TPTP Problem File: SWW476^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW476^1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 197, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_100_thf_l197 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 469 ( 93 unt; 164 typ; 0 def)
% Number of atoms : 737 ( 365 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 3211 ( 97 ~; 2 |; 12 &;2671 @)
% ( 40 <=>; 375 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 31 ( 30 usr)
% Number of type conns : 921 ( 921 >; 0 *; 0 +; 0 <<)
% Number of symbols : 137 ( 134 usr; 8 con; 0-5 aty)
% ( 7 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 1263 ( 0 ^;1228 !; 35 ?;1263 :)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:07:10
%------------------------------------------------------------------------------
%----Should-be-implicit typings (30)
thf(ty_ty_tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
exp_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_J,type,
list_exp_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
list_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J,type,
list_option_ty: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J,type,
list_option_val: $tType ).
thf(ty_ty_tc__List__Olist_Itc__String__Ochar_J,type,
list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Type__Oty_J,type,
list_ty: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Value__Oval_J,type,
list_val: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
list_P1999446415t_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
list_P1964248404on_val: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
nat: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__Type__Oty_J,type,
option_ty: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__Value__Oval_J,type,
option_val: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_,type,
option1728594148on_val: $tType ).
thf(ty_ty_tc__Type__Oty,type,
ty: $tType ).
thf(ty_ty_tc__Value__Oval,type,
val: $tType ).
thf(ty_ty_tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
produc2090907612on_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
produc1282892786on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__pro,type,
produc1285161482t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_Itc__List__,type,
produc2088785539on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc__Strin,type,
produc1278157519t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Olist_Itc_,type,
produc220283002t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__List__Ol,type,
produc662261637t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
produc1581780743on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
produc1746408499on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_,type,
produc349695911t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_I,type,
produc1368416213on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__,type,
produc1406897475t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc,type,
produc1826280281t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
produc652964533on_val: $tType ).
%----Explicit typings (148)
thf(sy_c_BigStep_Oeval,type,
eval: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J,type,
final_list_char: exp_list_char > $o ).
thf(sy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
conf_P373316194t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > val > ty > $o ).
thf(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
hconf_97414254t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
lconf_496643946t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_val ) > ( list_char > option_ty ) > $o ).
thf(sy_c_Expr_Oexp_OTryCatch_000tc__List__Olist_Itc__String__Ochar_J,type,
tryCatch_list_char: exp_list_char > list_char > list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
val_list_char: val > exp_list_char ).
thf(sy_c_Fun_Ocomp_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J_000t,type,
comp_l1825390573t_char: ( list_option_val > list_val ) > ( list_list_char > list_option_val ) > list_list_char > list_val ).
thf(sy_c_Fun_Ocomp_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval_000t,type,
comp_o1129292306t_char: ( option_val > val ) > ( list_char > option_val ) > list_char > val ).
thf(sy_c_Fun_Ooverride__on_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oo,type,
overri2012515291on_val: ( list_char > option_val ) > ( list_char > option_val ) > ( list_char > $o ) > list_char > option_val ).
thf(sy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J,type,
distinct_list_char: list_list_char > $o ).
thf(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
list_a52822260ion_ty: ( exp_list_char > option_ty > $o ) > list_exp_list_char > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oop,type,
list_a1834344429ion_ty: ( list_char > option_ty > $o ) > list_list_char > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_,type,
list_a283687028t_char: ( option_ty > exp_list_char > $o ) > list_option_ty > list_exp_list_char > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist,type,
list_a839443437t_char: ( option_ty > list_char > $o ) > list_option_ty > list_list_char > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
list_a2039389316_ty_ty: ( option_ty > ty > $o ) > list_option_ty > list_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
list_a1073113293ty_val: ( option_ty > val > $o ) > list_option_ty > list_val > $o ).
thf(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
list_a1880637950ion_ty: ( ty > option_ty > $o ) > list_ty > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty,type,
list_all2_ty_ty: ( ty > ty > $o ) > list_ty > list_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
list_a1462908359ion_ty: ( val > option_ty > $o ) > list_val > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Type__Oty,type,
list_all2_val_ty: ( val > ty > $o ) > list_val > list_ty > $o ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__,type,
map_ex101166958t_char: ( exp_list_char > exp_list_char ) > list_exp_list_char > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___001,type,
map_ex2109939687t_char: ( exp_list_char > list_char ) > list_exp_list_char > list_list_char ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___002,type,
map_ex1548475405ion_ty: ( exp_list_char > option_ty ) > list_exp_list_char > list_option_ty ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___003,type,
map_ex1598883030on_val: ( exp_list_char > option_val ) > list_exp_list_char > list_option_val ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___004,type,
map_exp_list_char_ty: ( exp_list_char > ty ) > list_exp_list_char > list_ty ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___005,type,
map_ex740158547ar_val: ( exp_list_char > val ) > list_exp_list_char > list_val ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___006,type,
map_ex920537562on_val: ( exp_list_char > produc1746408499on_val ) > list_exp_list_char > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Expr__Oexp_Itc__Li,type,
map_li1249123943t_char: ( list_char > exp_list_char ) > list_list_char > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__S,type,
map_li1333403488t_char: ( list_char > list_char ) > list_list_char > list_list_char ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It,type,
map_li771939206ion_ty: ( list_char > option_ty ) > list_list_char > list_option_ty ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It_007,type,
map_li50976719on_val: ( list_char > option_val ) > list_list_char > list_option_val ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_list_char_ty: ( list_char > ty ) > list_list_char > list_ty ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_list_char_val: ( list_char > val ) > list_list_char > list_val ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc,type,
map_li772299987on_val: ( list_char > produc1746408499on_val ) > list_list_char > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_Itc__Li,type,
map_op1779340173t_char: ( option_ty > exp_list_char ) > list_option_ty > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_Itc__S,type,
map_op1924521862t_char: ( option_ty > list_char ) > list_option_ty > list_list_char ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Option__Ooption_It,type,
map_op1363057580ion_ty: ( option_ty > option_ty ) > list_option_ty > list_option_ty ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
map_option_ty_ty: ( option_ty > ty ) > list_option_ty > list_ty ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
map_option_ty_val: ( option_ty > val ) > list_option_ty > list_val ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval,type,
map_option_val_val: ( option_val > val ) > list_option_val > list_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
map_ty_exp_list_char: ( ty > exp_list_char ) > list_ty > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__List__Olist_Itc__String__Ochar_J,type,
map_ty_list_char: ( ty > list_char ) > list_ty > list_list_char ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
map_ty_option_ty: ( ty > option_ty ) > list_ty > list_option_ty ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Value__Oval_J,type,
map_ty_option_val: ( ty > option_val ) > list_ty > list_option_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Type__Oty,type,
map_ty_ty: ( ty > ty ) > list_ty > list_ty ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Value__Oval,type,
map_ty_val: ( ty > val ) > list_ty > list_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
map_ty908261490on_val: ( ty > produc1746408499on_val ) > list_ty > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String,type,
map_va1934808527t_char: ( val > exp_list_char ) > list_val > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__List__Olist_Itc__String__Ochar_J,type,
map_val_list_char: ( val > list_char ) > list_val > list_list_char ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
map_val_option_ty: ( val > option_ty ) > list_val > list_option_ty ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Value__Oval_J,type,
map_val_option_val: ( val > option_val ) > list_val > list_option_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Type__Oty,type,
map_val_ty: ( val > ty ) > list_val > list_ty ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Value__Oval,type,
map_val_val: ( val > val ) > list_val > list_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
map_va32158779on_val: ( val > produc1746408499on_val ) > list_val > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
map_Pr816758342on_val: ( produc1746408499on_val > produc1746408499on_val ) > list_P1964248404on_val > list_P1964248404on_val ).
thf(sy_c_List_Oset_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
set_exp_list_char: list_exp_list_char > exp_list_char > $o ).
thf(sy_c_List_Oset_000tc__List__Olist_Itc__String__Ochar_J,type,
set_list_char: list_list_char > list_char > $o ).
thf(sy_c_List_Oset_000tc__Option__Ooption_Itc__Type__Oty_J,type,
set_option_ty: list_option_ty > option_ty > $o ).
thf(sy_c_List_Oset_000tc__Type__Oty,type,
set_ty: list_ty > ty > $o ).
thf(sy_c_List_Oset_000tc__Value__Oval,type,
set_val: list_val > val > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
set_Pr1184195362on_val: list_P1964248404on_val > produc1746408499on_val > $o ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_add_list_char_ty: ( list_char > option_ty ) > ( list_char > option_ty ) > list_char > option_ty ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_ad325961431ar_val: ( list_char > option_val ) > ( list_char > option_val ) > list_char > option_val ).
thf(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_up891053837har_ty: ( list_char > option_ty ) > list_list_char > list_ty > list_char > option_ty ).
thf(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_up1085636310ar_val: ( list_char > option_val ) > list_list_char > list_val > list_char > option_val ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
size_s1143674878t_char: list_exp_list_char > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
size_s2113983095t_char: list_list_char > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__O,type,
size_s1050794909ion_ty: list_option_ty > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__,type,
size_s1595297126on_val: list_option_val > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Type__Oty_J,type,
size_size_list_ty: list_ty > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Value__Oval_J,type,
size_size_list_val: list_val > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oe,type,
size_s350851178on_val: list_P1964248404on_val > nat ).
thf(sy_c_Objects_Ohext,type,
hext: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Objects_Otypeof__h,type,
typeof_h: ( nat > option1728594148on_val ) > val > option_ty ).
thf(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
some_ty: ty > option_ty ).
thf(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
some_val: val > option_val ).
thf(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_06,type,
some_P451527732on_val: produc2088785539on_val > option1728594148on_val ).
thf(sy_c_Option_Othe_000tc__Type__Oty,type,
the_ty: option_ty > ty ).
thf(sy_c_Option_Othe_000tc__Value__Oval,type,
the_val: option_val > val ).
thf(sy_c_Option_Othe_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__pr,type,
the_Pr1885945130on_val: option1728594148on_val > produc2088785539on_val ).
thf(sy_c_Product__Type_OPair_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
produc755559506on_val: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc235638504on_val: exp_list_char > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
produc921874948t_char: list_list_char > produc220283002t_char > produc1285161482t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__pr,type,
produc926070009on_val: list_char > ( produc1278157519t_char > option_val ) > produc2088785539on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
produc1909267824t_char: list_ty > produc662261637t_char > produc220283002t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
produc1916172923t_char: list_val > exp_list_char > produc662261637t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
produc259392253on_val: produc2090907612on_val > produc2090907612on_val > produc1581780743on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc833389609on_val: produc1282892786on_val > produc1282892786on_val > produc1746408499on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
produc24551831t_char: produc1285161482t_char > produc1285161482t_char > produc349695911t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062,type,
produc1773146955on_val: produc2088785539on_val > produc2088785539on_val > produc1368416213on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
produc57279289t_char: produc220283002t_char > produc220283002t_char > produc1406897475t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
produc1299387215t_char: produc662261637t_char > produc662261637t_char > produc1826280281t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
produc345758123on_val: produc1746408499on_val > produc1746408499on_val > produc652964533on_val ).
thf(sy_c_Product__Type_Ocurry_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
produc1402621651_val_o: ( produc2090907612on_val > $o ) > ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_,type,
produc1287763389_val_o: ( produc1282892786on_val > $o ) > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar,type,
produc193646727char_o: ( produc1285161482t_char > $o ) > list_list_char > produc220283002t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__p,type,
produc1177570924_val_o: ( produc2088785539on_val > $o ) > list_char > ( produc1278157519t_char > option_val ) > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__L,type,
produc786676533char_o: ( produc220283002t_char > $o ) > list_ty > produc662261637t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oex,type,
produc1072551658char_o: ( produc662261637t_char > $o ) > list_val > exp_list_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc803302844_val_o: ( produc1746408499on_val > $o ) > produc1282892786on_val > produc1282892786on_val > $o ).
thf(sy_c_SmallStep_Oblocks,type,
blocks: produc1285161482t_char > exp_list_char ).
thf(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > produc1746408499on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__,type,
transi466770671on_val: ( produc1581780743on_val > $o ) > produc1581780743on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
transi2118771717on_val: ( produc1746408499on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist_,type,
transi122195895t_char: ( produc349695911t_char > $o ) > produc349695911t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
transi1669211542on_val: ( produc1368416213on_val > $o ) > produc1368416213on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_,type,
transi1257872013t_char: ( produc1406897475t_char > $o ) > produc1406897475t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Value__Oval_,type,
transi1789604888t_char: ( produc1826280281t_char > $o ) > produc1826280281t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
transi130214086on_val: ( produc652964533on_val > $o ) > produc652964533on_val > $o ).
thf(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
widen_2090681816t_char: list_P1999446415t_char > ty > ty > $o ).
thf(sy_c_WellTypeRT_OWTrt,type,
wTrt: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > exp_list_char > ty > $o ).
thf(sy_c_WellTypeRT_OWTrts,type,
wTrts: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > list_exp_list_char > list_ty > $o ).
thf(sy_c_fequal_000tc__Type__Oty,type,
fequal_ty: ty > ty > $o ).
thf(sy_c_member_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
member_exp_list_char: exp_list_char > ( exp_list_char > $o ) > $o ).
thf(sy_c_member_000tc__List__Olist_Itc__String__Ochar_J,type,
member_list_char: list_char > ( list_char > $o ) > $o ).
thf(sy_c_member_000tc__Option__Ooption_Itc__Type__Oty_J,type,
member_option_ty: option_ty > ( option_ty > $o ) > $o ).
thf(sy_c_member_000tc__Type__Oty,type,
member_ty: ty > ( ty > $o ) > $o ).
thf(sy_c_member_000tc__Value__Oval,type,
member_val: val > ( val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_,type,
member565037556on_val: produc1581780743on_val > ( produc1581780743on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
member1913460000on_val: produc1746408499on_val > ( produc1746408499on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
member1420286996t_char: produc349695911t_char > ( produc349695911t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_It,type,
member1235075778on_val: produc1368416213on_val > ( produc1368416213on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
member125098544t_char: produc1406897475t_char > ( produc1406897475t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
member1161907014t_char: produc1826280281t_char > ( produc1826280281t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
member1714424482on_val: produc652964533on_val > ( produc652964533on_val > $o ) > $o ).
thf(sy_v_E,type,
e_1: list_char > option_ty ).
thf(sy_v_P,type,
p: list_P1999446415t_char ).
thf(sy_v_T,type,
t: ty ).
thf(sy_v_Ts,type,
ts: list_ty ).
thf(sy_v_Vs,type,
vs_1: list_list_char ).
thf(sy_v_e,type,
e: exp_list_char ).
thf(sy_v_h,type,
h: nat > option1728594148on_val ).
thf(sy_v_vs,type,
vs: list_val ).
