6v1_2E0),s(tyop_2Esptree_2Espt(A_27a),V7t2_2E0)))))) = mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum),mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F1_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V5t1_2E0)))))),mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(F3_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V7t2_2E0)))))) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Espt__fold__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u,V1acc_2E0: u] : ( s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0))) = s(A_27a,V1acc_2E0) )
      & ! [V2f_2E0: u,V3acc_2E0: u,V4a_2E0: u] : ( s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27a,V3acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELS_2E1(s(A_27b,V4a_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27b,V4a_2E0))),s(A_27a,V3acc_2E0))) )
      & ! [V5f_2E0: u,V6acc_2E0: u,V7t1_2E0: u,V8t2_2E0: u] : ( s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V5f_2E0),s(A_27a,V6acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V8t2_2E0))))) = s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V5f_2E0),s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V5f_2E0),s(A_27a,V6acc_2E0),s(tyop_2Esptree_2Espt(A_27b),V7t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),V8t2_2E0))) )
      & ! [V9f_2E0: u,V10acc_2E0: u,V11t1_2E0: u,V12a_2E0: u,V13t2_2E0: u] : ( s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V9f_2E0),s(A_27a,V10acc_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27b),V11t1_2E0),s(A_27b,V12a_2E0),s(tyop_2Esptree_2Espt(A_27b),V13t2_2E0))))) = s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V9f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V9f_2E0),s(A_27b,V12a_2E0))),s(A_27a,c_2Esptree_2Espt__fold_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V9f_2E0),s(A_27a,V10acc_2E0),s(tyop_2Esptree_2Espt(A_27b),V11t1_2E0))))),s(tyop_2Esptree_2Espt(A_27b),V13t2_2E0))) ) ) ).

tff(thm_2Esptree_2Elist__to__num__set__def,axiom,
    ( ( mono_2Ec_2Esptree_2Elist__to__num__set_2E1(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum) = mono_2Ec_2Esptree_2ELN_2E0_2Emono_2Etyop_2Eone_2Eone )
    & ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ns_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Esptree_2Elist__to__num__set_2E1(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(V0n_2E0,V1ns_2E0)) = mono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone(V0n_2E0,mono_2Ec_2Eone_2Eone_2E0,mono_2Ec_2Esptree_2Elist__to__num__set_2E1(V1ns_2E0)) ) ) ).

tff(thm_2Esptree_2Elist__insert__def,axiom,
    ( ! [V0t_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Elist__insert_2E2(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,V0t_2E0) = V0t_2E0 )
    & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2ns_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V3t_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Elist__insert_2E2(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum(V1n_2E0,V2ns_2E0),V3t_2E0) = mono_2Ec_2Esptree_2Elist__insert_2E2(V2ns_2E0,mono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone(V1n_2E0,mono_2Ec_2Eone_2Eone_2E0,V3t_2E0)) ) ) ).

tff(thm_2Esptree_2Elookup__fromList__outside,axiom,
    ! [A_27a: d,V0args_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0args_2E0)))),V1k_2E0))
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0args_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Esptree_2Esize__delete,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) )
     => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))),mono_2Ec_2Earithmetic_2E_2D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))) ) ) ).

tff(thm_2Esptree_2Edelete__fail,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))))
     => ( ~ p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0n_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))))
      <=> ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),V1t_2E0) ) ) ) ).

tff(thm_2Esptree_2Ewf__difference,axiom,
    ! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))))) ) ).

tff(thm_2Esptree_2Edifference__sub,axiom,
    ! [A_27a: d,A_27b: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V1a_2E0),s(tyop_2Esptree_2Espt(A_27b),V0b_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
     => p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1a_2E0)))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V0b_2E0)))))) ) ).

tff(thm_2Esptree_2Eunion__num__set__sym,axiom,
    ! [V0t1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1t2_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone(V0t1_2E0,V1t2_2E0) = mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone(V1t2_2E0,V0t1_2E0) ) ).

tff(thm_2Esptree_2Enum__set__domain__eq,axiom,
    ! [V0t1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1t2_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( p(mono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone(V0t1_2E0))
        & p(mono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone(V1t2_2E0)) )
     => ( ( mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(V0t1_2E0) = mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(V1t2_2E0) )
      <=> ( V0t1_2E0 = V1t2_2E0 ) ) ) ).

tff(thm_2Esptree_2Esize__domain,axiom,
    ! [A_27a: d,V0t_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) = mono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))) ) ).

tff(thm_2Esptree_2Edomain__mapi,axiom,
    ! [A_27a: d,A_27b: d,V0pt_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0)))))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0)))) ) ).

tff(thm_2Esptree_2Emapi__Alist,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2kv_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),V2kv_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),V2kv_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),V2kv_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),V2kv_2E0))))))) )
     => ! [V0pt_2E0: u,V1f_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0))))))) ) ) ).

tff(thm_2Esptree_2EMAP__foldi,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V4k_2E0: mono_2Etyop_2Enum_2Enum,V5v_2E0: u,V6a_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4k_2E0)))),s(A_27a,V5v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V6a_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4k_2E0)),s(A_27a,V5v_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V6a_2E0))) )
     => ( ! [V1f_2E0: u,V7k_2E0: mono_2Etyop_2Enum_2Enum,V8v_2E0: u,V9a_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7k_2E0)))),s(A_27a,V8v_2E0))),s(tyop_2Elist_2Elist(A_27b),V9a_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V1f_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7k_2E0)),s(A_27a,V8v_2E0))))),s(tyop_2Elist_2Elist(A_27b),V9a_2E0))) )
       => ! [V0pt_2E0: u,V1f_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3acc_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V3acc_2E0),s(tyop_2Esptree_2Espt(A_27a),V0pt_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V3acc_2E0))),s(tyop_2Esptree_2Espt(A_27a),V0pt_2E0))) ) ) ) ).

tff(thm_2Esptree_2Elookup__mk__BN,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V2i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V2i_2E0))
        <=> ( V2i_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0t2_2E0: u,V1t1_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V2i_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V2i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V2i_2E0))),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))))) ) ) ).

tff(thm_2Esptree_2Ewf__mapi,axiom,
    ! [A_27a: d,A_27b: d,V0pt_2E0: u,V1f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0))))))) ).

tff(thm_2Esptree_2Ewf__mk__BS,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2a_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V2a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))))) ) ).

tff(thm_2Esptree_2Ewf__mk__BN,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))))) ) ).

tff(thm_2Esptree_2Ewf__filter__v,axiom,
    ! [A_27a: d,V0t_2E0: u,V1f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))))) ) ).

tff(thm_2Esptree_2Elookup__filter__v,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V2f_2E0: u,V3v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0))),s(A_27a,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0),s(A_27a,V3v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) )
     => ! [V0k_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: u,V2f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Efilter__v_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0))))) ) ) ).

tff(thm_2Esptree_2Esubspt__LN,axiom,
    ! [A_27a: d,V0sp_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),V0sp_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V0sp_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
      <=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0sp_2E0)))) = mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum ) ) ) ).

