% 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_665__5342984_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:09.457

% Could-be-implicit typings (31)
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thf(ty_n_t__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,
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thf(ty_n_t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_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,
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thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
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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__Option__Ooption_It__Type__Oty_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__Set__Oset_It__Nat__Onat_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (76)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Oconf_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,
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thf(sy_c_Conform_Ohconf_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,
    hconf_1244167010t_char : list_P1234162913t_char > (nat > option2118145160on_val) > $o).
thf(sy_c_Conform_Olconf_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,
    lconf_485928294t_char : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_val) > (list_char > option_ty) > $o).
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_DefAss_Ohyper__isin_001t__List__Olist_It__String__Ochar_J, type,
    hyper_isin_list_char : list_char > option_set_list_char > $o).
thf(sy_c_Expr_Obinop, type,
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thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_OVar_001t__List__Olist_It__String__Ochar_J, type,
    var_list_char : list_char > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Map_Odom_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,
    dom_na451844572on_val : (nat > option2118145160on_val) > set_nat).
thf(sy_c_Map_Odom_001t__Nat__Onat_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_na736636731t_char : (nat > option_set_list_char) > set_nat).
thf(sy_c_Map_Odom_001t__Nat__Onat_001t__Type__Oty, type,
    dom_nat_ty : (nat > option_ty) > set_nat).
thf(sy_c_Map_Odom_001t__Nat__Onat_001t__Value__Oval, type,
    dom_nat_val : (nat > option_val) > set_nat).
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__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,
    dom_Pr269338893on_val : (produc1172664615on_val > option2118145160on_val) > set_Pr1189492743on_val).
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    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__Type__Oty, type,
    dom_Pr1796446476val_ty : (produc1172664615on_val > option_ty) > 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_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__Type__Oty, type,
    some_ty : ty > option_ty).
thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
    some_val : val > option_val).
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__Obop_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    produc1753769388al_val : bop > product_prod_val_val > produc1373793468al_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__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    produc1304532571t_char : list_char > list_char > produc1257910179t_char).
thf(sy_c_Product__Type_OPair_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_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,
    produc2106877847on_val : produc515445032on_val > produc515445032on_val > produc744932519on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    produc1144711447al_val : produc1373793468al_val > produc1373793468al_val > produc674182439al_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_Product__Type_OPair_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_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,
    produc881885833on_val : produc266837688on_val > produc266837688on_val > produc1085126737on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc395356247t_char : produc1257910179t_char > produc1257910179t_char > produc442406631t_char).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Value__Oval, type,
    product_Pair_val_val : val > val > product_prod_val_val).
thf(sy_c_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
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_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_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_State_Olcl, type,
    lcl : produc515445032on_val > list_char > option_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__String__Ochar_J, type,
    transi1879726366t_char : set_Pr164112643t_char > set_Pr164112643t_char).
thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    transi531594559al_val : set_Pr711661575al_val > set_Pr711661575al_val).
thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi2071064181on_val : set_Pr2110063281on_val > set_Pr2110063281on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    transi858104614t_char : set_Pr729957319t_char > set_Pr729957319t_char).
thf(sy_c_TypeRel_Owiden_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,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Owf__config, type,
    typeSa1969945757config : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > exp_list_char > ty > $o).
thf(sy_c_Value_Oval_OAddr, type,
    addr : nat > val).
thf(sy_c_WWellForm_Owwf__J__mdecl, type,
    wwf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $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_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $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__Nat__Onat, type,
    member_nat : nat > set_nat > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_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_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,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_Mt__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J_J, type,
    member1528603216al_val : produc674182439al_val > set_Pr711661575al_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_c_member_001t__Product____Type__Oprod_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_Mt__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,
    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    member803902992t_char : produc442406631t_char > set_Pr729957319t_char > $o).
thf(sy_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T, type,
    t : ty).
thf(sy_v_T_H, type,
    t2 : ty).
