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thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr148564103on_val : $tType).
thf(ty_n_t__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,
    produc744932519on_val : $tType).
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J_Mt__List__Olist_It__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_J_J_J_J_J, type,
    list_P1234162913t_char : $tType).
thf(ty_n_t__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,
    produc1097884484on_val : $tType).
thf(ty_n_t__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,
    produc515445032on_val : $tType).
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__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__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    option_set_list_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    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__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (65)
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_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_Ofv, type,
    fv : exp_list_char > set_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    sup_su1099679555t_char : set_list_char > set_list_char > set_list_char).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__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_J, type,
    sup_su499610203on_val : set_Pr148564103on_val > set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    sup_su886787547on_val : set_Pr1189492743on_val > set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_J, type,
    sup_su2093213339on_val : set_Pr1368603847on_val > set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_li665594572t_char : (list_char > option_set_list_char) > set_list_char).
thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    dom_list_char_ty : (list_char > option_ty) > set_list_char).
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__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__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_Pr2060832492t_char : (produc744932519on_val > option_set_list_char) > set_Pr148564103on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_Pr1335625324t_char : (produc1172664615on_val > option_set_list_char) > set_Pr1189492743on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_Pr911909676t_char : (produc1161703655on_val > option_set_list_char) > set_Pr1368603847on_val).
thf(sy_c_Map_Orestrict__map_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    restri1468981139ar_val : (list_char > option_val) > set_list_char > list_char > option_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_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__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_J, type,
    ord_le1661771815on_val : set_Pr148564103on_val > set_Pr148564103on_val > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    ord_le837504935on_val : set_Pr1189492743on_val > set_Pr1189492743on_val > $o).
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thf(sy_c_State_Olcl, type,
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thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__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,
    transi2142918570on_val : set_Pr777589959on_val > set_Pr777589959on_val).
thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    transi1260223466on_val : set_Pr718570695on_val > set_Pr718570695on_val).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Owf__config, type,
    typeSa1969945757config : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > exp_list_char > ty > $o).
thf(sy_c_WWellForm_Owwf__J__mdecl, type,
    wwf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J, type,
    member_list_char : list_char > set_list_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__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_Mt__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_J, type,
    member2048912144on_val : produc1682558695on_val > set_Pr777589959on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J_J, type,
    member364223248on_val : produc669986535on_val > set_Pr718570695on_val > $o).
thf(sy_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T, type,
    t : ty).
thf(sy_v_T_H, type,
    t2 : ty).
thf(sy_v_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (249)
thf(fact_0_Progress, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, S : produc515445032on_val, E2 : exp_list_char, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((typeSa1969945757config @ P @ E @ S @ E2 @ T) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S)))) => ((~ ((final_list_char @ E2))) => (?[E3 : exp_list_char, S2 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)))))))))). % Progress
