% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_150__5335402_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:41.554

% Could-be-implicit typings (20)
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
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    option2118145160on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    option_set_list_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (55)
thf(sy_c_DefAss_O_092_060D_062_001t__List__Olist_It__String__Ochar_J, type,
    d_list_char : exp_list_char > option_set_list_char > $o).
thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
    block_list_char : list_char > ty > exp_list_char > exp_list_char).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
    fun_up1252458416on_val : (list_char > option_val) > list_char > option_val > list_char > option_val).
thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    fun_up262443479on_val : (nat > option2118145160on_val) > nat > option2118145160on_val > nat > option2118145160on_val).
thf(sy_c_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    if_opt451925058on_val : $o > option2118145160on_val > option2118145160on_val > option2118145160on_val).
thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
    if_option_val : $o > option_val > option_val > option_val).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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    dom_Pr269338893on_val : (produc1172664615on_val > option2118145160on_val) > set_Pr1189492743on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_Pr1335625324t_char : (produc1172664615on_val > option_set_list_char) > set_Pr1189492743on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Value__Oval, type,
    dom_Pr162898261al_val : (produc1172664615on_val > option_val) > set_Pr1189492743on_val).
thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Map_Omap__add_001t__Nat__Onat_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    map_ad109059391on_val : (nat > option2118145160on_val) > (nat > option2118145160on_val) > nat > option2118145160on_val).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    none_P1535574167on_val : option2118145160on_val).
thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    none_set_list_char : option_set_list_char).
thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
    none_val : option_val).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    some_set_list_char : set_list_char > option_set_list_char).
thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
    some_val : val > option_val).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_Eo_J_J, type,
    ord_le752245279_val_o : ((nat > option2118145160on_val) > (list_char > option_val) > $o) > ((nat > option2118145160on_val) > (list_char > option_val) > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_M_062_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_M_Eo_J_J, type,
    ord_le383107121_val_o : (exp_list_char > produc515445032on_val > $o) > (exp_list_char > produc515445032on_val > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__List__Olist_It__String__Ochar_J_M_062_I_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_Eo_J_J, type,
    ord_le1192209529_val_o : (list_char > (produc1257910179t_char > option_val) > $o) > (list_char > (produc1257910179t_char > option_val) > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J, type,
    ord_le1945897678char_o : (list_char > $o) > (list_char > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_M_062_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_M_Eo_J_J, type,
    ord_le1677030286_val_o : (produc1097884484on_val > produc1097884484on_val > $o) > (produc1097884484on_val > produc1097884484on_val > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_Eo_J, type,
    ord_le14618614_val_o : (produc1172664615on_val > $o) > (produc1172664615on_val > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    ord_le1836582007t_char : set_list_char > set_list_char > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    ord_le930806568on_val : set_Pr723149704on_val > set_Pr723149704on_val > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    ord_le131203268on_val : set_Pr556513572on_val > set_Pr556513572on_val > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    ord_le1071216206on_val : set_Pr2075231726on_val > set_Pr2075231726on_val > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    ord_le837504935on_val : set_Pr1189492743on_val > set_Pr1189492743on_val > $o).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc904988266on_val : list_char > (produc1257910179t_char > option_val) > produc266837688on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J, type,
    collect_list_char : (list_char > $o) > set_list_char).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oassigned, type,
    assigned : list_char > exp_list_char > $o).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oredp, type,
    redp : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J, type,
    member_list_char : list_char > set_list_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T______, type,
    t : ty).
thf(sy_v_V______, type,
    v : list_char).
thf(sy_v_e_Ha______, type,
    e_a : exp_list_char).
thf(sy_v_ea______, type,
    ea : exp_list_char).
thf(sy_v_h_Ha______, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha______, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha______, type,
    l_a : list_char > option_val).
thf(sy_v_la______, type,
    la : list_char > option_val).