%----Relevant facts (300)
thf(fact_0_widens__refl,axiom,
! [P: list_P1999446415t_char,Xs_16: list_ty] : ( list_all2_ty_ty @ ( widen_2090681816t_char @ P ) @ Xs_16 @ Xs_16 ) ).
thf(fact_1_widen__refl,axiom,
! [P_26: list_P1999446415t_char,T_9: ty] : ( widen_2090681816t_char @ P_26 @ T_9 @ T_9 ) ).
thf(fact_2_widens__trans,axiom,
! [Us: list_ty,P_25: list_P1999446415t_char,Ss: list_ty,Ts_7: list_ty] :
( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_25 ) @ Ss @ Ts_7 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_25 ) @ Ts_7 @ Us )
=> ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_25 ) @ Ss @ Us ) ) ) ).
thf(fact_3_list__all2__lengthD,axiom,
! [P_24: val > ty > $o,Xs_15: list_val,Ys_10: list_ty] :
( ( list_all2_val_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_val @ Xs_15 )
= ( size_size_list_ty @ Ys_10 ) ) ) ).
thf(fact_4_list__all2__lengthD,axiom,
! [P_24: ty > ty > $o,Xs_15: list_ty,Ys_10: list_ty] :
( ( list_all2_ty_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_ty @ Xs_15 )
= ( size_size_list_ty @ Ys_10 ) ) ) ).
thf(fact_5_list__all2__lengthD,axiom,
! [P_24: option_ty > exp_list_char > $o,Xs_15: list_option_ty,Ys_10: list_exp_list_char] :
( ( list_a283687028t_char @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_s1143674878t_char @ Ys_10 ) ) ) ).
thf(fact_6_list__all2__lengthD,axiom,
! [P_24: option_ty > val > $o,Xs_15: list_option_ty,Ys_10: list_val] :
( ( list_a1073113293ty_val @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_size_list_val @ Ys_10 ) ) ) ).
thf(fact_7_list__all2__lengthD,axiom,
! [P_24: option_ty > ty > $o,Xs_15: list_option_ty,Ys_10: list_ty] :
( ( list_a2039389316_ty_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_size_list_ty @ Ys_10 ) ) ) ).
thf(fact_8_list__all2__lengthD,axiom,
! [P_24: option_ty > list_char > $o,Xs_15: list_option_ty,Ys_10: list_list_char] :
( ( list_a839443437t_char @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_s2113983095t_char @ Ys_10 ) ) ) ).
thf(fact_9_list__all2__lengthD,axiom,
! [P_24: exp_list_char > option_ty > $o,Xs_15: list_exp_list_char,Ys_10: list_option_ty] :
( ( list_a52822260ion_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_s1143674878t_char @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_10_list__all2__lengthD,axiom,
! [P_24: val > option_ty > $o,Xs_15: list_val,Ys_10: list_option_ty] :
( ( list_a1462908359ion_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_val @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_11_list__all2__lengthD,axiom,
! [P_24: ty > option_ty > $o,Xs_15: list_ty,Ys_10: list_option_ty] :
( ( list_a1880637950ion_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_ty @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_12_list__all2__lengthD,axiom,
! [P_24: list_char > option_ty > $o,Xs_15: list_list_char,Ys_10: list_option_ty] :
( ( list_a1834344429ion_ty @ P_24 @ Xs_15 @ Ys_10 )
=> ( ( size_s2113983095t_char @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_13_length__map,axiom,
! [F_14: list_char > val,Xs_14: list_list_char] :
( ( size_size_list_val @ ( map_list_char_val @ F_14 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_14_length__map,axiom,
! [F_14: val > exp_list_char,Xs_14: list_val] :
( ( size_s1143674878t_char @ ( map_va1934808527t_char @ F_14 @ Xs_14 ) )
= ( size_size_list_val @ Xs_14 ) ) ).
thf(fact_15_length__map,axiom,
! [F_14: ty > option_ty,Xs_14: list_ty] :
( ( size_s1050794909ion_ty @ ( map_ty_option_ty @ F_14 @ Xs_14 ) )
= ( size_size_list_ty @ Xs_14 ) ) ).
thf(fact_16_length__map,axiom,
! [F_14: val > option_ty,Xs_14: list_val] :
( ( size_s1050794909ion_ty @ ( map_val_option_ty @ F_14 @ Xs_14 ) )
= ( size_size_list_val @ Xs_14 ) ) ).
thf(fact_17_length__map,axiom,
! [F_14: exp_list_char > option_ty,Xs_14: list_exp_list_char] :
( ( size_s1050794909ion_ty @ ( map_ex1548475405ion_ty @ F_14 @ Xs_14 ) )
= ( size_s1143674878t_char @ Xs_14 ) ) ).
thf(fact_18_length__map,axiom,
! [F_14: list_char > option_ty,Xs_14: list_list_char] :
( ( size_s1050794909ion_ty @ ( map_li771939206ion_ty @ F_14 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_19_length__map,axiom,
! [F_14: option_ty > exp_list_char,Xs_14: list_option_ty] :
( ( size_s1143674878t_char @ ( map_op1779340173t_char @ F_14 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_20_length__map,axiom,
! [F_14: option_ty > val,Xs_14: list_option_ty] :
( ( size_size_list_val @ ( map_option_ty_val @ F_14 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_21_length__map,axiom,
! [F_14: option_ty > ty,Xs_14: list_option_ty] :
( ( size_size_list_ty @ ( map_option_ty_ty @ F_14 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_22_length__map,axiom,
! [F_14: option_ty > list_char,Xs_14: list_option_ty] :
( ( size_s2113983095t_char @ ( map_op1924521862t_char @ F_14 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_23_length__map,axiom,
! [F_14: list_char > list_char,Xs_14: list_list_char] :
( ( size_s2113983095t_char @ ( map_li1333403488t_char @ F_14 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_24_length__map,axiom,
! [F_14: produc1746408499on_val > produc1746408499on_val,Xs_14: list_P1964248404on_val] :
( ( size_s350851178on_val @ ( map_Pr816758342on_val @ F_14 @ Xs_14 ) )
= ( size_s350851178on_val @ Xs_14 ) ) ).
thf(fact_25_length__map,axiom,
! [F_14: option_val > val,Xs_14: list_option_val] :
( ( size_size_list_val @ ( map_option_val_val @ F_14 @ Xs_14 ) )
= ( size_s1595297126on_val @ Xs_14 ) ) ).
thf(fact_26_length__map,axiom,
! [F_14: list_char > option_val,Xs_14: list_list_char] :
( ( size_s1595297126on_val @ ( map_li50976719on_val @ F_14 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_27_length__map,axiom,
! [F_14: option_ty > option_ty,Xs_14: list_option_ty] :
( ( size_s1050794909ion_ty @ ( map_op1363057580ion_ty @ F_14 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_28_map__eq__imp__length__eq,axiom,
! [F_13: val > option_ty,Xs_13: list_val,G_7: option_ty > option_ty,Ys_9: list_option_ty] :
( ( ( map_val_option_ty @ F_13 @ Xs_13 )
= ( map_op1363057580ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_29_map__eq__imp__length__eq,axiom,
! [F_13: ty > option_ty,Xs_13: list_ty,G_7: option_ty > option_ty,Ys_9: list_option_ty] :
( ( ( map_ty_option_ty @ F_13 @ Xs_13 )
= ( map_op1363057580ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_30_map__eq__imp__length__eq,axiom,
! [F_13: val > exp_list_char,Xs_13: list_val,G_7: option_ty > exp_list_char,Ys_9: list_option_ty] :
( ( ( map_va1934808527t_char @ F_13 @ Xs_13 )
= ( map_op1779340173t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_31_map__eq__imp__length__eq,axiom,
! [F_13: list_char > val,Xs_13: list_list_char,G_7: option_ty > val,Ys_9: list_option_ty] :
( ( ( map_list_char_val @ F_13 @ Xs_13 )
= ( map_option_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_32_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > option_ty,Xs_13: list_option_ty,G_7: val > option_ty,Ys_9: list_val] :
( ( ( map_op1363057580ion_ty @ F_13 @ Xs_13 )
= ( map_val_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_33_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > option_ty,Xs_13: list_option_ty,G_7: ty > option_ty,Ys_9: list_ty] :
( ( ( map_op1363057580ion_ty @ F_13 @ Xs_13 )
= ( map_ty_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_34_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > exp_list_char,Xs_13: list_option_ty,G_7: val > exp_list_char,Ys_9: list_val] :
( ( ( map_op1779340173t_char @ F_13 @ Xs_13 )
= ( map_va1934808527t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_35_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > val,Xs_13: list_option_ty,G_7: list_char > val,Ys_9: list_list_char] :
( ( ( map_option_ty_val @ F_13 @ Xs_13 )
= ( map_list_char_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_36_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_val,Xs_13: list_list_char,G_7: exp_list_char > option_val,Ys_9: list_exp_list_char] :
( ( ( map_li50976719on_val @ F_13 @ Xs_13 )
= ( map_ex1598883030on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_37_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > option_ty,Xs_13: list_option_ty,G_7: exp_list_char > option_ty,Ys_9: list_exp_list_char] :
( ( ( map_op1363057580ion_ty @ F_13 @ Xs_13 )
= ( map_ex1548475405ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_38_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > exp_list_char,Xs_13: list_option_ty,G_7: exp_list_char > exp_list_char,Ys_9: list_exp_list_char] :
( ( ( map_op1779340173t_char @ F_13 @ Xs_13 )
= ( map_ex101166958t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_39_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > val,Xs_13: list_option_ty,G_7: exp_list_char > val,Ys_9: list_exp_list_char] :
( ( ( map_option_ty_val @ F_13 @ Xs_13 )
= ( map_ex740158547ar_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_40_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > list_char,Xs_13: list_option_ty,G_7: exp_list_char > list_char,Ys_9: list_exp_list_char] :
( ( ( map_op1924521862t_char @ F_13 @ Xs_13 )
= ( map_ex2109939687t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_41_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > ty,Xs_13: list_option_ty,G_7: exp_list_char > ty,Ys_9: list_exp_list_char] :
( ( ( map_option_ty_ty @ F_13 @ Xs_13 )
= ( map_exp_list_char_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_42_map__eq__imp__length__eq,axiom,
! [F_13: list_char > list_char,Xs_13: list_list_char,G_7: val > list_char,Ys_9: list_val] :
( ( ( map_li1333403488t_char @ F_13 @ Xs_13 )
= ( map_val_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_43_map__eq__imp__length__eq,axiom,
! [F_13: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: val > produc1746408499on_val,Ys_9: list_val] :
( ( ( map_Pr816758342on_val @ F_13 @ Xs_13 )
= ( map_va32158779on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_44_map__eq__imp__length__eq,axiom,
! [F_13: option_val > val,Xs_13: list_option_val,G_7: val > val,Ys_9: list_val] :
( ( ( map_option_val_val @ F_13 @ Xs_13 )
= ( map_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_45_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_val,Xs_13: list_list_char,G_7: val > option_val,Ys_9: list_val] :
( ( ( map_li50976719on_val @ F_13 @ Xs_13 )
= ( map_val_option_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_46_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > val,Xs_13: list_option_ty,G_7: val > val,Ys_9: list_val] :
( ( ( map_option_ty_val @ F_13 @ Xs_13 )
= ( map_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_47_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > list_char,Xs_13: list_option_ty,G_7: val > list_char,Ys_9: list_val] :
( ( ( map_op1924521862t_char @ F_13 @ Xs_13 )
= ( map_val_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_48_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > ty,Xs_13: list_option_ty,G_7: val > ty,Ys_9: list_val] :
( ( ( map_option_ty_ty @ F_13 @ Xs_13 )
= ( map_val_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_49_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_ty,Xs_13: list_list_char,G_7: val > option_ty,Ys_9: list_val] :
( ( ( map_li771939206ion_ty @ F_13 @ Xs_13 )
= ( map_val_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_50_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > option_ty,Xs_13: list_exp_list_char,G_7: val > option_ty,Ys_9: list_val] :
( ( ( map_ex1548475405ion_ty @ F_13 @ Xs_13 )
= ( map_val_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_51_map__eq__imp__length__eq,axiom,
! [F_13: list_char > list_char,Xs_13: list_list_char,G_7: ty > list_char,Ys_9: list_ty] :
( ( ( map_li1333403488t_char @ F_13 @ Xs_13 )
= ( map_ty_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_52_map__eq__imp__length__eq,axiom,
! [F_13: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: ty > produc1746408499on_val,Ys_9: list_ty] :
( ( ( map_Pr816758342on_val @ F_13 @ Xs_13 )
= ( map_ty908261490on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_53_map__eq__imp__length__eq,axiom,
! [F_13: option_val > val,Xs_13: list_option_val,G_7: ty > val,Ys_9: list_ty] :
( ( ( map_option_val_val @ F_13 @ Xs_13 )
= ( map_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_54_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_val,Xs_13: list_list_char,G_7: ty > option_val,Ys_9: list_ty] :
( ( ( map_li50976719on_val @ F_13 @ Xs_13 )
= ( map_ty_option_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_55_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > exp_list_char,Xs_13: list_option_ty,G_7: ty > exp_list_char,Ys_9: list_ty] :
( ( ( map_op1779340173t_char @ F_13 @ Xs_13 )