thf(fact_1_Subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((typeSa1969945757config @ P @ E @ S @ E2 @ T) => (?[T2 : ty]: ((typeSa1969945757config @ P @ E @ S3 @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T))))))))). % Subject_reduction
thf(fact_2_Subject__reductions, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1969945757config @ P @ E @ S @ E2 @ T) => (?[T2 : ty]: ((typeSa1969945757config @ P @ E @ S3 @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T))))))))). % Subject_reductions
thf(fact_3_Red__preserves__defass, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S)))) => (d_list_char @ E4 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ S3)))))))))). % Red_preserves_defass
thf(fact_4_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) => ((![A : produc515445032on_val, B : produc515445032on_val, Aa : produc515445032on_val, Ba : produc515445032on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Ax @ Ay) @ (produc2106877847on_val @ A @ B)) @ (transi2142918570on_val @ R)) => ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ A @ B) @ (produc2106877847on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_5_rtrancl__induct2, axiom,
    ((![Ax : produc1172664615on_val, Ay : produc1172664615on_val, Bx : produc1172664615on_val, By : produc1172664615on_val, R : set_Pr718570695on_val, P : produc1172664615on_val > produc1172664615on_val > $o]: ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ Ax @ Ay) @ (produc564964183on_val @ Bx @ By)) @ (transi1260223466on_val @ R)) => ((P @ Ax @ Ay) => ((![A : produc1172664615on_val, B : produc1172664615on_val, Aa : produc1172664615on_val, Ba : produc1172664615on_val]: ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ Ax @ Ay) @ (produc564964183on_val @ A @ B)) @ (transi1260223466on_val @ R)) => ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ A @ B) @ (produc564964183on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_6_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_7_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) => ((![A : 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 @ A @ B)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_8_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_9_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)))) => (~ ((![A : produc515445032on_val, B : produc515445032on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ Xa @ Xb) @ (produc2106877847on_val @ A @ B)) @ R) => (~ ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ A @ B) @ (produc2106877847on_val @ Za @ Zb)) @ (transi2142918570on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_10_converse__rtranclE2, axiom,
    ((![Xa : produc1172664615on_val, Xb : produc1172664615on_val, Za : produc1172664615on_val, Zb : produc1172664615on_val, R : set_Pr718570695on_val]: ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ Xa @ Xb) @ (produc564964183on_val @ Za @ Zb)) @ (transi1260223466on_val @ R)) => ((~ (((produc564964183on_val @ Xa @ Xb) = (produc564964183on_val @ Za @ Zb)))) => (~ ((![A : produc1172664615on_val, B : produc1172664615on_val]: ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ Xa @ Xb) @ (produc564964183on_val @ A @ B)) @ R) => (~ ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ A @ B) @ (produc564964183on_val @ Za @ Zb)) @ (transi1260223466on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_11_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)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_12_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)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_13_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)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_14_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) => ((![A : produc515445032on_val, B : produc515445032on_val, Aa : produc515445032on_val, Ba : produc515445032on_val]: ((member2048912144on_val @ (produc253850455on_val @ (produc2106877847on_val @ A @ 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 @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_15_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1172664615on_val, Ay : produc1172664615on_val, Bx : produc1172664615on_val, By : produc1172664615on_val, R : set_Pr718570695on_val, P : produc1172664615on_val > produc1172664615on_val > $o]: ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ Ax @ Ay) @ (produc564964183on_val @ Bx @ By)) @ (transi1260223466on_val @ R)) => ((P @ Bx @ By) => ((![A : produc1172664615on_val, B : produc1172664615on_val, Aa : produc1172664615on_val, Ba : produc1172664615on_val]: ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ A @ B) @ (produc564964183on_val @ Aa @ Ba)) @ R) => ((member364223248on_val @ (produc1100907351on_val @ (produc564964183on_val @ Aa @ Ba) @ (produc564964183on_val @ Bx @ By)) @ (transi1260223466on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_16_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ 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 @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_17_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ 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 @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_18_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ 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 @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_19_prod__cases4, axiom,