% Relevant facts (212)
thf(fact_0_BlockRedNone_Ohyps_I4_J, axiom,
    ((~ ((assigned @ v @ ea))))). % BlockRedNone.hyps(4)
thf(fact_1_BlockRedNone_Ohyps_I3_J, axiom,
    (((l_a @ v) = none_val))). % BlockRedNone.hyps(3)
thf(fact_2_BlockRedNone_Oprems, axiom,
    ((d_list_char @ (block_list_char @ v @ t @ ea) @ (some_set_list_char @ (dom_list_char_val @ la))))). % BlockRedNone.prems
thf(fact_3_BlockRedNone_Ohyps_I2_J, axiom,
    (((d_list_char @ ea @ (some_set_list_char @ (dom_list_char_val @ (fun_up1252458416on_val @ la @ v @ none_val)))) => (d_list_char @ e_a @ (some_set_list_char @ (dom_list_char_val @ l_a)))))). % BlockRedNone.hyps(2)
thf(fact_4_BlockRedNone_Ohyps_I1_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % BlockRedNone.hyps(1)
thf(fact_5_exp_Oinject_I10_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, Y101 : list_char, Y102 : ty, Y103 : exp_list_char]: (((block_list_char @ X101 @ X102 @ X103) = (block_list_char @ Y101 @ Y102 @ Y103)) = (((X101 = Y101)) & ((((X102 = Y102)) & ((X103 = Y103))))))))). % exp.inject(10)
thf(fact_6_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X @ Y) @ X @ Z) = (fun_up1252458416on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_7_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_8_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X : list_char]: ((fun_up1252458416on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_9_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_10_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_11_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X2 : nat]: (^[Y2 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_12_option_Oinject, axiom,
    ((![X22 : set_list_char, Y22 : set_list_char]: (((some_set_list_char @ X22) = (some_set_list_char @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_13_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_14_domD, axiom,
    ((![A : list_char, M : list_char > option_val]: ((member_list_char @ A @ (dom_list_char_val @ M)) => (?[B : val]: ((M @ A) = (some_val @ B))))))). % domD
thf(fact_15_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option_set_list_char]: ((member354538064on_val @ A @ (dom_Pr1335625324t_char @ M)) => (?[B : set_list_char]: ((M @ A) = (some_set_list_char @ B))))))). % domD
thf(fact_16_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A @ (dom_Pr269338893on_val @ M)) => (?[B : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B))))))). % domD
thf(fact_17_domI, axiom,
    ((![M : list_char > option_val, A : list_char, B2 : val]: (((M @ A) = (some_val @ B2)) => (member_list_char @ A @ (dom_list_char_val @ M)))))). % domI
thf(fact_18_domI, axiom,
    ((![M : produc1172664615on_val > option_set_list_char, A : produc1172664615on_val, B2 : set_list_char]: (((M @ A) = (some_set_list_char @ B2)) => (member354538064on_val @ A @ (dom_Pr1335625324t_char @ M)))))). % domI
thf(fact_19_domI, axiom,
    ((![M : produc1172664615on_val > option2118145160on_val, A : produc1172664615on_val, B2 : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B2)) => (member354538064on_val @ A @ (dom_Pr269338893on_val @ M)))))). % domI
thf(fact_20_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A : list_char, X : val, N : list_char > option_val, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ X)) = (fun_up1252458416on_val @ N @ A @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_21_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_22_map__upd__triv, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (((T @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = T))))). % map_upd_triv
thf(fact_23_map__upd__triv, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_24_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A : list_char, B2 : val, X : list_char, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ B2) @ X) = (some_val @ Y)) = (((((X = A)) & ((B2 = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_25_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B2 : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B2) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B2 = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_26_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1252458416on_val @ (^[X2 : list_char]: none_val) @ X @ none_val) = (^[X2 : list_char]: none_val))))). % empty_upd_none
thf(fact_27_empty__upd__none, axiom,
    ((![X : nat]: ((fun_up262443479on_val @ (^[X2 : nat]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X2 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_28_map__upd__nonempty, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (~ (((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = (^[X2 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_29_map__upd__nonempty, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = (^[X2 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_30_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_31_not__Some__eq, axiom,
    ((![X : option_set_list_char]: ((![Y2 : set_list_char]: (~ ((X = (some_set_list_char @ Y2))))) = (X = none_set_list_char))))). % not_Some_eq
