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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__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_J_J_J, type,
    produc1259892823t_char : $tType).
thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr711661575al_val : $tType).
thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr729957319t_char : $tType).
thf(ty_n_t__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,
    produc674182439al_val : $tType).
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,
    option2118145160on_val : $tType).
thf(ty_n_t__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,
    produc442406631t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc266837688on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    set_Pr164112643t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Expr__Obop_Mt__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    produc1373793468al_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1257910179t_char : $tType).
thf(ty_n_t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    option_set_list_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    product_prod_val_val : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_list_char : $tType).
thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    set_list_char : $tType).
thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $tType).
thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
    option_ty : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
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 (80)
thf(sy_c_BigStep_Oeval, type,
    eval : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
    final_list_char : exp_list_char > $o).
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,
    conf_P93989998t_char : list_P1234162913t_char > (nat > option2118145160on_val) > val > ty > $o).
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_Expr_Obinop, type,
    binop : produc1373793468al_val > option_val).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
    binOp_list_char : exp_list_char > bop > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
    block_list_char : list_char > ty > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
    fAcc_list_char : exp_list_char > list_char > list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
    fAss_list_char : exp_list_char > list_char > list_char > exp_list_char > exp_list_char).
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,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    dom_list_char_val : (list_char > option_val) > set_list_char).
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_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_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    ord_le1836582007t_char : set_list_char > set_list_char > $o).
thf(sy_c_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__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_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,
    produc253850455on_val : produc744932519on_val > produc744932519on_val > produc1682558695on_val).
thf(sy_c_Product__Type_OPair_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_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,
    produc1500810071al_val : produc674182439al_val > produc674182439al_val > produc1212913895al_val).
thf(sy_c_Product__Type_OPair_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__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,
    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_val).
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thf(sy_c_member_001t__Product____Type__Oprod_It__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_Mt__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_J, type,
    member983186192t_char : produc1751401703t_char > set_Pr226680007t_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_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 (249)
thf(fact_0_Red__preserves__defass, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => ((d_list_char @ E @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S)))) => (d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S2)))))))))). % Red_preserves_defass
thf(fact_1_ThrowReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_2_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_3_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_4_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_5_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A2 @ B)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_6_rtrancl__induct2, axiom,
    ((![Ax : produc515445032on_val, Ay : produc515445032on_val, Bx : produc515445032on_val, By : produc515445032on_val, R : set_Pr777589959on_val, P : produc515445032on_val > produc515445032on_val > $o]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Ax @ Ay) @ (produc2106877847on_val @ Bx @ By)) @ (transi2142918570on_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : produc515445032on_val, B : produc515445032on_val, Aa : produc515445032on_val, Ba : produc515445032on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Ax @ Ay) @ (produc2106877847on_val @ A2 @ B)) @ (transi2142918570on_val @ R)) => ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ A2 @ B) @ (produc2106877847on_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_7_rtrancl__induct2, axiom,
    ((![Ax : produc1373793468al_val, Ay : produc1373793468al_val, Bx : produc1373793468al_val, By : produc1373793468al_val, R : set_Pr699325639al_val, P : produc1373793468al_val > produc1373793468al_val > $o]: ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ Ax @ Ay) @ (produc1144711447al_val @ Bx @ By)) @ (transi1750069546al_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : produc1373793468al_val, B : produc1373793468al_val, Aa : produc1373793468al_val, Ba : produc1373793468al_val]: ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ Ax @ Ay) @ (produc1144711447al_val @ A2 @ B)) @ (transi1750069546al_val @ R)) => ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ A2 @ B) @ (produc1144711447al_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_8_rtrancl__induct2, axiom,
    ((![Ax : produc266837688on_val, Ay : produc266837688on_val, Bx : produc266837688on_val, By : produc266837688on_val, R : set_Pr1774869831on_val, P : produc266837688on_val > produc266837688on_val > $o]: ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ Ax @ Ay) @ (produc881885833on_val @ Bx @ By)) @ (transi239281108on_val @ R)) => ((P @ Ax @ Ay) => ((![A2 : produc266837688on_val, B : produc266837688on_val, Aa : produc266837688on_val, Ba : produc266837688on_val]: ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ Ax @ Ay) @ (produc881885833on_val @ A2 @ B)) @ (transi239281108on_val @ R)) => ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ A2 @ B) @ (produc881885833on_val @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_9_rtrancl__induct2, axiom,
    ((![Ax : produc1257910179t_char, Ay : produc1257910179t_char, Bx : produc1257910179t_char, By : produc1257910179t_char, R : set_Pr226680007t_char, P : produc1257910179t_char > produc1257910179t_char > $o]: ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ Ax @ Ay) @ (produc395356247t_char @ Bx @ By)) @ (transi1018566890t_char @ R)) => ((P @ Ax @ Ay) => ((![A2 : produc1257910179t_char, B : produc1257910179t_char, Aa : produc1257910179t_char, Ba : produc1257910179t_char]: ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ Ax @ Ay) @ (produc395356247t_char @ A2 @ B)) @ (transi1018566890t_char @ R)) => ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ A2 @ B) @ (produc395356247t_char @ Aa @ Ba)) @ R) => ((P @ A2 @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