= ( map_ty_exp_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_56_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > val,Xs_13: list_option_ty,G_7: ty > val,Ys_9: list_ty] :
( ( ( map_option_ty_val @ F_13 @ Xs_13 )
= ( map_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_57_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > list_char,Xs_13: list_option_ty,G_7: ty > list_char,Ys_9: list_ty] :
( ( ( map_op1924521862t_char @ F_13 @ Xs_13 )
= ( map_ty_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_58_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > ty,Xs_13: list_option_ty,G_7: ty > ty,Ys_9: list_ty] :
( ( ( map_option_ty_ty @ F_13 @ Xs_13 )
= ( map_ty_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_59_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_ty,Xs_13: list_list_char,G_7: ty > option_ty,Ys_9: list_ty] :
( ( ( map_li771939206ion_ty @ F_13 @ Xs_13 )
= ( map_ty_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_60_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > option_ty,Xs_13: list_exp_list_char,G_7: ty > option_ty,Ys_9: list_ty] :
( ( ( map_ex1548475405ion_ty @ F_13 @ Xs_13 )
= ( map_ty_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_61_map__eq__imp__length__eq,axiom,
! [F_13: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: list_char > produc1746408499on_val,Ys_9: list_list_char] :
( ( ( map_Pr816758342on_val @ F_13 @ Xs_13 )
= ( map_li772299987on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_62_map__eq__imp__length__eq,axiom,
! [F_13: option_val > val,Xs_13: list_option_val,G_7: list_char > val,Ys_9: list_list_char] :
( ( ( map_option_val_val @ F_13 @ Xs_13 )
= ( map_list_char_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_63_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > option_ty,Xs_13: list_option_ty,G_7: list_char > option_ty,Ys_9: list_list_char] :
( ( ( map_op1363057580ion_ty @ F_13 @ Xs_13 )
= ( map_li771939206ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_64_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > exp_list_char,Xs_13: list_option_ty,G_7: list_char > exp_list_char,Ys_9: list_list_char] :
( ( ( map_op1779340173t_char @ F_13 @ Xs_13 )
= ( map_li1249123943t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_65_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > list_char,Xs_13: list_option_ty,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_op1924521862t_char @ F_13 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_66_map__eq__imp__length__eq,axiom,
! [F_13: option_ty > ty,Xs_13: list_option_ty,G_7: list_char > ty,Ys_9: list_list_char] :
( ( ( map_option_ty_ty @ F_13 @ Xs_13 )
= ( map_list_char_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_67_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > list_char,Xs_13: list_exp_list_char,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_ex2109939687t_char @ F_13 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_68_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > produc1746408499on_val,Xs_13: list_exp_list_char,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_ex920537562on_val @ F_13 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_69_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > val,Xs_13: list_exp_list_char,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_ex740158547ar_val @ F_13 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_70_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > option_val,Xs_13: list_exp_list_char,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_ex1598883030on_val @ F_13 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_71_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > option_ty,Xs_13: list_exp_list_char,G_7: list_char > option_ty,Ys_9: list_list_char] :
( ( ( map_ex1548475405ion_ty @ F_13 @ Xs_13 )
= ( map_li771939206ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_72_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > option_ty,Xs_13: list_exp_list_char,G_7: exp_list_char > option_ty,Ys_9: list_exp_list_char] :
( ( ( map_ex1548475405ion_ty @ F_13 @ Xs_13 )
= ( map_ex1548475405ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_73_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > option_ty,Xs_13: list_exp_list_char,G_7: option_ty > option_ty,Ys_9: list_option_ty] :
( ( ( map_ex1548475405ion_ty @ F_13 @ Xs_13 )
= ( map_op1363057580ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_74_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > exp_list_char,Xs_13: list_exp_list_char,G_7: option_ty > exp_list_char,Ys_9: list_option_ty] :
( ( ( map_ex101166958t_char @ F_13 @ Xs_13 )
= ( map_op1779340173t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_75_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > val,Xs_13: list_exp_list_char,G_7: option_ty > val,Ys_9: list_option_ty] :
( ( ( map_ex740158547ar_val @ F_13 @ Xs_13 )
= ( map_option_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_76_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > list_char,Xs_13: list_exp_list_char,G_7: option_ty > list_char,Ys_9: list_option_ty] :
( ( ( map_ex2109939687t_char @ F_13 @ Xs_13 )
= ( map_op1924521862t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_77_map__eq__imp__length__eq,axiom,
! [F_13: exp_list_char > ty,Xs_13: list_exp_list_char,G_7: option_ty > ty,Ys_9: list_option_ty] :
( ( ( map_exp_list_char_ty @ F_13 @ Xs_13 )
= ( map_option_ty_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_78_map__eq__imp__length__eq,axiom,
! [F_13: val > list_char,Xs_13: list_val,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_val_list_char @ F_13 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_79_map__eq__imp__length__eq,axiom,
! [F_13: val > produc1746408499on_val,Xs_13: list_val,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_va32158779on_val @ F_13 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_80_map__eq__imp__length__eq,axiom,
! [F_13: val > val,Xs_13: list_val,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_val_val @ F_13 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_81_map__eq__imp__length__eq,axiom,
! [F_13: val > option_val,Xs_13: list_val,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_val_option_val @ F_13 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_82_map__eq__imp__length__eq,axiom,
! [F_13: val > val,Xs_13: list_val,G_7: option_ty > val,Ys_9: list_option_ty] :
( ( ( map_val_val @ F_13 @ Xs_13 )
= ( map_option_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_83_map__eq__imp__length__eq,axiom,
! [F_13: val > list_char,Xs_13: list_val,G_7: option_ty > list_char,Ys_9: list_option_ty] :
( ( ( map_val_list_char @ F_13 @ Xs_13 )
= ( map_op1924521862t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_84_map__eq__imp__length__eq,axiom,
! [F_13: val > ty,Xs_13: list_val,G_7: option_ty > ty,Ys_9: list_option_ty] :
( ( ( map_val_ty @ F_13 @ Xs_13 )
= ( map_option_ty_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_85_map__eq__imp__length__eq,axiom,
! [F_13: val > option_ty,Xs_13: list_val,G_7: list_char > option_ty,Ys_9: list_list_char] :
( ( ( map_val_option_ty @ F_13 @ Xs_13 )
= ( map_li771939206ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_86_map__eq__imp__length__eq,axiom,
! [F_13: val > option_ty,Xs_13: list_val,G_7: exp_list_char > option_ty,Ys_9: list_exp_list_char] :
( ( ( map_val_option_ty @ F_13 @ Xs_13 )
= ( map_ex1548475405ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_87_map__eq__imp__length__eq,axiom,
! [F_13: ty > list_char,Xs_13: list_ty,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_ty_list_char @ F_13 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_88_map__eq__imp__length__eq,axiom,
! [F_13: ty > produc1746408499on_val,Xs_13: list_ty,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_ty908261490on_val @ F_13 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_89_map__eq__imp__length__eq,axiom,
! [F_13: ty > val,Xs_13: list_ty,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_ty_val @ F_13 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_90_map__eq__imp__length__eq,axiom,
! [F_13: ty > option_val,Xs_13: list_ty,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_ty_option_val @ F_13 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_91_map__eq__imp__length__eq,axiom,
! [F_13: ty > exp_list_char,Xs_13: list_ty,G_7: option_ty > exp_list_char,Ys_9: list_option_ty] :
( ( ( map_ty_exp_list_char @ F_13 @ Xs_13 )
= ( map_op1779340173t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_92_map__eq__imp__length__eq,axiom,
! [F_13: ty > val,Xs_13: list_ty,G_7: option_ty > val,Ys_9: list_option_ty] :
( ( ( map_ty_val @ F_13 @ Xs_13 )
= ( map_option_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_93_map__eq__imp__length__eq,axiom,
! [F_13: ty > list_char,Xs_13: list_ty,G_7: option_ty > list_char,Ys_9: list_option_ty] :
( ( ( map_ty_list_char @ F_13 @ Xs_13 )
= ( map_op1924521862t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_94_map__eq__imp__length__eq,axiom,
! [F_13: ty > ty,Xs_13: list_ty,G_7: option_ty > ty,Ys_9: list_option_ty] :
( ( ( map_ty_ty @ F_13 @ Xs_13 )
= ( map_option_ty_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_95_map__eq__imp__length__eq,axiom,
! [F_13: ty > option_ty,Xs_13: list_ty,G_7: list_char > option_ty,Ys_9: list_list_char] :
( ( ( map_ty_option_ty @ F_13 @ Xs_13 )
= ( map_li771939206ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_96_map__eq__imp__length__eq,axiom,
! [F_13: ty > option_ty,Xs_13: list_ty,G_7: exp_list_char > option_ty,Ys_9: list_exp_list_char] :
( ( ( map_ty_option_ty @ F_13 @ Xs_13 )
= ( map_ex1548475405ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_97_map__eq__imp__length__eq,axiom,
! [F_13: list_char > list_char,Xs_13: list_list_char,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_li1333403488t_char @ F_13 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_98_map__eq__imp__length__eq,axiom,
! [F_13: list_char > produc1746408499on_val,Xs_13: list_list_char,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_li772299987on_val @ F_13 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_99_map__eq__imp__length__eq,axiom,
! [F_13: list_char > val,Xs_13: list_list_char,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_list_char_val @ F_13 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_100_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_val,Xs_13: list_list_char,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_li50976719on_val @ F_13 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_101_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_ty,Xs_13: list_list_char,G_7: option_ty > option_ty,Ys_9: list_option_ty] :
( ( ( map_li771939206ion_ty @ F_13 @ Xs_13 )
= ( map_op1363057580ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_102_map__eq__imp__length__eq,axiom,
! [F_13: list_char > exp_list_char,Xs_13: list_list_char,G_7: option_ty > exp_list_char,Ys_9: list_option_ty] :
( ( ( map_li1249123943t_char @ F_13 @ Xs_13 )
= ( map_op1779340173t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_103_map__eq__imp__length__eq,axiom,
! [F_13: list_char > list_char,Xs_13: list_list_char,G_7: option_ty > list_char,Ys_9: list_option_ty] :
( ( ( map_li1333403488t_char @ F_13 @ Xs_13 )
= ( map_op1924521862t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_104_map__eq__imp__length__eq,axiom,
! [F_13: list_char > ty,Xs_13: list_list_char,G_7: option_ty > ty,Ys_9: list_option_ty] :
( ( ( map_list_char_ty @ F_13 @ Xs_13 )
= ( map_option_ty_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_105_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_ty,Xs_13: list_list_char,G_7: list_char > option_ty,Ys_9: list_list_char] :
( ( ( map_li771939206ion_ty @ F_13 @ Xs_13 )
= ( map_li771939206ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_106_map__eq__imp__length__eq,axiom,
! [F_13: list_char > option_ty,Xs_13: list_list_char,G_7: exp_list_char > option_ty,Ys_9: list_exp_list_char] :
( ( ( map_li771939206ion_ty @ F_13 @ Xs_13 )
= ( map_ex1548475405ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_107_prod__induct4,axiom,
! [X_7: produc1285161482t_char,P_23: produc1285161482t_char > $o] :
( ! [A: list_list_char,B_3: list_ty,C_5: list_val,D: exp_list_char] : ( P_23 @ ( produc921874948t_char @ A @ ( produc1909267824t_char @ B_3 @ ( produc1916172923t_char @ C_5 @ D ) ) ) )
=> ( P_23 @ X_7 ) ) ).
thf(fact_108_prod__induct4,axiom,
! [X_7: produc1746408499on_val,P_23: produc1746408499on_val > $o] :
( ! [A: produc1282892786on_val,B_3: exp_list_char,C_5: nat > option1728594148on_val,D: list_char > option_val] : ( P_23 @ ( produc833389609on_val @ A @ ( produc235638504on_val @ B_3 @ ( produc755559506on_val @ C_5 @ D ) ) ) )
=> ( P_23 @ X_7 ) ) ).
