ITP001 Axioms: ITP102_5.ax
%------------------------------------------------------------------------------
% File : ITP102_5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : sptree_2.ax [Gau20]
% : HL4102_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 475 ( 81 unt; 153 typ; 0 def)
% Number of atoms : 7239 ( 456 equ)
% Maximal formula atoms : 42 ( 15 avg)
% Number of connectives : 1161 ( 30 ~; 9 |; 246 &)
% ( 41 <=>; 835 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5786 (5786 fml; 0 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 374 ( 142 >; 232 *; 0 +; 0 <<)
% Number of predicates : 93 ( 90 usr; 27 prp; 0-3 aty)
% Number of functors : 152 ( 152 usr; 10 con; 0-8 aty)
% Number of variables : 1438 (1422 !; 16 ?;1438 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_ty_2Esptree_2Espt,type,
ty_2Esptree_2Espt: del > del ).
tff(tp_c_2Esptree_2EBN,type,
c_2Esptree_2EBN: del > $i ).
tff(mem_c_2Esptree_2EBN,axiom,
! [A_27a: del] : mem(c_2Esptree_2EBN(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2EBS,type,
c_2Esptree_2EBS: del > $i ).
tff(mem_c_2Esptree_2EBS,axiom,
! [A_27a: del] : mem(c_2Esptree_2EBS(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))))) ).
tff(tp_c_2Esptree_2ELN,type,
c_2Esptree_2ELN: del > $i ).
tff(mem_c_2Esptree_2ELN,axiom,
! [A_27a: del] : mem(c_2Esptree_2ELN(A_27a),ty_2Esptree_2Espt(A_27a)) ).
tff(tp_c_2Esptree_2ELS,type,
c_2Esptree_2ELS: del > $i ).
tff(mem_c_2Esptree_2ELS,axiom,
! [A_27a: del] : mem(c_2Esptree_2ELS(A_27a),arr(A_27a,ty_2Esptree_2Espt(A_27a))) ).
tff(tp_c_2Esptree_2Edelete,type,
c_2Esptree_2Edelete: del > $i ).
tff(mem_c_2Esptree_2Edelete,axiom,
! [A_27a: del] : mem(c_2Esptree_2Edelete(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Edifference,type,
c_2Esptree_2Edifference: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Edifference,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Edifference(A_27a,A_27b),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27b),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Edomain,type,
c_2Esptree_2Edomain: del > $i ).
tff(mem_c_2Esptree_2Edomain,axiom,
! [A_27a: del] : mem(c_2Esptree_2Edomain(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Enum_2Enum,bool))) ).
tff(tp_c_2Esptree_2Efilter__v,type,
c_2Esptree_2Efilter__v: del > $i ).
tff(mem_c_2Esptree_2Efilter__v,axiom,
! [A_27a: del] : mem(c_2Esptree_2Efilter__v(A_27a),arr(arr(A_27a,bool),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Efoldi,type,
c_2Esptree_2Efoldi: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Efoldi,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Efoldi(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))),arr(ty_2Enum_2Enum,arr(A_27a,arr(ty_2Esptree_2Espt(A_27b),A_27a))))) ).
tff(tp_c_2Esptree_2EfromAList,type,
c_2Esptree_2EfromAList: del > $i ).
tff(mem_c_2Esptree_2EfromAList,axiom,
! [A_27a: del] : mem(c_2Esptree_2EfromAList(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a))) ).
tff(tp_c_2Esptree_2EfromList,type,
c_2Esptree_2EfromList: del > $i ).
tff(mem_c_2Esptree_2EfromList,axiom,
! [A_27a: del] : mem(c_2Esptree_2EfromList(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Esptree_2Espt(A_27a))) ).
tff(tp_c_2Esptree_2Einsert,type,
c_2Esptree_2Einsert: del > $i ).
tff(mem_c_2Esptree_2Einsert,axiom,
! [A_27a: del] : mem(c_2Esptree_2Einsert(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))))) ).
tff(tp_c_2Esptree_2Einter,type,
c_2Esptree_2Einter: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Einter,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Einter(A_27a,A_27b),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27b),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Einter__eq,type,
c_2Esptree_2Einter__eq: del > $i ).
tff(mem_c_2Esptree_2Einter__eq,axiom,
! [A_27a: del] : mem(c_2Esptree_2Einter__eq(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))) ).
tff(stp_c_ty_2Esptree_2Espt_ty_2Eone_2Eone,type,
tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone: $tType ).
tff(stp_inj_c_ty_2Esptree_2Espt_ty_2Eone_2Eone,type,
inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone > $i ).
tff(stp_surj_c_ty_2Esptree_2Espt_ty_2Eone_2Eone,type,
surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone: $i > tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone ).
tff(stp_inj_surj_c_ty_2Esptree_2Espt_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] : ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Esptree_2Espt_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] : mem(inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(X),ty_2Esptree_2Espt(ty_2Eone_2Eone)) ).
tff(stp_iso_mem_c_ty_2Esptree_2Espt_ty_2Eone_2Eone,axiom,
! [X: $i] :
( mem(X,ty_2Esptree_2Espt(ty_2Eone_2Eone))
=> ( X = inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(X)) ) ) ).
tff(tp_c_2Esptree_2Elist__insert,type,
c_2Esptree_2Elist__insert: $i ).
tff(mem_c_2Esptree_2Elist__insert,axiom,
mem(c_2Esptree_2Elist__insert,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),arr(ty_2Esptree_2Espt(ty_2Eone_2Eone),ty_2Esptree_2Espt(ty_2Eone_2Eone)))) ).
tff(tp_c_2Esptree_2Elist__to__num__set,type,
c_2Esptree_2Elist__to__num__set: $i ).
tff(mem_c_2Esptree_2Elist__to__num__set,axiom,
mem(c_2Esptree_2Elist__to__num__set,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Esptree_2Espt(ty_2Eone_2Eone))) ).
tff(tp_c_2Esptree_2Elookup,type,
c_2Esptree_2Elookup: del > $i ).
tff(mem_c_2Esptree_2Elookup,axiom,
! [A_27a: del] : mem(c_2Esptree_2Elookup(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Esptree_2Espt(A_27a),ty_2Eoption_2Eoption(A_27a)))) ).
tff(tp_c_2Esptree_2Elrnext,type,
c_2Esptree_2Elrnext: $i ).
tff(mem_c_2Esptree_2Elrnext,axiom,
mem(c_2Esptree_2Elrnext,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Esptree_2Elrnext,type,
fo__c_2Esptree_2Elrnext: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Esptree_2Elrnext,axiom,
! [X0: tp__ty_2Enum_2Enum] : ( inj__ty_2Enum_2Enum(fo__c_2Esptree_2Elrnext(X0)) = ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(X0)) ) ).
tff(tp_c_2Esptree_2Emap,type,
c_2Esptree_2Emap: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Emap,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Emap(A_27a,A_27b),arr(arr(A_27b,A_27a),arr(ty_2Esptree_2Espt(A_27b),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Emapi,type,
c_2Esptree_2Emapi: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Emapi,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Emapi(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,arr(A_27b,A_27a)),arr(ty_2Esptree_2Espt(A_27b),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Emapi0,type,
c_2Esptree_2Emapi0: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Emapi0,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Emapi0(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,arr(A_27b,A_27a)),arr(ty_2Enum_2Enum,arr(ty_2Esptree_2Espt(A_27b),ty_2Esptree_2Espt(A_27a))))) ).
tff(tp_c_2Esptree_2Emk__BN,type,
c_2Esptree_2Emk__BN: del > $i ).
tff(mem_c_2Esptree_2Emk__BN,axiom,
! [A_27a: del] : mem(c_2Esptree_2Emk__BN(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Emk__BS,type,
c_2Esptree_2Emk__BS: del > $i ).
tff(mem_c_2Esptree_2Emk__BS,axiom,
! [A_27a: del] : mem(c_2Esptree_2Emk__BS(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))))) ).
tff(tp_c_2Esptree_2Emk__wf,type,
c_2Esptree_2Emk__wf: del > $i ).
tff(mem_c_2Esptree_2Emk__wf,axiom,
! [A_27a: del] : mem(c_2Esptree_2Emk__wf(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))) ).
tff(tp_c_2Esptree_2Esize,type,
c_2Esptree_2Esize: del > $i ).
tff(mem_c_2Esptree_2Esize,axiom,
! [A_27a: del] : mem(c_2Esptree_2Esize(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Enum_2Enum)) ).
tff(tp_c_2Esptree_2Espt__CASE,type,
c_2Esptree_2Espt__CASE: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Espt__CASE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Espt__CASE(A_27a,A_27b),arr(ty_2Esptree_2Espt(A_27a),arr(A_27b,arr(arr(A_27a,A_27b),arr(arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)),arr(arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))),A_27b)))))) ).
tff(tp_c_2Esptree_2Espt__acc,type,
c_2Esptree_2Espt__acc: $i ).
tff(mem_c_2Esptree_2Espt__acc,axiom,
mem(c_2Esptree_2Espt__acc,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
tff(stp_fo_c_2Esptree_2Espt__acc,type,
fo__c_2Esptree_2Espt__acc: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Esptree_2Espt__acc,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : ( inj__ty_2Enum_2Enum(fo__c_2Esptree_2Espt__acc(X0,X1)) = ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ) ).
tff(tp_c_2Esptree_2Espt__center,type,
c_2Esptree_2Espt__center: del > $i ).
tff(mem_c_2Esptree_2Espt__center,axiom,
! [A_27a: del] : mem(c_2Esptree_2Espt__center(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Eoption_2Eoption(A_27a))) ).
tff(tp_c_2Esptree_2Espt__fold,type,
c_2Esptree_2Espt__fold: ( del * del ) > $i ).
tff(mem_c_2Esptree_2Espt__fold,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Esptree_2Espt__fold(A_27a,A_27b),arr(arr(A_27b,arr(A_27a,A_27a)),arr(A_27a,arr(ty_2Esptree_2Espt(A_27b),A_27a)))) ).
tff(tp_c_2Esptree_2Espt__left,type,
c_2Esptree_2Espt__left: del > $i ).
tff(mem_c_2Esptree_2Espt__left,axiom,
! [A_27a: del] : mem(c_2Esptree_2Espt__left(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))) ).
tff(tp_c_2Esptree_2Espt__right,type,
c_2Esptree_2Espt__right: del > $i ).
tff(mem_c_2Esptree_2Espt__right,axiom,
! [A_27a: del] : mem(c_2Esptree_2Espt__right(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))) ).
tff(tp_c_2Esptree_2Espt__size,type,
c_2Esptree_2Espt__size: del > $i ).
tff(mem_c_2Esptree_2Espt__size,axiom,
! [A_27a: del] : mem(c_2Esptree_2Espt__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Esptree_2Espt(A_27a),ty_2Enum_2Enum))) ).
tff(tp_c_2Esptree_2Esubspt,type,
c_2Esptree_2Esubspt: del > $i ).
tff(mem_c_2Esptree_2Esubspt,axiom,
! [A_27a: del] : mem(c_2Esptree_2Esubspt(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),bool))) ).
tff(tp_c_2Esptree_2EtoAList,type,
c_2Esptree_2EtoAList: del > $i ).
tff(mem_c_2Esptree_2EtoAList,axiom,
! [A_27a: del] : mem(c_2Esptree_2EtoAList(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))) ).
tff(tp_c_2Esptree_2EtoList,type,
c_2Esptree_2EtoList: del > $i ).
tff(mem_c_2Esptree_2EtoList,axiom,
! [A_27a: del] : mem(c_2Esptree_2EtoList(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Elist_2Elist(A_27a))) ).
tff(tp_c_2Esptree_2EtoListA,type,
c_2Esptree_2EtoListA: del > $i ).
tff(mem_c_2Esptree_2EtoListA,axiom,
! [A_27a: del] : mem(c_2Esptree_2EtoListA(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Elist_2Elist(A_27a)))) ).
tff(tp_c_2Esptree_2Eunion,type,
c_2Esptree_2Eunion: del > $i ).
tff(mem_c_2Esptree_2Eunion,axiom,
! [A_27a: del] : mem(c_2Esptree_2Eunion(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))) ).
tff(tp_c_2Esptree_2Ewf,type,
c_2Esptree_2Ewf: del > $i ).
tff(mem_c_2Esptree_2Ewf,axiom,
! [A_27a: del] : mem(c_2Esptree_2Ewf(A_27a),arr(ty_2Esptree_2Espt(A_27a),bool)) ).
tff(lamtp_f2331,type,
f2331: del > $i ).
tff(lameq_f2331,axiom,
! [A_27a: del,V6a: $i] : ( ap(f2331(A_27a),V6a) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),V6a),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))) ) ).
tff(lamtp_f2332,type,
f2332: ( del * $i ) > $i ).
tff(lameq_f2332,axiom,
! [A_27a: del,V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V5a: $i] : ( ap(f2332(A_27a,V3a0_27),V5a) = ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(f2331(A_27a),V5a)) ) ) ).
tff(lamtp_f2333,type,
f2333: ( del * $i ) > $i ).
tff(lameq_f2333,axiom,
! [A_27a: del,V10a0: $i] :
( mem(V10a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V11a1: $i] : ( ap(f2333(A_27a,V10a0),V11a1) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),c_2Ebool_2EARB(A_27a)),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V10a0),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V11a1),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))) ) ) ).
tff(lamtp_f2334,type,
f2334: del > $i ).
tff(lameq_f2334,axiom,
! [A_27a: del,V10a0: $i] : ( ap(f2334(A_27a),V10a0) = f2333(A_27a,V10a0) ) ).
tff(lamtp_f2335,type,
f2335: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2335,axiom,
! [A_27a: del,V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V8a0: $i] :
( mem(V8a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27spt_27: $i] :
( mem(V2_27spt_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V9a1: $i] : ( ap(f2335(A_27a,V3a0_27,V8a0,V2_27spt_27),V9a1) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(f2334(A_27a),V8a0),V9a1))),ap(ap(c_2Ebool_2E_2F_5C,ap(V2_27spt_27,V8a0)),ap(V2_27spt_27,V9a1))) ) ) ) ) ).
tff(lamtp_f2336,type,
f2336: ( del * $i * $i ) > $i ).
tff(lameq_f2336,axiom,
! [A_27a: del,V2_27spt_27: $i] :
( mem(V2_27spt_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V8a0: $i] : ( ap(f2336(A_27a,V2_27spt_27,V3a0_27),V8a0) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2335(A_27a,V3a0_27,V8a0,V2_27spt_27)) ) ) ) ).
tff(lamtp_f2337,type,
f2337: ( del * $i * $i ) > $i ).
tff(lameq_f2337,axiom,
! [A_27a: del,V16a0: $i] :
( mem(V16a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V17a1: $i] :
( mem(V17a1,A_27a)
=> ! [V18a2: $i] : ( ap(f2337(A_27a,V16a0,V17a1),V18a2) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))),V17a1),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V16a0),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V18a2),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))) ) ) ) ).
tff(lamtp_f2338,type,
f2338: ( del * $i ) > $i ).
tff(lameq_f2338,axiom,
! [A_27a: del,V16a0: $i] :
( mem(V16a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V17a1: $i] : ( ap(f2338(A_27a,V16a0),V17a1) = f2337(A_27a,V16a0,V17a1) ) ) ).
tff(lamtp_f2339,type,
f2339: del > $i ).
tff(lameq_f2339,axiom,
! [A_27a: del,V16a0: $i] : ( ap(f2339(A_27a),V16a0) = f2338(A_27a,V16a0) ) ).
tff(lamtp_f2340,type,
f2340: ( del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2340,axiom,
! [A_27a: del,V14a1: $i] :
( mem(V14a1,A_27a)
=> ! [V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V13a0: $i] :
( mem(V13a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27spt_27: $i] :
( mem(V2_27spt_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V15a2: $i] : ( ap(f2340(A_27a,V14a1,V3a0_27,V13a0,V2_27spt_27),V15a2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(f2339(A_27a),V13a0),V14a1),V15a2))),ap(ap(c_2Ebool_2E_2F_5C,ap(V2_27spt_27,V13a0)),ap(V2_27spt_27,V15a2))) ) ) ) ) ) ).
tff(lamtp_f2341,type,
f2341: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2341,axiom,
! [A_27a: del,V2_27spt_27: $i] :
( mem(V2_27spt_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V13a0: $i] :
( mem(V13a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V14a1: $i] : ( ap(f2341(A_27a,V2_27spt_27,V13a0,V3a0_27),V14a1) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2340(A_27a,V14a1,V3a0_27,V13a0,V2_27spt_27)) ) ) ) ) ).
tff(lamtp_f2342,type,
f2342: ( del * $i * $i ) > $i ).
tff(lameq_f2342,axiom,
! [A_27a: del,V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27spt_27: $i] :
( mem(V2_27spt_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V13a0: $i] : ( ap(f2342(A_27a,V3a0_27,V2_27spt_27),V13a0) = ap(c_2Ebool_2E_3F(A_27a),f2341(A_27a,V2_27spt_27,V13a0,V3a0_27)) ) ) ) ).
tff(lamtp_f2343,type,
f2343: ( del * $i ) > $i ).
tff(lameq_f2343,axiom,
! [A_27a: del,V2_27spt_27: $i] :
( mem(V2_27spt_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27: $i] : ( ap(f2343(A_27a,V2_27spt_27),V3a0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Ebool_2EARB(A_27a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f2332(A_27a,V3a0_27))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2336(A_27a,V2_27spt_27,V3a0_27))),ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2342(A_27a,V3a0_27,V2_27spt_27)))))),ap(V2_27spt_27,V3a0_27)) ) ) ).
tff(lamtp_f2344,type,
f2344: ( del * $i ) > $i ).
tff(lameq_f2344,axiom,
! [A_27a: del,V1a0_27: $i] :
( mem(V1a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27spt_27: $i] : ( ap(f2344(A_27a,V1a0_27),V2_27spt_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f2343(A_27a,V2_27spt_27))),ap(V2_27spt_27,V1a0_27)) ) ) ).
tff(lamtp_f2345,type,
f2345: del > $i ).
tff(lameq_f2345,axiom,
! [A_27a: del,V1a0_27: $i] : ( ap(f2345(A_27a),V1a0_27) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f2344(A_27a,V1a0_27)) ) ).
tff(ax_thm_2Esptree_2Espt__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Esptree_2Espt(A_27a),ty_2Eind__type_2Erecspace(A_27a)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(A_27a),ty_2Esptree_2Espt(A_27a)),f2345(A_27a)),V0rep)) ) ).
tff(ax_thm_2Esptree_2Espt__case__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( mem(V0v,A_27b)
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2f1: $i] :
( mem(V2f1,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V3f2: $i] :
( mem(V3f2,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ( ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),c_2Esptree_2ELN(A_27a)),V0v),V1f),V2f1),V3f2) = V0v ) ) ) ) )
& ! [V4a: $i] :
( mem(V4a,A_27a)
=> ! [V5v: $i] :
( mem(V5v,A_27b)
=> ! [V6f: $i] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7f1: $i] :
( mem(V7f1,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V8f2: $i] :
( mem(V8f2,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ( ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),ap(c_2Esptree_2ELS(A_27a),V4a)),V5v),V6f),V7f1),V8f2) = ap(V6f,V4a) ) ) ) ) ) )
& ! [V9a0: $i] :
( mem(V9a0,ty_2Esptree_2Espt(A_27a))
=> ! [V10a1: $i] :
( mem(V10a1,ty_2Esptree_2Espt(A_27a))
=> ! [V11v: $i] :
( mem(V11v,A_27b)
=> ! [V12f: $i] :
( mem(V12f,arr(A_27a,A_27b))
=> ! [V13f1: $i] :
( mem(V13f1,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V14f2: $i] :
( mem(V14f2,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ( ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),ap(ap(c_2Esptree_2EBN(A_27a),V9a0),V10a1)),V11v),V12f),V13f1),V14f2) = ap(ap(V13f1,V9a0),V10a1) ) ) ) ) ) ) )
& ! [V15a0: $i] :
( mem(V15a0,ty_2Esptree_2Espt(A_27a))
=> ! [V16a1: $i] :
( mem(V16a1,A_27a)
=> ! [V17a2: $i] :
( mem(V17a2,ty_2Esptree_2Espt(A_27a))
=> ! [V18v: $i] :
( mem(V18v,A_27b)
=> ! [V19f: $i] :
( mem(V19f,arr(A_27a,A_27b))
=> ! [V20f1: $i] :
( mem(V20f1,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V21f2: $i] :
( mem(V21f2,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ( ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),ap(ap(ap(c_2Esptree_2EBS(A_27a),V15a0),V16a1),V17a2)),V18v),V19f),V20f1),V21f2) = ap(ap(ap(V21f2,V15a0),V16a1),V17a2) ) ) ) ) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Espt__size__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__size(A_27a),V0f),c_2Esptree_2ELN(A_27a))) = fo__c_2Enum_2E0 ) )
& ! [V1f: $i] :
( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__size(A_27a),V1f),ap(c_2Esptree_2ELS(A_27a),V2a))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(V1f,V2a))) ) ) )
& ! [V3f: $i] :
( mem(V3f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V4a0: $i] :
( mem(V4a0,ty_2Esptree_2Espt(A_27a))
=> ! [V5a1: $i] :
( mem(V5a1,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__size(A_27a),V3f),ap(ap(c_2Esptree_2EBN(A_27a),V4a0),V5a1))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esptree_2Espt__size(A_27a),V3f),V4a0)),ap(ap(c_2Esptree_2Espt__size(A_27a),V3f),V5a1)))) ) ) ) )
& ! [V6f: $i] :
( mem(V6f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V7a0: $i] :
( mem(V7a0,ty_2Esptree_2Espt(A_27a))
=> ! [V8a1: $i] :
( mem(V8a1,A_27a)
=> ! [V9a2: $i] :
( mem(V9a2,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__size(A_27a),V6f),ap(ap(ap(c_2Esptree_2EBS(A_27a),V7a0),V8a1),V9a2))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esptree_2Espt__size(A_27a),V6f),V7a0)),ap(ap(c_2Earithmetic_2E_2B,ap(V6f,V8a1)),ap(ap(c_2Esptree_2Espt__size(A_27a),V6f),V9a2))))) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Edatatype__spt,axiom,
! [A_27a: del,V0spt: $i] :
( mem(V0spt,arr(ty_2Esptree_2Espt(A_27a),arr(arr(A_27a,ty_2Esptree_2Espt(A_27a)),arr(arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a))),arr(arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),ty_2Esptree_2Espt(A_27a)))),bool)))))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(V0spt,c_2Esptree_2ELN(A_27a)),c_2Esptree_2ELS(A_27a)),c_2Esptree_2EBN(A_27a)),c_2Esptree_2EBS(A_27a)))) ) ).