thf(sy_v_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (213)
thf(fact_0_Progress, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, S : produc515445032on_val, E2 : exp_list_char, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((typeSa1969945757config @ P @ E @ S @ E2 @ T) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S)))) => ((~ ((final_list_char @ E2))) => (?[E3 : exp_list_char, S2 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)))))))))). % Progress
thf(fact_1_Subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((typeSa1969945757config @ P @ E @ S @ E2 @ T) => (?[T2 : ty]: ((typeSa1969945757config @ P @ E @ S3 @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T))))))))). % Subject_reduction
thf(fact_2_Subject__reductions, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1969945757config @ P @ E @ S @ E2 @ T) => (?[T2 : ty]: ((typeSa1969945757config @ P @ E @ S3 @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T))))))))). % Subject_reductions
thf(fact_3_Red__preserves__defass, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S)))) => (d_list_char @ E4 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S3)))))))))). % Red_preserves_defass
thf(fact_4_ThrowReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_5_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_6_finalE, axiom,
    ((![E2 : exp_list_char]: ((final_list_char @ E2) => ((![V : val]: (~ ((E2 = (val_list_char @ V))))) => (~ ((![A2 : nat]: (~ ((E2 = (throw_list_char @ (val_list_char @ (addr @ A2)))))))))))))). % finalE
thf(fact_7_final__def, axiom,
    ((final_list_char = (^[E5 : exp_list_char]: (((?[V2 : val]: (E5 = (val_list_char @ V2)))) | ((?[A3 : nat]: (E5 = (throw_list_char @ (val_list_char @ (addr @ A3))))))))))). % final_def
thf(fact_8_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_9_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_10_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Ax @ Ay) => ((![A2 : list_char, B : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A2 @ B)) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A2 @ B) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_11_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : list_char, B : produc1257910179t_char > option_val, Aa : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A2 @ B)) @ (transi2071064181on_val @ R)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B) @ (produc904988266on_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_12_rtrancl__induct2, axiom,
    ((![Ax : bop, Ay : product_prod_val_val, Bx : bop, By : product_prod_val_val, R : set_Pr711661575al_val, P : bop > product_prod_val_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : bop, B : product_prod_val_val, Aa : bop, Ba : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ A2 @ B)) @ (transi531594559al_val @ R)) => ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A2 @ B) @ (produc1753769388al_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_13_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A2 @ B)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_14_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A2 @ B)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_15_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A2 : list_char, B : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A2 @ B)) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A2 @ B) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_16_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A2 : list_char, B : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A2 @ B)) @ R) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_17_converse__rtranclE2, axiom,
    ((![Xa : bop, Xb : product_prod_val_val, Za : bop, Zb : product_prod_val_val, R : set_Pr711661575al_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Xa @ Xb) @ (produc1753769388al_val @ Za @ Zb)) @ (transi531594559al_val @ R)) => ((~ (((produc1753769388al_val @ Xa @ Xb) = (produc1753769388al_val @ Za @ Zb)))) => (~ ((![A2 : bop, B : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Xa @ Xb) @ (produc1753769388al_val @ A2 @ B)) @ R) => (~ ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A2 @ B) @ (produc1753769388al_val @ Za @ Zb)) @ (transi531594559al_val @ R))))))))))))). % converse_rtranclE2
thf(fact_18_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A2 @ B)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_19_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A2 : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A2 @ B)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_20_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Bx @ By) => ((![A2 : list_char, B : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A2 @ B) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_21_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R)) => ((P @ Bx @ By) => ((![A2 : list_char, B : produc1257910179t_char > option_val, Aa : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B) @ (produc904988266on_val @ Aa @ Ba)) @ R) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_22_converse__rtrancl__induct2, axiom,