thf(fact_109_prod__cases4,axiom,
! [Y_4: produc1285161482t_char] :
~ ! [A: list_list_char,B_3: list_ty,C_5: list_val,D: exp_list_char] :
( Y_4
!= ( produc921874948t_char @ A @ ( produc1909267824t_char @ B_3 @ ( produc1916172923t_char @ C_5 @ D ) ) ) ) ).
thf(fact_110_prod__cases4,axiom,
! [Y_4: produc1746408499on_val] :
~ ! [A: produc1282892786on_val,B_3: exp_list_char,C_5: nat > option1728594148on_val,D: list_char > option_val] :
( Y_4
!= ( produc833389609on_val @ A @ ( produc235638504on_val @ B_3 @ ( produc755559506on_val @ C_5 @ D ) ) ) ) ).
thf(fact_111_Pair__inject,axiom,
! [A_18: list_list_char,B_13: produc220283002t_char,A_17: list_list_char,B_12: produc220283002t_char] :
( ( ( produc921874948t_char @ A_18 @ B_13 )
= ( produc921874948t_char @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_112_Pair__inject,axiom,
! [A_18: list_ty,B_13: produc662261637t_char,A_17: list_ty,B_12: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_18 @ B_13 )
= ( produc1909267824t_char @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_113_Pair__inject,axiom,
! [A_18: list_val,B_13: exp_list_char,A_17: list_val,B_12: exp_list_char] :
( ( ( produc1916172923t_char @ A_18 @ B_13 )
= ( produc1916172923t_char @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_114_Pair__inject,axiom,
! [A_18: nat > option1728594148on_val,B_13: list_char > option_val,A_17: nat > option1728594148on_val,B_12: list_char > option_val] :
( ( ( produc755559506on_val @ A_18 @ B_13 )
= ( produc755559506on_val @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_115_Pair__inject,axiom,
! [A_18: produc1282892786on_val,B_13: produc1282892786on_val,A_17: produc1282892786on_val,B_12: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_18 @ B_13 )
= ( produc833389609on_val @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_116_Pair__inject,axiom,
! [A_18: exp_list_char,B_13: produc2090907612on_val,A_17: exp_list_char,B_12: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_18 @ B_13 )
= ( produc235638504on_val @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_117_Pair__inject,axiom,
! [A_18: list_char,B_13: produc1278157519t_char > option_val,A_17: list_char,B_12: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_18 @ B_13 )
= ( produc926070009on_val @ A_17 @ B_12 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_13 != B_12 ) ) ) ).
thf(fact_118_Pair__eq,axiom,
! [A_16: list_list_char,B_11: produc220283002t_char,A_15: list_list_char,B_10: produc220283002t_char] :
( ( ( produc921874948t_char @ A_16 @ B_11 )
= ( produc921874948t_char @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_119_Pair__eq,axiom,
! [A_16: list_ty,B_11: produc662261637t_char,A_15: list_ty,B_10: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_16 @ B_11 )
= ( produc1909267824t_char @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_120_Pair__eq,axiom,
! [A_16: list_val,B_11: exp_list_char,A_15: list_val,B_10: exp_list_char] :
( ( ( produc1916172923t_char @ A_16 @ B_11 )
= ( produc1916172923t_char @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_121_Pair__eq,axiom,
! [A_16: nat > option1728594148on_val,B_11: list_char > option_val,A_15: nat > option1728594148on_val,B_10: list_char > option_val] :
( ( ( produc755559506on_val @ A_16 @ B_11 )
= ( produc755559506on_val @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_122_Pair__eq,axiom,
! [A_16: produc1282892786on_val,B_11: produc1282892786on_val,A_15: produc1282892786on_val,B_10: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_16 @ B_11 )
= ( produc833389609on_val @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_123_Pair__eq,axiom,
! [A_16: exp_list_char,B_11: produc2090907612on_val,A_15: exp_list_char,B_10: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_16 @ B_11 )
= ( produc235638504on_val @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_124_Pair__eq,axiom,
! [A_16: list_char,B_11: produc1278157519t_char > option_val,A_15: list_char,B_10: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_16 @ B_11 )
= ( produc926070009on_val @ A_15 @ B_10 ) )
<=> ( ( A_16 = A_15 )
& ( B_11 = B_10 ) ) ) ).
thf(fact_125_split__paired__All,axiom,
! [P_22: produc1285161482t_char > $o] :
( ( !! @ produc1285161482t_char @ P_22 )
<=> ! [A: list_list_char,B_3: produc220283002t_char] : ( P_22 @ ( produc921874948t_char @ A @ B_3 ) ) ) ).
thf(fact_126_split__paired__All,axiom,
! [P_22: produc220283002t_char > $o] :
( ( !! @ produc220283002t_char @ P_22 )
<=> ! [A: list_ty,B_3: produc662261637t_char] : ( P_22 @ ( produc1909267824t_char @ A @ B_3 ) ) ) ).
thf(fact_127_split__paired__All,axiom,
! [P_22: produc662261637t_char > $o] :
( ( !! @ produc662261637t_char @ P_22 )
<=> ! [A: list_val,B_3: exp_list_char] : ( P_22 @ ( produc1916172923t_char @ A @ B_3 ) ) ) ).
thf(fact_128_split__paired__All,axiom,
! [P_22: produc2090907612on_val > $o] :
( ( !! @ produc2090907612on_val @ P_22 )
<=> ! [A: nat > option1728594148on_val,B_3: list_char > option_val] : ( P_22 @ ( produc755559506on_val @ A @ B_3 ) ) ) ).
thf(fact_129_split__paired__All,axiom,
! [P_22: produc1746408499on_val > $o] :
( ( !! @ produc1746408499on_val @ P_22 )
<=> ! [A: produc1282892786on_val,B_3: produc1282892786on_val] : ( P_22 @ ( produc833389609on_val @ A @ B_3 ) ) ) ).
thf(fact_130_split__paired__All,axiom,
! [P_22: produc1282892786on_val > $o] :
( ( !! @ produc1282892786on_val @ P_22 )
<=> ! [A: exp_list_char,B_3: produc2090907612on_val] : ( P_22 @ ( produc235638504on_val @ A @ B_3 ) ) ) ).
thf(fact_131_split__paired__All,axiom,
! [P_22: produc2088785539on_val > $o] :
( ( !! @ produc2088785539on_val @ P_22 )
<=> ! [A: list_char,B_3: produc1278157519t_char > option_val] : ( P_22 @ ( produc926070009on_val @ A @ B_3 ) ) ) ).
thf(fact_132_neq__if__length__neq,axiom,
! [Xs_12: list_option_ty,Ys_8: list_option_ty] :
( ( ( size_s1050794909ion_ty @ Xs_12 )
!= ( size_s1050794909ion_ty @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_133_neq__if__length__neq,axiom,
! [Xs_12: list_list_char,Ys_8: list_list_char] :
( ( ( size_s2113983095t_char @ Xs_12 )
!= ( size_s2113983095t_char @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_134_neq__if__length__neq,axiom,
! [Xs_12: list_ty,Ys_8: list_ty] :
( ( ( size_size_list_ty @ Xs_12 )
!= ( size_size_list_ty @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_135_neq__if__length__neq,axiom,
! [Xs_12: list_val,Ys_8: list_val] :
( ( ( size_size_list_val @ Xs_12 )
!= ( size_size_list_val @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_136_neq__if__length__neq,axiom,
! [Xs_12: list_exp_list_char,Ys_8: list_exp_list_char] :
( ( ( size_s1143674878t_char @ Xs_12 )
!= ( size_s1143674878t_char @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_137_list__all2__eq,axiom,
! [Xs_11: list_ty,Ys_7: list_ty] :
( ( Xs_11 = Ys_7 )
<=> ( list_all2_ty_ty @ fequal_ty @ Xs_11 @ Ys_7 ) ) ).
thf(fact_138_widen__trans,axiom,
! [T_8: ty,P_21: list_P1999446415t_char,S_2: ty,U: ty] :
( ( widen_2090681816t_char @ P_21 @ S_2 @ U )
=> ( ( widen_2090681816t_char @ P_21 @ U @ T_8 )
=> ( widen_2090681816t_char @ P_21 @ S_2 @ T_8 ) ) ) ).
thf(fact_139_prod__cases3,axiom,
! [Y_3: produc1285161482t_char] :
~ ! [A: list_list_char,B_3: list_ty,C_5: produc662261637t_char] :
( Y_3
!= ( produc921874948t_char @ A @ ( produc1909267824t_char @ B_3 @ C_5 ) ) ) ).
thf(fact_140_prod__cases3,axiom,
! [Y_3: produc220283002t_char] :
~ ! [A: list_ty,B_3: list_val,C_5: exp_list_char] :
( Y_3
!= ( produc1909267824t_char @ A @ ( produc1916172923t_char @ B_3 @ C_5 ) ) ) ).
thf(fact_141_prod__cases3,axiom,
! [Y_3: produc1746408499on_val] :
~ ! [A: produc1282892786on_val,B_3: exp_list_char,C_5: produc2090907612on_val] :
( Y_3
!= ( produc833389609on_val @ A @ ( produc235638504on_val @ B_3 @ C_5 ) ) ) ).
thf(fact_142_prod__cases3,axiom,
! [Y_3: produc1282892786on_val] :
~ ! [A: exp_list_char,B_3: nat > option1728594148on_val,C_5: list_char > option_val] :
( Y_3
!= ( produc235638504on_val @ A @ ( produc755559506on_val @ B_3 @ C_5 ) ) ) ).
thf(fact_143_prod__induct3,axiom,
! [X_6: produc1285161482t_char,P_20: produc1285161482t_char > $o] :
( ! [A: list_list_char,B_3: list_ty,C_5: produc662261637t_char] : ( P_20 @ ( produc921874948t_char @ A @ ( produc1909267824t_char @ B_3 @ C_5 ) ) )
=> ( P_20 @ X_6 ) ) ).
thf(fact_144_prod__induct3,axiom,
! [X_6: produc220283002t_char,P_20: produc220283002t_char > $o] :
( ! [A: list_ty,B_3: list_val,C_5: exp_list_char] : ( P_20 @ ( produc1909267824t_char @ A @ ( produc1916172923t_char @ B_3 @ C_5 ) ) )
=> ( P_20 @ X_6 ) ) ).
thf(fact_145_prod__induct3,axiom,
! [X_6: produc1746408499on_val,P_20: produc1746408499on_val > $o] :
( ! [A: produc1282892786on_val,B_3: exp_list_char,C_5: produc2090907612on_val] : ( P_20 @ ( produc833389609on_val @ A @ ( produc235638504on_val @ B_3 @ C_5 ) ) )
=> ( P_20 @ X_6 ) ) ).
thf(fact_146_prod__induct3,axiom,
! [X_6: produc1282892786on_val,P_20: produc1282892786on_val > $o] :
( ! [A: exp_list_char,B_3: nat > option1728594148on_val,C_5: list_char > option_val] : ( P_20 @ ( produc235638504on_val @ A @ ( produc755559506on_val @ B_3 @ C_5 ) ) )
=> ( P_20 @ X_6 ) ) ).
thf(fact_147_confs__conv__map,axiom,
! [P_19: list_P1999446415t_char,H_14: nat > option1728594148on_val,Vs_4: list_val,Ts_5: list_ty] :
( ( list_all2_val_ty @ ( conf_P373316194t_char @ P_19 @ H_14 ) @ Vs_4 @ Ts_5 )
<=> ? [Ts_6: list_ty] :
( ( ( map_val_option_ty @ ( typeof_h @ H_14 ) @ Vs_4 )
= ( map_ty_option_ty @ some_ty @ Ts_6 ) )
& ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_19 ) @ Ts_6 @ Ts_5 ) ) ) ).
thf(fact_148_list__all2__mono,axiom,
! [Q_1: ty > ty > $o,P_18: ty > ty > $o,Xs_10: list_ty,Ys_5: list_ty] :
( ( list_all2_ty_ty @ P_18 @ Xs_10 @ Ys_5 )
=> ( ! [Xs_5: ty,Ys_6: ty] :
( ( P_18 @ Xs_5 @ Ys_6 )
=> ( Q_1 @ Xs_5 @ Ys_6 ) )
=> ( list_all2_ty_ty @ Q_1 @ Xs_10 @ Ys_5 ) ) ) ).
thf(fact_149_list__all2__mono,axiom,
! [Q_1: val > ty > $o,P_18: val > ty > $o,Xs_10: list_val,Ys_5: list_ty] :
( ( list_all2_val_ty @ P_18 @ Xs_10 @ Ys_5 )
=> ( ! [Xs_5: val,Ys_6: ty] :
( ( P_18 @ Xs_5 @ Ys_6 )
=> ( Q_1 @ Xs_5 @ Ys_6 ) )
=> ( list_all2_val_ty @ Q_1 @ Xs_10 @ Ys_5 ) ) ) ).
thf(fact_150_list__all2__refl,axiom,
! [Xs_9: list_ty,P_17: ty > ty > $o] :
( ! [X_2: ty] : ( P_17 @ X_2 @ X_2 )
=> ( list_all2_ty_ty @ P_17 @ Xs_9 @ Xs_9 ) ) ).