tff(thm_2Esptree_2Esubspt__trans,axiom,
    ! [A_27a: d,V0sp3_2E0: u,V1sp2_2E0: u,V2sp1_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V2sp1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1sp2_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V1sp2_2E0),s(tyop_2Esptree_2Espt(A_27a),V0sp3_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V2sp1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0sp3_2E0))))) ) ).

tff(thm_2Esptree_2Esubspt__refl,axiom,
    ! [A_27a: d,V0sp_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V0sp_2E0),s(tyop_2Esptree_2Espt(A_27a),V0sp_2E0))))) ).

tff(thm_2Esptree_2Esubspt__def,axiom,
    ! [A_27a: d,V0sp1_2E0: u,V1sp2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V0sp1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1sp2_2E0)))))
    <=> ! [V2k_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V2k_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0sp1_2E0))))))
         => ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V2k_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1sp2_2E0))))))
            & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1sp2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0sp1_2E0))) ) ) ) ) ).

tff(thm_2Esptree_2Espt__center__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1v2_2E0: u,V2v1_2E0: u,V3t2_2E0: u,V4t1_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2v1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1v2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Esptree_2Espt__center__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1x_2E0)))))))
        & ! [V2t1_2E0: u,V3x_2E0: u,V4t2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0),s(A_27a,V3x_2E0),s(tyop_2Esptree_2Espt(A_27a),V4t2_2E0)))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V5v1_2E0: u,V6v2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V5v1_2E0),s(tyop_2Esptree_2Espt(A_27a),V6v2_2E0))))))) )
     => ! [V7v_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V7v_2E0))))) ) ).

tff(thm_2Esptree_2Einsert__shadow,axiom,
    ! [A_27a: d,V0t_2E0: u,V1a_2E0: mono_2Etyop_2Enum_2Enum,V2b_2E0: u,V3c_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V2b_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V3c_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V2b_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) ) ).

tff(thm_2Esptree_2Einsert__insert,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ! [V0x1_2E0: mono_2Etyop_2Enum_2Enum,V1x2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V0x1_2E0),V1x2_2E0))
        <=> ( V0x1_2E0 = V1x2_2E0 ) )
     => ! [V0x1_2E0: mono_2Etyop_2Enum_2Enum,V1x2_2E0: mono_2Etyop_2Enum_2Enum,V2v1_2E0: u,V3v2_2E0: u,V4t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x1_2E0)),s(A_27a,V2v1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x2_2E0)),s(A_27a,V3v2_2E0),s(tyop_2Esptree_2Espt(A_27a),V4t_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V0x1_2E0),V1x2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x1_2E0)),s(A_27a,V2v1_2E0),s(tyop_2Esptree_2Espt(A_27a),V4t_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x2_2E0)),s(A_27a,V3v2_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x1_2E0)),s(A_27a,V2v1_2E0),s(tyop_2Esptree_2Espt(A_27a),V4t_2E0))))))) ) ) ).

tff(thm_2Esptree_2Emap__fromAList,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum,V3v_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(A_27b,V3v_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V3v_2E0))))) )
     => ! [V0ls_2E0: u,V1f_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),V0ls_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),V0ls_2E0))))) ) ) ).

tff(thm_2Esptree_2Emap__insert,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: mono_2Etyop_2Enum_2Enum,V2y_2E0: u,V3z_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(A_27a,V2y_2E0),s(tyop_2Esptree_2Espt(A_27a),V3z_2E0))))) = s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),V3z_2E0))))) ) ).

tff(thm_2Esptree_2Emap__map__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t_2E0: u,V1f_2E0: u,V2g_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))) = s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0))),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) ) ).

tff(thm_2Esptree_2Ewf__map,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) ) ).

tff(thm_2Esptree_2Emap__LN,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))) = s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0) )
    <=> ( s(tyop_2Esptree_2Espt(A_27a),V1t_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) ) ) ).

tff(thm_2Esptree_2Elookup__map,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u,V2x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),V1s_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1s_2E0))))) ) ).

tff(thm_2Esptree_2Edomain__map,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),V1s_2E0)))))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1s_2E0)))) ) ).

tff(thm_2Esptree_2EtoList__map,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),V1s_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27a),V1s_2E0))))) ) ).

tff(thm_2Esptree_2EfromAList__append,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V1l2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0l1_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V1l2_2E0))))) ) ).

tff(thm_2Esptree_2Eunion__insert__LN,axiom,
    ! [A_27a: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1y_2E0: u,V2t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(A_27a,V1y_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(A_27a,V1y_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t2_2E0))) ) ).

tff(thm_2Esptree_2EfromAList__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) ) ) ).

tff(thm_2Esptree_2Ewf__fromAList,axiom,
    ! [A_27a: d,V0ls_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0ls_2E0))))))) ).

tff(thm_2Esptree_2Elookup__fromAList__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u,V1x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) ) ).

tff(thm_2Esptree_2Edomain__fromAList,axiom,
    ! [A_27a: d,V0ls_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0ls_2E0)))))) = mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0ls_2E0))))) ) ).

tff(thm_2Esptree_2Elookup__fromAList,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0ls_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ealist_2EALOOKUP_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0ls_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)))) ) ).

tff(thm_2Esptree_2EfromAList__def,axiom,
    ! [A_27a: d] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ! [V0y_2E0: u,V1xs_2E0: u,V2x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(A_27a,V0y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V1xs_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(A_27a,V0y_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V1xs_2E0))))) ) ) ).

tff(thm_2Esptree_2EfromAList__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ENIL_2E0)))))
        & ! [V1x_2E0: mono_2Etyop_2Enum_2Enum,V2y_2E0: u,V3xs_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V3xs_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(A_27a,V2y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V3xs_2E0))))))) ) )
     => ! [V4v_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V4v_2E0))))) ) ).

tff(thm_2Esptree_2Edelete__compute,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum,V4a_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) ) ) ).

tff(thm_2Esptree_2Einsert__compute,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum,V4a_27_2E0: u,V5a_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5a_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_27_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5a_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5a_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_27_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5a_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_27_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_27_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))),s(A_27a,V4a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) ) ) ).

tff(thm_2Esptree_2Elookup__compute,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum,V4a_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4a_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4a_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4a_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EZERO_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4a_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3n_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0))) ) ) ).

tff(thm_2Esptree_2Einter__assoc,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t1_2E0: u,V1t2_2E0: u,V2t3_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0),s(tyop_2Esptree_2Espt(A_27c),V2t3_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))),s(tyop_2Esptree_2Espt(A_27c),V2t3_2E0))) ) ).

tff(thm_2Esptree_2Eunion__assoc,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u,V2t3_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t3_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t3_2E0))) ) ).

tff(thm_2Esptree_2Einter__LN,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2ELN_2E0) ) ) ).

tff(thm_2Esptree_2Eunion__LN,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) ) ) ).

tff(thm_2Esptree_2Edelete__mk__wf,axiom,
    ! [A_27a: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))) ) ).

tff(thm_2Esptree_2Einsert__mk__wf,axiom,
    ! [A_27a: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(A_27a,V1v_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(A_27a,V1v_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) ) ).