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 : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A2 @ B)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_16_converse__rtranclE2, axiom,
    ((![Xa : produc515445032on_val, Xb : produc515445032on_val, Za : produc515445032on_val, Zb : produc515445032on_val, R : set_Pr777589959on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Xa @ Xb) @ (produc2106877847on_val @ Za @ Zb)) @ (transi2142918570on_val @ R)) => ((~ (((produc2106877847on_val @ Xa @ Xb) = (produc2106877847on_val @ Za @ Zb)))) => (~ ((![A2 : produc515445032on_val, B : produc515445032on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Xa @ Xb) @ (produc2106877847on_val @ A2 @ B)) @ R) => (~ ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ A2 @ B) @ (produc2106877847on_val @ Za @ Zb)) @ (transi2142918570on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_17_converse__rtranclE2, axiom,
    ((![Xa : produc1373793468al_val, Xb : produc1373793468al_val, Za : produc1373793468al_val, Zb : produc1373793468al_val, R : set_Pr699325639al_val]: ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ Xa @ Xb) @ (produc1144711447al_val @ Za @ Zb)) @ (transi1750069546al_val @ R)) => ((~ (((produc1144711447al_val @ Xa @ Xb) = (produc1144711447al_val @ Za @ Zb)))) => (~ ((![A2 : produc1373793468al_val, B : produc1373793468al_val]: ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ Xa @ Xb) @ (produc1144711447al_val @ A2 @ B)) @ R) => (~ ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ A2 @ B) @ (produc1144711447al_val @ Za @ Zb)) @ (transi1750069546al_val @ R))))))))))))). % converse_rtranclE2
thf(fact_18_converse__rtranclE2, axiom,
    ((![Xa : produc266837688on_val, Xb : produc266837688on_val, Za : produc266837688on_val, Zb : produc266837688on_val, R : set_Pr1774869831on_val]: ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ Xa @ Xb) @ (produc881885833on_val @ Za @ Zb)) @ (transi239281108on_val @ R)) => ((~ (((produc881885833on_val @ Xa @ Xb) = (produc881885833on_val @ Za @ Zb)))) => (~ ((![A2 : produc266837688on_val, B : produc266837688on_val]: ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ Xa @ Xb) @ (produc881885833on_val @ A2 @ B)) @ R) => (~ ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ A2 @ B) @ (produc881885833on_val @ Za @ Zb)) @ (transi239281108on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_19_converse__rtranclE2, axiom,
    ((![Xa : produc1257910179t_char, Xb : produc1257910179t_char, Za : produc1257910179t_char, Zb : produc1257910179t_char, R : set_Pr226680007t_char]: ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ Xa @ Xb) @ (produc395356247t_char @ Za @ Zb)) @ (transi1018566890t_char @ R)) => ((~ (((produc395356247t_char @ Xa @ Xb) = (produc395356247t_char @ Za @ Zb)))) => (~ ((![A2 : produc1257910179t_char, B : produc1257910179t_char]: ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ Xa @ Xb) @ (produc395356247t_char @ A2 @ B)) @ R) => (~ ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ A2 @ B) @ (produc395356247t_char @ Za @ Zb)) @ (transi1018566890t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_20_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_21_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_22_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_23_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_24_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_25_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Bx @ By) => ((![A2 : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_26_converse__rtrancl__induct2, axiom,
    ((![Ax : produc515445032on_val, Ay : produc515445032on_val, Bx : produc515445032on_val, By : produc515445032on_val, R : set_Pr777589959on_val, P : produc515445032on_val > produc515445032on_val > $o]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Ax @ Ay) @ (produc2106877847on_val @ Bx @ By)) @ (transi2142918570on_val @ R)) => ((P @ Bx @ By) => ((![A2 : produc515445032on_val, B : produc515445032on_val, Aa : produc515445032on_val, Ba : produc515445032on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ A2 @ B) @ (produc2106877847on_val @ Aa @ Ba)) @ R) => ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Aa @ Ba) @ (produc2106877847on_val @ Bx @ By)) @ (transi2142918570on_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_27_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1373793468al_val, Ay : produc1373793468al_val, Bx : produc1373793468al_val, By : produc1373793468al_val, R : set_Pr699325639al_val, P : produc1373793468al_val > produc1373793468al_val > $o]: ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ Ax @ Ay) @ (produc1144711447al_val @ Bx @ By)) @ (transi1750069546al_val @ R)) => ((P @ Bx @ By) => ((![A2 : produc1373793468al_val, B : produc1373793468al_val, Aa : produc1373793468al_val, Ba : produc1373793468al_val]: ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ A2 @ B) @ (produc1144711447al_val @ Aa @ Ba)) @ R) => ((member1200384784al_val @ (produc1500810071al_val @ (produc1144711447al_val @ Aa @ Ba) @ (produc1144711447al_val @ Bx @ By)) @ (transi1750069546al_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_28_converse__rtrancl__induct2, axiom,
    ((![Ax : produc266837688on_val, Ay : produc266837688on_val, Bx : produc266837688on_val, By : produc266837688on_val, R : set_Pr1774869831on_val, P : produc266837688on_val > produc266837688on_val > $o]: ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ Ax @ Ay) @ (produc881885833on_val @ Bx @ By)) @ (transi239281108on_val @ R)) => ((P @ Bx @ By) => ((![A2 : produc266837688on_val, B : produc266837688on_val, Aa : produc266837688on_val, Ba : produc266837688on_val]: ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ A2 @ B) @ (produc881885833on_val @ Aa @ Ba)) @ R) => ((member1591193488on_val @ (produc1716418775on_val @ (produc881885833on_val @ Aa @ Ba) @ (produc881885833on_val @ Bx @ By)) @ (transi239281108on_val @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_29_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1257910179t_char, Ay : produc1257910179t_char, Bx : produc1257910179t_char, By : produc1257910179t_char, R : set_Pr226680007t_char, P : produc1257910179t_char > produc1257910179t_char > $o]: ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ Ax @ Ay) @ (produc395356247t_char @ Bx @ By)) @ (transi1018566890t_char @ R)) => ((P @ Bx @ By) => ((![A2 : produc1257910179t_char, B : produc1257910179t_char, Aa : produc1257910179t_char, Ba : produc1257910179t_char]: ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ A2 @ B) @ (produc395356247t_char @ Aa @ Ba)) @ R) => ((member983186192t_char @ (produc1908198231t_char @ (produc395356247t_char @ Aa @ Ba) @ (produc395356247t_char @ Bx @ By)) @ (transi1018566890t_char @ R)) => ((P @ Aa @ Ba) => (P @ A2 @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_30_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_31_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_32_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_33_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_34_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_35_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_36_prod__cases4, axiom,
    ((![Y : produc674182439al_val]: (~ ((![A2 : produc1373793468al_val, B : bop, C : val, D : val]: (~ ((Y = (produc1144711447al_val @ A2 @ (produc1753769388al_val @ B @ (product_Pair_val_val @ C @ D)))))))))))). % prod_cases4