    ((![Ax : bop, Ay : product_prod_val_val, Bx : bop, By : product_prod_val_val, R : set_Pr711661575al_val, P : bop > product_prod_val_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Ax @ Ay) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R)) => ((P @ Bx @ By) => ((![A2 : bop, B : product_prod_val_val, Aa : bop, Ba : product_prod_val_val]: ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ A2 @ B) @ (produc1753769388al_val @ Aa @ Ba)) @ R) => ((member1528603216al_val @ (produc1144711447al_val @ (produc1753769388al_val @ Aa @ Ba) @ (produc1753769388al_val @ Bx @ By)) @ (transi531594559al_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_23_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Bx @ By) => ((![A2 : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_24_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Bx @ By) => ((![A2 : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_25_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : list_char, A4 : list_char, B3 : list_char]: (((produc1304532571t_char @ A @ B2) = (produc1304532571t_char @ A4 @ B3)) = (((A = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_26_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A4 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A4 @ B3)) = (((A = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_27_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A4 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A4 @ B3)) = (((A = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_28_old_Oprod_Oinject, axiom,
    ((![A : bop, B2 : product_prod_val_val, A4 : bop, B3 : product_prod_val_val]: (((produc1753769388al_val @ A @ B2) = (produc1753769388al_val @ A4 @ B3)) = (((A = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_29_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A4 @ B3)) = (((A = A4)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_30_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : list_char, Y1 : list_char, Y2 : list_char]: (((produc1304532571t_char @ X1 @ X2) = (produc1304532571t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_31_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_32_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_33_prod_Oinject, axiom,
    ((![X1 : bop, X2 : product_prod_val_val, Y1 : bop, Y2 : product_prod_val_val]: (((produc1753769388al_val @ X1 @ X2) = (produc1753769388al_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_34_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_35_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R) => (member354538064on_val @ P2 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_36_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_37_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E6 @ H3 @ L3 @ E6 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E3 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_1 @ H_1 @ L_1 @ E3 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E3 @ H4 @ L4)))) => (R2 @ E2 @ H @ L @ E4 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_38_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A2 : list_char, B : list_char]: (P @ (produc1304532571t_char @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_39_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_40_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_41_old_Oprod_Oinducts, axiom,
    ((![P : produc1373793468al_val > $o, Prod : produc1373793468al_val]: ((![A2 : bop, B : product_prod_val_val]: (P @ (produc1753769388al_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_42_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_43_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A2 : list_char, B : list_char]: (~ ((Y = (produc1304532571t_char @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_44_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_45_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_46_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1373793468al_val]: (~ ((![A2 : bop, B : product_prod_val_val]: (~ ((Y = (produc1753769388al_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_47_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_48_Pair__inject, axiom,
    ((![A : list_char, B2 : list_char, A4 : list_char, B3 : list_char]: (((produc1304532571t_char @ A @ B2) = (produc1304532571t_char @ A4 @ B3)) => (~ (((A = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_49_Pair__inject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A4 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_50_Pair__inject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A4 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_51_Pair__inject, axiom,
    ((![A : bop, B2 : product_prod_val_val, A4 : bop, B3 : product_prod_val_val]: (((produc1753769388al_val @ A @ B2) = (produc1753769388al_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_52_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_53_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P2 : produc1257910179t_char]: ((![A2 : list_char, B : list_char]: (P @ (produc1304532571t_char @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_54_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A2 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_55_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_56_prod__cases, axiom,
    ((![P : produc1373793468al_val > $o, P2 : produc1373793468al_val]: ((![A2 : bop, B : product_prod_val_val]: (P @ (produc1753769388al_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_57_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_58_surj__pair, axiom,
    ((![P2 : produc1257910179t_char]: (?[X : list_char, Y3 : list_char]: (P2 = (produc1304532571t_char @ X @ Y3)))))). % surj_pair
thf(fact_59_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X : list_char, Y3 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X @ Y3)))))). % surj_pair
thf(fact_60_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X @ Y3)))))). % surj_pair
thf(fact_61_surj__pair, axiom,