tff(conj_thm_2Esptree_2Espt__11,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ! [V1a_27: $i] :
( mem(V1a_27,A_27a)
=> ( ( ap(c_2Esptree_2ELS(A_27a),V0a) = ap(c_2Esptree_2ELS(A_27a),V1a_27) )
<=> ( V0a = V1a_27 ) ) ) )
& ! [V2a0: $i] :
( mem(V2a0,ty_2Esptree_2Espt(A_27a))
=> ! [V3a1: $i] :
( mem(V3a1,ty_2Esptree_2Espt(A_27a))
=> ! [V4a0_27: $i] :
( mem(V4a0_27,ty_2Esptree_2Espt(A_27a))
=> ! [V5a1_27: $i] :
( mem(V5a1_27,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2EBN(A_27a),V2a0),V3a1) = ap(ap(c_2Esptree_2EBN(A_27a),V4a0_27),V5a1_27) )
<=> ( ( V2a0 = V4a0_27 )
& ( V3a1 = V5a1_27 ) ) ) ) ) ) )
& ! [V6a0: $i] :
( mem(V6a0,ty_2Esptree_2Espt(A_27a))
=> ! [V7a1: $i] :
( mem(V7a1,A_27a)
=> ! [V8a2: $i] :
( mem(V8a2,ty_2Esptree_2Espt(A_27a))
=> ! [V9a0_27: $i] :
( mem(V9a0_27,ty_2Esptree_2Espt(A_27a))
=> ! [V10a1_27: $i] :
( mem(V10a1_27,A_27a)
=> ! [V11a2_27: $i] :
( mem(V11a2_27,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(ap(c_2Esptree_2EBS(A_27a),V6a0),V7a1),V8a2) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V9a0_27),V10a1_27),V11a2_27) )
<=> ( ( V6a0 = V9a0_27 )
& ( V7a1 = V10a1_27 )
& ( V8a2 = V11a2_27 ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__distinct,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ( c_2Esptree_2ELN(A_27a) != ap(c_2Esptree_2ELS(A_27a),V0a) ) )
& ! [V1a1: $i] :
( mem(V1a1,ty_2Esptree_2Espt(A_27a))
=> ! [V2a0: $i] :
( mem(V2a0,ty_2Esptree_2Espt(A_27a))
=> ( c_2Esptree_2ELN(A_27a) != ap(ap(c_2Esptree_2EBN(A_27a),V2a0),V1a1) ) ) )
& ! [V3a2: $i] :
( mem(V3a2,ty_2Esptree_2Espt(A_27a))
=> ! [V4a1: $i] :
( mem(V4a1,A_27a)
=> ! [V5a0: $i] :
( mem(V5a0,ty_2Esptree_2Espt(A_27a))
=> ( c_2Esptree_2ELN(A_27a) != ap(ap(ap(c_2Esptree_2EBS(A_27a),V5a0),V4a1),V3a2) ) ) ) )
& ! [V6a1: $i] :
( mem(V6a1,ty_2Esptree_2Espt(A_27a))
=> ! [V7a0: $i] :
( mem(V7a0,ty_2Esptree_2Espt(A_27a))
=> ! [V8a: $i] :
( mem(V8a,A_27a)
=> ( ap(c_2Esptree_2ELS(A_27a),V8a) != ap(ap(c_2Esptree_2EBN(A_27a),V7a0),V6a1) ) ) ) )
& ! [V9a2: $i] :
( mem(V9a2,ty_2Esptree_2Espt(A_27a))
=> ! [V10a1: $i] :
( mem(V10a1,A_27a)
=> ! [V11a0: $i] :
( mem(V11a0,ty_2Esptree_2Espt(A_27a))
=> ! [V12a: $i] :
( mem(V12a,A_27a)
=> ( ap(c_2Esptree_2ELS(A_27a),V12a) != ap(ap(ap(c_2Esptree_2EBS(A_27a),V11a0),V10a1),V9a2) ) ) ) ) )
& ! [V13a2: $i] :
( mem(V13a2,ty_2Esptree_2Espt(A_27a))
=> ! [V14a1_27: $i] :
( mem(V14a1_27,A_27a)
=> ! [V15a1: $i] :
( mem(V15a1,ty_2Esptree_2Espt(A_27a))
=> ! [V16a0_27: $i] :
( mem(V16a0_27,ty_2Esptree_2Espt(A_27a))
=> ! [V17a0: $i] :
( mem(V17a0,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2EBN(A_27a),V17a0),V15a1) != ap(ap(ap(c_2Esptree_2EBS(A_27a),V16a0_27),V14a1_27),V13a2) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__nchotomy,axiom,
! [A_27a: del,V0ss: $i] :
( mem(V0ss,ty_2Esptree_2Espt(A_27a))
=> ( ( V0ss = c_2Esptree_2ELN(A_27a) )
| ? [V1a: $i] :
( mem(V1a,A_27a)
& ( V0ss = ap(c_2Esptree_2ELS(A_27a),V1a) ) )
| ? [V2s: $i] :
( mem(V2s,ty_2Esptree_2Espt(A_27a))
& ? [V3s0: $i] :
( mem(V3s0,ty_2Esptree_2Espt(A_27a))
& ( V0ss = ap(ap(c_2Esptree_2EBN(A_27a),V2s),V3s0) ) ) )
| ? [V4s: $i] :
( mem(V4s,ty_2Esptree_2Espt(A_27a))
& ? [V5a: $i] :
( mem(V5a,A_27a)
& ? [V6s0: $i] :
( mem(V6s0,ty_2Esptree_2Espt(A_27a))
& ( V0ss = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4s),V5a),V6s0) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f0: $i] :
( mem(V0f0,A_27b)
=> ! [V1f1: $i] :
( mem(V1f1,arr(A_27a,A_27b))
=> ! [V2f2: $i] :
( mem(V2f2,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(A_27b,arr(A_27b,A_27b)))))
=> ! [V3f3: $i] :
( mem(V3f3,arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),arr(A_27b,arr(A_27b,A_27b))))))
=> ? [V4fn: $i] :
( mem(V4fn,arr(ty_2Esptree_2Espt(A_27a),A_27b))
& ( ap(V4fn,c_2Esptree_2ELN(A_27a)) = V0f0 )
& ! [V5a: $i] :
( mem(V5a,A_27a)
=> ( ap(V4fn,ap(c_2Esptree_2ELS(A_27a),V5a)) = ap(V1f1,V5a) ) )
& ! [V6a0: $i] :
( mem(V6a0,ty_2Esptree_2Espt(A_27a))
=> ! [V7a1: $i] :
( mem(V7a1,ty_2Esptree_2Espt(A_27a))
=> ( ap(V4fn,ap(ap(c_2Esptree_2EBN(A_27a),V6a0),V7a1)) = ap(ap(ap(ap(V2f2,V6a0),V7a1),ap(V4fn,V6a0)),ap(V4fn,V7a1)) ) ) )
& ! [V8a0: $i] :
( mem(V8a0,ty_2Esptree_2Espt(A_27a))
=> ! [V9a1: $i] :
( mem(V9a1,A_27a)
=> ! [V10a2: $i] :
( mem(V10a2,ty_2Esptree_2Espt(A_27a))
=> ( ap(V4fn,ap(ap(ap(c_2Esptree_2EBS(A_27a),V8a0),V9a1),V10a2)) = ap(ap(ap(ap(ap(V3f3,V9a1),V8a0),V10a2),ap(V4fn,V8a0)),ap(V4fn,V10a2)) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__induction,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Esptree_2Espt(A_27a),bool))
=> ( ( p(ap(V0P,c_2Esptree_2ELN(A_27a)))
& ! [V1a: $i] :
( mem(V1a,A_27a)
=> p(ap(V0P,ap(c_2Esptree_2ELS(A_27a),V1a))) )
& ! [V2s: $i] :
( mem(V2s,ty_2Esptree_2Espt(A_27a))
=> ! [V3s0: $i] :
( mem(V3s0,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(V0P,V2s))
& p(ap(V0P,V3s0)) )
=> p(ap(V0P,ap(ap(c_2Esptree_2EBN(A_27a),V2s),V3s0))) ) ) )
& ! [V4s: $i] :
( mem(V4s,ty_2Esptree_2Espt(A_27a))
=> ! [V5s0: $i] :
( mem(V5s0,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(V0P,V4s))
& p(ap(V0P,V5s0)) )
=> ! [V6a: $i] :
( mem(V6a,A_27a)
=> p(ap(V0P,ap(ap(ap(c_2Esptree_2EBS(A_27a),V4s),V6a),V5s0))) ) ) ) ) )
=> ! [V7s: $i] :
( mem(V7s,ty_2Esptree_2Espt(A_27a))
=> p(ap(V0P,V7s)) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__case__cong,axiom,
! [A_27a: del,A_27b: del,V0v_27: $i] :
( mem(V0v_27,A_27b)
=> ! [V1f_27: $i] :
( mem(V1f_27,arr(A_27a,A_27b))
=> ! [V2f1_27: $i] :
( mem(V2f1_27,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V3f2_27: $i] :
( mem(V3f2_27,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ! [V4M: $i] :
( mem(V4M,ty_2Esptree_2Espt(A_27a))
=> ! [V5M_27: $i] :
( mem(V5M_27,ty_2Esptree_2Espt(A_27a))
=> ! [V6v: $i] :
( mem(V6v,A_27b)
=> ! [V7f: $i] :
( mem(V7f,arr(A_27a,A_27b))
=> ! [V8f1: $i] :
( mem(V8f1,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V9f2: $i] :
( mem(V9f2,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ( ( ( V4M = V5M_27 )
& ( ( V5M_27 = c_2Esptree_2ELN(A_27a) )
=> ( V6v = V0v_27 ) )
& ! [V10a: $i] :
( mem(V10a,A_27a)
=> ( ( V5M_27 = ap(c_2Esptree_2ELS(A_27a),V10a) )
=> ( ap(V7f,V10a) = ap(V1f_27,V10a) ) ) )
& ! [V11a0: $i] :
( mem(V11a0,ty_2Esptree_2Espt(A_27a))
=> ! [V12a1: $i] :
( mem(V12a1,ty_2Esptree_2Espt(A_27a))
=> ( ( V5M_27 = ap(ap(c_2Esptree_2EBN(A_27a),V11a0),V12a1) )
=> ( ap(ap(V8f1,V11a0),V12a1) = ap(ap(V2f1_27,V11a0),V12a1) ) ) ) )
& ! [V13a0: $i] :
( mem(V13a0,ty_2Esptree_2Espt(A_27a))
=> ! [V14a1: $i] :
( mem(V14a1,A_27a)
=> ! [V15a2: $i] :
( mem(V15a2,ty_2Esptree_2Espt(A_27a))
=> ( ( V5M_27 = ap(ap(ap(c_2Esptree_2EBS(A_27a),V13a0),V14a1),V15a2) )
=> ( ap(ap(ap(V9f2,V13a0),V14a1),V15a2) = ap(ap(ap(V3f2_27,V13a0),V14a1),V15a2) ) ) ) ) ) )
=> ( ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),V4M),V6v),V7f),V8f1),V9f2) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),V5M_27),V0v_27),V1f_27),V2f1_27),V3f2_27) ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__case__eq,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Esptree_2Espt(A_27a))
=> ! [V1v: $i] :
( mem(V1v,A_27b)
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3f1: $i] :
( mem(V3f1,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),A_27b)))
=> ! [V4f2: $i] :
( mem(V4f2,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),A_27b))))
=> ! [V5v_27: $i] :
( mem(V5v_27,A_27b)
=> ( ( ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,A_27b),V0x),V1v),V2f),V3f1),V4f2) = V5v_27 )
<=> ( ( ( V0x = c_2Esptree_2ELN(A_27a) )
& ( V1v = V5v_27 ) )
| ? [V6a: $i] :
( mem(V6a,A_27a)
& ( V0x = ap(c_2Esptree_2ELS(A_27a),V6a) )
& ( ap(V2f,V6a) = V5v_27 ) )
| ? [V7s: $i] :
( mem(V7s,ty_2Esptree_2Espt(A_27a))
& ? [V8s0: $i] :
( mem(V8s0,ty_2Esptree_2Espt(A_27a))
& ( V0x = ap(ap(c_2Esptree_2EBN(A_27a),V7s),V8s0) )
& ( ap(ap(V3f1,V7s),V8s0) = V5v_27 ) ) )
| ? [V9s: $i] :
( mem(V9s,ty_2Esptree_2Espt(A_27a))
& ? [V10a: $i] :
( mem(V10a,A_27a)
& ? [V11s0: $i] :
( mem(V11s0,ty_2Esptree_2Espt(A_27a))
& ( V0x = ap(ap(ap(c_2Esptree_2EBS(A_27a),V9s),V10a),V11s0) )
& ( ap(ap(ap(V4f2,V9s),V10a),V11s0) = V5v_27 ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Ewf__def,axiom,
! [A_27a: del] :
( ( p(ap(c_2Esptree_2Ewf(A_27a),c_2Esptree_2ELN(A_27a)))
<=> $true )
& ! [V0a: $i] :
( mem(V0a,A_27a)
=> ( p(ap(c_2Esptree_2Ewf(A_27a),ap(c_2Esptree_2ELS(A_27a),V0a)))
<=> $true ) )
& ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V1t1),V2t2)))
<=> ( p(ap(c_2Esptree_2Ewf(A_27a),V1t1))
& p(ap(c_2Esptree_2Ewf(A_27a),V2t2))
& ~ ( ( V1t1 = c_2Esptree_2ELN(A_27a) )
& ( V2t2 = c_2Esptree_2ELN(A_27a) ) ) ) ) ) )
& ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4a: $i] :
( mem(V4a,A_27a)
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V4a),V5t2)))
<=> ( p(ap(c_2Esptree_2Ewf(A_27a),V3t1))
& p(ap(c_2Esptree_2Ewf(A_27a),V5t2))
& ~ ( ( V3t1 = c_2Esptree_2ELN(A_27a) )
& ( V5t2 = c_2Esptree_2ELN(A_27a) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Esptree_2Espt(A_27a),bool)))
=> ( ( ! [V1k: tp__ty_2Enum_2Enum] : p(ap(ap(V0P,inj__ty_2Enum_2Enum(V1k)),c_2Esptree_2ELN(A_27a)))
& ! [V2k: tp__ty_2Enum_2Enum,V3a: $i] :
( mem(V3a,A_27a)
=> p(ap(ap(V0P,inj__ty_2Enum_2Enum(V2k)),ap(c_2Esptree_2ELS(A_27a),V3a))) )
& ! [V4k: tp__ty_2Enum_2Enum,V5t1: $i] :
( mem(V5t1,ty_2Esptree_2Espt(A_27a))
=> ! [V6t2: $i] :
( mem(V6t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ( V4k != fo__c_2Enum_2E0 )
=> p(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V4k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V4k))),V5t1),V6t2))) )
=> p(ap(ap(V0P,inj__ty_2Enum_2Enum(V4k)),ap(ap(c_2Esptree_2EBN(A_27a),V5t1),V6t2))) ) ) )
& ! [V7k: tp__ty_2Enum_2Enum,V8t1: $i] :
( mem(V8t1,ty_2Esptree_2Espt(A_27a))
=> ! [V9a: $i] :
( mem(V9a,A_27a)
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ( V7k != fo__c_2Enum_2E0 )
=> p(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V7k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V7k))),V8t1),V10t2))) )
=> p(ap(ap(V0P,inj__ty_2Enum_2Enum(V7k)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V8t1),V9a),V10t2))) ) ) ) ) )
=> ! [V11v: tp__ty_2Enum_2Enum,V12v1: $i] :
( mem(V12v1,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,inj__ty_2Enum_2Enum(V11v)),V12v1)) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__def,axiom,
! [A_27a: del] :
( ! [V0k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0k)),c_2Esptree_2ELN(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ! [V1k: tp__ty_2Enum_2Enum,V2a: $i] :
( mem(V2a,A_27a)
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1k)),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Eoption_2ESOME(A_27a),V2a)),c_2Eoption_2ENONE(A_27a)) ) )
& ! [V3t2: $i] :
( mem(V3t2,ty_2Esptree_2Espt(A_27a))
=> ! [V4t1: $i] :
( mem(V4t1,ty_2Esptree_2Espt(A_27a))
=> ! [V5k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V5k)),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V3t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V5k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),c_2Eoption_2ENONE(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V5k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V5k))),V4t1),V3t2))) ) ) )
& ! [V6t2: $i] :
( mem(V6t2,ty_2Esptree_2Espt(A_27a))
=> ! [V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27a))
=> ! [V8k: tp__ty_2Enum_2Enum,V9a: $i] :
( mem(V9a,A_27a)
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V8k)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V7t1),V9a),V6t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V8k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Eoption_2ESOME(A_27a),V9a)),ap(ap(c_2Esptree_2Elookup(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V8k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V8k))),V7t1),V6t2))) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),bool))))
=> ( ( ! [V1k: tp__ty_2Enum_2Enum,V2a: $i] :
( mem(V2a,A_27a)
=> ( ( ( ( ( V1k != fo__c_2Enum_2E0 )
& p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V1k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V2a),c_2Esptree_2ELN(A_27a))) )
& ( ( ( V1k != fo__c_2Enum_2E0 )
& ~ p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V1k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V2a),c_2Esptree_2ELN(A_27a))) ) )
=> p(ap(ap(ap(V0P,inj__ty_2Enum_2Enum(V1k)),V2a),c_2Esptree_2ELN(A_27a))) ) )
& ! [V3k: tp__ty_2Enum_2Enum,V4a: $i] :
( mem(V4a,A_27a)
=> ! [V5a_27: $i] :
( mem(V5a_27,A_27a)
=> ( ( ( ( ( V3k != fo__c_2Enum_2E0 )
& p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V3k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V4a),c_2Esptree_2ELN(A_27a))) )
& ( ( ( V3k != fo__c_2Enum_2E0 )
& ~ p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V3k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V4a),c_2Esptree_2ELN(A_27a))) ) )
=> p(ap(ap(ap(V0P,inj__ty_2Enum_2Enum(V3k)),V4a),ap(c_2Esptree_2ELS(A_27a),V5a_27))) ) ) )
& ! [V6k: tp__ty_2Enum_2Enum,V7a: $i] :
( mem(V7a,A_27a)
=> ! [V8t1: $i] :
( mem(V8t1,ty_2Esptree_2Espt(A_27a))
=> ! [V9t2: $i] :
( mem(V9t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ( ( ( V6k != fo__c_2Enum_2E0 )
& p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V6k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V6k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V7a),V8t1)) )
& ( ( ( V6k != fo__c_2Enum_2E0 )
& ~ p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V6k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V6k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V7a),V9t2)) ) )
=> p(ap(ap(ap(V0P,inj__ty_2Enum_2Enum(V6k)),V7a),ap(ap(c_2Esptree_2EBN(A_27a),V8t1),V9t2))) ) ) ) )
& ! [V10k: tp__ty_2Enum_2Enum,V11a: $i] :
( mem(V11a,A_27a)
=> ! [V12t1: $i] :
( mem(V12t1,ty_2Esptree_2Espt(A_27a))
=> ! [V13a_27: $i] :
( mem(V13a_27,A_27a)
=> ! [V14t2: $i] :
( mem(V14t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ( ( ( V10k != fo__c_2Enum_2E0 )
& p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V10k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V10k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V11a),V12t1)) )
& ( ( ( V10k != fo__c_2Enum_2E0 )
& ~ p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V10k))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V10k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V11a),V14t2)) ) )
=> p(ap(ap(ap(V0P,inj__ty_2Enum_2Enum(V10k)),V11a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V12t1),V13a_27),V14t2))) ) ) ) ) ) )
=> ! [V15v: tp__ty_2Enum_2Enum,V16v1: $i] :
( mem(V16v1,A_27a)
=> ! [V17v2: $i] :
( mem(V17v2,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(ap(V0P,inj__ty_2Enum_2Enum(V15v)),V16v1),V17v2)) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__def,axiom,
! [A_27a: del] :
( ! [V0k: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,A_27a)
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1a),c_2Esptree_2ELN(A_27a)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Esptree_2ELS(A_27a),V1a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V0k))),ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V1a),c_2Esptree_2ELN(A_27a))),c_2Esptree_2ELN(A_27a))),ap(ap(c_2Esptree_2EBN(A_27a),c_2Esptree_2ELN(A_27a)),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V1a),c_2Esptree_2ELN(A_27a))))) ) )
& ! [V2k: tp__ty_2Enum_2Enum,V3a_27: $i] :
( mem(V3a_27,A_27a)
=> ! [V4a: $i] :
( mem(V4a,A_27a)
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V2k)),V4a),ap(c_2Esptree_2ELS(A_27a),V3a_27)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Esptree_2ELS(A_27a),V4a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V2k))),ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V4a),c_2Esptree_2ELN(A_27a))),V3a_27),c_2Esptree_2ELN(A_27a))),ap(ap(ap(c_2Esptree_2EBS(A_27a),c_2Esptree_2ELN(A_27a)),V3a_27),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V4a),c_2Esptree_2ELN(A_27a))))) ) ) )
& ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ! [V6t1: $i] :
( mem(V6t1,ty_2Esptree_2Espt(A_27a))
=> ! [V7k: tp__ty_2Enum_2Enum,V8a: $i] :
( mem(V8a,A_27a)
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V7k)),V8a),ap(ap(c_2Esptree_2EBN(A_27a),V6t1),V5t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V7k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(ap(c_2Esptree_2EBS(A_27a),V6t1),V8a),V5t2)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V7k))),ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V7k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V8a),V6t1)),V5t2)),ap(ap(c_2Esptree_2EBN(A_27a),V6t1),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V7k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V8a),V5t2)))) ) ) ) )
& ! [V9t2: $i] :
( mem(V9t2,ty_2Esptree_2Espt(A_27a))
=> ! [V10t1: $i] :
( mem(V10t1,ty_2Esptree_2Espt(A_27a))
=> ! [V11k: tp__ty_2Enum_2Enum,V12a_27: $i] :
( mem(V12a_27,A_27a)
=> ! [V13a: $i] :
( mem(V13a,A_27a)
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V11k)),V13a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V10t1),V12a_27),V9t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V11k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(ap(c_2Esptree_2EBS(A_27a),V10t1),V13a),V9t2)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V11k))),ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V11k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V13a),V10t1)),V12a_27),V9t2)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V10t1),V12a_27),ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V11k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V13a),V9t2)))) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Emk__BN__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),bool)))
=> ( ( p(ap(ap(V0P,c_2Esptree_2ELN(A_27a)),c_2Esptree_2ELN(A_27a)))
& ! [V1v14: $i] :
( mem(V1v14,A_27a)
=> p(ap(ap(V0P,c_2Esptree_2ELN(A_27a)),ap(c_2Esptree_2ELS(A_27a),V1v14))) )
& ! [V2v15: $i] :
( mem(V2v15,ty_2Esptree_2Espt(A_27a))
=> ! [V3v16: $i] :
( mem(V3v16,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,c_2Esptree_2ELN(A_27a)),ap(ap(c_2Esptree_2EBN(A_27a),V2v15),V3v16))) ) )
& ! [V4v17: $i] :
( mem(V4v17,ty_2Esptree_2Espt(A_27a))
=> ! [V5v18: $i] :
( mem(V5v18,A_27a)
=> ! [V6v19: $i] :
( mem(V6v19,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,c_2Esptree_2ELN(A_27a)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4v17),V5v18),V6v19))) ) ) )
& ! [V7v2: $i] :
( mem(V7v2,A_27a)
=> ! [V8t2: $i] :
( mem(V8t2,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,ap(c_2Esptree_2ELS(A_27a),V7v2)),V8t2)) ) )
& ! [V9v3: $i] :
( mem(V9v3,ty_2Esptree_2Espt(A_27a))
=> ! [V10v4: $i] :
( mem(V10v4,ty_2Esptree_2Espt(A_27a))
=> ! [V11t2: $i] :
( mem(V11t2,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,ap(ap(c_2Esptree_2EBN(A_27a),V9v3),V10v4)),V11t2)) ) ) )
& ! [V12v5: $i] :
( mem(V12v5,ty_2Esptree_2Espt(A_27a))
=> ! [V13v6: $i] :
( mem(V13v6,A_27a)
=> ! [V14v7: $i] :
( mem(V14v7,ty_2Esptree_2Espt(A_27a))
=> ! [V15t2: $i] :
( mem(V15t2,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,ap(ap(ap(c_2Esptree_2EBS(A_27a),V12v5),V13v6),V14v7)),V15t2)) ) ) ) ) )
=> ! [V16v: $i] :
( mem(V16v,ty_2Esptree_2Espt(A_27a))
=> ! [V17v1: $i] :
( mem(V17v1,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(V0P,V16v),V17v1)) ) ) ) ) ).