thf(fact_151_list__all2__antisym,axiom,
! [Xs_8: list_ty,Ys_4: list_ty,Q: ty > ty > $o,P_16: ty > ty > $o] :
( ! [X_2: ty,Y_1: ty] :
( ( P_16 @ X_2 @ Y_1 )
=> ( ( Q @ Y_1 @ X_2 )
=> ( X_2 = Y_1 ) ) )
=> ( ( list_all2_ty_ty @ P_16 @ Xs_8 @ Ys_4 )
=> ( ( list_all2_ty_ty @ Q @ Ys_4 @ Xs_8 )
=> ( Xs_8 = Ys_4 ) ) ) ) ).
thf(fact_152_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_5: list_option_ty] :
( ( size_s1050794909ion_ty @ Xs_5 )
= N_1 ) ).
thf(fact_153_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_5: list_exp_list_char] :
( ( size_s1143674878t_char @ Xs_5 )
= N_1 ) ).
thf(fact_154_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_5: list_val] :
( ( size_size_list_val @ Xs_5 )
= N_1 ) ).
thf(fact_155_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_5: list_ty] :
( ( size_size_list_ty @ Xs_5 )
= N_1 ) ).
thf(fact_156_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_5: list_list_char] :
( ( size_s2113983095t_char @ Xs_5 )
= N_1 ) ).
thf(fact_157_conf__widen,axiom,
! [T_7: ty,P_15: list_P1999446415t_char,H_13: nat > option1728594148on_val,V_7: val,T_6: ty] :
( ( conf_P373316194t_char @ P_15 @ H_13 @ V_7 @ T_6 )
=> ( ( widen_2090681816t_char @ P_15 @ T_6 @ T_7 )
=> ( conf_P373316194t_char @ P_15 @ H_13 @ V_7 @ T_7 ) ) ) ).
thf(fact_158_typeof__conf,axiom,
! [P_14: list_P1999446415t_char,H_12: nat > option1728594148on_val,V_6: val,T_5: ty] :
( ( ( typeof_h @ H_12 @ V_6 )
= ( some_ty @ T_5 ) )
=> ( conf_P373316194t_char @ P_14 @ H_12 @ V_6 @ T_5 ) ) ).
thf(fact_159_confs__widens,axiom,
! [Ts_4: list_ty,P_13: list_P1999446415t_char,H_11: nat > option1728594148on_val,Vs_3: list_val,Ts_3: list_ty] :
( ( list_all2_val_ty @ ( conf_P373316194t_char @ P_13 @ H_11 ) @ Vs_3 @ Ts_3 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_13 ) @ Ts_3 @ Ts_4 )
=> ( list_all2_val_ty @ ( conf_P373316194t_char @ P_13 @ H_11 ) @ Vs_3 @ Ts_4 ) ) ) ).
thf(fact_160_conf__def,axiom,
! [P_12: list_P1999446415t_char,H_10: nat > option1728594148on_val,V_5: val,T_3: ty] :
( ( conf_P373316194t_char @ P_12 @ H_10 @ V_5 @ T_3 )
<=> ? [T_4: ty] :
( ( ( typeof_h @ H_10 @ V_5 )
= ( some_ty @ T_4 ) )
& ( widen_2090681816t_char @ P_12 @ T_4 @ T_3 ) ) ) ).
thf(fact_161_split__paired__Ex,axiom,
! [P_11: produc2088785539on_val > $o] :
( ( ?? @ produc2088785539on_val @ P_11 )
<=> ? [A: list_char,B_3: produc1278157519t_char > option_val] : ( P_11 @ ( produc926070009on_val @ A @ B_3 ) ) ) ).
thf(fact_162_split__paired__Ex,axiom,
! [P_11: produc1282892786on_val > $o] :
( ( ?? @ produc1282892786on_val @ P_11 )
<=> ? [A: exp_list_char,B_3: produc2090907612on_val] : ( P_11 @ ( produc235638504on_val @ A @ B_3 ) ) ) ).
thf(fact_163_split__paired__Ex,axiom,
! [P_11: produc1746408499on_val > $o] :
( ( ?? @ produc1746408499on_val @ P_11 )
<=> ? [A: produc1282892786on_val,B_3: produc1282892786on_val] : ( P_11 @ ( produc833389609on_val @ A @ B_3 ) ) ) ).
thf(fact_164_split__paired__Ex,axiom,
! [P_11: produc2090907612on_val > $o] :
( ( ?? @ produc2090907612on_val @ P_11 )
<=> ? [A: nat > option1728594148on_val,B_3: list_char > option_val] : ( P_11 @ ( produc755559506on_val @ A @ B_3 ) ) ) ).
thf(fact_165_split__paired__Ex,axiom,
! [P_11: produc662261637t_char > $o] :
( ( ?? @ produc662261637t_char @ P_11 )
<=> ? [A: list_val,B_3: exp_list_char] : ( P_11 @ ( produc1916172923t_char @ A @ B_3 ) ) ) ).
thf(fact_166_split__paired__Ex,axiom,
! [P_11: produc220283002t_char > $o] :
( ( ?? @ produc220283002t_char @ P_11 )
<=> ? [A: list_ty,B_3: produc662261637t_char] : ( P_11 @ ( produc1909267824t_char @ A @ B_3 ) ) ) ).
thf(fact_167_split__paired__Ex,axiom,
! [P_11: produc1285161482t_char > $o] :
( ( ?? @ produc1285161482t_char @ P_11 )
<=> ? [A: list_list_char,B_3: produc220283002t_char] : ( P_11 @ ( produc921874948t_char @ A @ B_3 ) ) ) ).
thf(fact_168_PairE,axiom,
! [P_10: produc2088785539on_val] :
~ ! [X_2: list_char,Y_1: produc1278157519t_char > option_val] :
( P_10
!= ( produc926070009on_val @ X_2 @ Y_1 ) ) ).
thf(fact_169_PairE,axiom,
! [P_10: produc1282892786on_val] :
~ ! [X_2: exp_list_char,Y_1: produc2090907612on_val] :
( P_10
!= ( produc235638504on_val @ X_2 @ Y_1 ) ) ).
thf(fact_170_PairE,axiom,
! [P_10: produc1746408499on_val] :
~ ! [X_2: produc1282892786on_val,Y_1: produc1282892786on_val] :
( P_10
!= ( produc833389609on_val @ X_2 @ Y_1 ) ) ).
thf(fact_171_PairE,axiom,
! [P_10: produc2090907612on_val] :
~ ! [X_2: nat > option1728594148on_val,Y_1: list_char > option_val] :
( P_10
!= ( produc755559506on_val @ X_2 @ Y_1 ) ) ).
thf(fact_172_PairE,axiom,
! [P_10: produc662261637t_char] :
~ ! [X_2: list_val,Y_1: exp_list_char] :
( P_10
!= ( produc1916172923t_char @ X_2 @ Y_1 ) ) ).
thf(fact_173_PairE,axiom,
! [P_10: produc220283002t_char] :
~ ! [X_2: list_ty,Y_1: produc662261637t_char] :
( P_10
!= ( produc1909267824t_char @ X_2 @ Y_1 ) ) ).
thf(fact_174_PairE,axiom,
! [P_10: produc1285161482t_char] :
~ ! [X_2: list_list_char,Y_1: produc220283002t_char] :
( P_10
!= ( produc921874948t_char @ X_2 @ Y_1 ) ) ).
thf(fact_175_prod_Oexhaust,axiom,
! [Y_2: produc2088785539on_val] :
~ ! [A: list_char,B_3: produc1278157519t_char > option_val] :
( Y_2
!= ( produc926070009on_val @ A @ B_3 ) ) ).
thf(fact_176_prod_Oexhaust,axiom,
! [Y_2: produc1282892786on_val] :
~ ! [A: exp_list_char,B_3: produc2090907612on_val] :
( Y_2
!= ( produc235638504on_val @ A @ B_3 ) ) ).
thf(fact_177_prod_Oexhaust,axiom,
! [Y_2: produc1746408499on_val] :
~ ! [A: produc1282892786on_val,B_3: produc1282892786on_val] :
( Y_2
!= ( produc833389609on_val @ A @ B_3 ) ) ).
thf(fact_178_prod_Oexhaust,axiom,
! [Y_2: produc2090907612on_val] :
~ ! [A: nat > option1728594148on_val,B_3: list_char > option_val] :
( Y_2
!= ( produc755559506on_val @ A @ B_3 ) ) ).
thf(fact_179_prod_Oexhaust,axiom,
! [Y_2: produc662261637t_char] :
~ ! [A: list_val,B_3: exp_list_char] :
( Y_2
!= ( produc1916172923t_char @ A @ B_3 ) ) ).
thf(fact_180_prod_Oexhaust,axiom,
! [Y_2: produc220283002t_char] :
~ ! [A: list_ty,B_3: produc662261637t_char] :
( Y_2
!= ( produc1909267824t_char @ A @ B_3 ) ) ).
thf(fact_181_prod_Oexhaust,axiom,
! [Y_2: produc1285161482t_char] :
~ ! [A: list_list_char,B_3: produc220283002t_char] :
( Y_2
!= ( produc921874948t_char @ A @ B_3 ) ) ).
thf(fact_182_confs__hext,axiom,
! [H_9: nat > option1728594148on_val,P_9: list_P1999446415t_char,H_8: nat > option1728594148on_val,Vs_2: list_val,Ts_2: list_ty] :
( ( list_all2_val_ty @ ( conf_P373316194t_char @ P_9 @ H_8 ) @ Vs_2 @ Ts_2 )
=> ( ( hext @ H_8 @ H_9 )
=> ( list_all2_val_ty @ ( conf_P373316194t_char @ P_9 @ H_9 ) @ Vs_2 @ Ts_2 ) ) ) ).
thf(fact_183_blocksEval,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,Vs_1: list_val,Ps: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Ps )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_s2113983095t_char @ Ps )
= ( size_size_list_val @ Vs_1 ) )
=> ( ( eval @ P @ ( blocks @ ( produc921874948t_char @ Ps @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) @ E @ ( produc755559506on_val @ H_1 @ L ) )
=> ? [L_5: list_char > option_val] : ( eval @ P @ E_1 @ ( produc755559506on_val @ H @ ( map_up1085636310ar_val @ L_1 @ Ps @ Vs_1 ) ) @ E @ ( produc755559506on_val @ H_1 @ L_5 ) ) ) ) ) ).
thf(fact_184_conf__hext,axiom,
! [P_8: list_P1999446415t_char,V_4: val,T_2: ty,H_7: nat > option1728594148on_val,H_6: nat > option1728594148on_val] :
( ( hext @ H_7 @ H_6 )
=> ( ( conf_P373316194t_char @ P_8 @ H_7 @ V_4 @ T_2 )
=> ( conf_P373316194t_char @ P_8 @ H_6 @ V_4 @ T_2 ) ) ) ).
thf(fact_185_hext__typeof__mono,axiom,
! [V_1: val,T_1: ty,H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ( hext @ H @ H_1 )
=> ( ( ( typeof_h @ H @ V_1 )
= ( some_ty @ T_1 ) )
=> ( ( typeof_h @ H_1 @ V_1 )
= ( some_ty @ T_1 ) ) ) ) ).
thf(fact_186_eval__hext,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ ( produc755559506on_val @ H @ L_1 ) @ E @ ( produc755559506on_val @ H_1 @ L ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_187_hext__refl,axiom,
! [H: nat > option1728594148on_val] : ( hext @ H @ H ) ).
thf(fact_188_WTrt__hext__mono,axiom,
! [H_1: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_5: list_char > option_ty,E_1: exp_list_char,T_1: ty] :
( ( wTrt @ P @ H @ E_5 @ E_1 @ T_1 )
=> ( ( hext @ H @ H_1 )
=> ( wTrt @ P @ H_1 @ E_5 @ E_1 @ T_1 ) ) ) ).
thf(fact_189_hext__trans,axiom,
! [H_5: nat > option1728594148on_val,H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ( hext @ H @ H_1 )
=> ( ( hext @ H_1 @ H_5 )
=> ( hext @ H @ H_5 ) ) ) ).
thf(fact_190_WTrtVal,axiom,
! [P: list_P1999446415t_char,E_5: list_char > option_ty,H: nat > option1728594148on_val,V_1: val,T_1: ty] :
( ( ( typeof_h @ H @ V_1 )
= ( some_ty @ T_1 ) )
=> ( wTrt @ P @ H @ E_5 @ ( val_list_char @ V_1 ) @ T_1 ) ) ).
thf(fact_191_blocksFinal,axiom,
! [H: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,Vs_1: list_val,Vs: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( final_list_char @ E_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_192_WTrts__Val,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_5: list_char > option_ty,Vs_1: list_val,Ts_1: list_ty] :
( ( wTrts @ P @ H @ E_5 @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ Ts_1 )
<=> ( ( map_val_option_ty @ ( typeof_h @ H ) @ Vs_1 )
= ( map_ty_option_ty @ some_ty @ Ts_1 ) ) ) ).
thf(fact_193_option_Oinject,axiom,
! [A_14: val,A_13: val] :
( ( ( some_val @ A_14 )
= ( some_val @ A_13 ) )
<=> ( A_14 = A_13 ) ) ).
thf(fact_194_option_Oinject,axiom,
! [A_14: produc2088785539on_val,A_13: produc2088785539on_val] :
( ( ( some_P451527732on_val @ A_14 )
= ( some_P451527732on_val @ A_13 ) )
<=> ( A_14 = A_13 ) ) ).
thf(fact_195_option_Oinject,axiom,
! [A_14: ty,A_13: ty] :
( ( ( some_ty @ A_14 )
= ( some_ty @ A_13 ) )
<=> ( A_14 = A_13 ) ) ).