    ((![P2 : produc1373793468al_val]: (?[X : bop, Y3 : product_prod_val_val]: (P2 = (produc1753769388al_val @ X @ Y3)))))). % surj_pair
thf(fact_62_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X @ Y3)))))). % surj_pair
thf(fact_63_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_64_prod__induct3, axiom,
    ((![P : produc1373793468al_val > $o, X3 : produc1373793468al_val]: ((![A2 : bop, B : val, C : val]: (P @ (produc1753769388al_val @ A2 @ (product_Pair_val_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_65_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_66_prod__cases3, axiom,
    ((![Y : produc1373793468al_val]: (~ ((![A2 : bop, B : val, C : val]: (~ ((Y = (produc1753769388al_val @ A2 @ (product_Pair_val_val @ B @ C))))))))))). % prod_cases3
thf(fact_67_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B2 : list_char, R : set_Pr164112643t_char, C2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B2) @ R) => ((member89690956t_char @ (produc1304532571t_char @ B2 @ C2) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ A @ C2) @ (transi1879726366t_char @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_68_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_69_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B2 : list_char, R : set_Pr164112643t_char, C2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B2) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ B2 @ C2) @ R) => (member89690956t_char @ (produc1304532571t_char @ A @ C2) @ (transi1879726366t_char @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_70_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_71_converse__rtrancl__induct, axiom,
    ((![A : list_char, B2 : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B2) @ (transi1879726366t_char @ R)) => ((P @ B2) => ((![Y3 : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z @ B2) @ (transi1879726366t_char @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_72_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B2) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_73_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R))))). % rtrancl.rtrancl_refl
thf(fact_74_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_75_converse__rtranclE, axiom,
    ((![X3 : list_char, Z2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Z2) @ (transi1879726366t_char @ R)) => ((~ ((X3 = Z2))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_76_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X3 = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_77_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R)) => ((![A2 : list_char]: (P @ A2 @ A2)) => ((![A2 : list_char, B : list_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B) @ (transi1879726366t_char @ R)) => ((P @ A2 @ B) => ((member89690956t_char @ (produc1304532571t_char @ B @ C) @ R) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_78_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R)) => ((![A2 : produc1097884484on_val]: (P @ A2 @ A2)) => ((![A2 : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R)) => ((P @ A2 @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_79_rtrancl__induct, axiom,
    ((![A : list_char, B2 : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B2) @ (transi1879726366t_char @ R)) => ((P @ A) => ((![Y3 : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_80_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R)) => ((P @ A) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_81_rtrancl__trans, axiom,
    ((![X3 : list_char, Y : list_char, R : set_Pr164112643t_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z2) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Z2) @ (transi1879726366t_char @ R))))))). % rtrancl_trans
thf(fact_82_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_83_rtrancl_Osimps, axiom,
    ((![A1 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R)) = (((?[A3 : list_char]: (((A1 = A3)) & ((A22 = A3))))) | ((?[A3 : list_char]: (?[B4 : list_char]: (?[C3 : list_char]: (((A1 = A3)) & ((((A22 = C3)) & ((((member89690956t_char @ (produc1304532571t_char @ A3 @ B4) @ (transi1879726366t_char @ R))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_84_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A3 : produc1097884484on_val]: (((A1 = A3)) & ((A22 = A3))))) | ((?[A3 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A3)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A3 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_85_rtrancl_Ocases, axiom,
    ((![A1 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ A22) @ (transi1879726366t_char @ R)) => ((~ ((A22 = A1))) => (~ ((![B : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A1 @ B) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_86_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_87_rtranclE, axiom,
    ((![A : list_char, B2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B2) @ (transi1879726366t_char @ R)) => ((~ ((A = B2))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_88_rtranclE, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B2) @ (transi111096263on_val @ R)) => ((~ ((A = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_89_red__preserves__defass, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ L))) => (d_list_char @ E4 @ (some_set_list_char @ (dom_list_char_val @ L2))))))))). % red_preserves_defass
thf(fact_90_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_91_mem__Collect__eq, axiom,
    ((![A : nat, P : nat > $o]: ((member_nat @ A @ (collect_nat @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_92_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_93_Collect__mem__eq, axiom,