tff(conj_thm_2Esptree_2Emk__BN__def,axiom,
! [A_27a: del,V0v14: $i] :
( mem(V0v14,A_27a)
=> ! [V1v15: $i] :
( mem(V1v15,ty_2Esptree_2Espt(A_27a))
=> ! [V2v16: $i] :
( mem(V2v16,ty_2Esptree_2Espt(A_27a))
=> ! [V3v17: $i] :
( mem(V3v17,ty_2Esptree_2Espt(A_27a))
=> ! [V4v18: $i] :
( mem(V4v18,A_27a)
=> ! [V5v19: $i] :
( mem(V5v19,ty_2Esptree_2Espt(A_27a))
=> ! [V6v2: $i] :
( mem(V6v2,A_27a)
=> ! [V7t2: $i] :
( mem(V7t2,ty_2Esptree_2Espt(A_27a))
=> ! [V8v3: $i] :
( mem(V8v3,ty_2Esptree_2Espt(A_27a))
=> ! [V9v4: $i] :
( mem(V9v4,ty_2Esptree_2Espt(A_27a))
=> ! [V10v5: $i] :
( mem(V10v5,ty_2Esptree_2Espt(A_27a))
=> ! [V11v6: $i] :
( mem(V11v6,A_27a)
=> ! [V12v7: $i] :
( mem(V12v7,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Emk__BN(A_27a),c_2Esptree_2ELN(A_27a)),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Emk__BN(A_27a),c_2Esptree_2ELN(A_27a)),ap(c_2Esptree_2ELS(A_27a),V0v14)) = ap(ap(c_2Esptree_2EBN(A_27a),c_2Esptree_2ELN(A_27a)),ap(c_2Esptree_2ELS(A_27a),V0v14)) )
& ( ap(ap(c_2Esptree_2Emk__BN(A_27a),c_2Esptree_2ELN(A_27a)),ap(ap(c_2Esptree_2EBN(A_27a),V1v15),V2v16)) = ap(ap(c_2Esptree_2EBN(A_27a),c_2Esptree_2ELN(A_27a)),ap(ap(c_2Esptree_2EBN(A_27a),V1v15),V2v16)) )
& ( ap(ap(c_2Esptree_2Emk__BN(A_27a),c_2Esptree_2ELN(A_27a)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3v17),V4v18),V5v19)) = ap(ap(c_2Esptree_2EBN(A_27a),c_2Esptree_2ELN(A_27a)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3v17),V4v18),V5v19)) )
& ( ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(c_2Esptree_2ELS(A_27a),V6v2)),V7t2) = ap(ap(c_2Esptree_2EBN(A_27a),ap(c_2Esptree_2ELS(A_27a),V6v2)),V7t2) )
& ( ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V8v3),V9v4)),V7t2) = ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V8v3),V9v4)),V7t2) )
& ( ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V10v5),V11v6),V12v7)),V7t2) = ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V10v5),V11v6),V12v7)),V7t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Emk__BS__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Esptree_2Espt(A_27a),arr(A_27a,arr(ty_2Esptree_2Espt(A_27a),bool))))
=> ( ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> p(ap(ap(ap(V0P,c_2Esptree_2ELN(A_27a)),V1x),c_2Esptree_2ELN(A_27a))) )
& ! [V2v16: $i] :
( mem(V2v16,A_27a)
=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> p(ap(ap(ap(V0P,ap(c_2Esptree_2ELS(A_27a),V2v16)),V3x),c_2Esptree_2ELN(A_27a))) ) )
& ! [V4v17: $i] :
( mem(V4v17,ty_2Esptree_2Espt(A_27a))
=> ! [V5v18: $i] :
( mem(V5v18,ty_2Esptree_2Espt(A_27a))
=> ! [V6x: $i] :
( mem(V6x,A_27a)
=> p(ap(ap(ap(V0P,ap(ap(c_2Esptree_2EBN(A_27a),V4v17),V5v18)),V6x),c_2Esptree_2ELN(A_27a))) ) ) )
& ! [V7v19: $i] :
( mem(V7v19,ty_2Esptree_2Espt(A_27a))
=> ! [V8v20: $i] :
( mem(V8v20,A_27a)
=> ! [V9v21: $i] :
( mem(V9v21,ty_2Esptree_2Espt(A_27a))
=> ! [V10x: $i] :
( mem(V10x,A_27a)
=> p(ap(ap(ap(V0P,ap(ap(ap(c_2Esptree_2EBS(A_27a),V7v19),V8v20),V9v21)),V10x),c_2Esptree_2ELN(A_27a))) ) ) ) )
& ! [V11t1: $i] :
( mem(V11t1,ty_2Esptree_2Espt(A_27a))
=> ! [V12x: $i] :
( mem(V12x,A_27a)
=> ! [V13v4: $i] :
( mem(V13v4,A_27a)
=> p(ap(ap(ap(V0P,V11t1),V12x),ap(c_2Esptree_2ELS(A_27a),V13v4))) ) ) )
& ! [V14t1: $i] :
( mem(V14t1,ty_2Esptree_2Espt(A_27a))
=> ! [V15x: $i] :
( mem(V15x,A_27a)
=> ! [V16v5: $i] :
( mem(V16v5,ty_2Esptree_2Espt(A_27a))
=> ! [V17v6: $i] :
( mem(V17v6,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(ap(V0P,V14t1),V15x),ap(ap(c_2Esptree_2EBN(A_27a),V16v5),V17v6))) ) ) ) )
& ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V19x: $i] :
( mem(V19x,A_27a)
=> ! [V20v7: $i] :
( mem(V20v7,ty_2Esptree_2Espt(A_27a))
=> ! [V21v8: $i] :
( mem(V21v8,A_27a)
=> ! [V22v9: $i] :
( mem(V22v9,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(ap(V0P,V18t1),V19x),ap(ap(ap(c_2Esptree_2EBS(A_27a),V20v7),V21v8),V22v9))) ) ) ) ) ) )
=> ! [V23v: $i] :
( mem(V23v,ty_2Esptree_2Espt(A_27a))
=> ! [V24v1: $i] :
( mem(V24v1,A_27a)
=> ! [V25v2: $i] :
( mem(V25v2,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(ap(V0P,V23v),V24v1),V25v2)) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Emk__BS__def,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1v16: $i] :
( mem(V1v16,A_27a)
=> ! [V2v17: $i] :
( mem(V2v17,ty_2Esptree_2Espt(A_27a))
=> ! [V3v18: $i] :
( mem(V3v18,ty_2Esptree_2Espt(A_27a))
=> ! [V4v19: $i] :
( mem(V4v19,ty_2Esptree_2Espt(A_27a))
=> ! [V5v20: $i] :
( mem(V5v20,A_27a)
=> ! [V6v21: $i] :
( mem(V6v21,ty_2Esptree_2Espt(A_27a))
=> ! [V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27a))
=> ! [V8v4: $i] :
( mem(V8v4,A_27a)
=> ! [V9v5: $i] :
( mem(V9v5,ty_2Esptree_2Espt(A_27a))
=> ! [V10v6: $i] :
( mem(V10v6,ty_2Esptree_2Espt(A_27a))
=> ! [V11v7: $i] :
( mem(V11v7,ty_2Esptree_2Espt(A_27a))
=> ! [V12v8: $i] :
( mem(V12v8,A_27a)
=> ! [V13v9: $i] :
( mem(V13v9,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),c_2Esptree_2ELN(A_27a)),V0x),c_2Esptree_2ELN(A_27a)) = ap(c_2Esptree_2ELS(A_27a),V0x) )
& ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(c_2Esptree_2ELS(A_27a),V1v16)),V0x),c_2Esptree_2ELN(A_27a)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(c_2Esptree_2ELS(A_27a),V1v16)),V0x),c_2Esptree_2ELN(A_27a)) )
& ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V2v17),V3v18)),V0x),c_2Esptree_2ELN(A_27a)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V2v17),V3v18)),V0x),c_2Esptree_2ELN(A_27a)) )
& ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4v19),V5v20),V6v21)),V0x),c_2Esptree_2ELN(A_27a)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4v19),V5v20),V6v21)),V0x),c_2Esptree_2ELN(A_27a)) )
& ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),V7t1),V0x),ap(c_2Esptree_2ELS(A_27a),V8v4)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V7t1),V0x),ap(c_2Esptree_2ELS(A_27a),V8v4)) )
& ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),V7t1),V0x),ap(ap(c_2Esptree_2EBN(A_27a),V9v5),V10v6)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V7t1),V0x),ap(ap(c_2Esptree_2EBN(A_27a),V9v5),V10v6)) )
& ( ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),V7t1),V0x),ap(ap(ap(c_2Esptree_2EBS(A_27a),V11v7),V12v8),V13v9)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V7t1),V0x),ap(ap(ap(c_2Esptree_2EBS(A_27a),V11v7),V12v8),V13v9)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Edelete__def,axiom,
! [A_27a: del] :
( ! [V0k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0k)),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ! [V1k: tp__ty_2Enum_2Enum,V2a: $i] :
( mem(V2a,A_27a)
=> ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V1k)),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),c_2Esptree_2ELN(A_27a)),ap(c_2Esptree_2ELS(A_27a),V2a)) ) )
& ! [V3k: tp__ty_2Enum_2Enum,V4t1: $i] :
( mem(V4t1,ty_2Esptree_2Espt(A_27a))
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V3k)),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V3k))),ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V4t1)),V5t2)),ap(ap(c_2Esptree_2Emk__BN(A_27a),V4t1),ap(ap(c_2Esptree_2Edelete(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V5t2)))) ) ) )
& ! [V6k: tp__ty_2Enum_2Enum,V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27a))
=> ! [V8a: $i] :
( mem(V8a,A_27a)
=> ! [V9t2: $i] :
( mem(V9t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V6k)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V7t1),V8a),V9t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V6k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Esptree_2EBN(A_27a),V7t1),V9t2)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V6k))),ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V6k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V7t1)),V8a),V9t2)),ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),V7t1),V8a),ap(ap(c_2Esptree_2Edelete(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V6k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V9t2)))) ) ) ) ) ) ).
tff(lamtp_f2346,type,
f2346: ( del * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2346,axiom,
! [A_27a: del,V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ! [V1i: tp__ty_2Enum_2Enum,V3a: $i] : ( ap(f2346(A_27a,V2t,V1i),V3a) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1i)),V3a),V2t)) ) ) ).
tff(lamtp_f2347,type,
f2347: ( del * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2347,axiom,
! [A_27a: del,V1i: tp__ty_2Enum_2Enum,V2t: $i] : ( ap(f2347(A_27a,V1i),V2t) = f2346(A_27a,V2t,V1i) ) ).
tff(lamtp_f2348,type,
f2348: del > $i ).
tff(lameq_f2348,axiom,
! [A_27a: del,V1i: tp__ty_2Enum_2Enum] : ( ap(f2348(A_27a),inj__ty_2Enum_2Enum(V1i)) = f2347(A_27a,V1i) ) ).
tff(ax_thm_2Esptree_2EfromList__def,axiom,
! [A_27a: del,V0l: $i] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Esptree_2EfromList(A_27a),V0l) = ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)),ap(ap(ap(c_2Elist_2EFOLDL(A_27a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a))),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a),arr(A_27a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)))),f2348(A_27a))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Esptree_2ELN(A_27a))),V0l)) ) ) ).
tff(ax_thm_2Esptree_2Esize__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),c_2Esptree_2ELN(A_27a))) = fo__c_2Enum_2E0 )
& ! [V0a: $i] :
( mem(V0a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),ap(c_2Esptree_2ELS(A_27a),V0a))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) )
& ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V1t1),V2t2))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Esptree_2Esize(A_27a),V1t1)),ap(c_2Esptree_2Esize(A_27a),V2t2))) ) ) )
& ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4a: $i] :
( mem(V4a,A_27a)
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V4a),V5t2))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Esptree_2Esize(A_27a),V3t1)),ap(c_2Esptree_2Esize(A_27a),V5t2))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__notEmpty,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1a),V2t) != c_2Esptree_2ELN(A_27a) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__insert,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V2t))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1a),V2t))) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__delete,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1k: tp__ty_2Enum_2Enum] :
( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V1k)),V0t))) ) ) ).
tff(conj_thm_2Esptree_2Elookup__insert1,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0k)),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1a),V2t)) = ap(c_2Eoption_2ESOME(A_27a),V1a) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__insert,axiom,
! [A_27a: del,V0k2: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ! [V3k1: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V3k1)),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k2)),V1v),V2t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3k1)),inj__ty_2Enum_2Enum(V0k2))),ap(c_2Eoption_2ESOME(A_27a),V1v)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V3k1)),V2t)) ) ) ) ).
tff(lamtp_f2349,type,
f2349: ( del * $i * $i ) > $i ).
tff(lameq_f2349,axiom,
! [A_27a: del,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V4t1: $i] :
( mem(V4t1,ty_2Esptree_2Espt(A_27a))
=> ! [V5t2: $i] : ( ap(f2349(A_27a,V1a,V4t1),V5t2) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V1a),V5t2) ) ) ) ).
tff(lamtp_f2350,type,
f2350: ( del * $i ) > $i ).
tff(lameq_f2350,axiom,
! [A_27a: del,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V4t1: $i] : ( ap(f2350(A_27a,V1a),V4t1) = f2349(A_27a,V1a,V4t1) ) ) ).
tff(lamtp_f2351,type,
f2351: ( del * $i * $i ) > $i ).
tff(lameq_f2351,axiom,
! [A_27a: del,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V6t1_27: $i] :
( mem(V6t1_27,ty_2Esptree_2Espt(A_27a))
=> ! [V8t2_27: $i] : ( ap(f2351(A_27a,V1a,V6t1_27),V8t2_27) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V6t1_27),V1a),V8t2_27) ) ) ) ).
tff(lamtp_f2352,type,
f2352: ( del * $i ) > $i ).
tff(lameq_f2352,axiom,
! [A_27a: del,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V6t1_27: $i] : ( ap(f2352(A_27a,V1a),V6t1_27) = k(A_27a,f2351(A_27a,V1a,V6t1_27)) ) ) ).
tff(lamtp_f2353,type,
f2353: ( del * $i * $i ) > $i ).
tff(lameq_f2353,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V12a: $i] : ( ap(f2353(A_27a,V9t1,V10t2),V12a) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V9t1),V12a),V10t2) ) ) ) ).
tff(lamtp_f2354,type,
f2354: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2354,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] :
( mem(V13t1_27,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V14t2_27: $i] : ( ap(f2354(A_27a,V9t1,V13t1_27,V10t2),V14t2_27) = ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V9t1),V13t1_27)),ap(ap(c_2Esptree_2Eunion(A_27a),V10t2),V14t2_27)) ) ) ) ) ).
tff(lamtp_f2355,type,
f2355: ( del * $i * $i ) > $i ).
tff(lameq_f2355,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] : ( ap(f2355(A_27a,V9t1,V10t2),V13t1_27) = f2354(A_27a,V9t1,V13t1_27,V10t2) ) ) ) ).
tff(lamtp_f2356,type,
f2356: ( del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2356,axiom,
! [A_27a: del,V16a_27_27: $i] :
( mem(V16a_27_27,A_27a)
=> ! [V15t1_27_27: $i] :
( mem(V15t1_27_27,ty_2Esptree_2Espt(A_27a))
=> ! [V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V17t2_27_27: $i] : ( ap(f2356(A_27a,V16a_27_27,V15t1_27_27,V9t1,V10t2),V17t2_27_27) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V9t1),V15t1_27_27)),V16a_27_27),ap(ap(c_2Esptree_2Eunion(A_27a),V10t2),V17t2_27_27)) ) ) ) ) ) ).