tff(thm_2Esptree_2Einter__mk__wf,axiom,
    ! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0))),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))) ) ).

tff(thm_2Esptree_2Eunion__mk__wf,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))))) ) ).

tff(thm_2Esptree_2Einter__eq,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t1_2E0: u,V1t2_2E0: u,V2t3_2E0: u,V3t4_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V2t3_2E0),s(tyop_2Esptree_2Espt(A_27c),V3t4_2E0))) )
    <=> ! [V4x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V2t3_2E0),s(tyop_2Esptree_2Espt(A_27c),V3t4_2E0))))) ) ) ).

tff(thm_2Esptree_2Emk__wf__eq,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))) )
    <=> ! [V2x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))) ) ) ).

tff(thm_2Esptree_2Edomain__mk__wf,axiom,
    ! [A_27a: d,V0t_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) ) ).

tff(thm_2Esptree_2Elookup__mk__wf,axiom,
    ! [A_27a: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))) ) ).

tff(thm_2Esptree_2Ewf__mk__id,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) ) ) ).

tff(thm_2Esptree_2Ewf__mk__wf,axiom,
    ! [A_27a: d,V0t_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))))) ).

tff(thm_2Esptree_2Espt__eq__thm,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))))) )
     => ( ( s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0) = s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0) )
      <=> ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))) ) ) ) ).

tff(thm_2Esptree_2EMEM__toList,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))))))))
    <=> ? [V2k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) ) ) ).

tff(thm_2Esptree_2EisEmpty__toList,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => ( ( s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ) ).

tff(thm_2Esptree_2EisEmpty__toListA,axiom,
    ! [A_27a: d,V0t_2E0: u,V1acc_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => ( ( s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V1acc_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1acc_2E0) ) ) ) ).

tff(thm_2Esptree_2EtoListA__append,axiom,
    ! [A_27a: d,V0t_2E0: u,V1acc_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),V1acc_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoListA_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))),s(tyop_2Elist_2Elist(A_27a),V1acc_2E0))) ) ).

tff(thm_2Esptree_2Efoldi__FOLDR__toAList,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2t_2E0: u] : ( s(A_27b,c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27b,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V0f_2E0))),s(A_27b,V1a_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) ) ).

tff(thm_2Esptree_2EALL__DISTINCT__MAP__FST__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u] : p(mono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))))) ).

tff(thm_2Esptree_2Edomain__empty,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => ( ( s(tyop_2Esptree_2Espt(A_27a),V0t_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      <=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) = mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum ) ) ) ).

tff(thm_2Esptree_2Einsert__union,axiom,
    ! [A_27a: d,V0k_2E0: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2s_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1v_2E0),s(tyop_2Esptree_2Espt(A_27a),V2s_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1v_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2s_2E0))) ) ).

tff(thm_2Esptree_2EALOOKUP__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u,V1x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ealist_2EALOOKUP_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) ) ).

tff(thm_2Esptree_2EMEM__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum,V2v_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(A_27a,V2v_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))))))
    <=> ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2v_2E0))) ) ) ).

tff(thm_2Esptree_2Elookup__mapi,axiom,
    ! [A_27a: d,A_27b: d,V0pt_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emapi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2f_2E0),s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)))),s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27b),V0pt_2E0))))) ) ).

tff(thm_2Esptree_2Elookup__mapi0,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum,V3k_2E0: mono_2Etyop_2Enum_2Enum,V4v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)))),s(A_27a,V4v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Espt__acc_2E2(V2i_2E0,V3k_2E0))))),s(A_27a,V4v_2E0))))) )
     => ! [V0f_2E0: u,V1pt_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum,V3k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emapi0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1pt_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1pt_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)))))) ) ) ).

tff(thm_2Esptree_2Edomain__foldi,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V2v_2E0: u,V3a_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)))),s(A_27a,V2v_2E0)))),V3a_2E0) = mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(V1k_2E0,V3a_2E0) )
     => ! [V0t_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) ) ) ).

tff(thm_2Esptree_2Eset__foldi__keys,axiom,
    ! [A_27a: d,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,F0_2E0: u] :
      ( ! [V2i_2E0: mono_2Etyop_2Enum_2Enum,V6n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(F1_2E0,V2i_2E0),V6n_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(V2i_2E0,mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0),V6n_2E0)) )
     => ( ! [V3k_2E0: mono_2Etyop_2Enum_2Enum,V4v_2E0: u,V5a_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)))),s(A_27a,V4v_2E0)))),V5a_2E0) = mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(V3k_2E0,V5a_2E0) )
       => ! [V0t_2E0: u,V1a_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Efoldi_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1a_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) = mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(V1a_2E0,mono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(F1_2E0,V2i_2E0),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))) ) ) ) ).

tff(thm_2Esptree_2Espt__acc__0,axiom,
    ! [V0k_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(mono_2Ec_2Enum_2E0_2E0,V0k_2E0) = V0k_2E0 ) ).

tff(thm_2Esptree_2Espt__acc__eqn,axiom,
    ! [V0k_2E0: mono_2Etyop_2Enum_2Enum,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V1i_2E0,V0k_2E0) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Esptree_2Elrnext_2E1(V1i_2E0),V0k_2E0),V1i_2E0) ) ).

tff(thm_2Esptree_2Espt__acc__thm,axiom,
    ! [F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V0k_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0k_2E0))
        <=> ( V0k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0k_2E0: mono_2Etyop_2Enum_2Enum,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V1i_2E0,V0k_2E0) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0k_2E0),V1i_2E0,mono_2Ec_2Esptree_2Espt__acc_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(V1i_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(V0k_2E0),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V1i_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V1i_2E0))),mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))) ) ) ).

tff(thm_2Esptree_2Espt__acc__def__compute,axiom,
    ( ! [V0i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V0i_2E0,mono_2Ec_2Enum_2E0_2E0) = V0i_2E0 )
    & ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V2i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1k_2E0))) = mono_2Ec_2Esptree_2Espt__acc_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(V2i_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1k_2E0))),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0))),mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1k_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))) )
    & ! [V3k_2E0: mono_2Etyop_2Enum_2Enum,V4i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V4i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3k_2E0))) = mono_2Ec_2Esptree_2Espt__acc_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(V4i_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V3k_2E0))),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V4i_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V4i_2E0))),mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3k_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))) ) ) ).

tff(thm_2Esptree_2Espt__acc__def,axiom,
    ( ! [V0i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V0i_2E0,mono_2Ec_2Enum_2E0_2E0) = V0i_2E0 )
    & ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Espt__acc_2E2(V2i_2E0,mono_2Ec_2Enum_2ESUC_2E1(V1k_2E0)) = mono_2Ec_2Esptree_2Espt__acc_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(V2i_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(V1k_2E0)),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0))),mono_2Ec_2Earithmetic_2EDIV_2E2(V1k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))) ) ) ).