thf(fact_32_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_33_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_34_not__None__eq, axiom,
    ((![X : option_set_list_char]: ((~ ((X = none_set_list_char))) = (?[Y2 : set_list_char]: (X = (some_set_list_char @ Y2))))))). % not_None_eq
thf(fact_35_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_36_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_val > $o, Y : option_val]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A2 : val, B : val]: ((X = (some_val @ A2)) => ((Y = (some_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_37_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A2 : val, B : set_list_char]: ((X = (some_val @ A2)) => ((Y = (some_set_list_char @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_38_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A2 : val, B : produc266837688on_val]: ((X = (some_val @ A2)) => ((Y = (some_P1299442195on_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_39_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_val > $o, Y : option_val]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A2 : set_list_char, B : val]: ((X = (some_set_list_char @ A2)) => ((Y = (some_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_40_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A2 : set_list_char, B : set_list_char]: ((X = (some_set_list_char @ A2)) => ((Y = (some_set_list_char @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_41_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A2 : set_list_char, B : produc266837688on_val]: ((X = (some_set_list_char @ A2)) => ((Y = (some_P1299442195on_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_42_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_val > $o, Y : option_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A2 : produc266837688on_val, B : val]: ((X = (some_P1299442195on_val @ A2)) => ((Y = (some_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_43_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A2 : produc266837688on_val, B : set_list_char]: ((X = (some_P1299442195on_val @ A2)) => ((Y = (some_set_list_char @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_44_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A2 : produc266837688on_val, B : produc266837688on_val]: ((X = (some_P1299442195on_val @ A2)) => ((Y = (some_P1299442195on_val @ B)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_45_split__option__all, axiom,
    (((^[P2 : option_val > $o]: (![X3 : option_val]: (P2 @ X3))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) & ((![X2 : val]: (P3 @ (some_val @ X2))))))))). % split_option_all
thf(fact_46_split__option__all, axiom,
    (((^[P2 : option_set_list_char > $o]: (![X3 : option_set_list_char]: (P2 @ X3))) = (^[P3 : option_set_list_char > $o]: (((P3 @ none_set_list_char)) & ((![X2 : set_list_char]: (P3 @ (some_set_list_char @ X2))))))))). % split_option_all
thf(fact_47_split__option__all, axiom,
    (((^[P2 : option2118145160on_val > $o]: (![X3 : option2118145160on_val]: (P2 @ X3))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_48_split__option__ex, axiom,
    (((^[P2 : option_val > $o]: (?[X3 : option_val]: (P2 @ X3))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) | ((?[X2 : val]: (P3 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_49_split__option__ex, axiom,
    (((^[P2 : option_set_list_char > $o]: (?[X3 : option_set_list_char]: (P2 @ X3))) = (^[P3 : option_set_list_char > $o]: (((P3 @ none_set_list_char)) | ((?[X2 : set_list_char]: (P3 @ (some_set_list_char @ X2))))))))). % split_option_ex
thf(fact_50_split__option__ex, axiom,
    (((^[P2 : option2118145160on_val > $o]: (?[X3 : option2118145160on_val]: (P2 @ X3))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_51_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X4 : val]: (P @ (some_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_52_option_Oinducts, axiom,
    ((![P : option_set_list_char > $o, Option : option_set_list_char]: ((P @ none_set_list_char) => ((![X4 : set_list_char]: (P @ (some_set_list_char @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_53_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X4 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_54_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_55_option_Oexhaust, axiom,
    ((![Y : option_set_list_char]: ((~ ((Y = none_set_list_char))) => (~ ((![X23 : set_list_char]: (~ ((Y = (some_set_list_char @ X23))))))))))). % option.exhaust
thf(fact_56_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_57_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_58_option_OdiscI, axiom,
    ((![Option : option_set_list_char, X22 : set_list_char]: ((Option = (some_set_list_char @ X22)) => (~ ((Option = none_set_list_char))))))). % option.discI
thf(fact_59_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_60_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_61_option_Odistinct_I1_J, axiom,
    ((![X22 : set_list_char]: (~ ((none_set_list_char = (some_set_list_char @ X22))))))). % option.distinct(1)
thf(fact_62_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_63_domIff, axiom,
    ((![A : list_char, M : list_char > option_val]: ((member_list_char @ A @ (dom_list_char_val @ M)) = (~ (((M @ A) = none_val))))))). % domIff