    ((![Y : produc1161703655on_val]: (~ ((![A : produc1172664615on_val, B : produc1097884484on_val, C : exp_list_char, D : produc515445032on_val]: (~ ((Y = (produc564964183on_val @ A @ (produc1069526295on_val @ B @ (produc2023458740on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_20_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_21_prod__cases5, axiom,
    ((![Y : produc1161703655on_val]: (~ ((![A : produc1172664615on_val, B : produc1097884484on_val, C : exp_list_char, D : nat > option2118145160on_val, E5 : list_char > option_val]: (~ ((Y = (produc564964183on_val @ A @ (produc1069526295on_val @ B @ (produc2023458740on_val @ C @ (produc52622304on_val @ D @ E5))))))))))))). % prod_cases5
thf(fact_22_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_23_prod__induct4, axiom,
    ((![P : produc1161703655on_val > $o, X : produc1161703655on_val]: ((![A : produc1172664615on_val, B : produc1097884484on_val, C : exp_list_char, D : produc515445032on_val]: (P @ (produc564964183on_val @ A @ (produc1069526295on_val @ B @ (produc2023458740on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_24_prod__induct5, axiom,
    ((![P : produc1161703655on_val > $o, X : produc1161703655on_val]: ((![A : produc1172664615on_val, B : produc1097884484on_val, C : exp_list_char, D : nat > option2118145160on_val, E5 : list_char > option_val]: (P @ (produc564964183on_val @ A @ (produc1069526295on_val @ B @ (produc2023458740on_val @ C @ (produc52622304on_val @ D @ E5)))))) => (P @ X))))). % prod_induct5
thf(fact_25_red__preserves__defass, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ L))) => (d_list_char @ E4 @ (some_set_list_char @ (dom_list_char_val @ L2))))))))). % red_preserves_defass
thf(fact_26_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_27_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_28_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_29_old_Oprod_Oinject, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, A3 : produc515445032on_val, B3 : produc515445032on_val]: (((produc2106877847on_val @ A2 @ B2) = (produc2106877847on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_30_old_Oprod_Oinject, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, A3 : produc1172664615on_val, B3 : produc1172664615on_val]: (((produc564964183on_val @ A2 @ B2) = (produc564964183on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_31_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_32_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_33_prod_Oinject, axiom,
    ((![X1 : 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_34_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_35_prod_Oinject, axiom,
    ((![X1 : produc1172664615on_val, X2 : produc1172664615on_val, Y1 : produc1172664615on_val, Y2 : produc1172664615on_val]: (((produc564964183on_val @ X1 @ X2) = (produc564964183on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_36_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_37_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_38_r__into__rtrancl, axiom,
    ((![P2 : produc1161703655on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ P2 @ R) => (member208988944on_val @ P2 @ (transi100378922on_val @ R)))))). % r_into_rtrancl
thf(fact_39_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_40_rtrancl__idemp, axiom,
    ((![R : set_Pr148564103on_val]: ((transi432893227on_val @ (transi432893227on_val @ R)) = (transi432893227on_val @ R))))). % rtrancl_idemp
thf(fact_41_rtrancl__idemp, axiom,
    ((![R : set_Pr1368603847on_val]: ((transi100378922on_val @ (transi100378922on_val @ R)) = (transi100378922on_val @ R))))). % rtrancl_idemp
thf(fact_42_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_43_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_44_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_45_old_Oprod_Oinducts, axiom,
    ((![P : produc744932519on_val > $o, Prod : produc744932519on_val]: ((![A : produc515445032on_val, B : produc515445032on_val]: (P @ (produc2106877847on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_46_old_Oprod_Oinducts, axiom,
    ((![P : produc1161703655on_val > $o, Prod : produc1161703655on_val]: ((![A : produc1172664615on_val, B : produc1172664615on_val]: (P @ (produc564964183on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_47_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_48_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_49_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_50_old_Oprod_Oexhaust, axiom,