tff(lamtp_f2357,type,
f2357: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2357,axiom,
! [A_27a: del,V15t1_27_27: $i] :
( mem(V15t1_27_27,ty_2Esptree_2Espt(A_27a))
=> ! [V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V16a_27_27: $i] : ( ap(f2357(A_27a,V15t1_27_27,V9t1,V10t2),V16a_27_27) = f2356(A_27a,V16a_27_27,V15t1_27_27,V9t1,V10t2) ) ) ) ) ).
tff(lamtp_f2358,type,
f2358: ( del * $i * $i ) > $i ).
tff(lameq_f2358,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] : ( ap(f2358(A_27a,V9t1,V10t2),V15t1_27_27) = f2357(A_27a,V15t1_27_27,V9t1,V10t2) ) ) ) ).
tff(lamtp_f2359,type,
f2359: ( del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2359,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V23t1_27: $i] :
( mem(V23t1_27,ty_2Esptree_2Espt(A_27a))
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V24t2_27: $i] : ( ap(f2359(A_27a,V19a,V23t1_27,V18t1,V20t2),V24t2_27) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V18t1),V23t1_27)),V19a),ap(ap(c_2Esptree_2Eunion(A_27a),V20t2),V24t2_27)) ) ) ) ) ) ).
tff(lamtp_f2360,type,
f2360: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2360,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V23t1_27: $i] : ( ap(f2360(A_27a,V19a,V18t1,V20t2),V23t1_27) = f2359(A_27a,V19a,V23t1_27,V18t1,V20t2) ) ) ) ) ).
tff(lamtp_f2361,type,
f2361: ( del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2361,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V25t1_27_27: $i] :
( mem(V25t1_27_27,ty_2Esptree_2Espt(A_27a))
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V27t2_27_27: $i] : ( ap(f2361(A_27a,V19a,V25t1_27_27,V18t1,V20t2),V27t2_27_27) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V18t1),V25t1_27_27)),V19a),ap(ap(c_2Esptree_2Eunion(A_27a),V20t2),V27t2_27_27)) ) ) ) ) ) ).
tff(lamtp_f2362,type,
f2362: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2362,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] : ( ap(f2362(A_27a,V19a,V18t1,V20t2),V25t1_27_27) = k(A_27a,f2361(A_27a,V19a,V25t1_27_27,V18t1,V20t2)) ) ) ) ) ).
tff(ax_thm_2Esptree_2Eunion__def,axiom,
! [A_27a: del] :
( ! [V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),c_2Esptree_2ELN(A_27a)),V0t) = V0t ) )
& ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),ap(c_2Esptree_2ELS(A_27a),V1a)),V2t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Esptree_2Espt(A_27a)),V2t),ap(c_2Esptree_2ELS(A_27a),V1a)),k(A_27a,ap(c_2Esptree_2ELS(A_27a),V1a))),f2350(A_27a,V1a)),f2352(A_27a,V1a)) ) ) )
& ! [V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V11t: $i] :
( mem(V11t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2)),V11t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Esptree_2Espt(A_27a)),V11t),ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2)),f2353(A_27a,V9t1,V10t2)),f2355(A_27a,V9t1,V10t2)),f2358(A_27a,V9t1,V10t2)) ) ) ) )
& ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V19a: $i] :
( mem(V19a,A_27a)
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V21t: $i] :
( mem(V21t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2)),V21t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Esptree_2Espt(A_27a)),V21t),ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2)),k(A_27a,ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2))),f2360(A_27a,V19a,V18t1,V20t2)),f2362(A_27a,V19a,V18t1,V20t2)) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2EisEmpty__union,axiom,
! [A_27a: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Eunion(A_27a),V0m1),V1m2) = c_2Esptree_2ELN(A_27a) )
<=> ( ( V0m1 = c_2Esptree_2ELN(A_27a) )
& ( V1m2 = c_2Esptree_2ELN(A_27a) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__union,axiom,
! [A_27a: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(c_2Esptree_2Ewf(A_27a),V0m1))
& p(ap(c_2Esptree_2Ewf(A_27a),V1m2)) )
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V0m1),V1m2))) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__union,axiom,
! [A_27a: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),ap(ap(c_2Esptree_2Eunion(A_27a),V0m1),V1m2)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V0m1)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V1m2)),f1905(A_27a)) ) ) ) ).
tff(lamtp_f2363,type,
f2363: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2363,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] :
( mem(V13t1_27,ty_2Esptree_2Espt(A_27b))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V14t2_27: $i] : ( ap(f2363(A_27a,A_27b,V9t1,V13t1_27,V10t2),V14t2_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V9t1),V13t1_27)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V10t2),V14t2_27)) ) ) ) ) ).
tff(lamtp_f2364,type,
f2364: ( del * del * $i * $i ) > $i ).
tff(lameq_f2364,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] : ( ap(f2364(A_27a,A_27b,V9t1,V10t2),V13t1_27) = f2363(A_27a,A_27b,V9t1,V13t1_27,V10t2) ) ) ) ).
tff(lamtp_f2365,type,
f2365: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2365,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] :
( mem(V15t1_27_27,ty_2Esptree_2Espt(A_27b))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V17t2_27_27: $i] : ( ap(f2365(A_27a,A_27b,V9t1,V15t1_27_27,V10t2),V17t2_27_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V9t1),V15t1_27_27)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V10t2),V17t2_27_27)) ) ) ) ) ).
tff(lamtp_f2366,type,
f2366: ( del * del * $i * $i ) > $i ).
tff(lameq_f2366,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] : ( ap(f2366(A_27a,A_27b,V9t1,V10t2),V15t1_27_27) = k(A_27b,f2365(A_27a,A_27b,V9t1,V15t1_27_27,V10t2)) ) ) ) ).
tff(lamtp_f2367,type,
f2367: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2367,axiom,
! [A_27a: del,A_27b: del,V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V23t1_27: $i] :
( mem(V23t1_27,ty_2Esptree_2Espt(A_27b))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V24t2_27: $i] : ( ap(f2367(A_27a,A_27b,V18t1,V23t1_27,V20t2),V24t2_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V18t1),V23t1_27)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V20t2),V24t2_27)) ) ) ) ) ).
tff(lamtp_f2368,type,
f2368: ( del * del * $i * $i ) > $i ).
tff(lameq_f2368,axiom,
! [A_27a: del,A_27b: del,V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V23t1_27: $i] : ( ap(f2368(A_27a,A_27b,V18t1,V20t2),V23t1_27) = f2367(A_27a,A_27b,V18t1,V23t1_27,V20t2) ) ) ) ).
tff(lamtp_f2369,type,
f2369: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2369,axiom,
! [A_27a: del,A_27b: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V25t1_27_27: $i] :
( mem(V25t1_27_27,ty_2Esptree_2Espt(A_27b))
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V27t2_27_27: $i] : ( ap(f2369(A_27a,A_27b,V19a,V25t1_27_27,V18t1,V20t2),V27t2_27_27) = ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V18t1),V25t1_27_27)),V19a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V20t2),V27t2_27_27)) ) ) ) ) ) ).
tff(lamtp_f2370,type,
f2370: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2370,axiom,
! [A_27a: del,A_27b: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] : ( ap(f2370(A_27a,A_27b,V19a,V18t1,V20t2),V25t1_27_27) = k(A_27b,f2369(A_27a,A_27b,V19a,V25t1_27_27,V18t1,V20t2)) ) ) ) ) ).
tff(ax_thm_2Esptree_2Einter__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),c_2Esptree_2ELN(A_27a)),V0t) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),ap(c_2Esptree_2ELS(A_27a),V1a)),V2t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27b,ty_2Esptree_2Espt(A_27a)),V2t),c_2Esptree_2ELN(A_27a)),k(A_27b,ap(c_2Esptree_2ELS(A_27a),V1a))),k(ty_2Esptree_2Espt(A_27b),k(ty_2Esptree_2Espt(A_27b),c_2Esptree_2ELN(A_27a)))),k(ty_2Esptree_2Espt(A_27b),k(A_27b,k(ty_2Esptree_2Espt(A_27b),ap(c_2Esptree_2ELS(A_27a),V1a))))) ) ) )
& ! [V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V11t: $i] :
( mem(V11t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2)),V11t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27b,ty_2Esptree_2Espt(A_27a)),V11t),c_2Esptree_2ELN(A_27a)),k(A_27b,c_2Esptree_2ELN(A_27a))),f2364(A_27a,A_27b,V9t1,V10t2)),f2366(A_27a,A_27b,V9t1,V10t2)) ) ) ) )
& ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V19a: $i] :
( mem(V19a,A_27a)
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V21t: $i] :
( mem(V21t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2)),V21t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27b,ty_2Esptree_2Espt(A_27a)),V21t),c_2Esptree_2ELN(A_27a)),k(A_27b,ap(c_2Esptree_2ELS(A_27a),V19a))),f2368(A_27a,A_27b,V18t1,V20t2)),f2370(A_27a,A_27b,V19a,V18t1,V20t2)) ) ) ) ) ) ) ).
tff(lamtp_f2371,type,
f2371: ( del * $i ) > $i ).
tff(lameq_f2371,axiom,
! [A_27a: del,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V3b: $i] : ( ap(f2371(A_27a,V1a),V3b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(A_27a),V1a),V3b)),ap(c_2Esptree_2ELS(A_27a),V1a)),c_2Esptree_2ELN(A_27a)) ) ) ).
tff(lamtp_f2372,type,
f2372: ( del * $i ) > $i ).
tff(lameq_f2372,axiom,
! [A_27a: del,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V7b_27: $i] : ( ap(f2372(A_27a,V1a),V7b_27) = k(ty_2Esptree_2Espt(A_27a),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(A_27a),V1a),V7b_27)),ap(c_2Esptree_2ELS(A_27a),V1a)),c_2Esptree_2ELN(A_27a))) ) ) ).
tff(lamtp_f2373,type,
f2373: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2373,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] :
( mem(V13t1_27,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V14t2_27: $i] : ( ap(f2373(A_27a,V9t1,V13t1_27,V10t2),V14t2_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter__eq(A_27a),V9t1),V13t1_27)),ap(ap(c_2Esptree_2Einter__eq(A_27a),V10t2),V14t2_27)) ) ) ) ) ).
tff(lamtp_f2374,type,
f2374: ( del * $i * $i ) > $i ).
tff(lameq_f2374,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] : ( ap(f2374(A_27a,V9t1,V10t2),V13t1_27) = f2373(A_27a,V9t1,V13t1_27,V10t2) ) ) ) ).
tff(lamtp_f2375,type,
f2375: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2375,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] :
( mem(V15t1_27_27,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V17t2_27_27: $i] : ( ap(f2375(A_27a,V9t1,V15t1_27_27,V10t2),V17t2_27_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter__eq(A_27a),V9t1),V15t1_27_27)),ap(ap(c_2Esptree_2Einter__eq(A_27a),V10t2),V17t2_27_27)) ) ) ) ) ).
tff(lamtp_f2376,type,
f2376: ( del * $i * $i ) > $i ).
tff(lameq_f2376,axiom,
! [A_27a: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] : ( ap(f2376(A_27a,V9t1,V10t2),V15t1_27_27) = k(A_27a,f2375(A_27a,V9t1,V15t1_27_27,V10t2)) ) ) ) ).
tff(lamtp_f2377,type,
f2377: ( del * $i ) > $i ).
tff(lameq_f2377,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V22a_27: $i] : ( ap(f2377(A_27a,V19a),V22a_27) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(A_27a),V22a_27),V19a)),ap(c_2Esptree_2ELS(A_27a),V19a)),c_2Esptree_2ELN(A_27a)) ) ) ).
tff(lamtp_f2378,type,
f2378: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2378,axiom,
! [A_27a: del,V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V23t1_27: $i] :
( mem(V23t1_27,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V24t2_27: $i] : ( ap(f2378(A_27a,V18t1,V23t1_27,V20t2),V24t2_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter__eq(A_27a),V18t1),V23t1_27)),ap(ap(c_2Esptree_2Einter__eq(A_27a),V20t2),V24t2_27)) ) ) ) ) ).
tff(lamtp_f2379,type,
f2379: ( del * $i * $i ) > $i ).
tff(lameq_f2379,axiom,
! [A_27a: del,V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V23t1_27: $i] : ( ap(f2379(A_27a,V18t1,V20t2),V23t1_27) = f2378(A_27a,V18t1,V23t1_27,V20t2) ) ) ) ).
tff(lamtp_f2380,type,
f2380: ( del * $i * $i * $i * $i * $i ) > $i ).
tff(lameq_f2380,axiom,
! [A_27a: del,V26a_27_27_27: $i] :
( mem(V26a_27_27_27,A_27a)
=> ! [V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] :
( mem(V25t1_27_27,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V27t2_27_27: $i] : ( ap(f2380(A_27a,V26a_27_27_27,V19a,V18t1,V25t1_27_27,V20t2),V27t2_27_27) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(A_27a),V26a_27_27_27),V19a)),ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2Einter__eq(A_27a),V18t1),V25t1_27_27)),V19a),ap(ap(c_2Esptree_2Einter__eq(A_27a),V20t2),V27t2_27_27))),ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Einter__eq(A_27a),V18t1),V25t1_27_27)),ap(ap(c_2Esptree_2Einter__eq(A_27a),V20t2),V27t2_27_27))) ) ) ) ) ) ) ).
tff(lamtp_f2381,type,
f2381: ( del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2381,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] :
( mem(V25t1_27_27,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V26a_27_27_27: $i] : ( ap(f2381(A_27a,V19a,V18t1,V25t1_27_27,V20t2),V26a_27_27_27) = f2380(A_27a,V26a_27_27_27,V19a,V18t1,V25t1_27_27,V20t2) ) ) ) ) ) ).
tff(lamtp_f2382,type,
f2382: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2382,axiom,
! [A_27a: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] : ( ap(f2382(A_27a,V19a,V18t1,V20t2),V25t1_27_27) = f2381(A_27a,V19a,V18t1,V25t1_27_27,V20t2) ) ) ) ) ).
tff(ax_thm_2Esptree_2Einter__eq__def,axiom,
! [A_27a: del] :
( ! [V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Einter__eq(A_27a),c_2Esptree_2ELN(A_27a)),V0t) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Einter__eq(A_27a),ap(c_2Esptree_2ELS(A_27a),V1a)),V2t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Esptree_2Espt(A_27a)),V2t),c_2Esptree_2ELN(A_27a)),f2371(A_27a,V1a)),k(ty_2Esptree_2Espt(A_27a),k(ty_2Esptree_2Espt(A_27a),c_2Esptree_2ELN(A_27a)))),k(ty_2Esptree_2Espt(A_27a),f2372(A_27a,V1a))) ) ) )
& ! [V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V11t: $i] :
( mem(V11t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Einter__eq(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2)),V11t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Esptree_2Espt(A_27a)),V11t),c_2Esptree_2ELN(A_27a)),k(A_27a,c_2Esptree_2ELN(A_27a))),f2374(A_27a,V9t1,V10t2)),f2376(A_27a,V9t1,V10t2)) ) ) ) )
& ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V19a: $i] :
( mem(V19a,A_27a)
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V21t: $i] :
( mem(V21t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Einter__eq(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2)),V21t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Esptree_2Espt(A_27a)),V21t),c_2Esptree_2ELN(A_27a)),f2377(A_27a,V19a)),f2379(A_27a,V18t1,V20t2)),f2382(A_27a,V19a,V18t1,V20t2)) ) ) ) ) ) ) ).
tff(lamtp_f2383,type,
f2383: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2383,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] :
( mem(V13t1_27,ty_2Esptree_2Espt(A_27b))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V14t2_27: $i] : ( ap(f2383(A_27a,A_27b,V9t1,V13t1_27,V10t2),V14t2_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V9t1),V13t1_27)),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V10t2),V14t2_27)) ) ) ) ) ).
tff(lamtp_f2384,type,
f2384: ( del * del * $i * $i ) > $i ).
tff(lameq_f2384,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V13t1_27: $i] : ( ap(f2384(A_27a,A_27b,V9t1,V10t2),V13t1_27) = f2383(A_27a,A_27b,V9t1,V13t1_27,V10t2) ) ) ) ).
tff(lamtp_f2385,type,
f2385: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2385,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] :
( mem(V15t1_27_27,ty_2Esptree_2Espt(A_27b))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V17t2_27_27: $i] : ( ap(f2385(A_27a,A_27b,V9t1,V15t1_27_27,V10t2),V17t2_27_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V9t1),V15t1_27_27)),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V10t2),V17t2_27_27)) ) ) ) ) ).
tff(lamtp_f2386,type,
f2386: ( del * del * $i * $i ) > $i ).
tff(lameq_f2386,axiom,
! [A_27a: del,A_27b: del,V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V15t1_27_27: $i] : ( ap(f2386(A_27a,A_27b,V9t1,V10t2),V15t1_27_27) = k(A_27b,f2385(A_27a,A_27b,V9t1,V15t1_27_27,V10t2)) ) ) ) ).
tff(lamtp_f2387,type,
f2387: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2387,axiom,
! [A_27a: del,A_27b: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V23t1_27: $i] :
( mem(V23t1_27,ty_2Esptree_2Espt(A_27b))
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V24t2_27: $i] : ( ap(f2387(A_27a,A_27b,V19a,V23t1_27,V18t1,V20t2),V24t2_27) = ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V18t1),V23t1_27)),V19a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V20t2),V24t2_27)) ) ) ) ) ) ).
tff(lamtp_f2388,type,
f2388: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2388,axiom,
! [A_27a: del,A_27b: del,V19a: $i] :
( mem(V19a,A_27a)
=> ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V23t1_27: $i] : ( ap(f2388(A_27a,A_27b,V19a,V18t1,V20t2),V23t1_27) = f2387(A_27a,A_27b,V19a,V23t1_27,V18t1,V20t2) ) ) ) ) ).
tff(lamtp_f2389,type,
f2389: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2389,axiom,
! [A_27a: del,A_27b: del,V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] :
( mem(V25t1_27_27,ty_2Esptree_2Espt(A_27b))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V27t2_27_27: $i] : ( ap(f2389(A_27a,A_27b,V18t1,V25t1_27_27,V20t2),V27t2_27_27) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V18t1),V25t1_27_27)),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V20t2),V27t2_27_27)) ) ) ) ) ).
tff(lamtp_f2390,type,
f2390: ( del * del * $i * $i ) > $i ).
tff(lameq_f2390,axiom,
! [A_27a: del,A_27b: del,V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V25t1_27_27: $i] : ( ap(f2390(A_27a,A_27b,V18t1,V20t2),V25t1_27_27) = k(A_27b,f2389(A_27a,A_27b,V18t1,V25t1_27_27,V20t2)) ) ) ) ).
tff(ax_thm_2Esptree_2Edifference__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),c_2Esptree_2ELN(A_27a)),V0t) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),ap(c_2Esptree_2ELS(A_27a),V1a)),V2t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27b,ty_2Esptree_2Espt(A_27a)),V2t),ap(c_2Esptree_2ELS(A_27a),V1a)),k(A_27b,c_2Esptree_2ELN(A_27a))),k(ty_2Esptree_2Espt(A_27b),k(ty_2Esptree_2Espt(A_27b),ap(c_2Esptree_2ELS(A_27a),V1a)))),k(ty_2Esptree_2Espt(A_27b),k(A_27b,k(ty_2Esptree_2Espt(A_27b),c_2Esptree_2ELN(A_27a))))) ) ) )
& ! [V9t1: $i] :
( mem(V9t1,ty_2Esptree_2Espt(A_27a))
=> ! [V10t2: $i] :
( mem(V10t2,ty_2Esptree_2Espt(A_27a))
=> ! [V11t: $i] :
( mem(V11t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2)),V11t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27b,ty_2Esptree_2Espt(A_27a)),V11t),ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2)),k(A_27b,ap(ap(c_2Esptree_2EBN(A_27a),V9t1),V10t2))),f2384(A_27a,A_27b,V9t1,V10t2)),f2386(A_27a,A_27b,V9t1,V10t2)) ) ) ) )
& ! [V18t1: $i] :
( mem(V18t1,ty_2Esptree_2Espt(A_27a))
=> ! [V19a: $i] :
( mem(V19a,A_27a)
=> ! [V20t2: $i] :
( mem(V20t2,ty_2Esptree_2Espt(A_27a))
=> ! [V21t: $i] :
( mem(V21t,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2)),V21t) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27b,ty_2Esptree_2Espt(A_27a)),V21t),ap(ap(ap(c_2Esptree_2EBS(A_27a),V18t1),V19a),V20t2)),k(A_27b,ap(ap(c_2Esptree_2EBN(A_27a),V18t1),V20t2))),f2388(A_27a,A_27b,V19a,V18t1,V20t2)),f2390(A_27a,A_27b,V18t1,V20t2)) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__inter,axiom,
! [A_27a: del,A_27b: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27b))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0m1),V1m2))) ) ) ).
tff(lamtp_f2391,type,
f2391: ( del * del * $i ) > $i ).