thf(fact_37_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_38_prod__induct4, axiom,
    ((![P : produc674182439al_val > $o, X : produc674182439al_val]: ((![A2 : produc1373793468al_val, B : bop, C : val, D : val]: (P @ (produc1144711447al_val @ A2 @ (produc1753769388al_val @ B @ (product_Pair_val_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_39_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : list_char, A3 : list_char, B3 : list_char]: (((produc1304532571t_char @ A @ B2) = (produc1304532571t_char @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_40_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_41_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_42_old_Oprod_Oinject, axiom,
    ((![A : bop, B2 : product_prod_val_val, A3 : bop, B3 : product_prod_val_val]: (((produc1753769388al_val @ A @ B2) = (produc1753769388al_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_43_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_44_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_45_old_Oprod_Oinject, axiom,
    ((![A : produc515445032on_val, B2 : produc515445032on_val, A3 : produc515445032on_val, B3 : produc515445032on_val]: (((produc2106877847on_val @ A @ B2) = (produc2106877847on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_46_old_Oprod_Oinject, axiom,
    ((![A : produc1373793468al_val, B2 : produc1373793468al_val, A3 : produc1373793468al_val, B3 : produc1373793468al_val]: (((produc1144711447al_val @ A @ B2) = (produc1144711447al_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_47_old_Oprod_Oinject, axiom,
    ((![A : produc266837688on_val, B2 : produc266837688on_val, A3 : produc266837688on_val, B3 : produc266837688on_val]: (((produc881885833on_val @ A @ B2) = (produc881885833on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_48_old_Oprod_Oinject, axiom,
    ((![A : produc1257910179t_char, B2 : produc1257910179t_char, A3 : produc1257910179t_char, B3 : produc1257910179t_char]: (((produc395356247t_char @ A @ B2) = (produc395356247t_char @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_49_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_50_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_51_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_52_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_53_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_54_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_55_prod_Oinject, axiom,
    ((![X1 : produc515445032on_val, X2 : produc515445032on_val, Y1 : produc515445032on_val, Y2 : produc515445032on_val]: (((produc2106877847on_val @ X1 @ X2) = (produc2106877847on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_56_prod_Oinject, axiom,
    ((![X1 : produc1373793468al_val, X2 : produc1373793468al_val, Y1 : produc1373793468al_val, Y2 : produc1373793468al_val]: (((produc1144711447al_val @ X1 @ X2) = (produc1144711447al_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_57_prod_Oinject, axiom,
    ((![X1 : produc266837688on_val, X2 : produc266837688on_val, Y1 : produc266837688on_val, Y2 : produc266837688on_val]: (((produc881885833on_val @ X1 @ X2) = (produc881885833on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_58_prod_Oinject, axiom,
    ((![X1 : produc1257910179t_char, X2 : produc1257910179t_char, Y1 : produc1257910179t_char, Y2 : produc1257910179t_char]: (((produc395356247t_char @ X1 @ X2) = (produc395356247t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_59_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_60_r__into__rtrancl, axiom,
    ((![P2 : produc744932519on_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ P2 @ R) => (member2027247312on_val @ P2 @ (transi432893227on_val @ R)))))). % r_into_rtrancl
thf(fact_61_r__into__rtrancl, axiom,
    ((![P2 : produc674182439al_val, R : set_Pr711661575al_val]: ((member1528603216al_val @ P2 @ R) => (member1528603216al_val @ P2 @ (transi531594559al_val @ R)))))). % r_into_rtrancl
thf(fact_62_r__into__rtrancl, axiom,
    ((![P2 : produc1085126737on_val, R : set_Pr2110063281on_val]: ((member197592058on_val @ P2 @ R) => (member197592058on_val @ P2 @ (transi2071064181on_val @ R)))))). % r_into_rtrancl
thf(fact_63_r__into__rtrancl, axiom,
    ((![P2 : produc442406631t_char, R : set_Pr729957319t_char]: ((member803902992t_char @ P2 @ R) => (member803902992t_char @ P2 @ (transi858104614t_char @ R)))))). % r_into_rtrancl
thf(fact_64_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_65_rtrancl__idemp, axiom,
    ((![R : set_Pr148564103on_val]: ((transi432893227on_val @ (transi432893227on_val @ R)) = (transi432893227on_val @ R))))). % rtrancl_idemp
thf(fact_66_rtrancl__idemp, axiom,
    ((![R : set_Pr711661575al_val]: ((transi531594559al_val @ (transi531594559al_val @ R)) = (transi531594559al_val @ R))))). % rtrancl_idemp
thf(fact_67_rtrancl__idemp, axiom,
    ((![R : set_Pr2110063281on_val]: ((transi2071064181on_val @ (transi2071064181on_val @ R)) = (transi2071064181on_val @ R))))). % rtrancl_idemp
thf(fact_68_rtrancl__idemp, axiom,
    ((![R : set_Pr729957319t_char]: ((transi858104614t_char @ (transi858104614t_char @ R)) = (transi858104614t_char @ R))))). % rtrancl_idemp
thf(fact_69_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, 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 @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E3 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E3 @ H3 @ L3 @ E3 @ 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, E4 : 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 @ E4 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E4 @ H4 @ L4)))) => (R2 @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_70_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_71_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_72_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_73_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_74_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_75_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_76_old_Oprod_Oinducts, axiom,
    ((![P : produc744932519on_val > $o, Prod : produc744932519on_val]: ((![A2 : produc515445032on_val, B : produc515445032on_val]: (P @ (produc2106877847on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_77_old_Oprod_Oinducts, axiom,
    ((![P : produc674182439al_val > $o, Prod : produc674182439al_val]: ((![A2 : produc1373793468al_val, B : produc1373793468al_val]: (P @ (produc1144711447al_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_78_old_Oprod_Oinducts, axiom,
    ((![P : produc1085126737on_val > $o, Prod : produc1085126737on_val]: ((![A2 : produc266837688on_val, B : produc266837688on_val]: (P @ (produc881885833on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_79_old_Oprod_Oinducts, axiom,
    ((![P : produc442406631t_char > $o, Prod : produc442406631t_char]: ((![A2 : produc1257910179t_char, B : produc1257910179t_char]: (P @ (produc395356247t_char @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_80_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A2 : list_char, B : list_char]: (~ ((Y = (produc1304532571t_char @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_81_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_82_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_83_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1373793468al_val]: (~ ((![A2 : bop, B : product_prod_val_val]: (~ ((Y = (produc1753769388al_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_84_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_85_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_86_old_Oprod_Oexhaust, axiom,