tff(thm_2Esptree_2Espt__acc__ind,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( ! [V1i_2E0: mono_2Etyop_2Enum_2Enum] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0P_2E0,V1i_2E0),mono_2Ec_2Enum_2E0_2E0))
        & ! [V2i_2E0: mono_2Etyop_2Enum_2Enum,V3k_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0P_2E0,mono_2Ec_2Earithmetic_2E_2B_2E2(V2i_2E0,mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(V3k_2E0)),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V2i_2E0)))),mono_2Ec_2Earithmetic_2EDIV_2E2(V3k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))))
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0P_2E0,V2i_2E0),mono_2Ec_2Enum_2ESUC_2E1(V3k_2E0))) ) )
     => ! [V4v_2E0: mono_2Etyop_2Enum_2Enum,V5v1_2E0: mono_2Etyop_2Enum_2Enum] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0P_2E0,V4v_2E0),V5v1_2E0)) ) ).

tff(thm_2Esptree_2Edomain__delete,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))) = mono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))),V1k_2E0) ) ).

tff(thm_2Esptree_2Elookup__delete,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ! [V1k1_2E0: mono_2Etyop_2Enum_2Enum,V2k2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V1k1_2E0),V2k2_2E0))
        <=> ( V1k1_2E0 = V2k2_2E0 ) )
     => ! [V0t_2E0: u,V1k1_2E0: mono_2Etyop_2Enum_2Enum,V2k2_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k1_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k2_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V1k1_2E0),V2k2_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k1_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))) ) ) ).

tff(thm_2Esptree_2Edomain__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = mono_2Ec_2Epred__set_2Ecount_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ).

tff(thm_2Esptree_2Edomain__sing,axiom,
    ! [A_27a: d,V0v_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(A_27a,V0v_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))) = mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(V1k_2E0,mono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum) ) ).

tff(thm_2Esptree_2Edomain__difference,axiom,
    ! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0)))))) = mono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0)))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))) ) ).

tff(thm_2Esptree_2Edomain__insert,axiom,
    ! [A_27a: d,V0v_2E0: u,V1t_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(A_27a,V0v_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0)))))) = mono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum(V2k_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))) ) ).

tff(thm_2Esptree_2Edomain__inter,axiom,
    ! [A_27a: d,A_27b: d,V0t2_2E0: u,V1t1_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V0t2_2E0)))))) = mono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0)))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V0t2_2E0))))) ) ).

tff(thm_2Esptree_2Edomain__union,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0)))))) = mono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t1_2E0)))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t2_2E0))))) ) ).

tff(thm_2Esptree_2Elookup__NONE__domain,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
    <=> ~ p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V1k_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))) ) ).

tff(thm_2Esptree_2Elookup__inter__alt,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1t2_2E0: u,V2t1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V1t2_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Esptree_2Edomain__lookup,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V1k_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))))
    <=> ? [V2v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2v_2E0))) ) ) ).

tff(thm_2Esptree_2Elookup__fromList,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Esptree_2Esize__insert,axiom,
    ! [A_27a: d,V0k_2E0: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2m_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1v_2E0),s(tyop_2Esptree_2Espt(A_27a),V2m_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0k_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V2m_2E0))))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V2m_2E0)))),mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V2m_2E0)))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))) ) ).

tff(thm_2Esptree_2Esubspt__domain,axiom,
    ! [V0t1_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1t2_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone(V0t1_2E0,V1t2_2E0) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(V0t1_2E0),mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(V1t2_2E0)) ) ).

tff(thm_2Esptree_2Esubspt__lookup,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0)))))
    <=> ! [V2x_2E0: mono_2Etyop_2Enum_2Enum,V3y_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3y_2E0))) )
         => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1t2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3y_2E0))) ) ) ) ).

tff(thm_2Esptree_2Esubspt__eq,axiom,
    ! [A_27a: d] :
      ( ! [V0t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V1x_2E0: u,V2t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1x_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) ) )
      & ! [V3t1_2E0: u,V4t2_2E0: u,V5t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V4t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5t_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),V5t_2E0)))))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V4t2_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),V5t_2E0))))))) ) )
      & ! [V6t1_2E0: u,V7x_2E0: u,V8t2_2E0: u,V9t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0),s(A_27a,V7x_2E0),s(tyop_2Esptree_2Espt(A_27a),V8t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V9t_2E0)))))
        <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E1(s(tyop_2Esptree_2Espt(A_27a),V9t_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E1(s(tyop_2Esptree_2Espt(A_27a),V9t_2E0)))))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V8t2_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E1(s(tyop_2Esptree_2Espt(A_27a),V9t_2E0))))))) ) ) ) ).

tff(thm_2Esptree_2Edatatype__spt,axiom,
    ! [A_27a: d,V0spt_2E0: u] : p(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool)))),V0spt_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2ELS_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2EBN_2E0))),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),c_2Esptree_2EBS_2E0)))))) ).

tff(thm_2Esptree_2Espt__11,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1a_27_2E0: u] :
          ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0a_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_27_2E0))) )
        <=> ( s(A_27a,V0a_2E0) = s(A_27a,V1a_27_2E0) ) )
      & ! [V2a0_2E0: u,V3a1_2E0: u,V4a0_27_2E0: u,V5a1_27_2E0: u] :
          ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V3a1_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4a0_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V5a1_27_2E0))) )
        <=> ( ( s(tyop_2Esptree_2Espt(A_27a),V2a0_2E0) = s(tyop_2Esptree_2Espt(A_27a),V4a0_27_2E0) )
            & ( s(tyop_2Esptree_2Espt(A_27a),V3a1_2E0) = s(tyop_2Esptree_2Espt(A_27a),V5a1_27_2E0) ) ) )
      & ! [V6a0_2E0: u,V7a1_2E0: u,V8a2_2E0: u,V9a0_27_2E0: u,V10a1_27_2E0: u,V11a2_27_2E0: u] :
          ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V6a0_2E0),s(A_27a,V7a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V8a2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V9a0_27_2E0),s(A_27a,V10a1_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V11a2_27_2E0))) )
        <=> ( ( s(tyop_2Esptree_2Espt(A_27a),V6a0_2E0) = s(tyop_2Esptree_2Espt(A_27a),V9a0_27_2E0) )
            & ( s(A_27a,V7a1_2E0) = s(A_27a,V10a1_27_2E0) )
            & ( s(tyop_2Esptree_2Espt(A_27a),V8a2_2E0) = s(tyop_2Esptree_2Espt(A_27a),V11a2_27_2E0) ) ) ) ) ).

tff(thm_2Esptree_2Espt__distinct,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0a_2E0))) )
      & ! [V1a1_2E0: u,V2a0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V1a1_2E0))) )
      & ! [V3a2_2E0: u,V4a1_2E0: u,V5a0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V5a0_2E0),s(A_27a,V4a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V3a2_2E0))) )
      & ! [V6a1_2E0: u,V7a0_2E0: u,V8a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V8a_2E0))) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V7a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V6a1_2E0))) )
      & ! [V9a2_2E0: u,V10a1_2E0: u,V11a0_2E0: u,V12a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V12a_2E0))) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V11a0_2E0),s(A_27a,V10a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9a2_2E0))) )
      & ! [V13a2_2E0: u,V14a1_27_2E0: u,V15a1_2E0: u,V16a0_27_2E0: u,V17a0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V17a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V15a1_2E0))) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V16a0_27_2E0),s(A_27a,V14a1_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V13a2_2E0))) ) ) ).