    ((![A5 : set_nat]: ((collect_nat @ (^[X4 : nat]: (member_nat @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_94_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_95_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_96_Red__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E @ E4 @ T2)))))))))). % Red_preserves_type
thf(fact_97_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_98_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_99_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_100_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_101_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_102_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V3 : val, T : ty, T3 : ty]: ((conf_P93989998t_char @ P @ H @ V3 @ T) => ((widen_917054840t_char @ P @ T @ T3) => (conf_P93989998t_char @ P @ H @ V3 @ T3)))))). % conf_widen
thf(fact_103_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => (?[T2 : ty]: ((wTrt @ P @ (hp @ S3) @ E @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_104_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S3)))))))). % Red_preserves_sconf
thf(fact_105_wf__config__def, axiom,
    ((typeSa1969945757config = (^[P3 : list_P1234162913t_char]: (^[E7 : list_char > option_ty]: (^[S4 : produc515445032on_val]: (^[E5 : exp_list_char]: (^[T4 : ty]: (((typeSa1777264139_sconf @ P3 @ E7 @ S4)) & ((wTrt @ P3 @ (hp @ S4) @ E7 @ E5 @ T4))))))))))). % wf_config_def
thf(fact_106_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_107_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E @ E2 @ T) => (?[T2 : ty]: ((wTrt @ P @ H2 @ E @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_108_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_109_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_110_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_111_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E @ E2 @ T) => (wTrt @ P @ H @ E @ E2 @ T))))). % WT_implies_WTrt
thf(fact_112__092_060D_062_Osimps_I14_J, axiom,
    ((![E2 : exp_list_char, A5 : option_set_list_char]: ((d_list_char @ (throw_list_char @ E2) @ A5) = (d_list_char @ E2 @ A5))))). % \<D>.simps(14)
thf(fact_113__092_060D_062_Osimps_I3_J, axiom,
    ((![V3 : val, A5 : option_set_list_char]: (d_list_char @ (val_list_char @ V3) @ A5)))). % \<D>.simps(3)
thf(fact_114_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P3 : list_P1234162913t_char]: (^[H5 : nat > option2118145160on_val]: (^[L5 : list_char > option_val]: (^[E7 : list_char > option_ty]: (![V4 : list_char]: (![V2 : val]: ((((L5 @ V4) = (some_val @ V2))) => ((?[T4 : ty]: ((((E7 @ V4) = (some_ty @ T4))) & ((conf_P93989998t_char @ P3 @ H5 @ V2 @ T4))))))))))))))). % lconf_def
thf(fact_115_progress, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, L : list_char > option_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((hconf_1244167010t_char @ P @ H) => ((wTrt @ P @ H @ E @ E2 @ T) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ L))) => ((~ ((final_list_char @ E2))) => (?[E3 : exp_list_char, S2 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P))))))))))). % progress
thf(fact_116_eval__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wt @ P @ E @ E2 @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E @ E4 @ T2)))))))))). % eval_preserves_type
thf(fact_117_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_118_domI, axiom,
    ((![M : nat > option_set_list_char, A : nat, B2 : set_list_char]: (((M @ A) = (some_set_list_char @ B2)) => (member_nat @ A @ (dom_na736636731t_char @ M)))))). % domI
thf(fact_119_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_120_domI, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B2 : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B2)) => (member_nat @ A @ (dom_na451844572on_val @ M)))))). % domI
thf(fact_121_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_122_domI, axiom,
    ((![M : produc1172664615on_val > option_val, A : produc1172664615on_val, B2 : val]: (((M @ A) = (some_val @ B2)) => (member354538064on_val @ A @ (dom_Pr162898261al_val @ M)))))). % domI
thf(fact_123_domI, axiom,
    ((![M : nat > option_val, A : nat, B2 : val]: (((M @ A) = (some_val @ B2)) => (member_nat @ A @ (dom_nat_val @ M)))))). % domI
thf(fact_124_domI, axiom,
    ((![M : produc1172664615on_val > option_ty, A : produc1172664615on_val, B2 : ty]: (((M @ A) = (some_ty @ B2)) => (member354538064on_val @ A @ (dom_Pr1796446476val_ty @ M)))))). % domI
thf(fact_125_domI, axiom,
    ((![M : nat > option_ty, A : nat, B2 : ty]: (((M @ A) = (some_ty @ B2)) => (member_nat @ A @ (dom_nat_ty @ M)))))). % domI
thf(fact_126_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_127_domD, axiom,
    ((![A : nat, M : nat > option_set_list_char]: ((member_nat @ A @ (dom_na736636731t_char @ M)) => (?[B : set_list_char]: ((M @ A) = (some_set_list_char @ B))))))). % domD
thf(fact_128_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_129_domD, axiom,
    ((![A : nat, M : nat > option2118145160on_val]: ((member_nat @ A @ (dom_na451844572on_val @ M)) => (?[B : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B))))))). % domD
thf(fact_130_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_131_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option_val]: ((member354538064on_val @ A @ (dom_Pr162898261al_val @ M)) => (?[B : val]: ((M @ A) = (some_val @ B))))))). % domD
thf(fact_132_domD, axiom,
    ((![A : nat, M : nat > option_val]: ((member_nat @ A @ (dom_nat_val @ M)) => (?[B : val]: ((M @ A) = (some_val @ B))))))). % domD