thf(fact_196_curryI,axiom,
! [F_12: produc2088785539on_val > $o,A_12: list_char,B_9: produc1278157519t_char > option_val] :
( ( F_12 @ ( produc926070009on_val @ A_12 @ B_9 ) )
=> ( produc1177570924_val_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_197_curryI,axiom,
! [F_12: produc1282892786on_val > $o,A_12: exp_list_char,B_9: produc2090907612on_val] :
( ( F_12 @ ( produc235638504on_val @ A_12 @ B_9 ) )
=> ( produc1287763389_val_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_198_curryI,axiom,
! [F_12: produc1746408499on_val > $o,A_12: produc1282892786on_val,B_9: produc1282892786on_val] :
( ( F_12 @ ( produc833389609on_val @ A_12 @ B_9 ) )
=> ( produc803302844_val_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_199_curryI,axiom,
! [F_12: produc2090907612on_val > $o,A_12: nat > option1728594148on_val,B_9: list_char > option_val] :
( ( F_12 @ ( produc755559506on_val @ A_12 @ B_9 ) )
=> ( produc1402621651_val_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_200_curryI,axiom,
! [F_12: produc662261637t_char > $o,A_12: list_val,B_9: exp_list_char] :
( ( F_12 @ ( produc1916172923t_char @ A_12 @ B_9 ) )
=> ( produc1072551658char_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_201_curryI,axiom,
! [F_12: produc220283002t_char > $o,A_12: list_ty,B_9: produc662261637t_char] :
( ( F_12 @ ( produc1909267824t_char @ A_12 @ B_9 ) )
=> ( produc786676533char_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_202_curryI,axiom,
! [F_12: produc1285161482t_char > $o,A_12: list_list_char,B_9: produc220283002t_char] :
( ( F_12 @ ( produc921874948t_char @ A_12 @ B_9 ) )
=> ( produc193646727char_o @ F_12 @ A_12 @ B_9 ) ) ).
thf(fact_203_Val,axiom,
! [P: list_P1999446415t_char,V_1: val,S_1: produc2090907612on_val] : ( eval @ P @ ( val_list_char @ V_1 ) @ S_1 @ ( val_list_char @ V_1 ) @ S_1 ) ).
thf(fact_204_eval__cases_I2_J,axiom,
! [P: list_P1999446415t_char,V_1: val,S_1: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( val_list_char @ V_1 ) @ S_1 @ E @ S )
=> ~ ( ( E
= ( val_list_char @ V_1 ) )
=> ( S != S_1 ) ) ) ).
thf(fact_205_WTrts__hext__mono,axiom,
! [H_1: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_5: list_char > option_ty,Es: list_exp_list_char,Ts_1: list_ty] :
( ( wTrts @ P @ H @ E_5 @ Es @ Ts_1 )
=> ( ( hext @ H @ H_1 )
=> ( wTrts @ P @ H_1 @ E_5 @ Es @ Ts_1 ) ) ) ).
thf(fact_206_WTrts__same__length,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_5: list_char > option_ty,Es: list_exp_list_char,Ts_1: list_ty] :
( ( wTrts @ P @ H @ E_5 @ Es @ Ts_1 )
=> ( ( size_s1143674878t_char @ Es )
= ( size_size_list_ty @ Ts_1 ) ) ) ).
thf(fact_207_eval__final,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_1: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_1 @ E @ S )
=> ( final_list_char @ E ) ) ).
thf(fact_208_eval__finalId,axiom,
! [P: list_P1999446415t_char,S_1: produc2090907612on_val,E_1: exp_list_char] :
( ( final_list_char @ E_1 )
=> ( eval @ P @ E_1 @ S_1 @ E_1 @ S_1 ) ) ).
thf(fact_209_curryE,axiom,
! [F_11: produc2088785539on_val > $o,A_11: list_char,B_8: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc926070009on_val @ A_11 @ B_8 ) ) ) ).
thf(fact_210_curryE,axiom,
! [F_11: produc1282892786on_val > $o,A_11: exp_list_char,B_8: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc235638504on_val @ A_11 @ B_8 ) ) ) ).
thf(fact_211_curryE,axiom,
! [F_11: produc1746408499on_val > $o,A_11: produc1282892786on_val,B_8: produc1282892786on_val] :
( ( produc803302844_val_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc833389609on_val @ A_11 @ B_8 ) ) ) ).
thf(fact_212_curryE,axiom,
! [F_11: produc2090907612on_val > $o,A_11: nat > option1728594148on_val,B_8: list_char > option_val] :
( ( produc1402621651_val_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc755559506on_val @ A_11 @ B_8 ) ) ) ).
thf(fact_213_curryE,axiom,
! [F_11: produc662261637t_char > $o,A_11: list_val,B_8: exp_list_char] :
( ( produc1072551658char_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc1916172923t_char @ A_11 @ B_8 ) ) ) ).
thf(fact_214_curryE,axiom,
! [F_11: produc220283002t_char > $o,A_11: list_ty,B_8: produc662261637t_char] :
( ( produc786676533char_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc1909267824t_char @ A_11 @ B_8 ) ) ) ).
thf(fact_215_curryE,axiom,
! [F_11: produc1285161482t_char > $o,A_11: list_list_char,B_8: produc220283002t_char] :
( ( produc193646727char_o @ F_11 @ A_11 @ B_8 )
=> ( F_11 @ ( produc921874948t_char @ A_11 @ B_8 ) ) ) ).
thf(fact_216_curryD,axiom,
! [F_10: produc2088785539on_val > $o,A_10: list_char,B_7: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc926070009on_val @ A_10 @ B_7 ) ) ) ).
thf(fact_217_curryD,axiom,
! [F_10: produc1282892786on_val > $o,A_10: exp_list_char,B_7: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc235638504on_val @ A_10 @ B_7 ) ) ) ).
thf(fact_218_curryD,axiom,
! [F_10: produc1746408499on_val > $o,A_10: produc1282892786on_val,B_7: produc1282892786on_val] :
( ( produc803302844_val_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc833389609on_val @ A_10 @ B_7 ) ) ) ).
thf(fact_219_curryD,axiom,
! [F_10: produc2090907612on_val > $o,A_10: nat > option1728594148on_val,B_7: list_char > option_val] :
( ( produc1402621651_val_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc755559506on_val @ A_10 @ B_7 ) ) ) ).
thf(fact_220_curryD,axiom,
! [F_10: produc662261637t_char > $o,A_10: list_val,B_7: exp_list_char] :
( ( produc1072551658char_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc1916172923t_char @ A_10 @ B_7 ) ) ) ).
thf(fact_221_curryD,axiom,
! [F_10: produc220283002t_char > $o,A_10: list_ty,B_7: produc662261637t_char] :
( ( produc786676533char_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc1909267824t_char @ A_10 @ B_7 ) ) ) ).
thf(fact_222_curryD,axiom,
! [F_10: produc1285161482t_char > $o,A_10: list_list_char,B_7: produc220283002t_char] :
( ( produc193646727char_o @ F_10 @ A_10 @ B_7 )
=> ( F_10 @ ( produc921874948t_char @ A_10 @ B_7 ) ) ) ).
thf(fact_223_red__hext__incr,axiom,
! [E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( red @ P ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_224_rtrancl_Ortrancl__refl,axiom,
! [A_9: produc1282892786on_val,R_12: produc1746408499on_val > $o] : ( member1913460000on_val @ ( produc833389609on_val @ A_9 @ A_9 ) @ ( transi2118771717on_val @ R_12 ) ) ).
thf(fact_225_r__into__rtrancl,axiom,
! [P_7: produc1746408499on_val,R_11: produc1746408499on_val > $o] :
( ( member1913460000on_val @ P_7 @ R_11 )
=> ( member1913460000on_val @ P_7 @ ( transi2118771717on_val @ R_11 ) ) ) ).
thf(fact_226_red__preserves__hconf,axiom,
! [E_5: list_char > option_ty,T_1: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_5 @ E_1 @ T_1 )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( hconf_97414254t_char @ P @ H_1 ) ) ) ) ).
thf(fact_227_rtrancl__idemp,axiom,
! [R_10: produc1746408499on_val > $o] :
( ( transi2118771717on_val @ ( transi2118771717on_val @ R_10 ) )
= ( transi2118771717on_val @ R_10 ) ) ).
thf(fact_228_converse__rtrancl__into__rtrancl,axiom,
! [C_4: produc1282892786on_val,A_8: produc1282892786on_val,B_6: produc1282892786on_val,R_9: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_8 @ B_6 ) @ R_9 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_6 @ C_4 ) @ ( transi2118771717on_val @ R_9 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_8 @ C_4 ) @ ( transi2118771717on_val @ R_9 ) ) ) ) ).
thf(fact_229_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_3: produc1282892786on_val,A_7: produc1282892786on_val,B_5: produc1282892786on_val,R_8: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_7 @ B_5 ) @ ( transi2118771717on_val @ R_8 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_5 @ C_3 ) @ R_8 )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_7 @ C_3 ) @ ( transi2118771717on_val @ R_8 ) ) ) ) ).
thf(fact_230_rtrancl__trans,axiom,
! [C_2: produc1282892786on_val,A_6: produc1282892786on_val,B_4: produc1282892786on_val,R_7: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_6 @ B_4 ) @ ( transi2118771717on_val @ R_7 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_4 @ C_2 ) @ ( transi2118771717on_val @ R_7 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_6 @ C_2 ) @ ( transi2118771717on_val @ R_7 ) ) ) ) ).
thf(fact_231_rtrancl__induct2,axiom,
! [P_6: exp_list_char > produc2090907612on_val > $o,Ax_1: exp_list_char,Ay_1: produc2090907612on_val,Bx_1: exp_list_char,By_1: produc2090907612on_val,R_6: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax_1 @ Ay_1 ) @ ( produc235638504on_val @ Bx_1 @ By_1 ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: exp_list_char,B_3: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax_1 @ Ay_1 ) @ ( produc235638504on_val @ A @ B_3 ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A @ B_3 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_232_rtrancl__induct2,axiom,
! [P_6: list_char > ( produc1278157519t_char > option_val ) > $o,Ax_1: list_char,Ay_1: produc1278157519t_char > option_val,Bx_1: list_char,By_1: produc1278157519t_char > option_val,R_6: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax_1 @ Ay_1 ) @ ( produc926070009on_val @ Bx_1 @ By_1 ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: list_char,B_3: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax_1 @ Ay_1 ) @ ( produc926070009on_val @ A @ B_3 ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A @ B_3 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_233_rtrancl__induct2,axiom,
! [P_6: produc1282892786on_val > produc1282892786on_val > $o,Ax_1: produc1282892786on_val,Ay_1: produc1282892786on_val,Bx_1: produc1282892786on_val,By_1: produc1282892786on_val,R_6: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax_1 @ Ay_1 ) @ ( produc833389609on_val @ Bx_1 @ By_1 ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: produc1282892786on_val,B_3: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax_1 @ Ay_1 ) @ ( produc833389609on_val @ A @ B_3 ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A @ B_3 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_234_rtrancl__induct2,axiom,
! [P_6: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Ax_1: nat > option1728594148on_val,Ay_1: list_char > option_val,Bx_1: nat > option1728594148on_val,By_1: list_char > option_val,R_6: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax_1 @ Ay_1 ) @ ( produc755559506on_val @ Bx_1 @ By_1 ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: nat > option1728594148on_val,B_3: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax_1 @ Ay_1 ) @ ( produc755559506on_val @ A @ B_3 ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A @ B_3 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_235_rtrancl__induct2,axiom,
! [P_6: list_val > exp_list_char > $o,Ax_1: list_val,Ay_1: exp_list_char,Bx_1: list_val,By_1: exp_list_char,R_6: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax_1 @ Ay_1 ) @ ( produc1916172923t_char @ Bx_1 @ By_1 ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: list_val,B_3: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax_1 @ Ay_1 ) @ ( produc1916172923t_char @ A @ B_3 ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A @ B_3 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_236_rtrancl__induct2,axiom,
! [P_6: list_ty > produc662261637t_char > $o,Ax_1: list_ty,Ay_1: produc662261637t_char,Bx_1: list_ty,By_1: produc662261637t_char,R_6: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax_1 @ Ay_1 ) @ ( produc1909267824t_char @ Bx_1 @ By_1 ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: list_ty,B_3: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax_1 @ Ay_1 ) @ ( produc1909267824t_char @ A @ B_3 ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A @ B_3 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_237_rtrancl__induct2,axiom,
! [P_6: list_list_char > produc220283002t_char > $o,Ax_1: list_list_char,Ay_1: produc220283002t_char,Bx_1: list_list_char,By_1: produc220283002t_char,R_6: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax_1 @ Ay_1 ) @ ( produc921874948t_char @ Bx_1 @ By_1 ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( P_6 @ Ax_1 @ Ay_1 )
=> ( ! [A: list_list_char,B_3: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax_1 @ Ay_1 ) @ ( produc921874948t_char @ A @ B_3 ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A @ B_3 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( P_6 @ A @ B_3 )
=> ( P_6 @ Aa @ Ba ) ) ) )
=> ( P_6 @ Bx_1 @ By_1 ) ) ) ) ).