thf(fact_64_domIff, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option_val]: ((member354538064on_val @ A @ (dom_Pr162898261al_val @ M)) = (~ (((M @ A) = none_val))))))). % domIff
thf(fact_65_domIff, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A @ (dom_Pr269338893on_val @ M)) = (~ (((M @ A) = none_P1535574167on_val))))))). % domIff
thf(fact_66_dom__def, axiom,
    ((dom_list_char_val = (^[M2 : list_char > option_val]: (collect_list_char @ (^[A3 : list_char]: (~ (((M2 @ A3) = none_val))))))))). % dom_def
thf(fact_67_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_68_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_69_fun__upd__twist, axiom,
    ((![A : list_char, C : list_char, M : list_char > option_val, B2 : option_val, D : option_val]: ((~ ((A = C))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A @ B2) @ C @ D) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C @ D) @ A @ B2)))))). % fun_upd_twist
thf(fact_70_fun__upd__twist, axiom,
    ((![A : nat, C : nat, M : nat > option2118145160on_val, B2 : option2118145160on_val, D : option2118145160on_val]: ((~ ((A = C))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B2) @ C @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C @ D) @ A @ B2)))))). % fun_upd_twist
thf(fact_71_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up1252458416on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_72_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_73_fun__upd__same, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: ((fun_up1252458416on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_74_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_75_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((F @ X) = Y) => ((fun_up1252458416on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_76_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((F @ X) = Y) => ((fun_up262443479on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_77_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = (fun_up1252458416on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_78_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = (fun_up262443479on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_79_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A3 : list_char]: (^[B3 : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A3) @ B3 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_80_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A3 : nat]: (^[B3 : option2118145160on_val]: (^[X2 : nat]: (if_opt451925058on_val @ (X2 = A3) @ B3 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_81_red__reds_OBlockRedNone, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T2 @ E) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T2 @ E2) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_82_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_83_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_84_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_85_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_86_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_87_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A5 @ B4)) = (((A = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_88_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A5 @ B4)) = (((A = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_89_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A5 @ B4)) = (((A = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_90_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A5 @ B4)) = (((A = A5)) & ((B2 = B4))))))). % old.prod.inject
thf(fact_91_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_92_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_93_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_94_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : produc1257910179t_char > option_val, Y1 : list_char, Y22 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X22) = (produc904988266on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_95_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_96_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_97_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_98_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_99_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_100_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_101_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_102_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A2 : list_char, B : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_103_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_104_Pair__inject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_105_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_106_Pair__inject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A5 @ B4)) => (~ (((A = A5) => (~ ((B2 = B4)))))))))). % Pair_inject
thf(fact_107_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P4 : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B))) => (P @ P4))))). % prod_cases
thf(fact_108_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ P4))))). % prod_cases