thf(fact_133_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option_ty]: ((member354538064on_val @ A @ (dom_Pr1796446476val_ty @ M)) => (?[B : ty]: ((M @ A) = (some_ty @ B))))))). % domD
thf(fact_134_domD, axiom,
    ((![A : nat, M : nat > option_ty]: ((member_nat @ A @ (dom_nat_ty @ M)) => (?[B : ty]: ((M @ A) = (some_ty @ B))))))). % domD
thf(fact_135_FAccRedsVal, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (val_list_char @ V3) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_136_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_137_exp_Odistinct_I61_J, axiom,
    ((![X32 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X32) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_138_exp_Odistinct_I151_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X14 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (throw_list_char @ X14))))))). % exp.distinct(151)
thf(fact_139_eval__evals_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E4 : exp_list_char, S_1 : produc515445032on_val, F : list_char, D : list_char]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E4) @ S_1) => (eval @ P @ (fAcc_list_char @ E2 @ F @ D) @ S_0 @ (throw_list_char @ E4) @ S_1))))). % eval_evals.FAccThrow
thf(fact_140_eval__evals_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E4 : exp_list_char, S_1 : produc515445032on_val]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E4) @ S_1) => (eval @ P @ (throw_list_char @ E2) @ S_0 @ (throw_list_char @ E4) @ S_1))))). % eval_evals.ThrowThrow
thf(fact_141_Val, axiom,
    ((![P : list_P1234162913t_char, V3 : val, S : produc515445032on_val]: (eval @ P @ (val_list_char @ V3) @ S @ (val_list_char @ V3) @ S)))). % Val
thf(fact_142_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V3 : val, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V3) @ S @ E4 @ S3) => (~ (((E4 = (val_list_char @ V3)) => (~ ((S3 = S)))))))))). % eval_cases(2)
thf(fact_143_eval__final, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E2 @ S @ E4 @ S3) => (final_list_char @ E4))))). % eval_final
thf(fact_144_eval__finalId, axiom,
    ((![E2 : exp_list_char, P : list_P1234162913t_char, S : produc515445032on_val]: ((final_list_char @ E2) => (eval @ P @ E2 @ S @ E2 @ S))))). % eval_finalId
thf(fact_145__092_060D_062_Osimps_I7_J, axiom,
    ((![E2 : exp_list_char, F : list_char, D : list_char, A5 : option_set_list_char]: ((d_list_char @ (fAcc_list_char @ E2 @ F @ D) @ A5) = (d_list_char @ E2 @ A5))))). % \<D>.simps(7)
thf(fact_146_FAcc, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A : nat, H : nat > option2118145160on_val, L : list_char > option_val, C4 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (addr @ A)) @ (produc52622304on_val @ H @ L)) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (eval @ P @ (fAcc_list_char @ E2 @ F @ D) @ S_0 @ (val_list_char @ V3) @ (produc52622304on_val @ H @ L)))))))). % FAcc
thf(fact_147_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E8 @ S5)) @ (red @ P)) => ((eval @ P @ E8 @ S5 @ E4 @ S3) => (eval @ P @ E2 @ S @ E4 @ S3))))))). % extend_1_eval
thf(fact_148_Throw, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (addr @ A)) @ S_1) => (eval @ P @ (throw_list_char @ E2) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A))) @ S_1))))). % Throw
thf(fact_149_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E8 @ S5)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E8 @ S5 @ E4 @ S3) => (eval @ P @ E2 @ S @ E4 @ S3))))))). % extend_eval
thf(fact_150_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_151_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F @ D) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_152_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E4) => (eval @ P @ E2 @ S @ E4 @ S3))))))). % small_by_big
thf(fact_153_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E4)))))))). % big_iff_small
thf(fact_154_red__reds_OFAccThrow, axiom,
    ((![E2 : exp_list_char, F : list_char, D : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E2) @ F @ D) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_155_FAccReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F @ D) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_156_eval__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) => ((wt @ P @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S3)))))))). % eval_preserves_sconf
thf(fact_157_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_158_red__reds_ORedFAcc, axiom,
    ((![S : produc515445032on_val, A : nat, C4 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val, P : list_P1234162913t_char]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F @ D) @ S) @ (produc2023458740on_val @ (val_list_char @ V3) @ S)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_159_wf__prog__wwf__prog, axiom,
    ((![P : list_P1234162913t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => (wf_pro1229751607t_char @ wwf_J_mdecl @ P))))). % wf_prog_wwf_prog
thf(fact_160_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C4 @ Md) => (wwf_J_mdecl @ P @ C4 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_161_redp__redsp_ORedFAcc, axiom,
    ((![S : produc515445032on_val, A : nat, C4 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D : list_char, V3 : val, P : list_P1234162913t_char]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D)) = (some_val @ V3)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F @ D) @ S @ (val_list_char @ V3) @ S)))))). % redp_redsp.RedFAcc
thf(fact_162_red__reds_ORedVar, axiom,