tff(lameq_f2391,axiom,
! [A_27b: del,A_27a: del,V4v4: $i] :
( mem(V4v4,ty_2Eoption_2Eoption(A_27b))
=> ! [V5v: $i] : ( ap(f2391(A_27b,A_27a,V4v4),V5v) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27b,ty_2Eoption_2Eoption(A_27a)),V4v4),c_2Eoption_2ENONE(A_27a)),k(A_27b,ap(c_2Eoption_2ESOME(A_27a),V5v))) ) ) ).
tff(lamtp_f2392,type,
f2392: ( del * del * $i ) > $i ).
tff(lameq_f2392,axiom,
! [A_27a: del,A_27b: del,V3v3: $i] :
( mem(V3v3,ty_2Eoption_2Eoption(A_27a))
=> ! [V4v4: $i] : ( ap(f2392(A_27a,A_27b,V3v3),V4v4) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V3v3),c_2Eoption_2ENONE(A_27a)),f2391(A_27b,A_27a,V4v4)) ) ) ).
tff(lamtp_f2393,type,
f2393: ( del * del ) > $i ).
tff(lameq_f2393,axiom,
! [A_27b: del,A_27a: del,V3v3: $i] : ( ap(f2393(A_27b,A_27a),V3v3) = f2392(A_27a,A_27b,V3v3) ) ).
tff(conj_thm_2Esptree_2Elookup__inter,axiom,
! [A_27a: del,A_27b: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27b))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0m1),V1m2)) = ap(ap(c_2Epair_2Epair__CASE(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Epair_2E_2C(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V0m1)),ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V2k)),V1m2))),f2393(A_27b,A_27a)) ) ) ) ).
tff(lamtp_f2394,type,
f2394: ( del * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2394,axiom,
! [A_27a: del,V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3v: $i] : ( ap(f2394(A_27a,V1m2,V2k),V3v) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V1m2)),ap(c_2Eoption_2ESOME(A_27a),V3v))),ap(c_2Eoption_2ESOME(A_27a),V3v)),c_2Eoption_2ENONE(A_27a)) ) ) ).
tff(conj_thm_2Esptree_2Elookup__inter__eq,axiom,
! [A_27a: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),ap(ap(c_2Esptree_2Einter__eq(A_27a),V0m1),V1m2)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V0m1)),c_2Eoption_2ENONE(A_27a)),f2394(A_27a,V1m2,V2k)) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__inter__EQ,axiom,
! [A_27a: del,A_27b: del,V0x: tp__ty_2Enum_2Enum,V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27b))
=> ! [V3y: $i] :
( mem(V3y,A_27a)
=> ( ( ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V1t1),V2t2)) = ap(c_2Eoption_2ESOME(A_27a),V3y) )
<=> ( ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),V1t1) = ap(c_2Eoption_2ESOME(A_27a),V3y) )
& ( ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V0x)),V2t2) != c_2Eoption_2ENONE(A_27b) ) ) )
& ( ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V1t1),V2t2)) = c_2Eoption_2ENONE(A_27a) )
<=> ( ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),V1t1) = c_2Eoption_2ENONE(A_27a) )
| ( ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V0x)),V2t2) = c_2Eoption_2ENONE(A_27b) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__inter__assoc,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: tp__ty_2Enum_2Enum,V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27b))
=> ! [V3t3: $i] :
( mem(V3t3,ty_2Esptree_2Espt(A_27c))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V1t1),ap(ap(c_2Esptree_2Einter(A_27b,A_27c),V2t2),V3t3))) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27c),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V1t1),V2t2)),V3t3)) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__difference,axiom,
! [A_27a: del,A_27b: del,V0m1: $i] :
( mem(V0m1,ty_2Esptree_2Espt(A_27a))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Esptree_2Espt(A_27b))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V0m1),V1m2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V2k)),V1m2)),c_2Eoption_2ENONE(A_27b))),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V0m1)),c_2Eoption_2ENONE(A_27a)) ) ) ) ).
tff(lamtp_f2395,type,
f2395: $i > $i ).
tff(lameq_f2395,axiom,
! [V0R: $i] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V1n: tp__ty_2Enum_2Enum] : ( ap(f2395(V0R),inj__ty_2Enum_2Enum(V1n)) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(V0R,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V1n))) ) ) ).
tff(lamtp_f2396,type,
f2396: $i ).
tff(lameq_f2396,axiom,
! [V0R: $i] : ( ap(f2396,V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Enum_2Enum),V0R)),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2395(V0R))) ) ).
tff(lamtp_f2397,type,
f2397: $i > $i ).
tff(lameq_f2397,axiom,
! [V2lrnext: $i] :
( mem(V2lrnext,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V3a: tp__ty_2Enum_2Enum] : ( ap(f2397(V2lrnext),inj__ty_2Enum_2Enum(V3a)) = ap(c_2Ecombin_2EI(ty_2Enum_2Enum),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3a)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(V2lrnext,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))) ) ) ).
tff(lamtp_f2398,type,
f2398: $i ).
tff(lameq_f2398,axiom,
! [V2lrnext: $i] : ( ap(f2398,V2lrnext) = f2397(V2lrnext) ) ).
tff(ax_thm_2Esptree_2Elrnext__primitive__def,axiom,
c_2Esptree_2Elrnext = ap(ap(c_2Erelation_2EWFREC(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))),f2396)),f2398) ).
tff(conj_thm_2Esptree_2Elrnext__ind,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ! [V1n: tp__ty_2Enum_2Enum] :
( ( ( V1n != fo__c_2Enum_2E0 )
=> p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) )
=> p(ap(V0P,inj__ty_2Enum_2Enum(V1n))) )
=> ! [V2v: tp__ty_2Enum_2Enum] : p(ap(V0P,inj__ty_2Enum_2Enum(V2v))) ) ) ).
tff(conj_thm_2Esptree_2Elrnext__def,axiom,
! [V0n: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))) ) ).
tff(conj_thm_2Esptree_2Elrnext__thm,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2a: $i] :
( mem(V2a,A_27b)
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V1n))) ) )
& ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) )
& ! [V3n: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3n)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V3n)))) )
& ! [V4n: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Elrnext,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V4n)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V4n)))) ) ) ).
tff(lamtp_f2399,type,
f2399: $i ).
tff(lameq_f2399,axiom,
! [V3n: tp__ty_2Enum_2Enum] : ( ap(f2399,inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) ).
tff(lamtp_f2400,type,
f2400: $i ).
tff(lameq_f2400,axiom,
! [V4n: tp__ty_2Enum_2Enum] : ( ap(f2400,inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V4n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) ).
tff(lamtp_f2401,type,
f2401: $i ).
tff(lameq_f2401,axiom,
! [V8n: tp__ty_2Enum_2Enum] : ( ap(f2401,inj__ty_2Enum_2Enum(V8n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V8n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) ).
tff(lamtp_f2402,type,
f2402: $i ).
tff(lameq_f2402,axiom,
! [V9n: tp__ty_2Enum_2Enum] : ( ap(f2402,inj__ty_2Enum_2Enum(V9n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V9n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) ).
tff(ax_thm_2Esptree_2Edomain__def,axiom,
! [A_27a: del] :
( ( ap(c_2Esptree_2Edomain(A_27a),c_2Esptree_2ELN(A_27a)) = c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) )
& ! [V0v0: $i] :
( mem(V0v0,A_27a)
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(c_2Esptree_2ELS(A_27a),V0v0)) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) ) )
& ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V1t1),V2t2)) = ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Enum_2Enum),f2399),ap(c_2Esptree_2Edomain(A_27a),V1t1))),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Enum_2Enum),f2400),ap(c_2Esptree_2Edomain(A_27a),V2t2))) ) ) )
& ! [V5t1: $i] :
( mem(V5t1,ty_2Esptree_2Espt(A_27a))
=> ! [V6v1: $i] :
( mem(V6v1,A_27a)
=> ! [V7t2: $i] :
( mem(V7t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V5t1),V6v1),V7t2)) = ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Enum_2Enum),f2401),ap(c_2Esptree_2Edomain(A_27a),V5t1)))),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Enum_2Enum),f2402),ap(c_2Esptree_2Edomain(A_27a),V7t2))) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2EFINITE__domain,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0t))) ) ).
tff(conj_thm_2Esptree_2Esize__insert,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2m: $i] :
( mem(V2m,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1v),V2m))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0k)),ap(c_2Esptree_2Edomain(A_27a),V2m))),ap(c_2Esptree_2Esize(A_27a),V2m)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Esptree_2Esize(A_27a),V2m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__fromList,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),ap(c_2Esptree_2EfromList(A_27a),V1l)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),ap(c_2Elist_2ELENGTH(A_27a),V1l))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V0n)),V1l))),c_2Eoption_2ENONE(A_27a)) ) ) ).
tff(conj_thm_2Esptree_2Edomain__lookup,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1k: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1k)),ap(c_2Esptree_2Edomain(A_27a),V0t)))
<=> ? [V2v: $i] :
( mem(V2v,A_27a)
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1k)),V0t) = ap(c_2Eoption_2ESOME(A_27a),V2v) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__inter__alt,axiom,
! [A_27a: del,A_27b: del,V0x: tp__ty_2Enum_2Enum,V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V1t1),V2t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0x)),ap(c_2Esptree_2Edomain(A_27b),V2t2))),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),V1t1)),c_2Eoption_2ENONE(A_27a)) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__NONE__domain,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0k)),V1t) = c_2Eoption_2ENONE(A_27a) )
<=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0k)),ap(c_2Esptree_2Edomain(A_27a),V1t))) ) ) ).
tff(conj_thm_2Esptree_2Edomain__union,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V0t1),V1t2)) = ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0t1)),ap(c_2Esptree_2Edomain(A_27a),V1t2)) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__inter,axiom,
! [A_27a: del,A_27b: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t1),V1t2)) = ap(ap(c_2Epred__set_2EINTER(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0t1)),ap(c_2Esptree_2Edomain(A_27b),V1t2)) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__insert,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1v),V2t)) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0k)),ap(c_2Esptree_2Edomain(A_27a),V2t)) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__difference,axiom,
! [A_27a: del,A_27b: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V0t1),V1t2)) = ap(ap(c_2Epred__set_2EDIFF(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0t1)),ap(c_2Esptree_2Edomain(A_27b),V1t2)) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__sing,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1v),c_2Esptree_2ELN(A_27a))) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0k)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) ) ) ).
tff(conj_thm_2Esptree_2Edomain__fromList,axiom,
! [A_27a: del,V0l: $i] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(c_2Esptree_2EfromList(A_27a),V0l)) = ap(c_2Epred__set_2Ecount,ap(c_2Elist_2ELENGTH(A_27a),V0l)) ) ) ).
tff(conj_thm_2Esptree_2Elookup__delete,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1k1: tp__ty_2Enum_2Enum,V2k2: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1k1)),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V2k2)),V0t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1k1)),inj__ty_2Enum_2Enum(V2k2))),c_2Eoption_2ENONE(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1k1)),V0t)) ) ) ).
tff(conj_thm_2Esptree_2Edomain__delete,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0k)),V1t)) = ap(ap(c_2Epred__set_2EDELETE(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V1t)),inj__ty_2Enum_2Enum(V0k)) ) ) ).
tff(lamtp_f2403,type,
f2403: ( del * del * $i * tp__ty_2Enum_2Enum * $i * $i * $i ) > $i ).
tff(lameq_f2403,axiom,
! [A_27b: del,A_27a: del,V7f: $i] :
( mem(V7f,arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))))
=> ! [V8i: tp__ty_2Enum_2Enum,V9acc: $i] :
( mem(V9acc,A_27a)
=> ! [V10t1: $i] :
( mem(V10t1,ty_2Esptree_2Espt(A_27b))
=> ! [V11t2: $i] :
( mem(V11t2,ty_2Esptree_2Espt(A_27b))
=> ! [V12inc: tp__ty_2Enum_2Enum] : ( ap(f2403(A_27b,A_27a,V7f,V8i,V9acc,V10t1,V11t2),inj__ty_2Enum_2Enum(V12inc)) = ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V7f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V8i)),inj__ty_2Enum_2Enum(V12inc))),ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V7f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V8i)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V12inc)))),V9acc),V10t1)),V11t2) ) ) ) ) ) ).
tff(lamtp_f2404,type,
f2404: ( del * del * $i * tp__ty_2Enum_2Enum * $i * $i * $i * $i ) > $i ).
tff(lameq_f2404,axiom,
! [A_27b: del,A_27a: del,V13f: $i] :
( mem(V13f,arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))))
=> ! [V14i: tp__ty_2Enum_2Enum,V16t1: $i] :
( mem(V16t1,ty_2Esptree_2Espt(A_27b))
=> ! [V15acc: $i] :
( mem(V15acc,A_27a)
=> ! [V17a: $i] :
( mem(V17a,A_27b)
=> ! [V18t2: $i] :
( mem(V18t2,ty_2Esptree_2Espt(A_27b))
=> ! [V19inc: tp__ty_2Enum_2Enum] : ( ap(f2404(A_27b,A_27a,V13f,V14i,V16t1,V15acc,V17a,V18t2),inj__ty_2Enum_2Enum(V19inc)) = ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V13f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V14i)),inj__ty_2Enum_2Enum(V19inc))),ap(ap(ap(V13f,inj__ty_2Enum_2Enum(V14i)),V17a),ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V13f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V14i)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V19inc)))),V15acc),V16t1))),V18t2) ) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Efoldi__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))))
=> ! [V1i: tp__ty_2Enum_2Enum,V2acc: $i] :
( mem(V2acc,A_27a)
=> ( ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V0f),inj__ty_2Enum_2Enum(V1i)),V2acc),c_2Esptree_2ELN(A_27b)) = V2acc ) ) )
& ! [V3f: $i] :
( mem(V3f,arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))))
=> ! [V4i: tp__ty_2Enum_2Enum,V5acc: $i] :
( mem(V5acc,A_27a)
=> ! [V6a: $i] :
( mem(V6a,A_27b)
=> ( ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V3f),inj__ty_2Enum_2Enum(V4i)),V5acc),ap(c_2Esptree_2ELS(A_27b),V6a)) = ap(ap(ap(V3f,inj__ty_2Enum_2Enum(V4i)),V6a),V5acc) ) ) ) )
& ! [V7f: $i] :
( mem(V7f,arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))))
=> ! [V8i: tp__ty_2Enum_2Enum,V9acc: $i] :
( mem(V9acc,A_27a)
=> ! [V10t1: $i] :
( mem(V10t1,ty_2Esptree_2Espt(A_27b))
=> ! [V11t2: $i] :
( mem(V11t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V7f),inj__ty_2Enum_2Enum(V8i)),V9acc),ap(ap(c_2Esptree_2EBN(A_27b),V10t1),V11t2)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,A_27a),f2403(A_27b,A_27a,V7f,V8i,V9acc,V10t1,V11t2)),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V8i))) ) ) ) ) )
& ! [V13f: $i] :
( mem(V13f,arr(ty_2Enum_2Enum,arr(A_27b,arr(A_27a,A_27a))))
=> ! [V14i: tp__ty_2Enum_2Enum,V15acc: $i] :
( mem(V15acc,A_27a)
=> ! [V16t1: $i] :
( mem(V16t1,ty_2Esptree_2Espt(A_27b))
=> ! [V17a: $i] :
( mem(V17a,A_27b)
=> ! [V18t2: $i] :
( mem(V18t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27a,A_27b),V13f),inj__ty_2Enum_2Enum(V14i)),V15acc),ap(ap(ap(c_2Esptree_2EBS(A_27b),V16t1),V17a),V18t2)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,A_27a),f2404(A_27b,A_27a,V13f,V14i,V16t1,V15acc,V17a,V18t2)),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V14i))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__acc__ind,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ( ( ! [V1i: tp__ty_2Enum_2Enum] : p(ap(ap(V0P,inj__ty_2Enum_2Enum(V1i)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
& ! [V2i: tp__ty_2Enum_2Enum,V3k: tp__ty_2Enum_2Enum] :
( p(ap(ap(V0P,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2i)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V3k)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i))))),ap(ap(c_2Earithmetic_2EDIV,inj__ty_2Enum_2Enum(V3k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))
=> p(ap(ap(V0P,inj__ty_2Enum_2Enum(V2i)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V3k)))) ) )
=> ! [V4v: tp__ty_2Enum_2Enum,V5v1: tp__ty_2Enum_2Enum] : p(ap(ap(V0P,inj__ty_2Enum_2Enum(V4v)),inj__ty_2Enum_2Enum(V5v1))) ) ) ).
tff(conj_thm_2Esptree_2Espt__acc__def,axiom,
( ! [V0i: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V0i)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V0i )
& ! [V1k: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V2i)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1k)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2i)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1k)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i))))),ap(ap(c_2Earithmetic_2EDIV,inj__ty_2Enum_2Enum(V1k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ) ).
tff(conj_thm_2Esptree_2Espt__acc__def__compute,axiom,
( ! [V0i: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V0i)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V0i )
& ! [V1k: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V2i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1k))))) = surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2i)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1k))))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i))))),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1k)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) )
& ! [V3k: tp__ty_2Enum_2Enum,V4i: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V4i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V3k))))) = surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V4i)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V3k))))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V4i)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V4i))))),ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3k)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ) ).
tff(conj_thm_2Esptree_2Espt__acc__thm,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V0i)),inj__ty_2Enum_2Enum(V1k))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1k)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Enum_2Enum(V0i)),ap(ap(c_2Esptree_2Espt__acc,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0i)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V1k))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V0i)))),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V0i))))),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1k)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ).
tff(conj_thm_2Esptree_2Espt__acc__eqn,axiom,
! [V0k: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V1i)),inj__ty_2Enum_2Enum(V0k))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V1i))),inj__ty_2Enum_2Enum(V0k))),inj__ty_2Enum_2Enum(V1i))) ) ).
tff(conj_thm_2Esptree_2Espt__acc__0,axiom,
! [V0k: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0k))) = V0k ) ).
tff(lamtp_f2405,type,
f2405: tp__ty_2Enum_2Enum > $i ).
tff(lameq_f2405,axiom,
! [V3k: tp__ty_2Enum_2Enum,V5a: $i] : ( ap(f2405(V3k),V5a) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3k)),V5a) ) ).
tff(lamtp_f2406,type,
f2406: del > $i ).
tff(lameq_f2406,axiom,
! [A_27a: del,V3k: tp__ty_2Enum_2Enum] : ( ap(f2406(A_27a),inj__ty_2Enum_2Enum(V3k)) = k(A_27a,f2405(V3k)) ) ).
tff(lamtp_f2407,type,
f2407: tp__ty_2Enum_2Enum > $i ).
tff(lameq_f2407,axiom,
! [V2i: tp__ty_2Enum_2Enum,V6n: tp__ty_2Enum_2Enum] : ( ap(f2407(V2i),inj__ty_2Enum_2Enum(V6n)) = ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2i)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V2i))),inj__ty_2Enum_2Enum(V6n))) ) ).
tff(conj_thm_2Esptree_2Eset__foldi__keys,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1a: $i] :
( mem(V1a,arr(ty_2Enum_2Enum,bool))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(ap(ap(ap(c_2Esptree_2Efoldi(arr(ty_2Enum_2Enum,bool),A_27a),f2406(A_27a)),inj__ty_2Enum_2Enum(V2i)),V1a),V0t) = ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),V1a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Enum_2Enum),f2407(V2i)),ap(c_2Esptree_2Edomain(A_27a),V0t))) ) ) ) ).
tff(lamtp_f2408,type,
f2408: tp__ty_2Enum_2Enum > $i ).
tff(lameq_f2408,axiom,
! [V1k: tp__ty_2Enum_2Enum,V3a: $i] : ( ap(f2408(V1k),V3a) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1k)),V3a) ) ).
tff(lamtp_f2409,type,
f2409: del > $i ).
tff(lameq_f2409,axiom,
! [A_27a: del,V1k: tp__ty_2Enum_2Enum] : ( ap(f2409(A_27a),inj__ty_2Enum_2Enum(V1k)) = k(A_27a,f2408(V1k)) ) ).
tff(conj_thm_2Esptree_2Edomain__foldi,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),V0t) = ap(ap(ap(ap(c_2Esptree_2Efoldi(arr(ty_2Enum_2Enum,bool),A_27a),f2409(A_27a)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)),V0t) ) ) ).
tff(lamtp_f2410,type,
f2410: ( del * del * $i * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2410,axiom,
! [A_27b: del,A_27a: del,V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27b))
=> ! [V5f: $i] :
( mem(V5f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V6i: tp__ty_2Enum_2Enum,V8t2: $i] :
( mem(V8t2,ty_2Esptree_2Espt(A_27b))
=> ! [V9inc: tp__ty_2Enum_2Enum] : ( ap(f2410(A_27b,A_27a,V7t1,V5f,V6i,V8t2),inj__ty_2Enum_2Enum(V9inc)) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V5f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V6i)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V9inc)))),V7t1)),ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V5f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V6i)),inj__ty_2Enum_2Enum(V9inc))),V8t2)) ) ) ) ) ).