thf(fact_238_converse__rtrancl__induct2,axiom,
! [P_5: exp_list_char > produc2090907612on_val > $o,Ax: exp_list_char,Ay: produc2090907612on_val,Bx: exp_list_char,By: produc2090907612on_val,R_5: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax @ Ay ) @ ( produc235638504on_val @ Bx @ By ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: exp_list_char,B_3: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A @ B_3 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Aa @ Ba ) @ ( produc235638504on_val @ Bx @ By ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_239_converse__rtrancl__induct2,axiom,
! [P_5: list_char > ( produc1278157519t_char > option_val ) > $o,Ax: list_char,Ay: produc1278157519t_char > option_val,Bx: list_char,By: produc1278157519t_char > option_val,R_5: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax @ Ay ) @ ( produc926070009on_val @ Bx @ By ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: list_char,B_3: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A @ B_3 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Aa @ Ba ) @ ( produc926070009on_val @ Bx @ By ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_240_converse__rtrancl__induct2,axiom,
! [P_5: produc1282892786on_val > produc1282892786on_val > $o,Ax: produc1282892786on_val,Ay: produc1282892786on_val,Bx: produc1282892786on_val,By: produc1282892786on_val,R_5: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax @ Ay ) @ ( produc833389609on_val @ Bx @ By ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: produc1282892786on_val,B_3: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A @ B_3 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Aa @ Ba ) @ ( produc833389609on_val @ Bx @ By ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_241_converse__rtrancl__induct2,axiom,
! [P_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Ax: nat > option1728594148on_val,Ay: list_char > option_val,Bx: nat > option1728594148on_val,By: list_char > option_val,R_5: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax @ Ay ) @ ( produc755559506on_val @ Bx @ By ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: nat > option1728594148on_val,B_3: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A @ B_3 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Aa @ Ba ) @ ( produc755559506on_val @ Bx @ By ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_242_converse__rtrancl__induct2,axiom,
! [P_5: list_val > exp_list_char > $o,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_5: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax @ Ay ) @ ( produc1916172923t_char @ Bx @ By ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: list_val,B_3: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A @ B_3 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Aa @ Ba ) @ ( produc1916172923t_char @ Bx @ By ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_243_converse__rtrancl__induct2,axiom,
! [P_5: list_ty > produc662261637t_char > $o,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_5: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax @ Ay ) @ ( produc1909267824t_char @ Bx @ By ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: list_ty,B_3: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A @ B_3 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Aa @ Ba ) @ ( produc1909267824t_char @ Bx @ By ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_244_converse__rtrancl__induct2,axiom,
! [P_5: list_list_char > produc220283002t_char > $o,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_5: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax @ Ay ) @ ( produc921874948t_char @ Bx @ By ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_5 @ Bx @ By )
=> ( ! [A: list_list_char,B_3: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A @ B_3 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Aa @ Ba ) @ ( produc921874948t_char @ Bx @ By ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_5 @ Aa @ Ba )
=> ( P_5 @ A @ B_3 ) ) ) )
=> ( P_5 @ Ax @ Ay ) ) ) ) ).
thf(fact_245_converse__rtranclE2,axiom,
! [Xa_1: exp_list_char,Xb: produc2090907612on_val,Za: exp_list_char,Zb: produc2090907612on_val,R_4: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_4 ) )
=> ( ( ( produc235638504on_val @ Xa_1 @ Xb )
!= ( produc235638504on_val @ Za @ Zb ) )
=> ~ ! [A: exp_list_char,B_3: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb ) @ ( produc235638504on_val @ A @ B_3 ) ) @ R_4 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A @ B_3 ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_4 ) ) ) ) ) ).
thf(fact_246_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb: produc1278157519t_char > option_val,Za: list_char,Zb: produc1278157519t_char > option_val,R_4: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_4 ) )
=> ( ( ( produc926070009on_val @ Xa_1 @ Xb )
!= ( produc926070009on_val @ Za @ Zb ) )
=> ~ ! [A: list_char,B_3: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb ) @ ( produc926070009on_val @ A @ B_3 ) ) @ R_4 )
=> ~ ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A @ B_3 ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_4 ) ) ) ) ) ).
thf(fact_247_converse__rtranclE2,axiom,
! [Xa_1: produc1282892786on_val,Xb: produc1282892786on_val,Za: produc1282892786on_val,Zb: produc1282892786on_val,R_4: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_4 ) )
=> ( ( ( produc833389609on_val @ Xa_1 @ Xb )
!= ( produc833389609on_val @ Za @ Zb ) )
=> ~ ! [A: produc1282892786on_val,B_3: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb ) @ ( produc833389609on_val @ A @ B_3 ) ) @ R_4 )
=> ~ ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A @ B_3 ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_4 ) ) ) ) ) ).
thf(fact_248_converse__rtranclE2,axiom,
! [Xa_1: nat > option1728594148on_val,Xb: list_char > option_val,Za: nat > option1728594148on_val,Zb: list_char > option_val,R_4: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_4 ) )
=> ( ( ( produc755559506on_val @ Xa_1 @ Xb )
!= ( produc755559506on_val @ Za @ Zb ) )
=> ~ ! [A: nat > option1728594148on_val,B_3: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb ) @ ( produc755559506on_val @ A @ B_3 ) ) @ R_4 )
=> ~ ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A @ B_3 ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_4 ) ) ) ) ) ).
thf(fact_249_converse__rtranclE2,axiom,
! [Xa_1: list_val,Xb: exp_list_char,Za: list_val,Zb: exp_list_char,R_4: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_4 ) )
=> ( ( ( produc1916172923t_char @ Xa_1 @ Xb )
!= ( produc1916172923t_char @ Za @ Zb ) )
=> ~ ! [A: list_val,B_3: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb ) @ ( produc1916172923t_char @ A @ B_3 ) ) @ R_4 )
=> ~ ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A @ B_3 ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_4 ) ) ) ) ) ).
thf(fact_250_converse__rtranclE2,axiom,
! [Xa_1: list_ty,Xb: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_4: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_4 ) )
=> ( ( ( produc1909267824t_char @ Xa_1 @ Xb )
!= ( produc1909267824t_char @ Za @ Zb ) )
=> ~ ! [A: list_ty,B_3: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb ) @ ( produc1909267824t_char @ A @ B_3 ) ) @ R_4 )
=> ~ ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A @ B_3 ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_4 ) ) ) ) ) ).
thf(fact_251_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R_4: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_4 ) )
=> ( ( ( produc921874948t_char @ Xa_1 @ Xb )
!= ( produc921874948t_char @ Za @ Zb ) )
=> ~ ! [A: list_list_char,B_3: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb ) @ ( produc921874948t_char @ A @ B_3 ) ) @ R_4 )
=> ~ ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A @ B_3 ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_4 ) ) ) ) ) ).
thf(fact_252_rtranclE,axiom,
! [A_5: produc1282892786on_val,B_2: produc1282892786on_val,R_3: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_5 @ B_2 ) @ ( transi2118771717on_val @ R_3 ) )
=> ( ( A_5 != B_2 )
=> ~ ! [Y_1: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_5 @ Y_1 ) @ ( transi2118771717on_val @ R_3 ) )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ B_2 ) @ R_3 ) ) ) ) ).
thf(fact_253_converse__rtranclE,axiom,
! [X_5: produc1282892786on_val,Z_1: produc1282892786on_val,R_2: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_5 @ Z_1 ) @ ( transi2118771717on_val @ R_2 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_5 @ Y_1 ) @ R_2 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z_1 ) @ ( transi2118771717on_val @ R_2 ) ) ) ) ) ).
thf(fact_254_converse__rtrancl__induct,axiom,
! [P_4: produc1282892786on_val > $o,A_4: produc1282892786on_val,B_1: produc1282892786on_val,R_1: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_4 @ B_1 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( P_4 @ B_1 )
=> ( ! [Y_1: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z ) @ R_1 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Z @ B_1 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( P_4 @ Z )
=> ( P_4 @ Y_1 ) ) ) )
=> ( P_4 @ A_4 ) ) ) ) ).
thf(fact_255_rtrancl__induct,axiom,
! [P_3: produc1282892786on_val > $o,A_3: produc1282892786on_val,B: produc1282892786on_val,R: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_3 @ B ) @ ( transi2118771717on_val @ R ) )
=> ( ( P_3 @ A_3 )
=> ( ! [Y_1: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_3 @ Y_1 ) @ ( transi2118771717on_val @ R ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z ) @ R )
=> ( ( P_3 @ Y_1 )
=> ( P_3 @ Z ) ) ) )
=> ( P_3 @ B ) ) ) ) ).
thf(fact_256_red__preserves__lconf,axiom,
! [E_5: list_char > option_ty,T_1: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_5 @ E_1 @ T_1 )
=> ( ( lconf_496643946t_char @ P @ H @ L_1 @ E_5 )
=> ( lconf_496643946t_char @ P @ H_1 @ L @ E_5 ) ) ) ) ).
thf(fact_257_blocksRedsFinal,axiom,
! [L_4: list_char > option_val,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( distinct_list_char @ Vs )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( map_up1085636310ar_val @ L_1 @ Vs @ Vs_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E )
=> ( ( L_4
= ( overri2012515291on_val @ L @ L_1 @ ( set_list_char @ Vs ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L_4 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ) ).
thf(fact_258_map__eq__conv,axiom,
! [F_9: list_char > val,Xs_7: list_list_char,G_6: list_char > val] :
( ( ( map_list_char_val @ F_9 @ Xs_7 )
= ( map_list_char_val @ G_6 @ Xs_7 ) )
<=> ! [X_2: list_char] :
( ( member_list_char @ X_2 @ ( set_list_char @ Xs_7 ) )
=> ( ( F_9 @ X_2 )
= ( G_6 @ X_2 ) ) ) ) ).
thf(fact_259_map__eq__conv,axiom,
! [F_9: val > exp_list_char,Xs_7: list_val,G_6: val > exp_list_char] :
( ( ( map_va1934808527t_char @ F_9 @ Xs_7 )
= ( map_va1934808527t_char @ G_6 @ Xs_7 ) )
<=> ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Xs_7 ) )
=> ( ( F_9 @ X_2 )
= ( G_6 @ X_2 ) ) ) ) ).
thf(fact_260_map__eq__conv,axiom,
! [F_9: ty > option_ty,Xs_7: list_ty,G_6: ty > option_ty] :
( ( ( map_ty_option_ty @ F_9 @ Xs_7 )
= ( map_ty_option_ty @ G_6 @ Xs_7 ) )
<=> ! [X_2: ty] :
( ( member_ty @ X_2 @ ( set_ty @ Xs_7 ) )
=> ( ( F_9 @ X_2 )
= ( G_6 @ X_2 ) ) ) ) ).
thf(fact_261_map__eq__conv,axiom,
! [F_9: val > option_ty,Xs_7: list_val,G_6: val > option_ty] :
( ( ( map_val_option_ty @ F_9 @ Xs_7 )
= ( map_val_option_ty @ G_6 @ Xs_7 ) )
<=> ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Xs_7 ) )
=> ( ( F_9 @ X_2 )
= ( G_6 @ X_2 ) ) ) ) ).
thf(fact_262_mem__def,axiom,
! [X_4: produc1746408499on_val,A_2: produc1746408499on_val > $o] :
( ( member1913460000on_val @ X_4 @ A_2 )
<=> ( A_2 @ X_4 ) ) ).
thf(fact_263_lconf__hext,axiom,
! [H_4: nat > option1728594148on_val,P_2: list_P1999446415t_char,H_3: nat > option1728594148on_val,L_3: list_char > option_val,E_4: list_char > option_ty] :
( ( lconf_496643946t_char @ P_2 @ H_3 @ L_3 @ E_4 )
=> ( ( hext @ H_3 @ H_4 )
=> ( lconf_496643946t_char @ P_2 @ H_4 @ L_3 @ E_4 ) ) ) ).
thf(fact_264_lconf__def,axiom,
! [P_1: list_P1999446415t_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,E_3: list_char > option_ty] :
( ( lconf_496643946t_char @ P_1 @ H_2 @ L_2 @ E_3 )
<=> ! [V_3: list_char,V_2: val] :
( ( ( L_2 @ V_3 )
= ( some_val @ V_2 ) )
=> ? [T: ty] :
( ( ( E_3 @ V_3 )
= ( some_ty @ T ) )
& ( conf_P373316194t_char @ P_1 @ H_2 @ V_2 @ T ) ) ) ) ).
thf(fact_265_blocksReds,axiom,
! [E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( distinct_list_char @ Vs )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( map_up1085636310ar_val @ L_1 @ Vs @ Vs_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ L ) @ Vs ) @ E ) ) ) ) @ ( produc755559506on_val @ H_1 @ ( overri2012515291on_val @ L @ L_1 @ ( set_list_char @ Vs ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ).
thf(fact_266_List_Omap_Ocomp,axiom,
! [F_8: option_val > val,G_5: list_char > option_val] :
( ( comp_l1825390573t_char @ ( map_option_val_val @ F_8 ) @ ( map_li50976719on_val @ G_5 ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_8 @ G_5 ) ) ) ).
thf(fact_267_map__comp__map,axiom,
! [F_7: option_val > val,G_4: list_char > option_val] :
( ( comp_l1825390573t_char @ ( map_option_val_val @ F_7 ) @ ( map_li50976719on_val @ G_4 ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_7 @ G_4 ) ) ) ).