    ((![Y : produc744932519on_val]: (~ ((![A2 : produc515445032on_val, B : produc515445032on_val]: (~ ((Y = (produc2106877847on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_87_old_Oprod_Oexhaust, axiom,
    ((![Y : produc674182439al_val]: (~ ((![A2 : produc1373793468al_val, B : produc1373793468al_val]: (~ ((Y = (produc1144711447al_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_88_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1085126737on_val]: (~ ((![A2 : produc266837688on_val, B : produc266837688on_val]: (~ ((Y = (produc881885833on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_89_old_Oprod_Oexhaust, axiom,
    ((![Y : produc442406631t_char]: (~ ((![A2 : produc1257910179t_char, B : produc1257910179t_char]: (~ ((Y = (produc395356247t_char @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_90_Pair__inject, axiom,
    ((![A : list_char, B2 : list_char, A3 : list_char, B3 : list_char]: (((produc1304532571t_char @ A @ B2) = (produc1304532571t_char @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_91_Pair__inject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_92_Pair__inject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_93_Pair__inject, axiom,
    ((![A : bop, B2 : product_prod_val_val, A3 : bop, B3 : product_prod_val_val]: (((produc1753769388al_val @ A @ B2) = (produc1753769388al_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_94_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_95_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_96_Pair__inject, axiom,
    ((![A : produc515445032on_val, B2 : produc515445032on_val, A3 : produc515445032on_val, B3 : produc515445032on_val]: (((produc2106877847on_val @ A @ B2) = (produc2106877847on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_97_Pair__inject, axiom,
    ((![A : produc1373793468al_val, B2 : produc1373793468al_val, A3 : produc1373793468al_val, B3 : produc1373793468al_val]: (((produc1144711447al_val @ A @ B2) = (produc1144711447al_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_98_Pair__inject, axiom,
    ((![A : produc266837688on_val, B2 : produc266837688on_val, A3 : produc266837688on_val, B3 : produc266837688on_val]: (((produc881885833on_val @ A @ B2) = (produc881885833on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_99_Pair__inject, axiom,
    ((![A : produc1257910179t_char, B2 : produc1257910179t_char, A3 : produc1257910179t_char, B3 : produc1257910179t_char]: (((produc395356247t_char @ A @ B2) = (produc395356247t_char @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_100_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_101_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_102_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_103_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_104_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_105_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_106_prod__cases, axiom,
    ((![P : produc744932519on_val > $o, P2 : produc744932519on_val]: ((![A2 : produc515445032on_val, B : produc515445032on_val]: (P @ (produc2106877847on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_107_prod__cases, axiom,
    ((![P : produc674182439al_val > $o, P2 : produc674182439al_val]: ((![A2 : produc1373793468al_val, B : produc1373793468al_val]: (P @ (produc1144711447al_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_108_prod__cases, axiom,
    ((![P : produc1085126737on_val > $o, P2 : produc1085126737on_val]: ((![A2 : produc266837688on_val, B : produc266837688on_val]: (P @ (produc881885833on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_109_prod__cases, axiom,
    ((![P : produc442406631t_char > $o, P2 : produc442406631t_char]: ((![A2 : produc1257910179t_char, B : produc1257910179t_char]: (P @ (produc395356247t_char @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_110_surj__pair, axiom,
    ((![P2 : produc1257910179t_char]: (?[X3 : list_char, Y3 : list_char]: (P2 = (produc1304532571t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_111_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X3 : list_char, Y3 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_112_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_113_surj__pair, axiom,
    ((![P2 : produc1373793468al_val]: (?[X3 : bop, Y3 : product_prod_val_val]: (P2 = (produc1753769388al_val @ X3 @ Y3)))))). % surj_pair
thf(fact_114_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_115_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_116_surj__pair, axiom,
    ((![P2 : produc744932519on_val]: (?[X3 : produc515445032on_val, Y3 : produc515445032on_val]: (P2 = (produc2106877847on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_117_surj__pair, axiom,
    ((![P2 : produc674182439al_val]: (?[X3 : produc1373793468al_val, Y3 : produc1373793468al_val]: (P2 = (produc1144711447al_val @ X3 @ Y3)))))). % surj_pair
thf(fact_118_surj__pair, axiom,
    ((![P2 : produc1085126737on_val]: (?[X3 : produc266837688on_val, Y3 : produc266837688on_val]: (P2 = (produc881885833on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_119_surj__pair, axiom,
    ((![P2 : produc442406631t_char]: (?[X3 : produc1257910179t_char, Y3 : produc1257910179t_char]: (P2 = (produc395356247t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_120_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_121_prod__induct3, axiom,
    ((![P : produc1373793468al_val > $o, X : produc1373793468al_val]: ((![A2 : bop, B : val, C : val]: (P @ (produc1753769388al_val @ A2 @ (product_Pair_val_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_122_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_123_prod__induct3, axiom,
    ((![P : produc744932519on_val > $o, X : produc744932519on_val]: ((![A2 : produc515445032on_val, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2106877847on_val @ A2 @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_124_prod__induct3, axiom,
    ((![P : produc674182439al_val > $o, X : produc674182439al_val]: ((![A2 : produc1373793468al_val, B : bop, C : product_prod_val_val]: (P @ (produc1144711447al_val @ A2 @ (produc1753769388al_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_125_prod__induct3, axiom,
    ((![P : produc1085126737on_val > $o, X : produc1085126737on_val]: ((![A2 : produc266837688on_val, B : list_char, C : produc1257910179t_char > option_val]: (P @ (produc881885833on_val @ A2 @ (produc904988266on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_126_prod__induct3, axiom,
    ((![P : produc442406631t_char > $o, X : produc442406631t_char]: ((![A2 : produc1257910179t_char, B : list_char, C : list_char]: (P @ (produc395356247t_char @ A2 @ (produc1304532571t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_127_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_128_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_129_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_130_prod__cases3, axiom,
    ((![Y : produc744932519on_val]: (~ ((![A2 : produc515445032on_val, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2106877847on_val @ A2 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_131_prod__cases3, axiom,
    ((![Y : produc674182439al_val]: (~ ((![A2 : produc1373793468al_val, B : bop, C : product_prod_val_val]: (~ ((Y = (produc1144711447al_val @ A2 @ (produc1753769388al_val @ B @ C))))))))))). % prod_cases3
thf(fact_132_prod__cases3, axiom,
    ((![Y : produc1085126737on_val]: (~ ((![A2 : produc266837688on_val, B : list_char, C : produc1257910179t_char > option_val]: (~ ((Y = (produc881885833on_val @ A2 @ (produc904988266on_val @ B @ C))))))))))). % prod_cases3