tff(thm_2Esptree_2Espt__nchotomy,axiom,
    ! [A_27a: d,V0ss_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),V0ss_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      | ? [V1a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),V0ss_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))) )
      | ? [V2s_2E0: u,V3s0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),V0ss_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2s_2E0),s(tyop_2Esptree_2Espt(A_27a),V3s0_2E0))) )
      | ? [V4s_2E0: u,V5a_2E0: u,V6s0_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),V0ss_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V4s_2E0),s(A_27a,V5a_2E0),s(tyop_2Esptree_2Espt(A_27a),V6s0_2E0))) ) ) ).

tff(thm_2Esptree_2Espt__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u,V3f3_2E0: u] :
    ? [V4fn_2E0: u] :
      ( ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(A_27b,V0f0_2E0) )
      & ! [V5a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f1_2E0),s(A_27a,V5a_2E0))) )
      & ! [V6a0_2E0: u,V7a1_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V6a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V7a1_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V2f2_2E0),s(tyop_2Esptree_2Espt(A_27a),V6a0_2E0))),s(tyop_2Esptree_2Espt(A_27a),V7a1_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),V6a0_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),V7a1_2E0))))) )
      & ! [V8a0_2E0: u,V9a1_2E0: u,V10a2_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V8a0_2E0),s(A_27a,V9a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10a2_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))))),V3f3_2E0),s(A_27a,V9a1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8a0_2E0))),s(tyop_2Esptree_2Espt(A_27a),V10a2_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),V8a0_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4fn_2E0),s(tyop_2Esptree_2Espt(A_27a),V10a2_2E0))))) ) ) ).

tff(thm_2Esptree_2Espt__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V1a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0)))))))
        & ! [V2s_2E0: u,V3s0_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V2s_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V3s0_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2s_2E0),s(tyop_2Esptree_2Espt(A_27a),V3s0_2E0))))))) )
        & ! [V4s_2E0: u,V5s0_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V4s_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V5s0_2E0))))) )
           => ! [V6a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V4s_2E0),s(A_27a,V6a_2E0),s(tyop_2Esptree_2Espt(A_27a),V5s0_2E0))))))) ) )
     => ! [V7s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V7s_2E0))))) ) ).

tff(thm_2Esptree_2Espt__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f2_27_2E0: u,V2f1_27_2E0: u,V3f_27_2E0: u,V4M_2E0: u,V5M_27_2E0: u,V6v_2E0: u,V7f_2E0: u,V8f1_2E0: u,V9f2_2E0: u] :
      ( ( ( s(tyop_2Esptree_2Espt(A_27a),V4M_2E0) = s(tyop_2Esptree_2Espt(A_27a),V5M_27_2E0) )
        & ( ( s(tyop_2Esptree_2Espt(A_27a),V5M_27_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
         => ( s(A_27b,V6v_2E0) = s(A_27b,V0v_27_2E0) ) )
        & ! [V10a_2E0: u] :
            ( ( s(tyop_2Esptree_2Espt(A_27a),V5M_27_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V10a_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7f_2E0),s(A_27a,V10a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(A_27a,V10a_2E0))) ) )
        & ! [V11a0_2E0: u,V12a1_2E0: u] :
            ( ( s(tyop_2Esptree_2Espt(A_27a),V5M_27_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V11a0_2E0),s(tyop_2Esptree_2Espt(A_27a),V12a1_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V8f1_2E0),s(tyop_2Esptree_2Espt(A_27a),V11a0_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12a1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V2f1_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V11a0_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12a1_2E0))) ) )
        & ! [V13a0_2E0: u,V14a1_2E0: u,V15a2_2E0: u] :
            ( ( s(tyop_2Esptree_2Espt(A_27a),V5M_27_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13a0_2E0),s(A_27a,V14a1_2E0),s(tyop_2Esptree_2Espt(A_27a),V15a2_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V9f2_2E0),s(tyop_2Esptree_2Espt(A_27a),V13a0_2E0))),s(A_27a,V14a1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V15a2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V1f2_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V13a0_2E0))),s(A_27a,V14a1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V15a2_2E0))) ) ) )
     => ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V4M_2E0),s(A_27b,V6v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V8f1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V9f2_2E0))) = s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V5M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V2f1_27_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V1f2_27_2E0))) ) ) ).

tff(thm_2Esptree_2Espt__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f2_2E0: u,V4f1_2E0: u,V5f_2E0: u] :
      ( ( s(A_27b,c_2Esptree_2Espt__CASE_2E5(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0),s(A_27b,V2v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V4f1_2E0),s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V3f2_2E0))) = s(A_27b,V1v_27_2E0) )
    <=> ( ( ( s(tyop_2Esptree_2Espt(A_27a),V0x_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
          & ( s(A_27b,V2v_2E0) = s(A_27b,V1v_27_2E0) ) )
        | ? [V6a_2E0: u] :
            ( ( s(tyop_2Esptree_2Espt(A_27a),V0x_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V6a_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(A_27a,V6a_2E0))) = s(A_27b,V1v_27_2E0) ) )
        | ? [V7s_2E0: u,V8s0_2E0: u] :
            ( ( s(tyop_2Esptree_2Espt(A_27a),V0x_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V7s_2E0),s(tyop_2Esptree_2Espt(A_27a),V8s0_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V4f1_2E0),s(tyop_2Esptree_2Espt(A_27a),V7s_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8s0_2E0))) = s(A_27b,V1v_27_2E0) ) )
        | ? [V9s_2E0: u,V10a_2E0: u,V11s0_2E0: u] :
            ( ( s(tyop_2Esptree_2Espt(A_27a),V0x_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V9s_2E0),s(A_27a,V10a_2E0),s(tyop_2Esptree_2Espt(A_27a),V11s0_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V3f2_2E0),s(tyop_2Esptree_2Espt(A_27a),V9s_2E0))),s(A_27a,V10a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V11s0_2E0))) = s(A_27b,V1v_27_2E0) ) ) ) ) ).

tff(thm_2Esptree_2Elookup__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1k_2E0: mono_2Etyop_2Enum_2Enum] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V2k_2E0: mono_2Etyop_2Enum_2Enum,V3a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V3a_2E0)))))))
        & ! [V4k_2E0: mono_2Etyop_2Enum_2Enum,V5t1_2E0: u,V6t2_2E0: u] :
            ( ( ( V4k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V4k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V4k_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V6t2_2E0))))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V5t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V6t2_2E0))))))) )
        & ! [V7k_2E0: mono_2Etyop_2Enum_2Enum,V8t1_2E0: u,V9a_2E0: u,V10t2_2E0: u] :
            ( ( ( V7k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V7k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V7k_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V8t1_2E0),s(A_27a,V9a_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t2_2E0))))))) ) )
     => ! [V11v_2E0: mono_2Etyop_2Enum_2Enum,V12v1_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V11v_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V12v1_2E0))))) ) ).