    ((![Y : produc744932519on_val]: (~ ((![A : produc515445032on_val, B : produc515445032on_val]: (~ ((Y = (produc2106877847on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_51_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1161703655on_val]: (~ ((![A : produc1172664615on_val, B : produc1172664615on_val]: (~ ((Y = (produc564964183on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_52_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_53_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_54_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_55_Pair__inject, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, A3 : produc515445032on_val, B3 : produc515445032on_val]: (((produc2106877847on_val @ A2 @ B2) = (produc2106877847on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_56_Pair__inject, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, A3 : produc1172664615on_val, B3 : produc1172664615on_val]: (((produc564964183on_val @ A2 @ B2) = (produc564964183on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_57_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_58_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_59_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_60_prod__cases, axiom,
    ((![P : produc744932519on_val > $o, P2 : produc744932519on_val]: ((![A : produc515445032on_val, B : produc515445032on_val]: (P @ (produc2106877847on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_61_prod__cases, axiom,
    ((![P : produc1161703655on_val > $o, P2 : produc1161703655on_val]: ((![A : produc1172664615on_val, B : produc1172664615on_val]: (P @ (produc564964183on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_62_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_63_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_64_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_65_surj__pair, axiom,
    ((![P2 : produc744932519on_val]: (?[X3 : produc515445032on_val, Y3 : produc515445032on_val]: (P2 = (produc2106877847on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_66_surj__pair, axiom,
    ((![P2 : produc1161703655on_val]: (?[X3 : produc1172664615on_val, Y3 : produc1172664615on_val]: (P2 = (produc564964183on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_67_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_68_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_69_prod__induct3, axiom,
    ((![P : produc744932519on_val > $o, X : produc744932519on_val]: ((![A : produc515445032on_val, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2106877847on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_70_prod__induct3, axiom,
    ((![P : produc1161703655on_val > $o, X : produc1161703655on_val]: ((![A : produc1172664615on_val, B : produc1097884484on_val, C : produc1097884484on_val]: (P @ (produc564964183on_val @ A @ (produc1069526295on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_71_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_72_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_73_prod__cases3, axiom,
    ((![Y : produc744932519on_val]: (~ ((![A : produc515445032on_val, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2106877847on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_74_prod__cases3, axiom,
    ((![Y : produc1161703655on_val]: (~ ((![A : produc1172664615on_val, B : produc1097884484on_val, C : produc1097884484on_val]: (~ ((Y = (produc564964183on_val @ A @ (produc1069526295on_val @ B @ C))))))))))). % prod_cases3
thf(fact_75_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_76_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, C2 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ B2) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ B2 @ C2) @ (transi432893227on_val @ R)) => (member2027247312on_val @ (produc2106877847on_val @ A2 @ C2) @ (transi432893227on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_77_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, R : set_Pr1368603847on_val, C2 : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ A2 @ B2) @ R) => ((member208988944on_val @ (produc564964183on_val @ B2 @ C2) @ (transi100378922on_val @ R)) => (member208988944on_val @ (produc564964183on_val @ A2 @ C2) @ (transi100378922on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_78_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_79_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, C2 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ B2) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ B2 @ C2) @ R) => (member2027247312on_val @ (produc2106877847on_val @ A2 @ C2) @ (transi432893227on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_80_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, R : set_Pr1368603847on_val, C2 : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ A2 @ B2) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ B2 @ C2) @ R) => (member208988944on_val @ (produc564964183on_val @ A2 @ C2) @ (transi100378922on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_81_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ 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 @ A2))))))). % converse_rtrancl_induct