tff(lamtp_f2411,type,
f2411: ( del * del * $i * $i * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2411,axiom,
! [A_27b: del,A_27a: del,V13a: $i] :
( mem(V13a,A_27b)
=> ! [V12t1: $i] :
( mem(V12t1,ty_2Esptree_2Espt(A_27b))
=> ! [V10f: $i] :
( mem(V10f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V11i: tp__ty_2Enum_2Enum,V14t2: $i] :
( mem(V14t2,ty_2Esptree_2Espt(A_27b))
=> ! [V15inc: tp__ty_2Enum_2Enum] : ( ap(f2411(A_27b,A_27a,V13a,V12t1,V10f,V11i,V14t2),inj__ty_2Enum_2Enum(V15inc)) = ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V10f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V11i)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V15inc)))),V12t1)),ap(ap(V10f,inj__ty_2Enum_2Enum(V11i)),V13a)),ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V10f),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V11i)),inj__ty_2Enum_2Enum(V15inc))),V14t2)) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Emapi0__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V1i: tp__ty_2Enum_2Enum] : ( ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V0f),inj__ty_2Enum_2Enum(V1i)),c_2Esptree_2ELN(A_27b)) = c_2Esptree_2ELN(A_27a) ) )
& ! [V2f: $i] :
( mem(V2f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V3i: tp__ty_2Enum_2Enum,V4a: $i] :
( mem(V4a,A_27b)
=> ( ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V2f),inj__ty_2Enum_2Enum(V3i)),ap(c_2Esptree_2ELS(A_27b),V4a)) = ap(c_2Esptree_2ELS(A_27a),ap(ap(V2f,inj__ty_2Enum_2Enum(V3i)),V4a)) ) ) )
& ! [V5f: $i] :
( mem(V5f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V6i: tp__ty_2Enum_2Enum,V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27b))
=> ! [V8t2: $i] :
( mem(V8t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V5f),inj__ty_2Enum_2Enum(V6i)),ap(ap(c_2Esptree_2EBN(A_27b),V7t1),V8t2)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)),f2410(A_27b,A_27a,V7t1,V5f,V6i,V8t2)),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V6i))) ) ) ) )
& ! [V10f: $i] :
( mem(V10f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V11i: tp__ty_2Enum_2Enum,V12t1: $i] :
( mem(V12t1,ty_2Esptree_2Espt(A_27b))
=> ! [V13a: $i] :
( mem(V13a,A_27b)
=> ! [V14t2: $i] :
( mem(V14t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V10f),inj__ty_2Enum_2Enum(V11i)),ap(ap(ap(c_2Esptree_2EBS(A_27b),V12t1),V13a),V14t2)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)),f2411(A_27b,A_27a,V13a,V12t1,V10f,V11i,V14t2)),ap(c_2Esptree_2Elrnext,inj__ty_2Enum_2Enum(V11i))) ) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Emapi__def,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V1pt: $i] :
( mem(V1pt,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Emapi(A_27a,A_27b),V0f),V1pt) = ap(ap(ap(c_2Esptree_2Emapi0(A_27a,A_27b),V0f),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V1pt) ) ) ) ).
tff(lamtp_f2412,type,
f2412: ( del * del * tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2412,axiom,
! [A_27b: del,A_27a: del,V3k: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27b)))
=> ! [V4v: $i] : ( ap(f2412(A_27b,A_27a,V3k,V2i,V0f),V4v) = ap(c_2Eoption_2ESOME(A_27b),ap(ap(V0f,ap(ap(c_2Esptree_2Espt__acc,inj__ty_2Enum_2Enum(V2i)),inj__ty_2Enum_2Enum(V3k))),V4v)) ) ) ).
tff(conj_thm_2Esptree_2Elookup__mapi0,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27b)))
=> ! [V1pt: $i] :
( mem(V1pt,ty_2Esptree_2Espt(A_27a))
=> ! [V2i: tp__ty_2Enum_2Enum,V3k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V3k)),ap(ap(ap(c_2Esptree_2Emapi0(A_27b,A_27a),V0f),inj__ty_2Enum_2Enum(V2i)),V1pt)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V3k)),V1pt)),c_2Eoption_2ENONE(A_27b)),f2412(A_27b,A_27a,V3k,V2i,V0f)) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__mapi,axiom,
! [A_27a: del,A_27b: del,V0k: tp__ty_2Enum_2Enum,V1f: $i] :
( mem(V1f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V2pt: $i] :
( mem(V2pt,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0k)),ap(ap(c_2Esptree_2Emapi(A_27a,A_27b),V1f),V2pt)) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),ap(V1f,inj__ty_2Enum_2Enum(V0k))),ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V0k)),V2pt)) ) ) ) ).
tff(lamtp_f2413,type,
f2413: ( del * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2413,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2a: $i] : ( ap(f2413(A_27a,V0k,V1v),V2a) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V0k)),V1v)),V2a) ) ) ).
tff(lamtp_f2414,type,
f2414: ( del * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2414,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1v: $i] : ( ap(f2414(A_27a,V0k),V1v) = f2413(A_27a,V0k,V1v) ) ).
tff(lamtp_f2415,type,
f2415: del > $i ).
tff(lameq_f2415,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum] : ( ap(f2415(A_27a),inj__ty_2Enum_2Enum(V0k)) = f2414(A_27a,V0k) ) ).
tff(ax_thm_2Esptree_2EtoAList__def,axiom,
! [A_27a: del] : ( c_2Esptree_2EtoAList(A_27a) = ap(ap(ap(c_2Esptree_2Efoldi(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),A_27a),f2415(A_27a)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Elist_2ENIL(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))) ) ).
tff(conj_thm_2Esptree_2EMEM__toAList,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1k: tp__ty_2Enum_2Enum,V2v: $i] :
( mem(V2v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V1k)),V2v)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(c_2Esptree_2EtoAList(A_27a),V0t))))
<=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1k)),V0t) = ap(c_2Eoption_2ESOME(A_27a),V2v) ) ) ) ) ).
tff(conj_thm_2Esptree_2EALOOKUP__toAList,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1x: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Ealist_2EALOOKUP(A_27a,ty_2Enum_2Enum),ap(c_2Esptree_2EtoAList(A_27a),V0t)),inj__ty_2Enum_2Enum(V1x)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1x)),V0t) ) ) ).
tff(conj_thm_2Esptree_2Einsert__union,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2s: $i] :
( mem(V2s,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1v),V2s) = ap(ap(c_2Esptree_2Eunion(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0k)),V1v),c_2Esptree_2ELN(A_27a))),V2s) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__empty,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> ( ( V0t = c_2Esptree_2ELN(A_27a) )
<=> ( ap(c_2Esptree_2Edomain(A_27a),V0t) = c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) ) ) ) ) ).
tff(conj_thm_2Esptree_2EALL__DISTINCT__MAP__FST__toAList,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Enum_2Enum),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),ty_2Enum_2Enum),c_2Epair_2EFST(ty_2Enum_2Enum,A_27a)),ap(c_2Esptree_2EtoAList(A_27a),V0t)))) ) ).
tff(conj_thm_2Esptree_2Efoldi__FOLDR__toAList,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,arr(A_27b,A_27b))))
=> ! [V1a: $i] :
( mem(V1a,A_27b)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(ap(ap(c_2Esptree_2Efoldi(A_27b,A_27a),V0f),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V1a),V2t) = ap(ap(ap(c_2Elist_2EFOLDR(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,A_27a,arr(A_27b,A_27b)),V0f)),V1a),ap(c_2Esptree_2EtoAList(A_27a),V2t)) ) ) ) ) ).
tff(ax_thm_2Esptree_2EtoListA__def,axiom,
! [A_27a: del] :
( ! [V0acc: $i] :
( mem(V0acc,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Esptree_2EtoListA(A_27a),V0acc),c_2Esptree_2ELN(A_27a)) = V0acc ) )
& ! [V1acc: $i] :
( mem(V1acc,ty_2Elist_2Elist(A_27a))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ( ap(ap(c_2Esptree_2EtoListA(A_27a),V1acc),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(ap(c_2Elist_2ECONS(A_27a),V2a),V1acc) ) ) )
& ! [V3acc: $i] :
( mem(V3acc,ty_2Elist_2Elist(A_27a))
=> ! [V4t1: $i] :
( mem(V4t1,ty_2Esptree_2Espt(A_27a))
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2EtoListA(A_27a),V3acc),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)) = ap(ap(c_2Esptree_2EtoListA(A_27a),ap(ap(c_2Esptree_2EtoListA(A_27a),V3acc),V5t2)),V4t1) ) ) ) )
& ! [V6acc: $i] :
( mem(V6acc,ty_2Elist_2Elist(A_27a))
=> ! [V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27a))
=> ! [V8a: $i] :
( mem(V8a,A_27a)
=> ! [V9t2: $i] :
( mem(V9t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2EtoListA(A_27a),V6acc),ap(ap(ap(c_2Esptree_2EBS(A_27a),V7t1),V8a),V9t2)) = ap(ap(c_2Esptree_2EtoListA(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V8a),ap(ap(c_2Esptree_2EtoListA(A_27a),V6acc),V9t2))),V7t1) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2EtoListA__append,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1acc: $i] :
( mem(V1acc,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Esptree_2EtoListA(A_27a),V1acc),V0t) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Esptree_2EtoListA(A_27a),c_2Elist_2ENIL(A_27a)),V0t)),V1acc) ) ) ) ).
tff(conj_thm_2Esptree_2EisEmpty__toListA,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1acc: $i] :
( mem(V1acc,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> ( ( V0t = c_2Esptree_2ELN(A_27a) )
<=> ( ap(ap(c_2Esptree_2EtoListA(A_27a),V1acc),V0t) = V1acc ) ) ) ) ) ).
tff(ax_thm_2Esptree_2EtoList__def,axiom,
! [A_27a: del,V0m: $i] :
( mem(V0m,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2EtoList(A_27a),V0m) = ap(ap(c_2Esptree_2EtoListA(A_27a),c_2Elist_2ENIL(A_27a)),V0m) ) ) ).
tff(conj_thm_2Esptree_2EisEmpty__toList,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> ( ( V0t = c_2Esptree_2ELN(A_27a) )
<=> ( ap(c_2Esptree_2EtoList(A_27a),V0t) = c_2Elist_2ENIL(A_27a) ) ) ) ) ).
tff(conj_thm_2Esptree_2EMEM__toList,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Esptree_2EtoList(A_27a),V1t))))
<=> ? [V2k: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V1t) = ap(c_2Eoption_2ESOME(A_27a),V0x) ) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__eq__thm,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(c_2Esptree_2Ewf(A_27a),V0t1))
& p(ap(c_2Esptree_2Ewf(A_27a),V1t2)) )
=> ( ( V0t1 = V1t2 )
<=> ! [V2n: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2n)),V0t1) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2n)),V1t2) ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Emk__wf__def,axiom,
! [A_27a: del] :
( ( ap(c_2Esptree_2Emk__wf(A_27a),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ! [V0x: $i] :
( mem(V0x,A_27a)
=> ( ap(c_2Esptree_2Emk__wf(A_27a),ap(c_2Esptree_2ELS(A_27a),V0x)) = ap(c_2Esptree_2ELS(A_27a),V0x) ) )
& ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Emk__wf(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V1t1),V2t2)) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(c_2Esptree_2Emk__wf(A_27a),V1t1)),ap(c_2Esptree_2Emk__wf(A_27a),V2t2)) ) ) )
& ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4x: $i] :
( mem(V4x,A_27a)
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Emk__wf(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V4x),V5t2)) = ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(c_2Esptree_2Emk__wf(A_27a),V3t1)),V4x),ap(c_2Esptree_2Emk__wf(A_27a),V5t2)) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__mk__wf,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(c_2Esptree_2Emk__wf(A_27a),V0t))) ) ).
tff(conj_thm_2Esptree_2Ewf__mk__id,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> ( ap(c_2Esptree_2Emk__wf(A_27a),V0t) = V0t ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__mk__wf,axiom,
! [A_27a: del,V0x: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(c_2Esptree_2Emk__wf(A_27a),V1t)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0x)),V1t) ) ) ).
tff(conj_thm_2Esptree_2Edomain__mk__wf,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(c_2Esptree_2Emk__wf(A_27a),V0t)) = ap(c_2Esptree_2Edomain(A_27a),V0t) ) ) ).
tff(conj_thm_2Esptree_2Emk__wf__eq,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(c_2Esptree_2Emk__wf(A_27a),V0t1) = ap(c_2Esptree_2Emk__wf(A_27a),V1t2) )
<=> ! [V2x: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2x)),V0t1) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2x)),V1t2) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einter__eq,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27b))
=> ! [V2t3: $i] :
( mem(V2t3,ty_2Esptree_2Espt(A_27a))
=> ! [V3t4: $i] :
( mem(V3t4,ty_2Esptree_2Espt(A_27c))
=> ( ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t1),V1t2) = ap(ap(c_2Esptree_2Einter(A_27a,A_27c),V2t3),V3t4) )
<=> ! [V4x: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V4x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t1),V1t2)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V4x)),ap(ap(c_2Esptree_2Einter(A_27a,A_27c),V2t3),V3t4)) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Eunion__mk__wf,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),ap(c_2Esptree_2Emk__wf(A_27a),V0t1)),ap(c_2Esptree_2Emk__wf(A_27a),V1t2)) = ap(c_2Esptree_2Emk__wf(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V0t1),V1t2)) ) ) ) ).
tff(conj_thm_2Esptree_2Einter__mk__wf,axiom,
! [A_27a: del,A_27b: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),ap(c_2Esptree_2Emk__wf(A_27a),V0t1)),ap(c_2Esptree_2Emk__wf(A_27b),V1t2)) = ap(c_2Esptree_2Emk__wf(A_27a),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t1),V1t2)) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__mk__wf,axiom,
! [A_27a: del,V0x: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x)),V1v),ap(c_2Esptree_2Emk__wf(A_27a),V2t)) = ap(c_2Esptree_2Emk__wf(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x)),V1v),V2t)) ) ) ) ).
tff(conj_thm_2Esptree_2Edelete__mk__wf,axiom,
! [A_27a: del,V0x: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0x)),ap(c_2Esptree_2Emk__wf(A_27a),V1t)) = ap(c_2Esptree_2Emk__wf(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0x)),V1t)) ) ) ).
tff(conj_thm_2Esptree_2Eunion__LN,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Eunion(A_27a),V0t),c_2Esptree_2ELN(A_27a)) = V0t )
& ( ap(ap(c_2Esptree_2Eunion(A_27a),c_2Esptree_2ELN(A_27a)),V0t) = V0t ) ) ) ).
tff(conj_thm_2Esptree_2Einter__LN,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t),c_2Esptree_2ELN(A_27b)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Einter(A_27c,A_27a),c_2Esptree_2ELN(A_27c)),V0t) = c_2Esptree_2ELN(A_27c) ) ) ) ).
tff(conj_thm_2Esptree_2Eunion__assoc,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ! [V2t3: $i] :
( mem(V2t3,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),V0t1),ap(ap(c_2Esptree_2Eunion(A_27a),V1t2),V2t3)) = ap(ap(c_2Esptree_2Eunion(A_27a),ap(ap(c_2Esptree_2Eunion(A_27a),V0t1),V1t2)),V2t3) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einter__assoc,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27b))
=> ! [V2t3: $i] :
( mem(V2t3,ty_2Esptree_2Espt(A_27c))
=> ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t1),ap(ap(c_2Esptree_2Einter(A_27b,A_27c),V1t2),V2t3)) = ap(ap(c_2Esptree_2Einter(A_27a,A_27c),ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0t1),V1t2)),V2t3) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__compute,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4t2: $i] :
( mem(V4t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V0n))),V1t) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),V1t) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Esptree_2ELN(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(c_2Eoption_2ESOME(A_27a),V2a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(c_2Eoption_2ESOME(A_27a),V2a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),c_2Esptree_2ELN(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(c_2Eoption_2ESOME(A_27a),V2a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(c_2Eoption_2ESOME(A_27a),V2a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),c_2Esptree_2ELN(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Esptree_2ELS(A_27a),V2a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),V4t2) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),V4t2) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),c_2Esptree_2ELN(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Esptree_2ELS(A_27a),V2a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),V3t1) )
& ( ap(ap(c_2Esptree_2Elookup(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),V3t1) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__compute,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ! [V3a_27: $i] :
( mem(V3a_27,A_27a)
=> ! [V4t1: $i] :
( mem(V4t1,ty_2Esptree_2Espt(A_27a))
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V0n))),V1a),V2t) = ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),V2t) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V1a),c_2Esptree_2ELN(A_27a)) = ap(c_2Esptree_2ELS(A_27a),V1a) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V1a),ap(c_2Esptree_2ELS(A_27a),V3a_27)) = ap(c_2Esptree_2ELS(A_27a),V1a) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V1a),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V1a),V5t2) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V1a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V3a_27),V5t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V1a),V5t2) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),V1a),c_2Esptree_2ELN(A_27a)) = ap(c_2Esptree_2ELS(A_27a),V1a) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),V1a),ap(c_2Esptree_2ELS(A_27a),V3a_27)) = ap(c_2Esptree_2ELS(A_27a),V1a) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),V1a),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V1a),V5t2) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),V1a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V3a_27),V5t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V1a),V5t2) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),V1a),c_2Esptree_2ELN(A_27a)) = ap(ap(c_2Esptree_2EBN(A_27a),c_2Esptree_2ELN(A_27a)),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),c_2Esptree_2ELN(A_27a))) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),V1a),ap(c_2Esptree_2ELS(A_27a),V3a_27)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),c_2Esptree_2ELN(A_27a)),V3a_27),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),c_2Esptree_2ELN(A_27a))) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),V1a),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)) = ap(ap(c_2Esptree_2EBN(A_27a),V4t1),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),V5t2)) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),V1a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V3a_27),V5t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V3a_27),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),V5t2)) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),V1a),c_2Esptree_2ELN(A_27a)) = ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),c_2Esptree_2ELN(A_27a))),c_2Esptree_2ELN(A_27a)) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),V1a),ap(c_2Esptree_2ELS(A_27a),V3a_27)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),c_2Esptree_2ELN(A_27a))),V3a_27),c_2Esptree_2ELN(A_27a)) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),V1a),ap(ap(c_2Esptree_2EBN(A_27a),V4t1),V5t2)) = ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),V4t1)),V5t2) )
& ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),V1a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V4t1),V3a_27),V5t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0n)),V1a),V4t1)),V3a_27),V5t2) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Edelete__compute,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4t2: $i] :
( mem(V4t2,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V0n))),V1t) = ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V1t) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Esptree_2ELS(A_27a),V2a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Esptree_2ELS(A_27a),V2a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(c_2Esptree_2ELS(A_27a),V2a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = ap(ap(c_2Esptree_2Emk__BN(A_27a),V3t1),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V4t2)) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),V3t1),V2a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V4t2)) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Esptree_2ELS(A_27a),V2a)) = ap(c_2Esptree_2ELS(A_27a),V2a) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V3t1)),V4t2) )
& ( ap(ap(c_2Esptree_2Edelete(A_27a),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V2a),V4t2)) = ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V3t1)),V2a),V4t2) ) ) ) ) ) ) ).
tff(lamtp_f2416,type,
f2416: ( del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2416,axiom,
! [A_27a: del,V1y: $i] :
( mem(V1y,A_27a)
=> ! [V2x: tp__ty_2Enum_2Enum,V0R: $i] :
( mem(V0R,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),bool)))
=> ! [V3xs: $i] : ( ap(f2416(A_27a,V1y,V2x,V0R),V3xs) = ap(ap(V0R,V3xs),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V2x)),V1y)),V3xs)) ) ) ) ).
tff(lamtp_f2417,type,
f2417: ( del * $i * $i ) > $i ).
tff(lameq_f2417,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),bool)))
=> ! [V1y: $i] :
( mem(V1y,A_27a)
=> ! [V2x: tp__ty_2Enum_2Enum] : ( ap(f2417(A_27a,V0R,V1y),inj__ty_2Enum_2Enum(V2x)) = ap(c_2Ebool_2E_21(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),f2416(A_27a,V1y,V2x,V0R)) ) ) ) ).
tff(lamtp_f2418,type,
f2418: ( del * $i ) > $i ).
tff(lameq_f2418,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),bool)))
=> ! [V1y: $i] : ( ap(f2418(A_27a,V0R),V1y) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2417(A_27a,V0R,V1y)) ) ) ).
tff(lamtp_f2419,type,
f2419: del > $i ).
tff(lameq_f2419,axiom,
! [A_27a: del,V0R: $i] : ( ap(f2419(A_27a),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),V0R)),ap(c_2Ebool_2E_21(A_27a),f2418(A_27a,V0R))) ) ).
tff(lamtp_f2420,type,
f2420: ( del * $i * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2420,axiom,
! [A_27a: del,V7xs: $i] :
( mem(V7xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ! [V4fromAList: $i] :
( mem(V4fromAList,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a)))
=> ! [V8x: tp__ty_2Enum_2Enum,V9y: $i] : ( ap(f2420(A_27a,V7xs,V4fromAList,V8x),V9y) = ap(c_2Ecombin_2EI(ty_2Esptree_2Espt(A_27a)),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V8x)),V9y),ap(V4fromAList,V7xs))) ) ) ) ).