    ((![S : produc515445032on_val, V5 : list_char, V3 : val, P : list_P1234162913t_char]: (((lcl @ S @ V5) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (var_list_char @ V5) @ S) @ (produc2023458740on_val @ (val_list_char @ V3) @ S)) @ (red @ P)))))). % red_reds.RedVar
thf(fact_163_exp_Oinject_I5_J, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((var_list_char @ X5) = (var_list_char @ Y5)) = (X5 = Y5))))). % exp.inject(5)
thf(fact_164_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, F : list_char, D : list_char]: ((redp @ P @ E2 @ S @ E4 @ S3) => (redp @ P @ (fAcc_list_char @ E2 @ F @ D) @ S @ (fAcc_list_char @ E4 @ F @ D) @ S3))))). % redp_redsp.FAccRed
thf(fact_165_exp_Odistinct_I103_J, axiom,
    ((![X5 : list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((var_list_char @ X5) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(103)
thf(fact_166_exp_Odistinct_I117_J, axiom,
    ((![X5 : list_char, X14 : exp_list_char]: (~ (((var_list_char @ X5) = (throw_list_char @ X14))))))). % exp.distinct(117)
thf(fact_167_exp_Odistinct_I57_J, axiom,
    ((![X32 : val, X5 : list_char]: (~ (((val_list_char @ X32) = (var_list_char @ X5))))))). % exp.distinct(57)
thf(fact_168_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((redp @ P @ E2 @ S @ E4 @ S3) => (redp @ P @ (throw_list_char @ E2) @ S @ (throw_list_char @ E4) @ S3))))). % redp_redsp.ThrowRed
thf(fact_169_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E2)) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.ThrowThrow
thf(fact_170_redp__redsp_ORedVar, axiom,
    ((![S : produc515445032on_val, V5 : list_char, V3 : val, P : list_P1234162913t_char]: (((lcl @ S @ V5) = (some_val @ V3)) => (redp @ P @ (var_list_char @ V5) @ S @ (val_list_char @ V3) @ S))))). % redp_redsp.RedVar
thf(fact_171_redp__redsp_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, F : list_char, D : list_char, S : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (throw_list_char @ E2) @ F @ D) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.FAccThrow
thf(fact_172_WTrtVar, axiom,
    ((![E : list_char > option_ty, V5 : list_char, T : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((E @ V5) = (some_ty @ T)) => (wTrt @ P @ H @ E @ (var_list_char @ V5) @ T))))). % WTrtVar
thf(fact_173_Var, axiom,
    ((![L : list_char > option_val, V5 : list_char, V3 : val, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((L @ V5) = (some_val @ V3)) => (eval @ P @ (var_list_char @ V5) @ (produc52622304on_val @ H @ L) @ (val_list_char @ V3) @ (produc52622304on_val @ H @ L)))))). % Var
thf(fact_174_WTVar, axiom,
    ((![E : list_char > option_ty, V5 : list_char, T : ty, P : list_P1234162913t_char]: (((E @ V5) = (some_ty @ T)) => (wt @ P @ E @ (var_list_char @ V5) @ T))))). % WTVar
thf(fact_175__092_060D_062_Osimps_I5_J, axiom,
    ((![V5 : list_char, A5 : option_set_list_char]: ((d_list_char @ (var_list_char @ V5) @ A5) = (hyper_isin_list_char @ V5 @ A5))))). % \<D>.simps(5)
thf(fact_176_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_177_exp_Oinject_I4_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (((binOp_list_char @ X41 @ X42 @ X43) = (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((X41 = Y41)) & ((((X42 = Y42)) & ((X43 = Y43))))))))). % exp.inject(4)
thf(fact_178_exp_Odistinct_I83_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(83)
thf(fact_179_exp_Odistinct_I79_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X5 : list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (var_list_char @ X5))))))). % exp.distinct(79)
thf(fact_180_redp__redsp_OBinOpRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((redp @ P @ E2 @ S @ E4 @ S3) => (redp @ P @ (binOp_list_char @ E2 @ Bop @ E_2) @ S @ (binOp_list_char @ E4 @ Bop @ E_2) @ S3))))). % redp_redsp.BinOpRed1
thf(fact_181_exp_Odistinct_I55_J, axiom,
    ((![X32 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X32) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_182_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)
thf(fact_183_eval__evals_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((eval @ P @ E_12 @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.BinOpThrow1
thf(fact_184_redp__redsp_OBinOpRed2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, V_1 : val, Bop : bop]: ((redp @ P @ E2 @ S @ E4 @ S3) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E4) @ S3))))). % redp_redsp.BinOpRed2
thf(fact_185_redp__redsp_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.BinOpThrow1
thf(fact_186_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E4 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_187_eval__evals_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((eval @ P @ E_12 @ S_0 @ (val_list_char @ V_1) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (throw_list_char @ E2) @ S_2) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E2) @ S_2)))))). % eval_evals.BinOpThrow2
thf(fact_188_redp__redsp_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, V_1 : val, Bop : bop, E2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.BinOpThrow2
thf(fact_189_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E4) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_190_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_191_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E4 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_192_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_193_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V3 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V3) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V3) @ Bop @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_194_BinOpRedsThrow1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_195_BinOpRedsVal, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, V_2 : val, S_2 : produc515445032on_val, Bop : bop, V3 : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V_2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ V3) @ S_2)) @ (transi111096263on_val @ (red @ P))))))))). % BinOpRedsVal