thf(fact_82_converse__rtrancl__induct, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, P : produc515445032on_val > $o]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ 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 @ A2))))))). % converse_rtrancl_induct
thf(fact_83_converse__rtrancl__induct, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, R : set_Pr1368603847on_val, P : produc1172664615on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ A2 @ B2) @ (transi100378922on_val @ R)) => ((P @ B2) => ((![Y3 : produc1172664615on_val, Z : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ Y3 @ Z) @ R) => ((member208988944on_val @ (produc564964183on_val @ Z @ B2) @ (transi100378922on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_84_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_85_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc515445032on_val, R : set_Pr148564103on_val]: (member2027247312on_val @ (produc2106877847on_val @ A2 @ A2) @ (transi432893227on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_86_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1172664615on_val, R : set_Pr1368603847on_val]: (member208988944on_val @ (produc564964183on_val @ A2 @ A2) @ (transi100378922on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_87_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_88_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_89_converse__rtranclE, axiom,
    ((![X : produc1172664615on_val, Z2 : produc1172664615on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ X @ Z2) @ (transi100378922on_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ X @ Y3) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ Y3 @ Z2) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE
thf(fact_90_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)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_91_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)) => ((![A : produc515445032on_val]: (P @ A @ A)) => ((![A : produc515445032on_val, B : produc515445032on_val, C : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A @ B) @ (transi432893227on_val @ R)) => ((P @ A @ B) => ((member2027247312on_val @ (produc2106877847on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_92_rtrancl_Oinducts, axiom,
    ((![X1 : produc1172664615on_val, X2 : produc1172664615on_val, R : set_Pr1368603847on_val, P : produc1172664615on_val > produc1172664615on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ X1 @ X2) @ (transi100378922on_val @ R)) => ((![A : produc1172664615on_val]: (P @ A @ A)) => ((![A : produc1172664615on_val, B : produc1172664615on_val, C : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ A @ B) @ (transi100378922on_val @ R)) => ((P @ A @ B) => ((member208988944on_val @ (produc564964183on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_93_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_94_rtrancl__induct, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val, P : produc515445032on_val > $o]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ B2) @ (transi432893227on_val @ R)) => ((P @ A2) => ((![Y3 : produc515445032on_val, Z : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ Y3) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_95_rtrancl__induct, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, R : set_Pr1368603847on_val, P : produc1172664615on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ A2 @ B2) @ (transi100378922on_val @ R)) => ((P @ A2) => ((![Y3 : produc1172664615on_val, Z : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ A2 @ Y3) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_96_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_97_rtrancl__trans, axiom,
    ((![X : produc515445032on_val, Y : produc515445032on_val, R : set_Pr148564103on_val, Z2 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ X @ Y) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ Y @ Z2) @ (transi432893227on_val @ R)) => (member2027247312on_val @ (produc2106877847on_val @ X @ Z2) @ (transi432893227on_val @ R))))))). % rtrancl_trans
thf(fact_98_rtrancl__trans, axiom,
    ((![X : produc1172664615on_val, Y : produc1172664615on_val, R : set_Pr1368603847on_val, Z2 : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ X @ Y) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ Y @ Z2) @ (transi100378922on_val @ R)) => (member208988944on_val @ (produc564964183on_val @ X @ Z2) @ (transi100378922on_val @ R))))))). % rtrancl_trans