thf(fact_109_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ P4))))). % prod_cases
thf(fact_110_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P4 : produc266837688on_val]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B))) => (P @ P4))))). % prod_cases
thf(fact_111_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_112_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X4 : exp_list_char, Y3 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_113_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P4 = (produc52622304on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_114_surj__pair, axiom,
    ((![P4 : produc266837688on_val]: (?[X4 : list_char, Y3 : produc1257910179t_char > option_val]: (P4 = (produc904988266on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_115_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_116_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A2 : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_117_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_118_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_119_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, T2 : ty]: ((redp @ P @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val)) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E))) => (redp @ P @ (block_list_char @ V @ T2 @ E) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T2 @ E2) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V)))))))))). % redp_redsp.BlockRedNone
thf(fact_120_red__lcl__incr, axiom,
    ((![E : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E2 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_0) @ (dom_list_char_val @ L_1)))))). % red_lcl_incr
thf(fact_121_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_122_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_123_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_124_subsetI, axiom,
    ((![A4 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: ((member354538064on_val @ X4 @ A4) => (member354538064on_val @ X4 @ B5))) => (ord_le837504935on_val @ A4 @ B5))))). % subsetI
thf(fact_125_subsetI, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((![X4 : list_char]: ((member_list_char @ X4 @ A4) => (member_list_char @ X4 @ B5))) => (ord_le1836582007t_char @ A4 @ B5))))). % subsetI
thf(fact_126_subset__antisym, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ A4 @ B5) => ((ord_le1836582007t_char @ B5 @ A4) => (A4 = B5)))))). % subset_antisym
thf(fact_127_order__refl, axiom,
    ((![X : set_list_char]: (ord_le1836582007t_char @ X @ X)))). % order_refl
thf(fact_128_Collect__subset, axiom,
    ((![A4 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A4)) & ((P @ X2))))) @ A4)))). % Collect_subset
thf(fact_129_Collect__subset, axiom,
    ((![A4 : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ A4)) & ((P @ X2))))) @ A4)))). % Collect_subset
thf(fact_130_less__eq__set__def, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (ord_le14618614_val_o @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A6)) @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ B6)))))))). % less_eq_set_def
thf(fact_131_less__eq__set__def, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (ord_le1945897678char_o @ (^[X2 : list_char]: (member_list_char @ X2 @ A6)) @ (^[X2 : list_char]: (member_list_char @ X2 @ B6)))))))). % less_eq_set_def
thf(fact_132_dual__order_Oantisym, axiom,
    ((![B2 : set_list_char, A : set_list_char]: ((ord_le1836582007t_char @ B2 @ A) => ((ord_le1836582007t_char @ A @ B2) => (A = B2)))))). % dual_order.antisym
thf(fact_133_dual__order_Oeq__iff, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[A3 : set_list_char]: (^[B3 : set_list_char]: (((ord_le1836582007t_char @ B3 @ A3)) & ((ord_le1836582007t_char @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_134_dual__order_Otrans, axiom,
    ((![B2 : set_list_char, A : set_list_char, C : set_list_char]: ((ord_le1836582007t_char @ B2 @ A) => ((ord_le1836582007t_char @ C @ B2) => (ord_le1836582007t_char @ C @ A)))))). % dual_order.trans
thf(fact_135_dual__order_Orefl, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ A)))). % dual_order.refl
thf(fact_136_order__trans, axiom,
    ((![X : set_list_char, Y : set_list_char, Z : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ Z) => (ord_le1836582007t_char @ X @ Z)))))). % order_trans
thf(fact_137_order__class_Oorder_Oantisym, axiom,
    ((![A : set_list_char, B2 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ B2 @ A) => (A = B2)))))). % order_class.order.antisym
thf(fact_138_ord__le__eq__trans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((B2 = C) => (ord_le1836582007t_char @ A @ C)))))). % ord_le_eq_trans
thf(fact_139_ord__eq__le__trans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C : set_list_char]: ((A = B2) => ((ord_le1836582007t_char @ B2 @ C) => (ord_le1836582007t_char @ A @ C)))))). % ord_eq_le_trans
thf(fact_140_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[A3 : set_list_char]: (^[B3 : set_list_char]: (((ord_le1836582007t_char @ A3 @ B3)) & ((ord_le1836582007t_char @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_141_antisym__conv, axiom,