tff(lamtp_f2421,type,
f2421: ( del * $i * $i ) > $i ).
tff(lameq_f2421,axiom,
! [A_27a: del,V7xs: $i] :
( mem(V7xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ! [V4fromAList: $i] :
( mem(V4fromAList,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a)))
=> ! [V8x: tp__ty_2Enum_2Enum] : ( ap(f2421(A_27a,V7xs,V4fromAList),inj__ty_2Enum_2Enum(V8x)) = f2420(A_27a,V7xs,V4fromAList,V8x) ) ) ) ).
tff(lamtp_f2422,type,
f2422: ( del * $i * $i ) > $i ).
tff(lameq_f2422,axiom,
! [A_27a: del,V4fromAList: $i] :
( mem(V4fromAList,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a)))
=> ! [V6v: $i] :
( mem(V6v,ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))
=> ! [V7xs: $i] : ( ap(f2422(A_27a,V4fromAList,V6v),V7xs) = ap(ap(c_2Epair_2Epair__CASE(ty_2Esptree_2Espt(A_27a),ty_2Enum_2Enum,A_27a),V6v),f2421(A_27a,V7xs,V4fromAList)) ) ) ) ).
tff(lamtp_f2423,type,
f2423: ( del * $i ) > $i ).
tff(lameq_f2423,axiom,
! [A_27a: del,V4fromAList: $i] :
( mem(V4fromAList,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a)))
=> ! [V6v: $i] : ( ap(f2423(A_27a,V4fromAList),V6v) = f2422(A_27a,V4fromAList,V6v) ) ) ).
tff(lamtp_f2424,type,
f2424: ( del * $i ) > $i ).
tff(lameq_f2424,axiom,
! [A_27a: del,V4fromAList: $i] :
( mem(V4fromAList,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a)))
=> ! [V5a: $i] : ( ap(f2424(A_27a,V4fromAList),V5a) = ap(ap(ap(c_2Elist_2Elist__CASE(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),ty_2Esptree_2Espt(A_27a)),V5a),ap(c_2Ecombin_2EI(ty_2Esptree_2Espt(A_27a)),c_2Esptree_2ELN(A_27a))),f2423(A_27a,V4fromAList)) ) ) ).
tff(lamtp_f2425,type,
f2425: del > $i ).
tff(lameq_f2425,axiom,
! [A_27a: del,V4fromAList: $i] : ( ap(f2425(A_27a),V4fromAList) = f2424(A_27a,V4fromAList) ) ).
tff(ax_thm_2Esptree_2EfromAList__primitive__def,axiom,
! [A_27a: del] : ( c_2Esptree_2EfromAList(A_27a) = ap(ap(c_2Erelation_2EWFREC(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ty_2Esptree_2Espt(A_27a)),ap(c_2Emin_2E_40(arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),bool))),f2419(A_27a))),f2425(A_27a)) ) ).
tff(conj_thm_2Esptree_2EfromAList__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))))
& ! [V1x: tp__ty_2Enum_2Enum,V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3xs: $i] :
( mem(V3xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ( p(ap(V0P,V3xs))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V1x)),V2y)),V3xs))) ) ) ) )
=> ! [V4v: $i] :
( mem(V4v,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> p(ap(V0P,V4v)) ) ) ) ).
tff(conj_thm_2Esptree_2EfromAList__def,axiom,
! [A_27a: del] :
( ( ap(c_2Esptree_2EfromAList(A_27a),c_2Elist_2ENIL(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))) = c_2Esptree_2ELN(A_27a) )
& ! [V0y: $i] :
( mem(V0y,A_27a)
=> ! [V1xs: $i] :
( mem(V1xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ! [V2x: tp__ty_2Enum_2Enum] : ( ap(c_2Esptree_2EfromAList(A_27a),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V2x)),V0y)),V1xs)) = ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V2x)),V0y),ap(c_2Esptree_2EfromAList(A_27a),V1xs)) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__fromAList,axiom,
! [A_27a: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ! [V1x: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1x)),ap(c_2Esptree_2EfromAList(A_27a),V0ls)) = ap(ap(c_2Ealist_2EALOOKUP(A_27a,ty_2Enum_2Enum),V0ls),inj__ty_2Enum_2Enum(V1x)) ) ) ).
tff(conj_thm_2Esptree_2Edomain__fromAList,axiom,
! [A_27a: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(c_2Esptree_2EfromAList(A_27a),V0ls)) = ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),ty_2Enum_2Enum),c_2Epair_2EFST(ty_2Enum_2Enum,A_27a)),V0ls)) ) ) ).
tff(conj_thm_2Esptree_2Elookup__fromAList__toAList,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1x: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1x)),ap(c_2Esptree_2EfromAList(A_27a),ap(c_2Esptree_2EtoAList(A_27a),V0t))) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1x)),V0t) ) ) ).
tff(conj_thm_2Esptree_2Ewf__fromAList,axiom,
! [A_27a: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(c_2Esptree_2EfromAList(A_27a),V0ls))) ) ).
tff(conj_thm_2Esptree_2EfromAList__toAList,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> ( ap(c_2Esptree_2EfromAList(A_27a),ap(c_2Esptree_2EtoAList(A_27a),V0t)) = V0t ) ) ) ).
tff(conj_thm_2Esptree_2Eunion__insert__LN,axiom,
! [A_27a: del,V0x: tp__ty_2Enum_2Enum,V1y: $i] :
( mem(V1y,A_27a)
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Eunion(A_27a),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x)),V1y),c_2Esptree_2ELN(A_27a))),V2t2) = ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x)),V1y),V2t2) ) ) ) ).
tff(conj_thm_2Esptree_2EfromAList__append,axiom,
! [A_27a: del,V0l1: $i] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ! [V1l2: $i] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ( ap(c_2Esptree_2EfromAList(A_27a),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),V0l1),V1l2)) = ap(ap(c_2Esptree_2Eunion(A_27a),ap(c_2Esptree_2EfromAList(A_27a),V0l1)),ap(c_2Esptree_2EfromAList(A_27a),V1l2)) ) ) ) ).
tff(ax_thm_2Esptree_2Emap__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27b,A_27a))
=> ( ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V0f),c_2Esptree_2ELN(A_27b)) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1f: $i] :
( mem(V1f,arr(A_27b,A_27a))
=> ! [V2a: $i] :
( mem(V2a,A_27b)
=> ( ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V1f),ap(c_2Esptree_2ELS(A_27b),V2a)) = ap(c_2Esptree_2ELS(A_27a),ap(V1f,V2a)) ) ) )
& ! [V3f: $i] :
( mem(V3f,arr(A_27b,A_27a))
=> ! [V4t1: $i] :
( mem(V4t1,ty_2Esptree_2Espt(A_27b))
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V3f),ap(ap(c_2Esptree_2EBN(A_27b),V4t1),V5t2)) = ap(ap(c_2Esptree_2EBN(A_27a),ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V3f),V4t1)),ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V3f),V5t2)) ) ) ) )
& ! [V6f: $i] :
( mem(V6f,arr(A_27b,A_27a))
=> ! [V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27b))
=> ! [V8a: $i] :
( mem(V8a,A_27b)
=> ! [V9t2: $i] :
( mem(V9t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V6f),ap(ap(ap(c_2Esptree_2EBS(A_27b),V7t1),V8a),V9t2)) = ap(ap(ap(c_2Esptree_2EBS(A_27a),ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V6f),V7t1)),ap(V6f,V8a)),ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V6f),V9t2)) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2EtoList__map,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2EtoList(A_27b),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V0f),V1s)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(c_2Esptree_2EtoList(A_27a),V1s)) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__map,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27b),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V0f),V1s)) = ap(c_2Esptree_2Edomain(A_27a),V1s) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__map,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,ty_2Esptree_2Espt(A_27a))
=> ! [V2x: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V2x)),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V0f),V1s)) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2x)),V1s)) ) ) ) ).
tff(conj_thm_2Esptree_2Emap__LN,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V0f),V1t) = c_2Esptree_2ELN(A_27b) )
<=> ( V1t = c_2Esptree_2ELN(A_27a) ) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__map,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ( p(ap(c_2Esptree_2Ewf(A_27b),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V1f),V0t)))
<=> p(ap(c_2Esptree_2Ewf(A_27a),V0t)) ) ) ) ).
tff(conj_thm_2Esptree_2Emap__map__o,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27b,A_27c))
=> ! [V2g: $i] :
( mem(V2g,arr(A_27a,A_27b))
=> ( ap(ap(c_2Esptree_2Emap(A_27c,A_27b),V1f),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V2g),V0t)) = ap(ap(c_2Esptree_2Emap(A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1f),V2g)),V0t) ) ) ) ) ).
tff(conj_thm_2Esptree_2Emap__insert,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x: tp__ty_2Enum_2Enum,V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V0f),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1x)),V2y),V3z)) = ap(ap(ap(c_2Esptree_2Einsert(A_27b),inj__ty_2Enum_2Enum(V1x)),ap(V0f,V2y)),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),V0f),V3z)) ) ) ) ) ).
tff(lamtp_f2426,type,
f2426: ( del * del * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2426,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3v: $i] : ( ap(f2426(A_27a,A_27b,V0f,V2k),V3v) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V2k)),ap(V0f,V3v)) ) ) ).
tff(lamtp_f2427,type,
f2427: ( del * del * $i ) > $i ).
tff(lameq_f2427,axiom,
! [A_27b: del,A_27a: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2427(A_27b,A_27a,V0f),inj__ty_2Enum_2Enum(V2k)) = f2426(A_27a,A_27b,V0f,V2k) ) ) ).
tff(conj_thm_2Esptree_2Emap__fromAList,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1ls: $i] :
( mem(V1ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27b)))
=> ( ap(ap(c_2Esptree_2Emap(A_27a,A_27b),V0f),ap(c_2Esptree_2EfromAList(A_27b),V1ls)) = ap(c_2Esptree_2EfromAList(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27b),ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,A_27b,ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),f2427(A_27b,A_27a,V0f))),V1ls)) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__insert,axiom,
! [A_27a: del,V0x1: tp__ty_2Enum_2Enum,V1x2: tp__ty_2Enum_2Enum,V2v1: $i] :
( mem(V2v1,A_27a)
=> ! [V3v2: $i] :
( mem(V3v2,A_27a)
=> ! [V4t: $i] :
( mem(V4t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x1)),V2v1),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1x2)),V3v2),V4t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0x1)),inj__ty_2Enum_2Enum(V1x2))),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x1)),V2v1),V4t)),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1x2)),V3v2),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V0x1)),V2v1),V4t))) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einsert__shadow,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1a: tp__ty_2Enum_2Enum,V2b: $i] :
( mem(V2b,A_27a)
=> ! [V3c: $i] :
( mem(V3c,A_27a)
=> ( ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1a)),V2b),ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1a)),V3c),V0t)) = ap(ap(ap(c_2Esptree_2Einsert(A_27a),inj__ty_2Enum_2Enum(V1a)),V2b),V0t) ) ) ) ) ).
tff(ax_thm_2Esptree_2Espt__left__def,axiom,
! [A_27a: del] :
( ( ap(c_2Esptree_2Espt__left(A_27a),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ! [V0x: $i] :
( mem(V0x,A_27a)
=> ( ap(c_2Esptree_2Espt__left(A_27a),ap(c_2Esptree_2ELS(A_27a),V0x)) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Espt__left(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V1t1),V2t2)) = V1t1 ) ) )
& ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4x: $i] :
( mem(V4x,A_27a)
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Espt__left(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V4x),V5t2)) = V3t1 ) ) ) ) ) ).
tff(ax_thm_2Esptree_2Espt__right__def,axiom,
! [A_27a: del] :
( ( ap(c_2Esptree_2Espt__right(A_27a),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) )
& ! [V0x: $i] :
( mem(V0x,A_27a)
=> ( ap(c_2Esptree_2Espt__right(A_27a),ap(c_2Esptree_2ELS(A_27a),V0x)) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Espt__right(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V1t1),V2t2)) = V2t2 ) ) )
& ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4x: $i] :
( mem(V4x,A_27a)
=> ! [V5t2: $i] :
( mem(V5t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Espt__right(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V3t1),V4x),V5t2)) = V5t2 ) ) ) ) ) ).
tff(lamtp_f2428,type,
f2428: del > $i ).
tff(lameq_f2428,axiom,
! [A_27a: del,V0R: $i] : ( ap(f2428(A_27a),V0R) = ap(c_2Erelation_2EWF(ty_2Esptree_2Espt(A_27a)),V0R) ) ).
tff(lamtp_f2429,type,
f2429: del > $i ).
tff(lameq_f2429,axiom,
! [A_27a: del,V3x: $i] : ( ap(f2429(A_27a),V3x) = ap(c_2Ecombin_2EI(ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V3x)) ) ).
tff(lamtp_f2430,type,
f2430: del > $i ).
tff(lameq_f2430,axiom,
! [A_27a: del,V7x_27: $i] : ( ap(f2430(A_27a),V7x_27) = k(ty_2Esptree_2Espt(A_27a),ap(c_2Ecombin_2EI(ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V7x_27))) ) ).
tff(lamtp_f2431,type,
f2431: del > $i ).
tff(lameq_f2431,axiom,
! [A_27a: del,V2a: $i] : ( ap(f2431(A_27a),V2a) = ap(ap(ap(ap(ap(c_2Esptree_2Espt__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V2a),ap(c_2Ecombin_2EI(ty_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE(A_27a))),f2429(A_27a)),k(ty_2Esptree_2Espt(A_27a),k(ty_2Esptree_2Espt(A_27a),ap(c_2Ecombin_2EI(ty_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE(A_27a))))),k(ty_2Esptree_2Espt(A_27a),f2430(A_27a))) ) ).
tff(ax_thm_2Esptree_2Espt__center__primitive__def,axiom,
! [A_27a: del] : ( c_2Esptree_2Espt__center(A_27a) = ap(ap(c_2Erelation_2EWFREC(ty_2Esptree_2Espt(A_27a),ty_2Eoption_2Eoption(A_27a)),ap(c_2Emin_2E_40(arr(ty_2Esptree_2Espt(A_27a),arr(ty_2Esptree_2Espt(A_27a),bool))),f2428(A_27a))),k(arr(ty_2Esptree_2Espt(A_27a),ty_2Eoption_2Eoption(A_27a)),f2431(A_27a))) ) ).
tff(conj_thm_2Esptree_2Espt__center__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Esptree_2Espt(A_27a),bool))
=> ( ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> p(ap(V0P,ap(c_2Esptree_2ELS(A_27a),V1x))) )
& ! [V2t1: $i] :
( mem(V2t1,ty_2Esptree_2Espt(A_27a))
=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4t2: $i] :
( mem(V4t2,ty_2Esptree_2Espt(A_27a))
=> p(ap(V0P,ap(ap(ap(c_2Esptree_2EBS(A_27a),V2t1),V3x),V4t2))) ) ) )
& p(ap(V0P,c_2Esptree_2ELN(A_27a)))
& ! [V5v1: $i] :
( mem(V5v1,ty_2Esptree_2Espt(A_27a))
=> ! [V6v2: $i] :
( mem(V6v2,ty_2Esptree_2Espt(A_27a))
=> p(ap(V0P,ap(ap(c_2Esptree_2EBN(A_27a),V5v1),V6v2))) ) ) )
=> ! [V7v: $i] :
( mem(V7v,ty_2Esptree_2Espt(A_27a))
=> p(ap(V0P,V7v)) ) ) ) ).
tff(conj_thm_2Esptree_2Espt__center__def,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ! [V3v1: $i] :
( mem(V3v1,ty_2Esptree_2Espt(A_27a))
=> ! [V4v2: $i] :
( mem(V4v2,ty_2Esptree_2Espt(A_27a))
=> ( ( ap(c_2Esptree_2Espt__center(A_27a),ap(c_2Esptree_2ELS(A_27a),V0x)) = ap(c_2Eoption_2ESOME(A_27a),V0x) )
& ( ap(c_2Esptree_2Espt__center(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V1t1),V0x),V2t2)) = ap(c_2Eoption_2ESOME(A_27a),V0x) )
& ( ap(c_2Esptree_2Espt__center(A_27a),c_2Esptree_2ELN(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ( ap(c_2Esptree_2Espt__center(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V3v1),V4v2)) = c_2Eoption_2ENONE(A_27a) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Esubspt__eq,axiom,
! [A_27a: del] :
( ! [V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),c_2Esptree_2ELN(A_27a)),V0t))
<=> $true ) )
& ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),ap(c_2Esptree_2ELS(A_27a),V1x)),V2t))
<=> ( ap(c_2Esptree_2Espt__center(A_27a),V2t) = ap(c_2Eoption_2ESOME(A_27a),V1x) ) ) ) )
& ! [V3t1: $i] :
( mem(V3t1,ty_2Esptree_2Espt(A_27a))
=> ! [V4t2: $i] :
( mem(V4t2,ty_2Esptree_2Espt(A_27a))
=> ! [V5t: $i] :
( mem(V5t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V3t1),V4t2)),V5t))
<=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),V3t1),ap(c_2Esptree_2Espt__left(A_27a),V5t)))
& p(ap(ap(c_2Esptree_2Esubspt(A_27a),V4t2),ap(c_2Esptree_2Espt__right(A_27a),V5t))) ) ) ) ) )
& ! [V6t1: $i] :
( mem(V6t1,ty_2Esptree_2Espt(A_27a))
=> ! [V7x: $i] :
( mem(V7x,A_27a)
=> ! [V8t2: $i] :
( mem(V8t2,ty_2Esptree_2Espt(A_27a))
=> ! [V9t: $i] :
( mem(V9t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V6t1),V7x),V8t2)),V9t))
<=> ( ( ap(c_2Esptree_2Espt__center(A_27a),V9t) = ap(c_2Eoption_2ESOME(A_27a),V7x) )
& p(ap(ap(c_2Esptree_2Esubspt(A_27a),V6t1),ap(c_2Esptree_2Espt__left(A_27a),V9t)))
& p(ap(ap(c_2Esptree_2Esubspt(A_27a),V8t2),ap(c_2Esptree_2Espt__right(A_27a),V9t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Esubspt__lookup,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0t1),V1t2))
<=> ! [V2x: tp__ty_2Enum_2Enum,V3y: $i] :
( mem(V3y,A_27a)
=> ( ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2x)),V0t1) = ap(c_2Eoption_2ESOME(A_27a),V3y) )
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2x)),V1t2) = ap(c_2Eoption_2ESOME(A_27a),V3y) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Esubspt__domain,axiom,
! [V0t1: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone,V1t2: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] :
( p(ap(ap(c_2Esptree_2Esubspt(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t1)),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V1t2)))
<=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t1))),ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V1t2)))) ) ).
tff(conj_thm_2Esptree_2Esubspt__def,axiom,
! [A_27a: del,V0sp1: $i] :
( mem(V0sp1,ty_2Esptree_2Espt(A_27a))
=> ! [V1sp2: $i] :
( mem(V1sp2,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0sp1),V1sp2))
<=> ! [V2k: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2k)),ap(c_2Esptree_2Edomain(A_27a),V0sp1)))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2k)),ap(c_2Esptree_2Edomain(A_27a),V1sp2)))
& ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V1sp2) = ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V2k)),V0sp1) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Esubspt__refl,axiom,
! [A_27a: del,V0sp: $i] :
( mem(V0sp,ty_2Esptree_2Espt(A_27a))
=> p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0sp),V0sp)) ) ).
tff(conj_thm_2Esptree_2Esubspt__trans,axiom,
! [A_27a: del,V0sp1: $i] :
( mem(V0sp1,ty_2Esptree_2Espt(A_27a))
=> ! [V1sp2: $i] :
( mem(V1sp2,ty_2Esptree_2Espt(A_27a))
=> ! [V2sp3: $i] :
( mem(V2sp3,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0sp1),V1sp2))
& p(ap(ap(c_2Esptree_2Esubspt(A_27a),V1sp2),V2sp3)) )
=> p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0sp1),V2sp3)) ) ) ) ) ).
tff(conj_thm_2Esptree_2Esubspt__LN,axiom,
! [A_27a: del,V0sp: $i] :
( mem(V0sp,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),c_2Esptree_2ELN(A_27a)),V0sp))
<=> $true )
& ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0sp),c_2Esptree_2ELN(A_27a)))
<=> ( ap(c_2Esptree_2Edomain(A_27a),V0sp) = c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) ) ) ) ) ).