thf(fact_99_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A4 : produc1097884484on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A4)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_100_rtrancl_Osimps, axiom,
    ((![A1 : produc515445032on_val, A22 : produc515445032on_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A1 @ A22) @ (transi432893227on_val @ R)) = (((?[A4 : produc515445032on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc515445032on_val]: (?[B4 : produc515445032on_val]: (?[C3 : produc515445032on_val]: (((A1 = A4)) & ((((A22 = C3)) & ((((member2027247312on_val @ (produc2106877847on_val @ A4 @ B4) @ (transi432893227on_val @ R))) & ((member2027247312on_val @ (produc2106877847on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_101_rtrancl_Osimps, axiom,
    ((![A1 : produc1172664615on_val, A22 : produc1172664615on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ A1 @ A22) @ (transi100378922on_val @ R)) = (((?[A4 : produc1172664615on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1172664615on_val]: (?[B4 : produc1172664615on_val]: (?[C3 : produc1172664615on_val]: (((A1 = A4)) & ((((A22 = C3)) & ((((member208988944on_val @ (produc564964183on_val @ A4 @ B4) @ (transi100378922on_val @ R))) & ((member208988944on_val @ (produc564964183on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_102_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_103_rtrancl_Ocases, axiom,
    ((![A1 : produc515445032on_val, A22 : produc515445032on_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A1 @ A22) @ (transi432893227on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A1 @ B) @ (transi432893227on_val @ R)) => (~ ((member2027247312on_val @ (produc2106877847on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_104_rtrancl_Ocases, axiom,
    ((![A1 : produc1172664615on_val, A22 : produc1172664615on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ A1 @ A22) @ (transi100378922on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ A1 @ B) @ (transi100378922on_val @ R)) => (~ ((member208988944on_val @ (produc564964183on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_105_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_106_rtranclE, axiom,
    ((![A2 : produc515445032on_val, B2 : produc515445032on_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ B2) @ (transi432893227on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc515445032on_val]: ((member2027247312on_val @ (produc2106877847on_val @ A2 @ Y3) @ (transi432893227on_val @ R)) => (~ ((member2027247312on_val @ (produc2106877847on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_107_rtranclE, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ A2 @ B2) @ (transi100378922on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1172664615on_val]: ((member208988944on_val @ (produc564964183on_val @ A2 @ Y3) @ (transi100378922on_val @ R)) => (~ ((member208988944on_val @ (produc564964183on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_108_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E5 @ H3 @ L3 @ E5 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E3 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_1 @ H_1 @ L_1 @ E3 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E3 @ H4 @ L4)))) => (R2 @ E2 @ H @ L @ E4 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_109_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_110_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E @ E2 @ T) => (?[T2 : ty]: ((wTrt @ P @ H2 @ E @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_111_domI, axiom,
    ((![M : list_char > option_val, A2 : list_char, B2 : val]: (((M @ A2) = (some_val @ B2)) => (member_list_char @ A2 @ (dom_list_char_val @ M)))))). % domI
thf(fact_112_domI, axiom,
    ((![M : list_char > option_ty, A2 : list_char, B2 : ty]: (((M @ A2) = (some_ty @ B2)) => (member_list_char @ A2 @ (dom_list_char_ty @ M)))))). % domI
thf(fact_113_domI, axiom,
    ((![M : produc1172664615on_val > option_set_list_char, A2 : produc1172664615on_val, B2 : set_list_char]: (((M @ A2) = (some_set_list_char @ B2)) => (member354538064on_val @ A2 @ (dom_Pr1335625324t_char @ M)))))). % domI
thf(fact_114_domI, axiom,
    ((![M : list_char > option_set_list_char, A2 : list_char, B2 : set_list_char]: (((M @ A2) = (some_set_list_char @ B2)) => (member_list_char @ A2 @ (dom_li665594572t_char @ M)))))). % domI
thf(fact_115_domI, axiom,
    ((![M : produc744932519on_val > option_set_list_char, A2 : produc744932519on_val, B2 : set_list_char]: (((M @ A2) = (some_set_list_char @ B2)) => (member2027247312on_val @ A2 @ (dom_Pr2060832492t_char @ M)))))). % domI
thf(fact_116_domI, axiom,
    ((![M : produc1161703655on_val > option_set_list_char, A2 : produc1161703655on_val, B2 : set_list_char]: (((M @ A2) = (some_set_list_char @ B2)) => (member208988944on_val @ A2 @ (dom_Pr911909676t_char @ M)))))). % domI