    ((![Y : set_list_char, X : set_list_char]: ((ord_le1836582007t_char @ Y @ X) => ((ord_le1836582007t_char @ X @ Y) = (X = Y)))))). % antisym_conv
thf(fact_142_order_Otrans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ B2 @ C) => (ord_le1836582007t_char @ A @ C)))))). % order.trans
thf(fact_143_eq__refl, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((X = Y) => (ord_le1836582007t_char @ X @ Y))))). % eq_refl
thf(fact_144_antisym, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ X) => (X = Y)))))). % antisym
thf(fact_145_eq__iff, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[X2 : set_list_char]: (^[Y2 : set_list_char]: (((ord_le1836582007t_char @ X2 @ Y2)) & ((ord_le1836582007t_char @ Y2 @ X2)))))))). % eq_iff
thf(fact_146_ord__le__eq__subst, axiom,
    ((![A : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => (((F @ B2) = C) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_147_ord__eq__le__subst, axiom,
    ((![A : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C : set_list_char]: ((A = (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_148_order__subst2, axiom,
    ((![A : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ (F @ B2) @ C) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ (F @ A) @ C))))))). % order_subst2
thf(fact_149_order__subst1, axiom,
    ((![A : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C : set_list_char]: ((ord_le1836582007t_char @ A @ (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ A @ (F @ C)))))))). % order_subst1
thf(fact_150_Collect__mono__iff, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)) = (![X2 : list_char]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_151_set__eq__subset, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (((ord_le1836582007t_char @ A6 @ B6)) & ((ord_le1836582007t_char @ B6 @ A6)))))))). % set_eq_subset
thf(fact_152_subset__trans, axiom,
    ((![A4 : set_list_char, B5 : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A4 @ B5) => ((ord_le1836582007t_char @ B5 @ C3) => (ord_le1836582007t_char @ A4 @ C3)))))). % subset_trans
thf(fact_153_Collect__mono, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((![X4 : list_char]: ((P @ X4) => (Q @ X4))) => (ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)))))). % Collect_mono
thf(fact_154_subset__refl, axiom,
    ((![A4 : set_list_char]: (ord_le1836582007t_char @ A4 @ A4)))). % subset_refl
thf(fact_155_subset__iff, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![T3 : produc1172664615on_val]: (((member354538064on_val @ T3 @ A6)) => ((member354538064on_val @ T3 @ B6))))))))). % subset_iff
thf(fact_156_subset__iff, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (![T3 : list_char]: (((member_list_char @ T3 @ A6)) => ((member_list_char @ T3 @ B6))))))))). % subset_iff
thf(fact_157_equalityD2, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((A4 = B5) => (ord_le1836582007t_char @ B5 @ A4))))). % equalityD2
thf(fact_158_equalityD1, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((A4 = B5) => (ord_le1836582007t_char @ A4 @ B5))))). % equalityD1
thf(fact_159_subset__eq, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A6)) => ((member354538064on_val @ X2 @ B6))))))))). % subset_eq
thf(fact_160_subset__eq, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (![X2 : list_char]: (((member_list_char @ X2 @ A6)) => ((member_list_char @ X2 @ B6))))))))). % subset_eq
thf(fact_161_equalityE, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((A4 = B5) => (~ (((ord_le1836582007t_char @ A4 @ B5) => (~ ((ord_le1836582007t_char @ B5 @ A4)))))))))). % equalityE
thf(fact_162_subsetD, axiom,
    ((![A4 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val, C : produc1172664615on_val]: ((ord_le837504935on_val @ A4 @ B5) => ((member354538064on_val @ C @ A4) => (member354538064on_val @ C @ B5)))))). % subsetD
thf(fact_163_subsetD, axiom,
    ((![A4 : set_list_char, B5 : set_list_char, C : list_char]: ((ord_le1836582007t_char @ A4 @ B5) => ((member_list_char @ C @ A4) => (member_list_char @ C @ B5)))))). % subsetD
thf(fact_164_in__mono, axiom,
    ((![A4 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val, X : produc1172664615on_val]: ((ord_le837504935on_val @ A4 @ B5) => ((member354538064on_val @ X @ A4) => (member354538064on_val @ X @ B5)))))). % in_mono
thf(fact_165_in__mono, axiom,
    ((![A4 : set_list_char, B5 : set_list_char, X : list_char]: ((ord_le1836582007t_char @ A4 @ B5) => ((member_list_char @ X @ A4) => (member_list_char @ X @ B5)))))). % in_mono
thf(fact_166_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: (((H @ A) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_167_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_168_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))). % hext_upd_obj
thf(fact_169_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3))))))))). % hext_objD
thf(fact_170_hext__def, axiom,
    ((hext = (^[H4 : nat > option2118145160on_val]: (^[H5 : nat > option2118145160on_val]: (![A3 : nat]: (![C4 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H4 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H5 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5)))))))))))))). % hext_def