thf(fact_133_prod__cases3, axiom,
    ((![Y : produc442406631t_char]: (~ ((![A2 : produc1257910179t_char, B : list_char, C : list_char]: (~ ((Y = (produc395356247t_char @ A2 @ (produc1304532571t_char @ B @ C))))))))))). % prod_cases3
thf(fact_134_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_135_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_136_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, C2 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A @ B2) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ B2 @ C2) @ (transi432893227on_val @ R)) => (member2027247312on_val @ (produc2106877847on_val @ A @ C2) @ (transi432893227on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_137_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1373793468al_val, B2 : produc1373793468al_val, R : set_Pr711661575al_val, C2 : produc1373793468al_val]: ((member1528603216al_val @ (produc1144711447al_val @ A @ B2) @ R) => ((member1528603216al_val @ (produc1144711447al_val @ B2 @ C2) @ (transi531594559al_val @ R)) => (member1528603216al_val @ (produc1144711447al_val @ A @ C2) @ (transi531594559al_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_138_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc266837688on_val, B2 : produc266837688on_val, R : set_Pr2110063281on_val, C2 : produc266837688on_val]: ((member197592058on_val @ (produc881885833on_val @ A @ B2) @ R) => ((member197592058on_val @ (produc881885833on_val @ B2 @ C2) @ (transi2071064181on_val @ R)) => (member197592058on_val @ (produc881885833on_val @ A @ C2) @ (transi2071064181on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_139_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1257910179t_char, B2 : produc1257910179t_char, R : set_Pr729957319t_char, C2 : produc1257910179t_char]: ((member803902992t_char @ (produc395356247t_char @ A @ B2) @ R) => ((member803902992t_char @ (produc395356247t_char @ B2 @ C2) @ (transi858104614t_char @ R)) => (member803902992t_char @ (produc395356247t_char @ A @ C2) @ (transi858104614t_char @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_140_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_141_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_142_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, C2 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A @ B2) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ B2 @ C2) @ R) => (member2027247312on_val @ (produc2106877847on_val @ A @ C2) @ (transi432893227on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_143_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1373793468al_val, B2 : produc1373793468al_val, R : set_Pr711661575al_val, C2 : produc1373793468al_val]: ((member1528603216al_val @ (produc1144711447al_val @ A @ B2) @ (transi531594559al_val @ R)) => ((member1528603216al_val @ (produc1144711447al_val @ B2 @ C2) @ R) => (member1528603216al_val @ (produc1144711447al_val @ A @ C2) @ (transi531594559al_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_144_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc266837688on_val, B2 : produc266837688on_val, R : set_Pr2110063281on_val, C2 : produc266837688on_val]: ((member197592058on_val @ (produc881885833on_val @ A @ B2) @ (transi2071064181on_val @ R)) => ((member197592058on_val @ (produc881885833on_val @ B2 @ C2) @ R) => (member197592058on_val @ (produc881885833on_val @ A @ C2) @ (transi2071064181on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_145_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1257910179t_char, B2 : produc1257910179t_char, R : set_Pr729957319t_char, C2 : produc1257910179t_char]: ((member803902992t_char @ (produc395356247t_char @ A @ B2) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ B2 @ C2) @ R) => (member803902992t_char @ (produc395356247t_char @ A @ C2) @ (transi858104614t_char @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_146_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_147_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_148_converse__rtrancl__induct, axiom,
    ((![A : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, P : produc515445032on_val > $o]: ((member2027247312on_val @ (produc2106877847on_val @ A @ B2) @ (transi432893227on_val @ R)) => ((P @ B2) => ((![Y3 : produc515445032on_val, Z : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ Y3 @ Z) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ Z @ B2) @ (transi432893227on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_149_converse__rtrancl__induct, axiom,
    ((![A : produc1373793468al_val, B2 : produc1373793468al_val, R : set_Pr711661575al_val, P : produc1373793468al_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ A @ B2) @ (transi531594559al_val @ R)) => ((P @ B2) => ((![Y3 : produc1373793468al_val, Z : produc1373793468al_val]: ((member1528603216al_val @ (produc1144711447al_val @ Y3 @ Z) @ R) => ((member1528603216al_val @ (produc1144711447al_val @ Z @ B2) @ (transi531594559al_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_150_converse__rtrancl__induct, axiom,
    ((![A : produc266837688on_val, B2 : produc266837688on_val, R : set_Pr2110063281on_val, P : produc266837688on_val > $o]: ((member197592058on_val @ (produc881885833on_val @ A @ B2) @ (transi2071064181on_val @ R)) => ((P @ B2) => ((![Y3 : produc266837688on_val, Z : produc266837688on_val]: ((member197592058on_val @ (produc881885833on_val @ Y3 @ Z) @ R) => ((member197592058on_val @ (produc881885833on_val @ Z @ B2) @ (transi2071064181on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_151_converse__rtrancl__induct, axiom,
    ((![A : produc1257910179t_char, B2 : produc1257910179t_char, R : set_Pr729957319t_char, P : produc1257910179t_char > $o]: ((member803902992t_char @ (produc395356247t_char @ A @ B2) @ (transi858104614t_char @ R)) => ((P @ B2) => ((![Y3 : produc1257910179t_char, Z : produc1257910179t_char]: ((member803902992t_char @ (produc395356247t_char @ Y3 @ Z) @ R) => ((member803902992t_char @ (produc395356247t_char @ Z @ B2) @ (transi858104614t_char @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_152_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_153_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_154_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc515445032on_val, R : set_Pr148564103on_val]: (member2027247312on_val @ (produc2106877847on_val @ A @ A) @ (transi432893227on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_155_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1373793468al_val, R : set_Pr711661575al_val]: (member1528603216al_val @ (produc1144711447al_val @ A @ A) @ (transi531594559al_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_156_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc266837688on_val, R : set_Pr2110063281on_val]: (member197592058on_val @ (produc881885833on_val @ A @ A) @ (transi2071064181on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_157_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1257910179t_char, R : set_Pr729957319t_char]: (member803902992t_char @ (produc395356247t_char @ A @ A) @ (transi858104614t_char @ R))))). % rtrancl.rtrancl_refl
thf(fact_158_converse__rtranclE, axiom,
    ((![X : list_char, Z2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Z2) @ (transi1879726366t_char @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y3) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_159_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_160_converse__rtranclE, axiom,
    ((![X : produc515445032on_val, Z2 : produc515445032on_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ X @ Z2) @ (transi432893227on_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ X @ Y3) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ Y3 @ Z2) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE
thf(fact_161_converse__rtranclE, axiom,
    ((![X : produc1373793468al_val, Z2 : produc1373793468al_val, R : set_Pr711661575al_val]: ((member1528603216al_val @ (produc1144711447al_val @ X @ Z2) @ (transi531594559al_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc1373793468al_val]: ((member1528603216al_val @ (produc1144711447al_val @ X @ Y3) @ R) => (~ ((member1528603216al_val @ (produc1144711447al_val @ Y3 @ Z2) @ (transi531594559al_val @ R))))))))))))). % converse_rtranclE
thf(fact_162_converse__rtranclE, axiom,
    ((![X : produc266837688on_val, Z2 : produc266837688on_val, R : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ X @ Z2) @ (transi2071064181on_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc266837688on_val]: ((member197592058on_val @ (produc881885833on_val @ X @ Y3) @ R) => (~ ((member197592058on_val @ (produc881885833on_val @ Y3 @ Z2) @ (transi2071064181on_val @ R))))))))))))). % converse_rtranclE
thf(fact_163_converse__rtranclE, axiom,
    ((![X : produc1257910179t_char, Z2 : produc1257910179t_char, R : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ X @ Z2) @ (transi858104614t_char @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc1257910179t_char]: ((member803902992t_char @ (produc395356247t_char @ X @ Y3) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ Y3 @ Z2) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE
thf(fact_164_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_165_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_166_rtrancl_Oinducts, axiom,
    ((![X1 : produc515445032on_val, X2 : produc515445032on_val, R : set_Pr148564103on_val, P : produc515445032on_val > produc515445032on_val > $o]: ((member2027247312on_val @ (produc2106877847on_val @ X1 @ X2) @ (transi432893227on_val @ R)) => ((![A2 : produc515445032on_val]: (P @ A2 @ A2)) => ((![A2 : produc515445032on_val, B : produc515445032on_val, C : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ B) @ (transi432893227on_val @ R)) => ((P @ A2 @ B) => ((member2027247312on_val @ (produc2106877847on_val @ B @ C) @ R) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_167_rtrancl_Oinducts, axiom,
    ((![X1 : produc1373793468al_val, X2 : produc1373793468al_val, R : set_Pr711661575al_val, P : produc1373793468al_val > produc1373793468al_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ X1 @ X2) @ (transi531594559al_val @ R)) => ((![A2 : produc1373793468al_val]: (P @ A2 @ A2)) => ((![A2 : produc1373793468al_val, B : produc1373793468al_val, C : produc1373793468al_val]: ((member1528603216al_val @ (produc1144711447al_val @ A2 @ B) @ (transi531594559al_val @ R)) => ((P @ A2 @ B) => ((member1528603216al_val @ (produc1144711447al_val @ B @ C) @ R) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_168_rtrancl_Oinducts, axiom,
    ((![X1 : produc266837688on_val, X2 : produc266837688on_val, R : set_Pr2110063281on_val, P : produc266837688on_val > produc266837688on_val > $o]: ((member197592058on_val @ (produc881885833on_val @ X1 @ X2) @ (transi2071064181on_val @ R)) => ((![A2 : produc266837688on_val]: (P @ A2 @ A2)) => ((![A2 : produc266837688on_val, B : produc266837688on_val, C : produc266837688on_val]: ((member197592058on_val @ (produc881885833on_val @ A2 @ B) @ (transi2071064181on_val @ R)) => ((P @ A2 @ B) => ((member197592058on_val @ (produc881885833on_val @ B @ C) @ R) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_169_rtrancl_Oinducts, axiom,
    ((![X1 : produc1257910179t_char, X2 : produc1257910179t_char, R : set_Pr729957319t_char, P : produc1257910179t_char > produc1257910179t_char > $o]: ((member803902992t_char @ (produc395356247t_char @ X1 @ X2) @ (transi858104614t_char @ R)) => ((![A2 : produc1257910179t_char]: (P @ A2 @ A2)) => ((![A2 : produc1257910179t_char, B : produc1257910179t_char, C : produc1257910179t_char]: ((member803902992t_char @ (produc395356247t_char @ A2 @ B) @ (transi858104614t_char @ R)) => ((P @ A2 @ B) => ((member803902992t_char @ (produc395356247t_char @ B @ C) @ R) => (P @ A2 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_170_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_171_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_172_rtrancl__induct, axiom,
    ((![A : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, P : produc515445032on_val > $o]: ((member2027247312on_val @ (produc2106877847on_val @ A @ B2) @ (transi432893227on_val @ R)) => ((P @ A) => ((![Y3 : produc515445032on_val, Z : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A @ Y3) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_173_rtrancl__induct, axiom,
    ((![A : produc1373793468al_val, B2 : produc1373793468al_val, R : set_Pr711661575al_val, P : produc1373793468al_val > $o]: ((member1528603216al_val @ (produc1144711447al_val @ A @ B2) @ (transi531594559al_val @ R)) => ((P @ A) => ((![Y3 : produc1373793468al_val, Z : produc1373793468al_val]: ((member1528603216al_val @ (produc1144711447al_val @ A @ Y3) @ (transi531594559al_val @ R)) => ((member1528603216al_val @ (produc1144711447al_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_174_rtrancl__induct, axiom,
    ((![A : produc266837688on_val, B2 : produc266837688on_val, R : set_Pr2110063281on_val, P : produc266837688on_val > $o]: ((member197592058on_val @ (produc881885833on_val @ A @ B2) @ (transi2071064181on_val @ R)) => ((P @ A) => ((![Y3 : produc266837688on_val, Z : produc266837688on_val]: ((member197592058on_val @ (produc881885833on_val @ A @ Y3) @ (transi2071064181on_val @ R)) => ((member197592058on_val @ (produc881885833on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_175_rtrancl__induct, axiom,
    ((![A : produc1257910179t_char, B2 : produc1257910179t_char, R : set_Pr729957319t_char, P : produc1257910179t_char > $o]: ((member803902992t_char @ (produc395356247t_char @ A @ B2) @ (transi858104614t_char @ R)) => ((P @ A) => ((![Y3 : produc1257910179t_char, Z : produc1257910179t_char]: ((member803902992t_char @ (produc395356247t_char @ A @ Y3) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_176_red__preserves__defass, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((d_list_char @ E @ (some_set_list_char @ (dom_list_char_val @ L))) => (d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ L2))))))))). % red_preserves_defass
thf(fact_177_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_178_Progress, axiom,
    ((![P : list_P1234162913t_char, E5 : list_char > option_ty, S : produc515445032on_val, E : exp_list_char, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((typeSa1969945757config @ P @ E5 @ S @ E @ T) => ((d_list_char @ E @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S)))) => ((~ ((final_list_char @ E))) => (?[E4 : exp_list_char, S3 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)))))))))). % Progress
thf(fact_179_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S) @ E5 @ E @ T) => ((typeSa1777264139_sconf @ P @ E5 @ S) => (typeSa1777264139_sconf @ P @ E5 @ S2)))))))). % Red_preserves_sconf
thf(fact_180_wf__config__def, axiom,
    ((typeSa1969945757config = (^[P3 : list_P1234162913t_char]: (^[E6 : list_char > option_ty]: (^[S4 : produc515445032on_val]: (^[E7 : exp_list_char]: (^[T2 : ty]: (((typeSa1777264139_sconf @ P3 @ E6 @ S4)) & ((wTrt @ P3 @ (hp @ S4) @ E6 @ E7 @ T2))))))))))). % wf_config_def
thf(fact_181_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E5 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E5 @ E @ T) => ((typeSa1777264139_sconf @ P @ E5 @ S) => (typeSa1777264139_sconf @ P @ E5 @ S2))))))). % red_preserves_sconf