tff(thm_2Esptree_2Elookup__def,axiom,
    ! [A_27a: d,F2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V8k_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V8k_2E0))
        <=> ( V8k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V5k_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V5k_2E0))
          <=> ( V5k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ! [V1k_2E0: mono_2Etyop_2Enum_2Enum] :
              ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1k_2E0))
            <=> ( V1k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
         => ( ! [V0k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
            & ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1k_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2a_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) )
            & ! [V3t2_2E0: u,V4t1_2E0: u,V5k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V5k_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V5k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V5k_2E0))),s(tyop_2Esptree_2Espt(A_27a),V4t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))))) )
            & ! [V6t2_2E0: u,V7t1_2E0: u,V8k_2E0: mono_2Etyop_2Enum_2Enum,V9a_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0),s(A_27a,V9a_2E0),s(tyop_2Esptree_2Espt(A_27a),V6t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V8k_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V9a_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V8k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V8k_2E0))),s(tyop_2Esptree_2Espt(A_27a),V7t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V6t2_2E0))))))) ) ) ) ) ) ).

tff(thm_2Esptree_2Einsert__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1k_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
            ( ( ( ( ( V1k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V1k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V1k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V2a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) )
              & ( ( ( V1k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V1k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V1k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V2a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) ) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)))),s(A_27a,V2a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) )
        & ! [V3k_2E0: mono_2Etyop_2Enum_2Enum,V4a_2E0: u,V5a_27_2E0: u] :
            ( ( ( ( ( V3k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V3k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V3k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V4a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) )
              & ( ( ( V3k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V3k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V3k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V4a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))) ) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k_2E0)))),s(A_27a,V4a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5a_27_2E0))))))) )
        & ! [V6k_2E0: mono_2Etyop_2Enum_2Enum,V7a_2E0: u,V8t1_2E0: u,V9t2_2E0: u] :
            ( ( ( ( ( V6k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V6k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V6k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V7a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V8t1_2E0))))) )
              & ( ( ( V6k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V6k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V6k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V7a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))) ) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6k_2E0)))),s(A_27a,V7a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V8t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))))) )
        & ! [V10k_2E0: mono_2Etyop_2Enum_2Enum,V11a_2E0: u,V12t1_2E0: u,V13a_27_2E0: u,V14t2_2E0: u] :
            ( ( ( ( ( V10k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V10k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V10k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V11a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t1_2E0))))) )
              & ( ( ( V10k_2E0 != mono_2Ec_2Enum_2E0_2E0 )
                  & ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(V10k_2E0)) )
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V10k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(A_27a,V11a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V14t2_2E0))))) ) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V10k_2E0)))),s(A_27a,V11a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V12t1_2E0),s(A_27a,V13a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V14t2_2E0))))))) ) )
     => ! [V15v_2E0: mono_2Etyop_2Enum_2Enum,V16v1_2E0: u,V17v2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V15v_2E0)))),s(A_27a,V16v1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V17v2_2E0))))) ) ).

tff(thm_2Esptree_2Einsert__def,axiom,
    ! [A_27a: d,F3_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V11k_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F3_2E0,V11k_2E0))
        <=> ( V11k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V7k_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V7k_2E0))
          <=> ( V7k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ! [V2k_2E0: mono_2Etyop_2Enum_2Enum] :
              ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V2k_2E0))
            <=> ( V2k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
         => ( ! [V0k_2E0: mono_2Etyop_2Enum_2Enum] :
                ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0k_2E0))
              <=> ( V0k_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
           => ( ! [V0k_2E0: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V0k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))))))) )
              & ! [V2k_2E0: mono_2Etyop_2Enum_2Enum,V3a_27_2E0: u,V4a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V3a_27_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V2k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V4a_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V2k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V2k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(A_27a,V3a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(A_27a,V3a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V2k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V4a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))))))))) )
              & ! [V5t2_2E0: u,V6t1_2E0: u,V7k_2E0: mono_2Etyop_2Enum_2Enum,V8a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7k_2E0)),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V7k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V7k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V7k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V6t1_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V7k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V8a_2E0),s(tyop_2Esptree_2Espt(A_27a),V5t2_2E0))))))))) )
              & ! [V9t2_2E0: u,V10t1_2E0: u,V11k_2E0: mono_2Etyop_2Enum_2Enum,V12a_27_2E0: u,V13a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V11k_2E0)),s(A_27a,V13a_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V10t1_2E0),s(A_27a,V12a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F3_2E0,V11k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V10t1_2E0),s(A_27a,V13a_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V11k_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V11k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V13a_2E0),s(tyop_2Esptree_2Espt(A_27a),V10t1_2E0))),s(A_27a,V12a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V10t1_2E0),s(A_27a,V12a_27_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V11k_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,V13a_2E0),s(tyop_2Esptree_2Espt(A_27a),V9t2_2E0))))))))) ) ) ) ) ) ) ).

tff(thm_2Esptree_2Emk__BN__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V1v14_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1v14_2E0)))))))
        & ! [V2v15_2E0: u,V3v16_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2v15_2E0),s(tyop_2Esptree_2Espt(A_27a),V3v16_2E0)))))))
        & ! [V4v17_2E0: u,V5v18_2E0: u,V6v19_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V4v17_2E0),s(A_27a,V5v18_2E0),s(tyop_2Esptree_2Espt(A_27a),V6v19_2E0)))))))
        & ! [V7v2_2E0: u,V8t2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V7v2_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V8t2_2E0)))))
        & ! [V9v3_2E0: u,V10v4_2E0: u,V11t2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V9v3_2E0),s(tyop_2Esptree_2Espt(A_27a),V10v4_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V11t2_2E0)))))
        & ! [V12v5_2E0: u,V13v6_2E0: u,V14v7_2E0: u,V15t2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V12v5_2E0),s(A_27a,V13v6_2E0),s(tyop_2Esptree_2Espt(A_27a),V14v7_2E0))))),s(tyop_2Esptree_2Espt(A_27a),V15t2_2E0))))) )
     => ! [V16v_2E0: u,V17v1_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V16v_2E0))),s(tyop_2Esptree_2Espt(A_27a),V17v1_2E0))))) ) ).

tff(thm_2Esptree_2Emk__BN__def,axiom,
    ! [A_27a: d,V0v7_2E0: u,V1v6_2E0: u,V2v5_2E0: u,V3v4_2E0: u,V4v3_2E0: u,V5v2_2E0: u,V6v19_2E0: u,V7v18_2E0: u,V8v17_2E0: u,V9v16_2E0: u,V10v15_2E0: u,V11v14_2E0: u,V12t2_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V11v14_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V11v14_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V10v15_2E0),s(tyop_2Esptree_2Espt(A_27a),V9v16_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V10v15_2E0),s(tyop_2Esptree_2Espt(A_27a),V9v16_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V8v17_2E0),s(A_27a,V7v18_2E0),s(tyop_2Esptree_2Espt(A_27a),V6v19_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V8v17_2E0),s(A_27a,V7v18_2E0),s(tyop_2Esptree_2Espt(A_27a),V6v19_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5v2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V5v2_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4v3_2E0),s(tyop_2Esptree_2Espt(A_27a),V3v4_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4v3_2E0),s(tyop_2Esptree_2Espt(A_27a),V3v4_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t2_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V2v5_2E0),s(A_27a,V1v6_2E0),s(tyop_2Esptree_2Espt(A_27a),V0v7_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V2v5_2E0),s(A_27a,V1v6_2E0),s(tyop_2Esptree_2Espt(A_27a),V0v7_2E0))),s(tyop_2Esptree_2Espt(A_27a),V12t2_2E0))) ) ) ).