thf(fact_268_map__map,axiom,
! [F_6: option_val > val,G_3: list_char > option_val,Xs_6: list_list_char] :
( ( map_option_val_val @ F_6 @ ( map_li50976719on_val @ G_3 @ Xs_6 ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_6 @ G_3 ) @ Xs_6 ) ) ).
thf(fact_269_List_Omap_Ocompositionality,axiom,
! [F_5: option_val > val,G_2: list_char > option_val,List: list_list_char] :
( ( map_option_val_val @ F_5 @ ( map_li50976719on_val @ G_2 @ List ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_5 @ G_2 ) @ List ) ) ).
thf(fact_270_the_Osimps,axiom,
! [X_3: val] :
( ( the_val @ ( some_val @ X_3 ) )
= X_3 ) ).
thf(fact_271_the_Osimps,axiom,
! [X_3: produc2088785539on_val] :
( ( the_Pr1885945130on_val @ ( some_P451527732on_val @ X_3 ) )
= X_3 ) ).
thf(fact_272_the_Osimps,axiom,
! [X_3: ty] :
( ( the_ty @ ( some_ty @ X_3 ) )
= X_3 ) ).
thf(fact_273_ex__map__conv,axiom,
! [Ys_3: list_val,F_4: list_char > val] :
( ? [Xs_5: list_list_char] :
( Ys_3
= ( map_list_char_val @ F_4 @ Xs_5 ) )
<=> ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Ys_3 ) )
=> ? [Xa: list_char] :
( X_2
= ( F_4 @ Xa ) ) ) ) ).
thf(fact_274_ex__map__conv,axiom,
! [Ys_3: list_exp_list_char,F_4: val > exp_list_char] :
( ? [Xs_5: list_val] :
( Ys_3
= ( map_va1934808527t_char @ F_4 @ Xs_5 ) )
<=> ! [X_2: exp_list_char] :
( ( member_exp_list_char @ X_2 @ ( set_exp_list_char @ Ys_3 ) )
=> ? [Xa: val] :
( X_2
= ( F_4 @ Xa ) ) ) ) ).
thf(fact_275_ex__map__conv,axiom,
! [Ys_3: list_option_ty,F_4: ty > option_ty] :
( ? [Xs_5: list_ty] :
( Ys_3
= ( map_ty_option_ty @ F_4 @ Xs_5 ) )
<=> ! [X_2: option_ty] :
( ( member_option_ty @ X_2 @ ( set_option_ty @ Ys_3 ) )
=> ? [Xa: ty] :
( X_2
= ( F_4 @ Xa ) ) ) ) ).
thf(fact_276_ex__map__conv,axiom,
! [Ys_3: list_option_ty,F_4: val > option_ty] :
( ? [Xs_5: list_val] :
( Ys_3
= ( map_val_option_ty @ F_4 @ Xs_5 ) )
<=> ! [X_2: option_ty] :
( ( member_option_ty @ X_2 @ ( set_option_ty @ Ys_3 ) )
=> ? [Xa: val] :
( X_2
= ( F_4 @ Xa ) ) ) ) ).
thf(fact_277_map__ext,axiom,
! [F_3: list_char > val,G_1: list_char > val,Xs_4: list_list_char] :
( ! [X_2: list_char] :
( ( member_list_char @ X_2 @ ( set_list_char @ Xs_4 ) )
=> ( ( F_3 @ X_2 )
= ( G_1 @ X_2 ) ) )
=> ( ( map_list_char_val @ F_3 @ Xs_4 )
= ( map_list_char_val @ G_1 @ Xs_4 ) ) ) ).
thf(fact_278_map__ext,axiom,
! [F_3: val > exp_list_char,G_1: val > exp_list_char,Xs_4: list_val] :
( ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Xs_4 ) )
=> ( ( F_3 @ X_2 )
= ( G_1 @ X_2 ) ) )
=> ( ( map_va1934808527t_char @ F_3 @ Xs_4 )
= ( map_va1934808527t_char @ G_1 @ Xs_4 ) ) ) ).
thf(fact_279_map__ext,axiom,
! [F_3: ty > option_ty,G_1: ty > option_ty,Xs_4: list_ty] :
( ! [X_2: ty] :
( ( member_ty @ X_2 @ ( set_ty @ Xs_4 ) )
=> ( ( F_3 @ X_2 )
= ( G_1 @ X_2 ) ) )
=> ( ( map_ty_option_ty @ F_3 @ Xs_4 )
= ( map_ty_option_ty @ G_1 @ Xs_4 ) ) ) ).
thf(fact_280_map__ext,axiom,
! [F_3: val > option_ty,G_1: val > option_ty,Xs_4: list_val] :
( ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Xs_4 ) )
=> ( ( F_3 @ X_2 )
= ( G_1 @ X_2 ) ) )
=> ( ( map_val_option_ty @ F_3 @ Xs_4 )
= ( map_val_option_ty @ G_1 @ Xs_4 ) ) ) ).
thf(fact_281_map__cong,axiom,
! [F_2: list_char > val,G: list_char > val,Xs_3: list_list_char,Ys_2: list_list_char] :
( ( Xs_3 = Ys_2 )
=> ( ! [X_2: list_char] :
( ( member_list_char @ X_2 @ ( set_list_char @ Ys_2 ) )
=> ( ( F_2 @ X_2 )
= ( G @ X_2 ) ) )
=> ( ( map_list_char_val @ F_2 @ Xs_3 )
= ( map_list_char_val @ G @ Ys_2 ) ) ) ) ).
thf(fact_282_map__cong,axiom,
! [F_2: val > exp_list_char,G: val > exp_list_char,Xs_3: list_val,Ys_2: list_val] :
( ( Xs_3 = Ys_2 )
=> ( ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Ys_2 ) )
=> ( ( F_2 @ X_2 )
= ( G @ X_2 ) ) )
=> ( ( map_va1934808527t_char @ F_2 @ Xs_3 )
= ( map_va1934808527t_char @ G @ Ys_2 ) ) ) ) ).
thf(fact_283_map__cong,axiom,
! [F_2: ty > option_ty,G: ty > option_ty,Xs_3: list_ty,Ys_2: list_ty] :
( ( Xs_3 = Ys_2 )
=> ( ! [X_2: ty] :
( ( member_ty @ X_2 @ ( set_ty @ Ys_2 ) )
=> ( ( F_2 @ X_2 )
= ( G @ X_2 ) ) )
=> ( ( map_ty_option_ty @ F_2 @ Xs_3 )
= ( map_ty_option_ty @ G @ Ys_2 ) ) ) ) ).
thf(fact_284_map__cong,axiom,
! [F_2: val > option_ty,G: val > option_ty,Xs_3: list_val,Ys_2: list_val] :
( ( Xs_3 = Ys_2 )
=> ( ! [X_2: val] :
( ( member_val @ X_2 @ ( set_val @ Ys_2 ) )
=> ( ( F_2 @ X_2 )
= ( G @ X_2 ) ) )
=> ( ( map_val_option_ty @ F_2 @ Xs_3 )
= ( map_val_option_ty @ G @ Ys_2 ) ) ) ) ).
thf(fact_285_map__idI,axiom,
! [F_1: list_char > list_char,Xs_2: list_list_char] :
( ! [X_2: list_char] :
( ( member_list_char @ X_2 @ ( set_list_char @ Xs_2 ) )
=> ( ( F_1 @ X_2 )
= X_2 ) )
=> ( ( map_li1333403488t_char @ F_1 @ Xs_2 )
= Xs_2 ) ) ).
thf(fact_286_map__idI,axiom,
! [F_1: produc1746408499on_val > produc1746408499on_val,Xs_2: list_P1964248404on_val] :
( ! [X_2: produc1746408499on_val] :
( ( member1913460000on_val @ X_2 @ ( set_Pr1184195362on_val @ Xs_2 ) )
=> ( ( F_1 @ X_2 )
= X_2 ) )
=> ( ( map_Pr816758342on_val @ F_1 @ Xs_2 )
= Xs_2 ) ) ).
thf(fact_287_map__upds__apply__nontin,axiom,
! [F: list_char > option_val,Ys_1: list_val,X_1: list_char,Xs_1: list_list_char] :
( ~ ( member_list_char @ X_1 @ ( set_list_char @ Xs_1 ) )
=> ( ( map_up1085636310ar_val @ F @ Xs_1 @ Ys_1 @ X_1 )
= ( F @ X_1 ) ) ) ).
thf(fact_288_map__upds__apply__nontin,axiom,
! [F: list_char > option_ty,Ys_1: list_ty,X_1: list_char,Xs_1: list_list_char] :
( ~ ( member_list_char @ X_1 @ ( set_list_char @ Xs_1 ) )
=> ( ( map_up891053837har_ty @ F @ Xs_1 @ Ys_1 @ X_1 )
= ( F @ X_1 ) ) ) ).
thf(fact_289_Red__lcl__add,axiom,
! [L_0: list_char > option_val,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ ( map_ad325961431ar_val @ L_0 @ L ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_290_map__add__find__right,axiom,
! [M: list_char > option_val,N: list_char > option_val,K: list_char,Xx: val] :
( ( ( N @ K )
= ( some_val @ Xx ) )
=> ( ( map_ad325961431ar_val @ M @ N @ K )
= ( some_val @ Xx ) ) ) ).
thf(fact_291_map__add__assoc,axiom,
! [M1_1: list_char > option_val,M2_1: list_char > option_val,M3: list_char > option_val] :
( ( map_ad325961431ar_val @ M1_1 @ ( map_ad325961431ar_val @ M2_1 @ M3 ) )
= ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ M1_1 @ M2_1 ) @ M3 ) ) ).
thf(fact_292_map__add__upds,axiom,
! [M1: list_char > option_val,M2: list_char > option_val,Xs: list_list_char,Ys: list_val] :
( ( map_ad325961431ar_val @ M1 @ ( map_up1085636310ar_val @ M2 @ Xs @ Ys ) )
= ( map_up1085636310ar_val @ ( map_ad325961431ar_val @ M1 @ M2 ) @ Xs @ Ys ) ) ).
thf(fact_293_map__add__upds,axiom,
! [M1: list_char > option_ty,M2: list_char > option_ty,Xs: list_list_char,Ys: list_ty] :
( ( map_add_list_char_ty @ M1 @ ( map_up891053837har_ty @ M2 @ Xs @ Ys ) )
= ( map_up891053837har_ty @ ( map_add_list_char_ty @ M1 @ M2 ) @ Xs @ Ys ) ) ).
thf(fact_294_red__lcl__add,axiom,
! [L_0: list_char > option_val,E_1: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H_1: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ L ) ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1 @ ( map_ad325961431ar_val @ L_0 @ L ) ) ) ) @ ( red @ P ) ) ) ).
thf(fact_295_hext__def,axiom,
! [H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ( hext @ H @ H_1 )
<=> ! [A: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ? [Fs_1: produc1278157519t_char > option_val] :
( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_1 ) ) ) ) ) ).
thf(fact_296_hext__objD,axiom,
! [A_1: nat,C: list_char,Fs_2: produc1278157519t_char > option_val,H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ( hext @ H @ H_1 )
=> ( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_2 ) ) )
=> ? [Fs_1: produc1278157519t_char > option_val] :
( ( H_1 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_1 ) ) ) ) ) ).
thf(fact_297_hextI,axiom,
! [H_1: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ! [A: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ? [Fs_1: produc1278157519t_char > option_val] :
( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_1 ) ) ) )
=> ( hext @ H @ H_1 ) ) ).
thf(fact_298_TryRedsVal,axiom,
! [C: list_char,V: list_char,E_2: exp_list_char,E_1: exp_list_char,S_1: produc2090907612on_val,V_1: val,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C @ V @ E_2 ) @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_299_red__reds_OTryRed,axiom,
! [C: list_char,V: list_char,E_2: exp_list_char,E_1: exp_list_char,S_1: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_1 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C @ V @ E_2 ) @ S_1 ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V @ E_2 ) @ S ) ) @ ( red @ P ) ) ) ).
%----Helper facts (2)
thf(help_fequal_1_1_fequal_000tc__Type__Oty_T,axiom,
! [X: ty,Y: ty] :
( ~ ( fequal_ty @ X @ Y )
| ( X = Y ) ) ).
thf(help_fequal_2_1_fequal_000tc__Type__Oty_T,axiom,
! [X: ty,Y: ty] :
( ( X != Y )
| ( fequal_ty @ X @ Y ) ) ).
%----Conjectures (3)
thf(conj_0,hypothesis,
( ( size_s2113983095t_char @ vs_1 )
= ( size_size_list_ty @ ts ) ) ).
thf(conj_1,hypothesis,
( ( size_size_list_val @ vs )
= ( size_size_list_ty @ ts ) ) ).
thf(conj_2,conjecture,
( ( wTrt @ p @ h @ e_1 @ ( blocks @ ( produc921874948t_char @ vs_1 @ ( produc1909267824t_char @ ts @ ( produc1916172923t_char @ vs @ e ) ) ) ) @ t )
<=> ( ( wTrt @ p @ h @ ( map_up891053837har_ty @ e_1 @ vs_1 @ ts ) @ e @ t )
& ? [Ts: list_ty] :
( ( ( map_val_option_ty @ ( typeof_h @ h ) @ vs )
= ( map_ty_option_ty @ some_ty @ Ts ) )
& ( list_all2_ty_ty @ ( widen_2090681816t_char @ p ) @ Ts @ ts ) ) ) ) ).
%------------------------------------------------------------------------------