thf(fact_117_domD, axiom,
    ((![A2 : list_char, M : list_char > option_val]: ((member_list_char @ A2 @ (dom_list_char_val @ M)) => (?[B : val]: ((M @ A2) = (some_val @ B))))))). % domD
thf(fact_118_domD, axiom,
    ((![A2 : list_char, M : list_char > option_ty]: ((member_list_char @ A2 @ (dom_list_char_ty @ M)) => (?[B : ty]: ((M @ A2) = (some_ty @ B))))))). % domD
thf(fact_119_domD, axiom,
    ((![A2 : produc1172664615on_val, M : produc1172664615on_val > option_set_list_char]: ((member354538064on_val @ A2 @ (dom_Pr1335625324t_char @ M)) => (?[B : set_list_char]: ((M @ A2) = (some_set_list_char @ B))))))). % domD
thf(fact_120_domD, axiom,
    ((![A2 : list_char, M : list_char > option_set_list_char]: ((member_list_char @ A2 @ (dom_li665594572t_char @ M)) => (?[B : set_list_char]: ((M @ A2) = (some_set_list_char @ B))))))). % domD
thf(fact_121_domD, axiom,
    ((![A2 : produc744932519on_val, M : produc744932519on_val > option_set_list_char]: ((member2027247312on_val @ A2 @ (dom_Pr2060832492t_char @ M)) => (?[B : set_list_char]: ((M @ A2) = (some_set_list_char @ B))))))). % domD
thf(fact_122_domD, axiom,
    ((![A2 : produc1161703655on_val, M : produc1161703655on_val > option_set_list_char]: ((member208988944on_val @ A2 @ (dom_Pr911909676t_char @ M)) => (?[B : set_list_char]: ((M @ A2) = (some_set_list_char @ B))))))). % domD
thf(fact_123_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_124_mem__Collect__eq, axiom,
    ((![A2 : list_char, P : list_char > $o]: ((member_list_char @ A2 @ (collect_list_char @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_125_mem__Collect__eq, axiom,
    ((![A2 : produc744932519on_val, P : produc744932519on_val > $o]: ((member2027247312on_val @ A2 @ (collec1161811218on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_126_mem__Collect__eq, axiom,
    ((![A2 : produc1161703655on_val, P : produc1161703655on_val > $o]: ((member208988944on_val @ A2 @ (collec608254290on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_127_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_128_Collect__mem__eq, axiom,
    ((![A5 : set_list_char]: ((collect_list_char @ (^[X4 : list_char]: (member_list_char @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_129_Collect__mem__eq, axiom,
    ((![A5 : set_Pr148564103on_val]: ((collec1161811218on_val @ (^[X4 : produc744932519on_val]: (member2027247312on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_130_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1368603847on_val]: ((collec608254290on_val @ (^[X4 : produc1161703655on_val]: (member208988944on_val @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_131_Red__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E @ E4 @ T2)))))))))). % Red_preserves_type
thf(fact_132_eval__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) => ((wt @ P @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S3)))))))). % eval_preserves_sconf
thf(fact_133_wf__config__def, axiom,
    ((typeSa1969945757config = (^[P3 : list_P1234162913t_char]: (^[E6 : list_char > option_ty]: (^[S4 : produc515445032on_val]: (^[E7 : exp_list_char]: (^[T3 : ty]: (((typeSa1777264139_sconf @ P3 @ E6 @ S4)) & ((wTrt @ P3 @ (hp @ S4) @ E6 @ E7 @ T3))))))))))). % wf_config_def
thf(fact_134_eval__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wt @ P @ E @ E2 @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E @ E4 @ T2)))))))))). % eval_preserves_type
thf(fact_135_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_136_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S3)))))))). % Red_preserves_sconf
thf(fact_137_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => (?[T2 : ty]: ((wTrt @ P @ (hp @ S3) @ E @ E4 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_138_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_139_eval__final, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E2 @ S @ E4 @ S3) => (final_list_char @ E4))))). % eval_final
thf(fact_140_eval__finalId, axiom,
    ((![E2 : exp_list_char, P : list_P1234162913t_char, S : produc515445032on_val]: ((final_list_char @ E2) => (eval @ P @ E2 @ S @ E2 @ S))))). % eval_finalId
thf(fact_141_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_142_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E4) => (eval @ P @ E2 @ S @ E4 @ S3))))))). % small_by_big
thf(fact_143_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E4)))))))). % big_iff_small
thf(fact_144_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E8 @ S5)) @ (red @ P)) => ((eval @ P @ E8 @ S5 @ E4 @ S3) => (eval @ P @ E2 @ S @ E4 @ S3))))))). % extend_1_eval
thf(fact_145_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S @ E4 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_146_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E8 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E8 @ S5)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E8 @ S5 @ E4 @ S3) => (eval @ P @ E2 @ S @ E4 @ S3))))))). % extend_eval