tff(ax_thm_2Esptree_2Efilter__v__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,bool))
=> ( ap(ap(c_2Esptree_2Efilter__v(A_27a),V0f),c_2Esptree_2ELN(A_27a)) = c_2Esptree_2ELN(A_27a) ) )
& ! [V1f: $i] :
( mem(V1f,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( ap(ap(c_2Esptree_2Efilter__v(A_27a),V1f),ap(c_2Esptree_2ELS(A_27a),V2x)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(V1f,V2x)),ap(c_2Esptree_2ELS(A_27a),V2x)),c_2Esptree_2ELN(A_27a)) ) ) )
& ! [V3f: $i] :
( mem(V3f,arr(A_27a,bool))
=> ! [V4l: $i] :
( mem(V4l,ty_2Esptree_2Espt(A_27a))
=> ! [V5r: $i] :
( mem(V5r,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Efilter__v(A_27a),V3f),ap(ap(c_2Esptree_2EBN(A_27a),V4l),V5r)) = ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Efilter__v(A_27a),V3f),V4l)),ap(ap(c_2Esptree_2Efilter__v(A_27a),V3f),V5r)) ) ) ) )
& ! [V6f: $i] :
( mem(V6f,arr(A_27a,bool))
=> ! [V7l: $i] :
( mem(V7l,ty_2Esptree_2Espt(A_27a))
=> ! [V8x: $i] :
( mem(V8x,A_27a)
=> ! [V9r: $i] :
( mem(V9r,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Efilter__v(A_27a),V6f),ap(ap(ap(c_2Esptree_2EBS(A_27a),V7l),V8x),V9r)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(V6f,V8x)),ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),ap(ap(c_2Esptree_2Efilter__v(A_27a),V6f),V7l)),V8x),ap(ap(c_2Esptree_2Efilter__v(A_27a),V6f),V9r))),ap(ap(c_2Esptree_2Emk__BN(A_27a),ap(ap(c_2Esptree_2Efilter__v(A_27a),V6f),V7l)),ap(ap(c_2Esptree_2Efilter__v(A_27a),V6f),V9r))) ) ) ) ) ) ) ).
tff(lamtp_f2432,type,
f2432: ( del * $i ) > $i ).
tff(lameq_f2432,axiom,
! [A_27a: del,V2f: $i] :
( mem(V2f,arr(A_27a,bool))
=> ! [V3v: $i] : ( ap(f2432(A_27a,V2f),V3v) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(V2f,V3v)),ap(c_2Eoption_2ESOME(A_27a),V3v)),c_2Eoption_2ENONE(A_27a)) ) ) ).
tff(conj_thm_2Esptree_2Elookup__filter__v,axiom,
! [A_27a: del,V0k: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,bool))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0k)),ap(ap(c_2Esptree_2Efilter__v(A_27a),V2f),V1t)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0k)),V1t)),c_2Eoption_2ENONE(A_27a)),f2432(A_27a,V2f)) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__filter__v,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,bool))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V0t))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Efilter__v(A_27a),V1f),V0t))) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__mk__BN,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(c_2Esptree_2Ewf(A_27a),V0t1))
& p(ap(c_2Esptree_2Ewf(A_27a),V1t2)) )
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Emk__BN(A_27a),V0t1),V1t2))) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__mk__BS,axiom,
! [A_27a: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27a))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ( ( p(ap(c_2Esptree_2Ewf(A_27a),V0t1))
& p(ap(c_2Esptree_2Ewf(A_27a),V1t2)) )
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(ap(c_2Esptree_2Emk__BS(A_27a),V0t1),V2a),V1t2))) ) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__mapi,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V1pt: $i] :
( mem(V1pt,ty_2Esptree_2Espt(A_27b))
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Emapi(A_27a,A_27b),V0f),V1pt))) ) ) ).
tff(conj_thm_2Esptree_2Elookup__mk__BN,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum,V1t1: $i] :
( mem(V1t1,ty_2Esptree_2Espt(A_27a))
=> ! [V2t2: $i] :
( mem(V2t2,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0i)),ap(ap(c_2Esptree_2Emk__BN(A_27a),V1t1),V2t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0i)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),c_2Eoption_2ENONE(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Esptree_2Espt(A_27a)),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V0i))),V1t1),V2t2))) ) ) ) ).
tff(lamtp_f2433,type,
f2433: ( del * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2433,axiom,
! [A_27a: del,V4k: tp__ty_2Enum_2Enum,V5v: $i] :
( mem(V5v,A_27a)
=> ! [V6a: $i] : ( ap(f2433(A_27a,V4k,V5v),V6a) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V4k)),V5v)),V6a) ) ) ).
tff(lamtp_f2434,type,
f2434: ( del * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2434,axiom,
! [A_27a: del,V4k: tp__ty_2Enum_2Enum,V5v: $i] : ( ap(f2434(A_27a,V4k),V5v) = f2433(A_27a,V4k,V5v) ) ).
tff(lamtp_f2435,type,
f2435: del > $i ).
tff(lameq_f2435,axiom,
! [A_27a: del,V4k: tp__ty_2Enum_2Enum] : ( ap(f2435(A_27a),inj__ty_2Enum_2Enum(V4k)) = f2434(A_27a,V4k) ) ).
tff(lamtp_f2436,type,
f2436: ( del * del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2436,axiom,
! [A_27a: del,A_27b: del,V8v: $i] :
( mem(V8v,A_27a)
=> ! [V7k: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b))
=> ! [V9a: $i] : ( ap(f2436(A_27a,A_27b,V8v,V7k,V0f),V9a) = ap(ap(c_2Elist_2ECONS(A_27b),ap(V0f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),inj__ty_2Enum_2Enum(V7k)),V8v))),V9a) ) ) ) ).
tff(lamtp_f2437,type,
f2437: ( del * del * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2437,axiom,
! [A_27b: del,A_27a: del,V7k: tp__ty_2Enum_2Enum,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b))
=> ! [V8v: $i] : ( ap(f2437(A_27b,A_27a,V7k,V0f),V8v) = f2436(A_27a,A_27b,V8v,V7k,V0f) ) ) ).
tff(lamtp_f2438,type,
f2438: ( del * del * $i ) > $i ).
tff(lameq_f2438,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b))
=> ! [V7k: tp__ty_2Enum_2Enum] : ( ap(f2438(A_27a,A_27b,V0f),inj__ty_2Enum_2Enum(V7k)) = f2437(A_27b,A_27a,V7k,V0f) ) ) ).
tff(conj_thm_2Esptree_2EMAP__foldi,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b))
=> ! [V1pt: $i] :
( mem(V1pt,ty_2Esptree_2Espt(A_27a))
=> ! [V2n: tp__ty_2Enum_2Enum,V3acc: $i] :
( mem(V3acc,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))
=> ( ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b),V0f),ap(ap(ap(ap(c_2Esptree_2Efoldi(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),A_27a),f2435(A_27a)),inj__ty_2Enum_2Enum(V2n)),V3acc),V1pt)) = ap(ap(ap(ap(c_2Esptree_2Efoldi(ty_2Elist_2Elist(A_27b),A_27a),f2438(A_27a,A_27b,V0f)),inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27b),V0f),V3acc)),V1pt) ) ) ) ) ).
tff(lamtp_f2439,type,
f2439: ( del * del * $i ) > $i ).
tff(lameq_f2439,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V2kv: $i] : ( ap(f2439(A_27a,A_27b,V0f),V2kv) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),ap(c_2Epair_2EFST(ty_2Enum_2Enum,A_27b),V2kv)),ap(ap(V0f,ap(c_2Epair_2EFST(ty_2Enum_2Enum,A_27b),V2kv)),ap(c_2Epair_2ESND(ty_2Enum_2Enum,A_27b),V2kv))) ) ) ).
tff(conj_thm_2Esptree_2Emapi__Alist,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V1pt: $i] :
( mem(V1pt,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(c_2Esptree_2Emapi(A_27a,A_27b),V0f),V1pt) = ap(c_2Esptree_2EfromAList(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27b),ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),f2439(A_27a,A_27b,V0f)),ap(c_2Esptree_2EtoAList(A_27b),V1pt))) ) ) ) ).
tff(conj_thm_2Esptree_2Edomain__mapi,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27b,A_27a)))
=> ! [V1pt: $i] :
( mem(V1pt,ty_2Esptree_2Espt(A_27b))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2Emapi(A_27a,A_27b),V0f),V1pt)) = ap(c_2Esptree_2Edomain(A_27b),V1pt) ) ) ) ).
tff(conj_thm_2Esptree_2Esize__domain,axiom,
! [A_27a: del,V0t: $i] :
( mem(V0t,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),V0t)) = surj__ty_2Enum_2Enum(ap(c_2Epred__set_2ECARD(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0t))) ) ) ).
tff(conj_thm_2Esptree_2Enum__set__domain__eq,axiom,
! [V0t1: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone,V1t2: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] :
( ( p(ap(c_2Esptree_2Ewf(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t1)))
& p(ap(c_2Esptree_2Ewf(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V1t2))) )
=> ( ( ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t1)) = ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V1t2)) )
<=> ( V0t1 = V1t2 ) ) ) ).
tff(conj_thm_2Esptree_2Eunion__num__set__sym,axiom,
! [V0t1: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone,V1t2: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] : ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Eunion(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t1)),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V1t2))) = surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Eunion(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V1t2)),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t1))) ) ).
tff(conj_thm_2Esptree_2Edifference__sub,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( mem(V0a,ty_2Esptree_2Espt(A_27a))
=> ! [V1b: $i] :
( mem(V1b,ty_2Esptree_2Espt(A_27b))
=> ( ( ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V0a),V1b) = c_2Esptree_2ELN(A_27a) )
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0a)),ap(c_2Esptree_2Edomain(A_27b),V1b))) ) ) ) ).
tff(conj_thm_2Esptree_2Ewf__difference,axiom,
! [A_27a: del,A_27b: del,V0t1: $i] :
( mem(V0t1,ty_2Esptree_2Espt(A_27a))
=> ! [V1t2: $i] :
( mem(V1t2,ty_2Esptree_2Espt(A_27b))
=> ( ( p(ap(c_2Esptree_2Ewf(A_27a),V0t1))
& p(ap(c_2Esptree_2Ewf(A_27b),V1t2)) )
=> p(ap(c_2Esptree_2Ewf(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V0t1),V1t2))) ) ) ) ).
tff(conj_thm_2Esptree_2Edelete__fail,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( p(ap(c_2Esptree_2Ewf(A_27a),V1t))
=> ( ~ p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),ap(c_2Esptree_2Edomain(A_27a),V1t)))
<=> ( ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V1t) = V1t ) ) ) ) ).
tff(conj_thm_2Esptree_2Esize__delete,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(c_2Esptree_2Esize(A_27a),ap(ap(c_2Esptree_2Edelete(A_27a),inj__ty_2Enum_2Enum(V0n)),V1t))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V0n)),V1t)),c_2Eoption_2ENONE(A_27a))),ap(c_2Esptree_2Esize(A_27a),V1t)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Esptree_2Esize(A_27a),V1t)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) ) ) ).
tff(conj_thm_2Esptree_2Elookup__fromList__outside,axiom,
! [A_27a: del,V0args: $i] :
( mem(V0args,ty_2Elist_2Elist(A_27a))
=> ! [V1k: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0args)),inj__ty_2Enum_2Enum(V1k)))
=> ( ap(ap(c_2Esptree_2Elookup(A_27a),inj__ty_2Enum_2Enum(V1k)),ap(c_2Esptree_2EfromList(A_27a),V0args)) = c_2Eoption_2ENONE(A_27a) ) ) ) ).
tff(conj_thm_2Esptree_2EIN__domain,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2t1: $i] :
( mem(V2t1,ty_2Esptree_2Espt(A_27a))
=> ! [V3t2: $i] :
( mem(V3t2,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),ap(c_2Esptree_2Edomain(A_27b),c_2Esptree_2ELN(A_27b))))
<=> $false )
& ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),ap(c_2Esptree_2Edomain(A_27a),ap(c_2Esptree_2ELS(A_27a),V1x))))
<=> ( V0n = fo__c_2Enum_2E0 ) )
& ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),ap(c_2Esptree_2Edomain(A_27a),ap(ap(c_2Esptree_2EBN(A_27a),V2t1),V3t2))))
<=> ( ( V0n != fo__c_2Enum_2E0 )
& p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Esptree_2Edomain(A_27a),V2t1))),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Esptree_2Edomain(A_27a),V3t2)))) ) )
& ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),ap(c_2Esptree_2Edomain(A_27a),ap(ap(ap(c_2Esptree_2EBS(A_27a),V2t1),V1x),V3t2))))
<=> ( ( V0n = fo__c_2Enum_2E0 )
| p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Esptree_2Edomain(A_27a),V2t1))),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Esptree_2Edomain(A_27a),V3t2)))) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2Emap__map__K,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0a: $i] :
( mem(V0a,A_27b)
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27c))
=> ! [V2t: $i] :
( mem(V2t,ty_2Esptree_2Espt(A_27a))
=> ( ap(ap(c_2Esptree_2Emap(A_27b,A_27c),ap(c_2Ecombin_2EK(A_27b,A_27c),V0a)),ap(ap(c_2Esptree_2Emap(A_27c,A_27a),V1f),V2t)) = ap(ap(c_2Esptree_2Emap(A_27b,A_27a),ap(c_2Ecombin_2EK(A_27b,A_27a),V0a)),V2t) ) ) ) ) ).
tff(conj_thm_2Esptree_2Elookup__map__K,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,A_27b)
=> ! [V1t: $i] :
( mem(V1t,ty_2Esptree_2Espt(A_27a))
=> ! [V2n: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Esptree_2Elookup(A_27b),inj__ty_2Enum_2Enum(V2n)),ap(ap(c_2Esptree_2Emap(A_27b,A_27a),ap(c_2Ecombin_2EK(A_27b,A_27a),V0x)),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2n)),ap(c_2Esptree_2Edomain(A_27a),V1t))),ap(c_2Eoption_2ESOME(A_27b),V0x)),c_2Eoption_2ENONE(A_27b)) ) ) ) ).
tff(ax_thm_2Esptree_2Espt__fold__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27b,arr(A_27a,A_27a)))
=> ! [V1acc: $i] :
( mem(V1acc,A_27a)
=> ( ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V0f),V1acc),c_2Esptree_2ELN(A_27b)) = V1acc ) ) )
& ! [V2f: $i] :
( mem(V2f,arr(A_27b,arr(A_27a,A_27a)))
=> ! [V3acc: $i] :
( mem(V3acc,A_27a)
=> ! [V4a: $i] :
( mem(V4a,A_27b)
=> ( ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V2f),V3acc),ap(c_2Esptree_2ELS(A_27b),V4a)) = ap(ap(V2f,V4a),V3acc) ) ) ) )
& ! [V5f: $i] :
( mem(V5f,arr(A_27b,arr(A_27a,A_27a)))
=> ! [V6acc: $i] :
( mem(V6acc,A_27a)
=> ! [V7t1: $i] :
( mem(V7t1,ty_2Esptree_2Espt(A_27b))
=> ! [V8t2: $i] :
( mem(V8t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V5f),V6acc),ap(ap(c_2Esptree_2EBN(A_27b),V7t1),V8t2)) = ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V5f),ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V5f),V6acc),V7t1)),V8t2) ) ) ) ) )
& ! [V9f: $i] :
( mem(V9f,arr(A_27b,arr(A_27a,A_27a)))
=> ! [V10acc: $i] :
( mem(V10acc,A_27a)
=> ! [V11t1: $i] :
( mem(V11t1,ty_2Esptree_2Espt(A_27b))
=> ! [V12a: $i] :
( mem(V12a,A_27b)
=> ! [V13t2: $i] :
( mem(V13t2,ty_2Esptree_2Espt(A_27b))
=> ( ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V9f),V10acc),ap(ap(ap(c_2Esptree_2EBS(A_27b),V11t1),V12a),V13t2)) = ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V9f),ap(ap(V9f,V12a),ap(ap(ap(c_2Esptree_2Espt__fold(A_27a,A_27b),V9f),V10acc),V11t1))),V13t2) ) ) ) ) ) ) ) ).
tff(conj_thm_2Esptree_2EIMP__size__LESS__size,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,ty_2Esptree_2Espt(A_27a))
=> ! [V1y: $i] :
( mem(V1y,ty_2Esptree_2Espt(A_27a))
=> ( ( p(ap(ap(c_2Esptree_2Esubspt(A_27a),V0x),V1y))
& ( ap(c_2Esptree_2Edomain(A_27a),V0x) != ap(c_2Esptree_2Edomain(A_27a),V1y) ) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Esptree_2Esize(A_27a),V0x)),ap(c_2Esptree_2Esize(A_27a),V1y))) ) ) ) ).
tff(conj_thm_2Esptree_2Esize__diff__less,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
( mem(V0x,ty_2Esptree_2Espt(A_27a))
=> ! [V1y: $i] :
( mem(V1y,ty_2Esptree_2Espt(A_27b))
=> ! [V2z: $i] :
( mem(V2z,ty_2Esptree_2Espt(A_27c))
=> ! [V3t: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27c),V2z)),ap(c_2Esptree_2Edomain(A_27b),V1y)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3t)),ap(c_2Esptree_2Edomain(A_27b),V1y)))
& ~ p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3t)),ap(c_2Esptree_2Edomain(A_27c),V2z)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3t)),ap(c_2Esptree_2Edomain(A_27a),V0x))) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Esptree_2Esize(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27b),V0x),V1y))),ap(c_2Esptree_2Esize(A_27a),ap(ap(c_2Esptree_2Edifference(A_27a,A_27c),V0x),V2z)))) ) ) ) ) ).
tff(conj_thm_2Esptree_2Einter__eq__LN,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Esptree_2Espt(A_27a))
=> ! [V1y: $i] :
( mem(V1y,ty_2Esptree_2Espt(A_27b))
=> ( ( ap(ap(c_2Esptree_2Einter(A_27a,A_27b),V0x),V1y) = c_2Esptree_2ELN(A_27a) )
<=> p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V0x)),ap(c_2Esptree_2Edomain(A_27b),V1y))) ) ) ) ).
tff(ax_thm_2Esptree_2Elist__to__num__set__def,axiom,
( ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(c_2Esptree_2Elist__to__num__set,c_2Elist_2ENIL(ty_2Enum_2Enum))) = surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(c_2Esptree_2ELN(ty_2Eone_2Eone)) )
& ! [V0n: tp__ty_2Enum_2Enum,V1ns: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] : ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(c_2Esptree_2Elist__to__num__set,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1ns)))) = surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(ap(c_2Esptree_2Einsert(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(V0n)),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)),ap(c_2Esptree_2Elist__to__num__set,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1ns)))) ) ) ).
tff(ax_thm_2Esptree_2Elist__insert__def,axiom,
( ! [V0t: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] : ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Elist__insert,c_2Elist_2ENIL(ty_2Enum_2Enum)),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V0t))) = V0t )
& ! [V1n: tp__ty_2Enum_2Enum,V2ns: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V3t: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] : ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Elist__insert,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V2ns))),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V3t))) = surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Elist__insert,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V2ns)),ap(ap(ap(c_2Esptree_2Einsert(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V3t)))) ) ) ).
tff(conj_thm_2Esptree_2Edomain__list__to__num__set,axiom,
! [V0x: tp__ty_2Enum_2Enum,V1xs: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0x)),ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),ap(c_2Esptree_2Elist__to__num__set,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1xs)))))
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0x)),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1xs)))) ) ).
tff(conj_thm_2Esptree_2Edomain__list__insert,axiom,
! [V0xs: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2t: tp__c_ty_2Esptree_2Espt_ty_2Eone_2Eone] :
( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1x)),ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),ap(ap(c_2Esptree_2Elist__insert,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V0xs)),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V2t)))))
<=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1x)),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V0xs))))
| p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1x)),ap(c_2Esptree_2Edomain(ty_2Eone_2Eone),inj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(V2t)))) ) ) ).
tff(conj_thm_2Esptree_2Edomain__FOLDR__delete,axiom,
! [A_27a: del,V0ls: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V1live: $i] :
( mem(V1live,ty_2Esptree_2Espt(A_27a))
=> ( ap(c_2Esptree_2Edomain(A_27a),ap(ap(ap(c_2Elist_2EFOLDR(ty_2Enum_2Enum,ty_2Esptree_2Espt(A_27a)),c_2Esptree_2Edelete(A_27a)),V1live),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V0ls))) = ap(ap(c_2Epred__set_2EDIFF(ty_2Enum_2Enum),ap(c_2Esptree_2Edomain(A_27a),V1live)),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V0ls))) ) ) ).
tff(conj_thm_2Esptree_2Elookup__list__to__num__set,axiom,
! [V0x: tp__ty_2Enum_2Enum,V1xs: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] : ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Elookup(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(V0x)),ap(c_2Esptree_2Elist__to__num__set,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1xs)))) = surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone(ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Eone_2Eone)),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0x)),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1xs)))),ap(c_2Eoption_2ESOME(ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone))),c_2Eoption_2ENONE(ty_2Eone_2Eone))) ) ).
tff(conj_thm_2Esptree_2Elist__to__num__set__append,axiom,
! [V0l1: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V1l2: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] : ( surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(c_2Esptree_2Elist__to__num__set,ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V0l1)),inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1l2)))) = surj__c_ty_2Esptree_2Espt_ty_2Eone_2Eone(ap(ap(c_2Esptree_2Eunion(ty_2Eone_2Eone),ap(c_2Esptree_2Elist__to__num__set,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V0l1))),ap(c_2Esptree_2Elist__to__num__set,inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum(V1l2)))) ) ).
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