thf(fact_196_red__reds_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V3 : val, S : produc515445032on_val, P : list_P1234162913t_char]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S) @ (produc2023458740on_val @ (val_list_char @ V3) @ S)) @ (red @ P)))))). % red_reds.RedBinOp
thf(fact_197_BinOp, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, E_2 : exp_list_char, V_2 : val, S_2 : produc515445032on_val, Bop : bop, V3 : val]: ((eval @ P @ E_12 @ S_0 @ (val_list_char @ V_1) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (val_list_char @ V_2) @ S_2) => (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V3)) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (val_list_char @ V3) @ S_2))))))). % BinOp
thf(fact_198_redp__redsp_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V3 : val, P : list_P1234162913t_char, S : produc515445032on_val]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V3)) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S @ (val_list_char @ V3) @ S))))). % redp_redsp.RedBinOp
thf(fact_199_eval__cases_I3_J, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S @ E4 @ S3) => ((![V_12 : val, S_12 : produc515445032on_val, V_22 : val, V : val]: ((E4 = (val_list_char @ V)) => ((eval @ P @ E_12 @ S @ (val_list_char @ V_12) @ S_12) => ((eval @ P @ E_2 @ S_12 @ (val_list_char @ V_22) @ S3) => (~ (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_12 @ V_22))) = (some_val @ V)))))))) => ((![E6 : exp_list_char]: ((E4 = (throw_list_char @ E6)) => (~ ((eval @ P @ E_12 @ S @ (throw_list_char @ E6) @ S3))))) => (~ ((![V_12 : val, S_12 : produc515445032on_val, E6 : exp_list_char]: ((E4 = (throw_list_char @ E6)) => ((eval @ P @ E_12 @ S @ (val_list_char @ V_12) @ S_12) => (~ ((eval @ P @ E_2 @ S_12 @ (throw_list_char @ E6) @ S3)))))))))))))). % eval_cases(3)
thf(fact_200_red__reds_OBlockThrow, axiom,
    ((![V5 : list_char, T : ty, A : nat, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V5 @ T @ (throw_list_char @ (val_list_char @ (addr @ A)))) @ S) @ (produc2023458740on_val @ (throw_list_char @ (val_list_char @ (addr @ A))) @ S)) @ (red @ P))))). % red_reds.BlockThrow
thf(fact_201_FAssRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V3 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V3) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_12 @ F @ D @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_202_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_203_exp_Oinject_I8_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((X84 = Y84))))))))))). % exp.inject(8)
thf(fact_204_exp_Odistinct_I89_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(89)
thf(fact_205_exp_Odistinct_I85_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(85)
thf(fact_206_exp_Odistinct_I143_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(143)
thf(fact_207_exp_Odistinct_I139_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(139)
thf(fact_208_redp__redsp_OFAssRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, F : list_char, D : list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S @ E4 @ S3) => (redp @ P @ (fAss_list_char @ E2 @ F @ D @ E_2) @ S @ (fAss_list_char @ E4 @ F @ D @ E_2) @ S3))))). % redp_redsp.FAssRed1
thf(fact_209_exp_Odistinct_I63_J, axiom,
    ((![X32 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X32) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_210_exp_Odistinct_I67_J, axiom,
    ((![X32 : val, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((val_list_char @ X32) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(67)
thf(fact_211_exp_Odistinct_I165_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X14 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (throw_list_char @ X14))))))). % exp.distinct(165)
thf(fact_212_exp_Odistinct_I187_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, X14 : exp_list_char]: (~ (((block_list_char @ X101 @ X102 @ X103) = (throw_list_char @ X14))))))). % exp.distinct(187)

% Conjectures (12)
thf(conj_0, hypothesis,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))).
thf(conj_1, hypothesis,
    ((typeSa1777264139_sconf @ p @ e @ s))).
thf(conj_2, hypothesis,
    ((wt @ p @ e @ e2 @ t))).
thf(conj_3, hypothesis,
    ((d_list_char @ e2 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ s)))))).
thf(conj_4, hypothesis,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ s) @ (produc2023458740on_val @ e3 @ s2)) @ (transi111096263on_val @ (red @ p))))).
thf(conj_5, hypothesis,
    ((~ ((?[E9 : exp_list_char, S6 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e3 @ s2) @ (produc2023458740on_val @ E9 @ S6)) @ (red @ p))))))).
thf(conj_6, hypothesis,
    ((typeSa1969945757config @ p @ e @ s @ e2 @ t))).
thf(conj_7, hypothesis,
    ((typeSa1969945757config @ p @ e @ s2 @ e3 @ t2))).
thf(conj_8, hypothesis,
    ((widen_917054840t_char @ p @ t2 @ t))).
thf(conj_9, hypothesis,
    ((d_list_char @ e3 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ s2)))))).
thf(conj_10, hypothesis,
    ((final_list_char @ e3))).
thf(conj_11, conjecture,
    (((?[V6 : val]: ((e3 = (val_list_char @ V6)) & (conf_P93989998t_char @ p @ (hp @ s2) @ V6 @ t))) | (?[A6 : nat]: ((e3 = (throw_list_char @ (val_list_char @ (addr @ A6)))) & (member_nat @ A6 @ (dom_na451844572on_val @ (hp @ s2)))))))).