thf(fact_171_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A2 : nat, C5 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H2 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs7)))))) => (hext @ H @ H2))))). % hextI
thf(fact_172_pred__subset__eq, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le14618614_val_o @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ R)) @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ S))) = (ord_le837504935on_val @ R @ S))))). % pred_subset_eq
thf(fact_173_pred__subset__eq, axiom,
    ((![R : set_list_char, S : set_list_char]: ((ord_le1945897678char_o @ (^[X2 : list_char]: (member_list_char @ X2 @ R)) @ (^[X2 : list_char]: (member_list_char @ X2 @ S))) = (ord_le1836582007t_char @ R @ S))))). % pred_subset_eq
thf(fact_174_subset__Collect__iff, axiom,
    ((![B5 : set_Pr1189492743on_val, A4 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: ((ord_le837504935on_val @ B5 @ A4) => ((ord_le837504935on_val @ B5 @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A4)) & ((P @ X2)))))) = (![X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ B5)) => ((P @ X2))))))))). % subset_Collect_iff
thf(fact_175_subset__Collect__iff, axiom,
    ((![B5 : set_list_char, A4 : set_list_char, P : list_char > $o]: ((ord_le1836582007t_char @ B5 @ A4) => ((ord_le1836582007t_char @ B5 @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ A4)) & ((P @ X2)))))) = (![X2 : list_char]: (((member_list_char @ X2 @ B5)) => ((P @ X2))))))))). % subset_Collect_iff
thf(fact_176_subset__CollectI, axiom,
    ((![B5 : set_Pr1189492743on_val, A4 : set_Pr1189492743on_val, Q : produc1172664615on_val > $o, P : produc1172664615on_val > $o]: ((ord_le837504935on_val @ B5 @ A4) => ((![X4 : produc1172664615on_val]: ((member354538064on_val @ X4 @ B5) => ((Q @ X4) => (P @ X4)))) => (ord_le837504935on_val @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ B5)) & ((Q @ X2))))) @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A4)) & ((P @ X2))))))))))). % subset_CollectI
thf(fact_177_subset__CollectI, axiom,
    ((![B5 : set_list_char, A4 : set_list_char, Q : list_char > $o, P : list_char > $o]: ((ord_le1836582007t_char @ B5 @ A4) => ((![X4 : list_char]: ((member_list_char @ X4 @ B5) => ((Q @ X4) => (P @ X4)))) => (ord_le1836582007t_char @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ B5)) & ((Q @ X2))))) @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ A4)) & ((P @ X2))))))))))). % subset_CollectI
thf(fact_178_Collect__restrict, axiom,
    ((![X5 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ X5)) & ((P @ X2))))) @ X5)))). % Collect_restrict
thf(fact_179_Collect__restrict, axiom,
    ((![X5 : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ X5)) & ((P @ X2))))) @ X5)))). % Collect_restrict
thf(fact_180_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S2 : produc1097884484on_val, R : set_Pr1189492743on_val, S3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_181_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S2 : produc515445032on_val, R : set_Pr556513572on_val, S3 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_182_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S2 : list_char > option_val, R : set_Pr723149704on_val, S3 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member652041809on_val @ (produc52622304on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_183_ssubst__Pair__rhs, axiom,
    ((![R2 : list_char, S2 : produc1257910179t_char > option_val, R : set_Pr2075231726on_val, S3 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ R2 @ S2) @ R) => ((S3 = S2) => (member1296415951on_val @ (produc904988266on_val @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_184_subrelI, axiom,
    ((![R2 : set_Pr1189492743on_val, S2 : set_Pr1189492743on_val]: ((![X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R2) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ S2))) => (ord_le837504935on_val @ R2 @ S2))))). % subrelI
thf(fact_185_subrelI, axiom,
    ((![R2 : set_Pr556513572on_val, S2 : set_Pr556513572on_val]: ((![X4 : exp_list_char, Y3 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X4 @ Y3) @ R2) => (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y3) @ S2))) => (ord_le131203268on_val @ R2 @ S2))))). % subrelI
thf(fact_186_subrelI, axiom,
    ((![R2 : set_Pr723149704on_val, S2 : set_Pr723149704on_val]: ((![X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ X4 @ Y3) @ R2) => (member652041809on_val @ (produc52622304on_val @ X4 @ Y3) @ S2))) => (ord_le930806568on_val @ R2 @ S2))))). % subrelI
thf(fact_187_subrelI, axiom,
    ((![R2 : set_Pr2075231726on_val, S2 : set_Pr2075231726on_val]: ((![X4 : list_char, Y3 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ X4 @ Y3) @ R2) => (member1296415951on_val @ (produc904988266on_val @ X4 @ Y3) @ S2))) => (ord_le1071216206on_val @ R2 @ S2))))). % subrelI
thf(fact_188_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_189_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_190_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_191_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_192_pred__subset__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le1677030286_val_o @ (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) @ (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (ord_le837504935on_val @ R @ S))))). % pred_subset_eq2