thf(fact_182_Red__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1777264139_sconf @ P @ E5 @ S) => ((wTrt @ P @ (hp @ S) @ E5 @ E @ T) => (?[T3 : ty]: ((widen_917054840t_char @ P @ T3 @ T) & (wTrt @ P @ (hp @ S2) @ E5 @ E2 @ T3)))))))))). % Red_preserves_type
thf(fact_183_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E5 @ S) => ((wTrt @ P @ (hp @ S) @ E5 @ E @ T) => (?[T3 : ty]: ((wTrt @ P @ (hp @ S2) @ E5 @ E2 @ T3) & (widen_917054840t_char @ P @ T3 @ T)))))))))). % subject_reduction
thf(fact_184_red__preserves__hconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E5 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E5 @ E @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_185_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E5 @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E5 @ E @ T) => (?[T3 : ty]: ((wTrt @ P @ H2 @ E5 @ E2 @ T3) & (widen_917054840t_char @ P @ T3 @ T)))))))))). % subject_reduction2
thf(fact_186_Subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => ((typeSa1969945757config @ P @ E5 @ S @ E @ T) => (?[T3 : ty]: ((typeSa1969945757config @ P @ E5 @ S2 @ E2 @ T3) & (widen_917054840t_char @ P @ T3 @ T))))))))). % Subject_reduction
thf(fact_187_Subject__reductions, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1969945757config @ P @ E5 @ S @ E @ T) => (?[T3 : ty]: ((typeSa1969945757config @ P @ E5 @ S2 @ E2 @ T3) & (widen_917054840t_char @ P @ T3 @ T))))))))). % Subject_reductions
thf(fact_188_progress, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E5 : list_char > option_ty, E : 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 @ E5 @ E @ T) => ((d_list_char @ E @ (some_set_list_char @ (dom_list_char_val @ L))) => ((~ ((final_list_char @ E))) => (?[E4 : exp_list_char, S3 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P))))))))))). % progress
thf(fact_189_red__preserves__lconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E5 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E5 @ E @ T) => ((lconf_485928294t_char @ P @ H @ L @ E5) => (lconf_485928294t_char @ P @ H2 @ L2 @ E5))))))). % red_preserves_lconf
thf(fact_190_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E5 : list_char > option_ty, E : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E5 @ E @ T) => (wTrt @ P @ H @ E5 @ E @ T))))). % WT_implies_WTrt
thf(fact_191_eval__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E @ S @ E2 @ S2) => ((typeSa1777264139_sconf @ P @ E5 @ S) => ((wt @ P @ E5 @ E @ T) => (?[T3 : ty]: ((widen_917054840t_char @ P @ T3 @ T) & (wTrt @ P @ (hp @ S2) @ E5 @ E2 @ T3)))))))))). % eval_preserves_type
thf(fact_192_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S @ E2 @ S2) => (~ (((E2 = (val_list_char @ V)) => (~ ((S2 = S)))))))))). % eval_cases(2)
thf(fact_193_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S @ (val_list_char @ V) @ S)))). % Val
thf(fact_194_eval__evals_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.ThrowThrow
thf(fact_195_eval__final, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((eval @ P @ E @ S @ E2 @ S2) => (final_list_char @ E2))))). % eval_final
thf(fact_196_eval__finalId, axiom,
    ((![E : exp_list_char, P : list_P1234162913t_char, S : produc515445032on_val]: ((final_list_char @ E) => (eval @ P @ E @ S @ E @ S))))). % eval_finalId
thf(fact_197_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E8 @ S5)) @ (red @ P)) => ((eval @ P @ E8 @ S5 @ E2 @ S2) => (eval @ P @ E @ S @ E2 @ S2))))))). % extend_1_eval
thf(fact_198_Throw, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A)) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ (val_list_char @ (addr @ A))) @ S_1))))). % Throw
thf(fact_199_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E8 @ S5)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E8 @ S5 @ E2 @ S2) => (eval @ P @ E @ S @ E2 @ S2))))))). % extend_eval
thf(fact_200_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E @ S @ E2 @ S2) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_201_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E2) => (eval @ P @ E @ S @ E2 @ S2))))))). % small_by_big
thf(fact_202_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E @ S @ E2 @ S2) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E2)))))))). % big_iff_small
thf(fact_203_eval__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E5 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E @ S @ E2 @ S2) => ((wt @ P @ E5 @ E @ T) => ((typeSa1777264139_sconf @ P @ E5 @ S) => (typeSa1777264139_sconf @ P @ E5 @ S2)))))))). % eval_preserves_sconf
thf(fact_204_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_205_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C3 @ Md) => (wwf_J_mdecl @ P @ C3 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_206_FAccRedsVal, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A : nat, S2 : produc515445032on_val, P : list_P1234162913t_char, C3 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S2)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D2) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_207_red__reds_ORedFAcc, axiom,
    ((![S : produc515445032on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F @ D2) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_208_eval__evals_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val, F : list_char, D2 : list_char]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (fAcc_list_char @ E @ F @ D2) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.FAccThrow
thf(fact_209_red__reds_OFAccRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D2) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_210_red__reds_OFAccThrow, axiom,
    ((![E : exp_list_char, F : list_char, D2 : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E) @ F @ D2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_211_FAccReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D2) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_212_FAcc, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A : nat, H : nat > option2118145160on_val, L : list_char > option_val, C3 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val]: ((eval @ P @ E @ S_0 @ (val_list_char @ (addr @ A)) @ (produc52622304on_val @ H @ L)) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (eval @ P @ (fAcc_list_char @ E @ F @ D2) @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L)))))))). % FAcc
thf(fact_213_FAccRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F @ D2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_214_redp__redsp_ORedFAcc, axiom,
    ((![S : produc515445032on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, F : list_char, D2 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (((Fs @ (produc1304532571t_char @ F @ D2)) = (some_val @ V)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F @ D2) @ S @ (val_list_char @ V) @ S)))))). % redp_redsp.RedFAcc
thf(fact_215_red__reds_ORedVar, axiom,
    ((![S : produc515445032on_val, V2 : list_char, V : val, P : list_P1234162913t_char]: (((lcl @ S @ V2) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (var_list_char @ V2) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S)) @ (red @ P)))))). % red_reds.RedVar
thf(fact_216_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, E : 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 @ E) @ 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 @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_217_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, F : list_char, D2 : list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (fAcc_list_char @ E @ F @ D2) @ S @ (fAcc_list_char @ E2 @ F @ D2) @ S2))))). % redp_redsp.FAccRed