tff(thm_2Esptree_2Emk__BS__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))),s(A_27a,V1x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V2v16_2E0: u,V3x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V2v16_2E0))))),s(A_27a,V3x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V4v17_2E0: u,V5v18_2E0: u,V6x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V4v17_2E0),s(tyop_2Esptree_2Espt(A_27a),V5v18_2E0))))),s(A_27a,V6x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V7v19_2E0: u,V8v20_2E0: u,V9v21_2E0: u,V10x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V7v19_2E0),s(A_27a,V8v20_2E0),s(tyop_2Esptree_2Espt(A_27a),V9v21_2E0))))),s(A_27a,V10x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0)))))
        & ! [V11t1_2E0: u,V12x_2E0: u,V13v4_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V11t1_2E0))),s(A_27a,V12x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V13v4_2E0)))))))
        & ! [V14t1_2E0: u,V15x_2E0: u,V16v5_2E0: u,V17v6_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V14t1_2E0))),s(A_27a,V15x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V16v5_2E0),s(tyop_2Esptree_2Espt(A_27a),V17v6_2E0)))))))
        & ! [V18t1_2E0: u,V19x_2E0: u,V20v7_2E0: u,V21v8_2E0: u,V22v9_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V18t1_2E0))),s(A_27a,V19x_2E0))),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V20v7_2E0),s(A_27a,V21v8_2E0),s(tyop_2Esptree_2Espt(A_27a),V22v9_2E0))))))) )
     => ! [V23v_2E0: u,V24v1_2E0: u,V25v2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Esptree_2Espt(A_27a),V23v_2E0))),s(A_27a,V24v1_2E0))),s(tyop_2Esptree_2Espt(A_27a),V25v2_2E0))))) ) ).

tff(thm_2Esptree_2Emk__BS__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1v9_2E0: u,V2v8_2E0: u,V3v7_2E0: u,V4v6_2E0: u,V5v5_2E0: u,V6v4_2E0: u,V7v21_2E0: u,V8v20_2E0: u,V9v19_2E0: u,V10v18_2E0: u,V11v17_2E0: u,V12v16_2E0: u,V13t1_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V0x_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V12v16_2E0))),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V12v16_2E0))),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V11v17_2E0),s(tyop_2Esptree_2Espt(A_27a),V10v18_2E0))),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V11v17_2E0),s(tyop_2Esptree_2Espt(A_27a),V10v18_2E0))),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V9v19_2E0),s(A_27a,V8v20_2E0),s(tyop_2Esptree_2Espt(A_27a),V7v21_2E0))),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V9v19_2E0),s(A_27a,V8v20_2E0),s(tyop_2Esptree_2Espt(A_27a),V7v21_2E0))),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V6v4_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V6v4_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V5v5_2E0),s(tyop_2Esptree_2Espt(A_27a),V4v6_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V5v5_2E0),s(tyop_2Esptree_2Espt(A_27a),V4v6_2E0))))) )
      & ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__BS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3v7_2E0),s(A_27a,V2v8_2E0),s(tyop_2Esptree_2Espt(A_27a),V1v9_2E0))))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V13t1_2E0),s(A_27a,V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V3v7_2E0),s(A_27a,V2v8_2E0),s(tyop_2Esptree_2Espt(A_27a),V1v9_2E0))))) ) ) ).

tff(thm_2Esptree_2Einsert__notEmpty,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(A_27a,V2a_2E0),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))) != s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) ) ).

tff(thm_2Esptree_2Ewf__insert,axiom,
    ! [A_27a: d,V0k_2E0: mono_2Etyop_2Enum_2Enum,V1a_2E0: u,V2t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))))) ) ).

tff(thm_2Esptree_2Ewf__delete,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0t_2E0))))))) ) ).

tff(thm_2Esptree_2Elookup__insert1,axiom,
    ! [A_27a: d,V0k_2E0: mono_2Etyop_2Enum_2Enum,V1a_2E0: u,V2t_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k_2E0)),s(A_27a,V1a_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1a_2E0))) ) ).

tff(thm_2Esptree_2Elookup__insert,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ! [V3k1_2E0: mono_2Etyop_2Enum_2Enum,V0k2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V3k1_2E0),V0k2_2E0))
        <=> ( V3k1_2E0 = V0k2_2E0 ) )
     => ! [V0k2_2E0: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2t_2E0: u,V3k1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k1_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k2_2E0)),s(A_27a,V1v_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V3k1_2E0),V0k2_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3k1_2E0)),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) ) ) ).

tff(thm_2Esptree_2EisEmpty__union,axiom,
    ! [A_27a: d,V0m2_2E0: u,V1m1_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V1m1_2E0),s(tyop_2Esptree_2Espt(A_27a),V0m2_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
    <=> ( ( s(tyop_2Esptree_2Espt(A_27a),V1m1_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
        & ( s(tyop_2Esptree_2Espt(A_27a),V0m2_2E0) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) ) ) ) ).

tff(thm_2Esptree_2Ewf__union,axiom,
    ! [A_27a: d,V0m1_2E0: u,V1m2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))))))) ) ).

tff(thm_2Esptree_2Elookup__union,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V3v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F0_2E0),s(A_27a,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3v_2E0))) )
     => ! [V0m1_2E0: u,V1m2_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Eunion_2E2(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F0_2E0))) ) ) ).

tff(thm_2Esptree_2Ewf__inter,axiom,
    ! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0))))))) ).

tff(thm_2Esptree_2Elookup__inter,axiom,
    ! [A_27a: d,A_27b: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V5v_2E0: u,V6w_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),F2_2E0),s(A_27a,V5v_2E0))),s(A_27b,V6w_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5v_2E0))) )
     => ( ! [V4v4_2E0: u,V5v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V4v4_2E0))),s(A_27a,V5v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27b),V4v4_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),F2_2E0),s(A_27a,V5v_2E0))))) )
       => ( ! [V3v3_2E0: u,V4v4_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),F0_2E0),s(tyop_2Eoption_2Eoption(A_27a),V3v3_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V4v4_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V3v3_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V4v4_2E0))))) )
         => ! [V0m1_2E0: u,V1m2_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0))))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),F0_2E0))) ) ) ) ) ).

tff(thm_2Esptree_2Elookup__inter__eq,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V2k_2E0: mono_2Etyop_2Enum_2Enum,V1m2_2E0: u,V3v_2E0: u] :
          ( p(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_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))),s(A_27a,V3v_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3v_2E0))) ) )
     => ( ! [V2k_2E0: mono_2Etyop_2Enum_2Enum,V1m2_2E0: u,V3v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))),s(A_27a,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))),s(A_27a,V3v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) )
       => ! [V0m1_2E0: u,V1m2_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter__eq_2E2(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27a),V1m2_2E0))))) ) ) ) ).