thf(fact_193_pred__subset__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: ((ord_le383107121_val_o @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (ord_le131203268on_val @ R @ S))))). % pred_subset_eq2
thf(fact_194_pred__subset__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: ((ord_le752245279_val_o @ (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) @ (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (ord_le930806568on_val @ R @ S))))). % pred_subset_eq2
thf(fact_195_pred__subset__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: ((ord_le1192209529_val_o @ (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) @ (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (ord_le1071216206on_val @ R @ S))))). % pred_subset_eq2
thf(fact_196_prop__restrict, axiom,
    ((![X : produc1172664615on_val, Z4 : set_Pr1189492743on_val, X5 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ X @ Z4) => ((ord_le837504935on_val @ Z4 @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ X5)) & ((P @ X2)))))) => (P @ X)))))). % prop_restrict
thf(fact_197_prop__restrict, axiom,
    ((![X : list_char, Z4 : set_list_char, X5 : set_list_char, P : list_char > $o]: ((member_list_char @ X @ Z4) => ((ord_le1836582007t_char @ Z4 @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ X5)) & ((P @ X2)))))) => (P @ X)))))). % prop_restrict
thf(fact_198_conj__subset__def, axiom,
    ((![A4 : set_list_char, P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ A4 @ (collect_list_char @ (^[X2 : list_char]: (((P @ X2)) & ((Q @ X2)))))) = (((ord_le1836582007t_char @ A4 @ (collect_list_char @ P))) & ((ord_le1836582007t_char @ A4 @ (collect_list_char @ Q)))))))). % conj_subset_def
thf(fact_199_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_200_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M22 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M22 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M22) @ M3))))). % map_add_assoc
thf(fact_201_map__add__find__right, axiom,
    ((![N : list_char > option_val, K : list_char, Xx : val, M : list_char > option_val]: (((N @ K) = (some_val @ Xx)) => ((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ Xx)))))). % map_add_find_right
thf(fact_202_map__add__eq__empty__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((map_ad1615113112ar_val @ F @ G) = (^[X2 : list_char]: none_val)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % map_add_eq_empty_iff
thf(fact_203_map__add__None, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char]: (((map_ad1615113112ar_val @ M @ N @ K) = none_val) = ((((N @ K) = none_val)) & (((M @ K) = none_val))))))). % map_add_None
thf(fact_204_empty__eq__map__add__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((^[X2 : list_char]: none_val) = (map_ad1615113112ar_val @ F @ G)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % empty_eq_map_add_iff
thf(fact_205_map__add__empty, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ M @ (^[X2 : list_char]: none_val)) = M)))). % map_add_empty
thf(fact_206_empty__map__add, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ (^[X2 : list_char]: none_val) @ M) = M)))). % empty_map_add
thf(fact_207_map__add__upd, axiom,
    ((![F : list_char > option_val, G : list_char > option_val, X : list_char, Y : val]: ((map_ad1615113112ar_val @ F @ (fun_up1252458416on_val @ G @ X @ (some_val @ Y))) = (fun_up1252458416on_val @ (map_ad1615113112ar_val @ F @ G) @ X @ (some_val @ Y)))))). % map_add_upd
thf(fact_208_map__add__upd, axiom,
    ((![F : nat > option2118145160on_val, G : nat > option2118145160on_val, X : nat, Y : produc266837688on_val]: ((map_ad109059391on_val @ F @ (fun_up262443479on_val @ G @ X @ (some_P1299442195on_val @ Y))) = (fun_up262443479on_val @ (map_ad109059391on_val @ F @ G) @ X @ (some_P1299442195on_val @ Y)))))). % map_add_upd
thf(fact_209_map__add__dom__app__simps_I3_J, axiom,
    ((![M : list_char, L22 : list_char > option_val, L1 : list_char > option_val]: ((~ ((member_list_char @ M @ (dom_list_char_val @ L22)))) => ((map_ad1615113112ar_val @ L1 @ L22 @ M) = (L1 @ M)))))). % map_add_dom_app_simps(3)
thf(fact_210_map__add__dom__app__simps_I2_J, axiom,
    ((![M : list_char, L1 : list_char > option_val, L22 : list_char > option_val]: ((~ ((member_list_char @ M @ (dom_list_char_val @ L1)))) => ((map_ad1615113112ar_val @ L1 @ L22 @ M) = (L22 @ M)))))). % map_add_dom_app_simps(2)
thf(fact_211_map__add__dom__app__simps_I1_J, axiom,
    ((![M : list_char, L22 : list_char > option_val, L1 : list_char > option_val]: ((member_list_char @ M @ (dom_list_char_val @ L22)) => ((map_ad1615113112ar_val @ L1 @ L22 @ M) = (L22 @ M)))))). % map_add_dom_app_simps(1)

% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_T, axiom,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((d_list_char @ (block_list_char @ v @ t @ e_a) @ (some_set_list_char @ (dom_list_char_val @ (fun_up1252458416on_val @ l_a @ v @ (la @ v))))))).