thf(fact_218_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E)) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.ThrowThrow
thf(fact_219_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (throw_list_char @ E) @ S @ (throw_list_char @ E2) @ S2))))). % redp_redsp.ThrowRed
thf(fact_220_redp__redsp_OBinOpRed1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (binOp_list_char @ E @ Bop @ E_2) @ S @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2))))). % redp_redsp.BinOpRed1
thf(fact_221_redp__redsp_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, V_1 : val, Bop : bop, E : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E)) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.BinOpThrow2
thf(fact_222_redp__redsp_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (throw_list_char @ E) @ Bop @ E_2) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.BinOpThrow1
thf(fact_223_redp__redsp_OBinOpRed2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, V_1 : val, Bop : bop]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2))))). % redp_redsp.BinOpRed2
thf(fact_224_redp__redsp_ORedVar, axiom,
    ((![S : produc515445032on_val, V2 : list_char, V : val, P : list_P1234162913t_char]: (((lcl @ S @ V2) = (some_val @ V)) => (redp @ P @ (var_list_char @ V2) @ S @ (val_list_char @ V) @ S))))). % redp_redsp.RedVar
thf(fact_225_eval__evals_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, S_0 : produc515445032on_val, E : exp_list_char, S_1 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((eval @ P @ E_12 @ S_0 @ (throw_list_char @ E) @ S_1) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E) @ S_1))))). % eval_evals.BinOpThrow1
thf(fact_226_redp__redsp_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, F : list_char, D2 : list_char, S : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (throw_list_char @ E) @ F @ D2) @ S @ (throw_list_char @ E) @ S)))). % redp_redsp.FAccThrow
thf(fact_227_WTrtVar, axiom,
    ((![E5 : list_char > option_ty, V2 : list_char, T : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((E5 @ V2) = (some_ty @ T)) => (wTrt @ P @ H @ E5 @ (var_list_char @ V2) @ T))))). % WTrtVar
thf(fact_228_red__reds_OBinOpRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_229_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, E : 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 @ E) @ S_2) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (throw_list_char @ E) @ S_2)))))). % eval_evals.BinOpThrow2
thf(fact_230_red__reds_OBinOpRed2, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_231_red__reds_OBinOpThrow1, axiom,
    ((![E : 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 @ E) @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_232_BinOp1Reds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_233_Var, axiom,
    ((![L : list_char > option_val, V2 : list_char, V : val, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((L @ V2) = (some_val @ V)) => (eval @ P @ (var_list_char @ V2) @ (produc52622304on_val @ H @ L) @ (val_list_char @ V) @ (produc52622304on_val @ H @ L)))))). % Var
thf(fact_234_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E : 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 @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_235_BinOp2Reds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_236_BinOpRedsThrow1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_237_WTVar, axiom,
    ((![E5 : list_char > option_ty, V2 : list_char, T : ty, P : list_P1234162913t_char]: (((E5 @ V2) = (some_ty @ T)) => (wt @ P @ E5 @ (var_list_char @ V2) @ T))))). % WTVar
thf(fact_238_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, V : 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 @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_2)) @ (transi111096263on_val @ (red @ P))))))))). % BinOpRedsVal
thf(fact_239_red__reds_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V : val, S : produc515445032on_val, P : list_P1234162913t_char]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (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 @ V) @ S)) @ (red @ P)))))). % red_reds.RedBinOp
thf(fact_240_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, V : 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 @ V)) => (eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0 @ (val_list_char @ V) @ S_2))))))). % BinOp
thf(fact_241_redp__redsp_ORedBinOp, axiom,
    ((![Bop : bop, V_1 : val, V_2 : val, V : val, P : list_P1234162913t_char, S : produc515445032on_val]: (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_1 @ V_2))) = (some_val @ V)) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (val_list_char @ V_2)) @ S @ (val_list_char @ V) @ S))))). % redp_redsp.RedBinOp
thf(fact_242_eval__cases_I3_J, axiom,
    ((![P : list_P1234162913t_char, E_12 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((eval @ P @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S @ E2 @ S2) => ((![V_12 : val, S_12 : produc515445032on_val, V_22 : val, V3 : val]: ((E2 = (val_list_char @ V3)) => ((eval @ P @ E_12 @ S @ (val_list_char @ V_12) @ S_12) => ((eval @ P @ E_2 @ S_12 @ (val_list_char @ V_22) @ S2) => (~ (((binop @ (produc1753769388al_val @ Bop @ (product_Pair_val_val @ V_12 @ V_22))) = (some_val @ V3)))))))) => ((![E3 : exp_list_char]: ((E2 = (throw_list_char @ E3)) => (~ ((eval @ P @ E_12 @ S @ (throw_list_char @ E3) @ S2))))) => (~ ((![V_12 : val, S_12 : produc515445032on_val, E3 : exp_list_char]: ((E2 = (throw_list_char @ E3)) => ((eval @ P @ E_12 @ S @ (val_list_char @ V_12) @ S_12) => (~ ((eval @ P @ E_2 @ S_12 @ (throw_list_char @ E3) @ S2)))))))))))))). % eval_cases(3)
thf(fact_243_red__reds_OBlockThrow, axiom,
    ((![V2 : list_char, T : ty, A : nat, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ 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_244_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T : ty, U : val, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T @ (val_list_char @ U)) @ S @ (val_list_char @ U) @ S)))). % redp_redsp.RedBlock
thf(fact_245_red__reds_ORedBlock, axiom,
    ((![V2 : list_char, T : ty, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T @ (val_list_char @ U)) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_246_redp__redsp_OBlockThrow, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T : ty, A : nat, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T @ (throw_list_char @ (val_list_char @ (addr @ A)))) @ S @ (throw_list_char @ (val_list_char @ (addr @ A))) @ S)))). % redp_redsp.BlockThrow
thf(fact_247_FAssRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E : exp_list_char, S_2 : produc515445032on_val, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_12 @ F @ D2 @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_248_red__lcl__incr, axiom,
    ((![E : exp_list_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, E2 : exp_list_char, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_12 @ L_12))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_02) @ (dom_list_char_val @ L_12)))))). % red_lcl_incr

% Conjectures (7)
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, conjecture,
    (((?[V4 : val]: ((e3 = (val_list_char @ V4)) & (conf_P93989998t_char @ p @ (hp @ s2) @ V4 @ t))) | (?[A4 : nat]: ((e3 = (throw_list_char @ (val_list_char @ (addr @ A4)))) & (member_nat @ A4 @ (dom_na451844572on_val @ (hp @ s2)))))))).