tff(thm_2Esptree_2Elookup__inter__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: mono_2Etyop_2Enum_2Enum,V2t2_2E0: u,V3t1_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V2t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) )
      <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) )
          & ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27b),V2t2_2E0))) != s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V2t2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
          | ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(tyop_2Esptree_2Espt(A_27b),V2t2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) ) ) ).

tff(thm_2Esptree_2Elookup__inter__assoc,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1t3_2E0: u,V2t2_2E0: u,V3t1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27b),V2t2_2E0),s(tyop_2Esptree_2Espt(A_27c),V1t3_2E0))))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V3t1_2E0),s(tyop_2Esptree_2Espt(A_27b),V2t2_2E0))),s(tyop_2Esptree_2Espt(A_27c),V1t3_2E0))))) ) ).

tff(thm_2Esptree_2Elookup__difference,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2k_2E0: mono_2Etyop_2Enum_2Enum,V1m2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) )
     => ! [V0m1_2E0: u,V1m2_2E0: u,V2k_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)))),s(tyop_2Esptree_2Espt(A_27b),V1m2_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2k_2E0)),s(tyop_2Esptree_2Espt(A_27a),V0m1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ) ).

tff(thm_2Esptree_2Elrnext__ind,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( ( V1n_2E0 != mono_2Ec_2Enum_2E0_2E0 )
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0P_2E0,mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V1n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))) )
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0P_2E0,V1n_2E0)) )
     => ! [V2v_2E0: mono_2Etyop_2Enum_2Enum] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0P_2E0,V2v_2E0)) ) ).

tff(thm_2Esptree_2Elrnext__def,axiom,
    ! [F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0n_2E0))
        <=> ( V0n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Elrnext_2E1(V0n_2E0) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0n_2E0),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))))) ) ) ).

tff(thm_2Esptree_2Elrnext__thm,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u] : ( mono_2Ec_2Esptree_2Elrnext_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] : ( mono_2Ec_2Esptree_2Elrnext_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(V1n_2E0)) = mono_2Ec_2Esptree_2Elrnext_2E1(V1n_2E0) )
      & ( mono_2Ec_2Esptree_2Elrnext_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
      & ! [V3n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Elrnext_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V3n_2E0)) = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V3n_2E0)) )
      & ! [V4n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Esptree_2Elrnext_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V4n_2E0)) = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),mono_2Ec_2Esptree_2Elrnext_2E1(V4n_2E0)) ) ) ).

tff(thm_2Esptree_2EFINITE__domain,axiom,
    ! [A_27a: d,V0t_2E0: u] : p(mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0t_2E0)))))) ).

tff(thm_2Esptree_2EIN__domain,axiom,
    ! [A_27a: d,A_27b: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1x_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
      ( ( mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0n_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELN_2E0))))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0n_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E1(s(A_27a,V1x_2E0))))))))
      <=> ( V0n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
      & ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0n_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBN_2E2(s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0),s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))))))
      <=> ( ( V0n_2E0 != mono_2Ec_2Enum_2E0_2E0 )
          & p(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V0n_2E0),mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0))))),mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))))) ) )
      & ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0n_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EBS_2E3(s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0),s(A_27a,V1x_2E0),s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))))))
      <=> ( ( V0n_2E0 = mono_2Ec_2Enum_2E0_2E0 )
          | p(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2EEVEN_2E1(V0n_2E0),mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V2t1_2E0))))),mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V3t2_2E0))))))) ) ) ) ).

tff(thm_2Esptree_2Emap__map__K,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1a_2E0: u,V2t_2E0: u] : ( s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2EK_2E1(s(A_27b,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27c),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))))) = s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EK_2E1(s(A_27b,V1a_2E0))),s(tyop_2Esptree_2Espt(A_27a),V2t_2E0))) ) ).

tff(thm_2Esptree_2Elookup__map__K,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1t_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EK_2E1(s(A_27b,V0x_2E0))),s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V2n_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1t_2E0))))))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Esptree_2EIMP__size__LESS__size,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Esptree_2Esubspt_2E2(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0),s(tyop_2Esptree_2Espt(A_27a),V1y_2E0)))))
        & ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0)))) != j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1y_2E0)))) ) )
     => p(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),V1y_2E0)))))) ) ).

tff(thm_2Esptree_2Esize__diff__less,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1y_2E0: u,V2z_2E0: u,V3t_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27c),V2z_2E0)))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V1y_2E0))))))
        & p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V3t_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V1y_2E0))))))
        & ~ p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V3t_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27c),V2z_2E0))))))
        & p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V3t_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0)))))) )
     => p(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0),s(tyop_2Esptree_2Espt(A_27b),V1y_2E0)))))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Esptree_2Esize_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edifference_2E2(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0),s(tyop_2Esptree_2Espt(A_27c),V2z_2E0)))))))) ) ).

tff(thm_2Esptree_2Einter__eq__LN,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einter_2E2(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0),s(tyop_2Esptree_2Espt(A_27b),V1y_2E0))) = s(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0) )
    <=> p(mono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V0x_2E0)))),j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27b),V1y_2E0)))))) ) ).

tff(thm_2Esptree_2Edomain__list__to__num__set,axiom,
    ! [V0x_2E0: mono_2Etyop_2Enum_2Enum,V1xs_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Esptree_2Elist__to__num__set_2E1(V1xs_2E0))) = mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V1xs_2E0)) ) ).

tff(thm_2Esptree_2Edomain__list__insert,axiom,
    ! [V0xs_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1x_2E0: mono_2Etyop_2Enum_2Enum,V2t_2E0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V1x_2E0,mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Esptree_2Elist__insert_2E2(V0xs_2E0,V2t_2E0))))
    <=> ( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V1x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V0xs_2E0)))
        | p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V1x_2E0,mono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone(V2t_2E0))) ) ) ).

tff(thm_2Esptree_2Edomain__FOLDR__delete,axiom,
    ! [A_27a: d,V0ls_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1live_2E0: u] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Edelete_2E0),s(tyop_2Esptree_2Espt(A_27a),V1live_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29(V0ls_2E0))))))) = mono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E1(s(tyop_2Esptree_2Espt(A_27a),V1live_2E0)))),mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V0ls_2E0)) ) ).

tff(thm_2Esptree_2Elookup__list__to__num__set,axiom,
    ! [V0x_2E0: mono_2Etyop_2Enum_2Enum,V1xs_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone(V0x_2E0,mono_2Ec_2Esptree_2Elist__to__num__set_2E1(V1xs_2E0)) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum(V0x_2E0,mono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum(V1xs_2E0)),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Eone_2Eone_2E0),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone) ) ).

tff(thm_2Esptree_2Elist__to__num__set__append,axiom,
    ! [V0l1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1l2_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Esptree_2Elist__to__num__set_2E1(mono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum(V0l1_2E0,V1l2_2E0)) = mono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Esptree_2Elist__to__num__set_2E1(V0l1_2E0),mono_2Ec_2Esptree_2Elist__to__num__set_2E1(V1l2_2E0)) ) ).

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