thf(fact_147_progress, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, L : list_char > option_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((hconf_1244167010t_char @ P @ H) => ((wTrt @ P @ H @ E @ E2 @ T) => ((d_list_char @ E2 @ (some_set_list_char @ (dom_list_char_val @ L))) => ((~ ((final_list_char @ E2))) => (?[E3 : exp_list_char, S2 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P))))))))))). % progress
thf(fact_148_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_149_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C4 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C4 @ Md) => (wwf_J_mdecl @ P @ C4 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_150_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty, H : nat > option2118145160on_val]: ((wt @ P @ E @ E2 @ T) => (wTrt @ P @ H @ E @ E2 @ T))))). % WT_implies_WTrt
thf(fact_151_red__lcl__incr, axiom,
    ((![E2 : exp_list_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, E4 : exp_list_char, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E4 @ (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
thf(fact_152_eval__lcl__incr, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, E4 : exp_list_char, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H_02 @ L_02) @ E4 @ (produc52622304on_val @ H_12 @ L_12)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_02) @ (dom_list_char_val @ L_12)))))). % eval_lcl_incr
thf(fact_153_Red__fv, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (ord_le1836582007t_char @ (fv @ E4) @ (fv @ E2))))))). % Red_fv
thf(fact_154_subset__antisym, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ A5 @ B5) => ((ord_le1836582007t_char @ B5 @ A5) => (A5 = B5)))))). % subset_antisym
thf(fact_155_subsetI, axiom,
    ((![A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((![X3 : produc1172664615on_val]: ((member354538064on_val @ X3 @ A5) => (member354538064on_val @ X3 @ B5))) => (ord_le837504935on_val @ A5 @ B5))))). % subsetI
thf(fact_156_subsetI, axiom,
    ((![A5 : set_Pr148564103on_val, B5 : set_Pr148564103on_val]: ((![X3 : produc744932519on_val]: ((member2027247312on_val @ X3 @ A5) => (member2027247312on_val @ X3 @ B5))) => (ord_le1661771815on_val @ A5 @ B5))))). % subsetI
thf(fact_157_subsetI, axiom,
    ((![A5 : set_Pr1368603847on_val, B5 : set_Pr1368603847on_val]: ((![X3 : produc1161703655on_val]: ((member208988944on_val @ X3 @ A5) => (member208988944on_val @ X3 @ B5))) => (ord_le403567719on_val @ A5 @ B5))))). % subsetI
thf(fact_158_subsetI, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: ((![X3 : list_char]: ((member_list_char @ X3 @ A5) => (member_list_char @ X3 @ B5))) => (ord_le1836582007t_char @ A5 @ B5))))). % subsetI
thf(fact_159_order__refl, axiom,
    ((![X : set_list_char]: (ord_le1836582007t_char @ X @ X)))). % order_refl
thf(fact_160_rtrancl__mono, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R @ S) => (ord_le837504935on_val @ (transi111096263on_val @ R) @ (transi111096263on_val @ S)))))). % rtrancl_mono
thf(fact_161_rtrancl__mono, axiom,
    ((![R : set_Pr148564103on_val, S : set_Pr148564103on_val]: ((ord_le1661771815on_val @ R @ S) => (ord_le1661771815on_val @ (transi432893227on_val @ R) @ (transi432893227on_val @ S)))))). % rtrancl_mono
thf(fact_162_rtrancl__mono, axiom,
    ((![R : set_Pr1368603847on_val, S : set_Pr1368603847on_val]: ((ord_le403567719on_val @ R @ S) => (ord_le403567719on_val @ (transi100378922on_val @ R) @ (transi100378922on_val @ S)))))). % rtrancl_mono
thf(fact_163_rtrancl__subset, axiom,
    ((![R2 : set_Pr1189492743on_val, S6 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R2 @ S6) => ((ord_le837504935on_val @ S6 @ (transi111096263on_val @ R2)) => ((transi111096263on_val @ S6) = (transi111096263on_val @ R2))))))). % rtrancl_subset
thf(fact_164_rtrancl__subset, axiom,
    ((![R2 : set_Pr148564103on_val, S6 : set_Pr148564103on_val]: ((ord_le1661771815on_val @ R2 @ S6) => ((ord_le1661771815on_val @ S6 @ (transi432893227on_val @ R2)) => ((transi432893227on_val @ S6) = (transi432893227on_val @ R2))))))). % rtrancl_subset
thf(fact_165_rtrancl__subset, axiom,
    ((![R2 : set_Pr1368603847on_val, S6 : set_Pr1368603847on_val]: ((ord_le403567719on_val @ R2 @ S6) => ((ord_le403567719on_val @ S6 @ (transi100378922on_val @ R2)) => ((transi100378922on_val @ S6) = (transi100378922on_val @ R2))))))). % rtrancl_subset
thf(fact_166_rtrancl__subset__rtrancl, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R @ (transi111096263on_val @ S)) => (ord_le837504935on_val @ (transi111096263on_val @ R) @ (transi111096263on_val @ S)))))). % rtrancl_subset_rtrancl
thf(fact_167_rtrancl__subset__rtrancl, axiom,
    ((![R : set_Pr148564103on_val, S : set_Pr148564103on_val]: ((ord_le1661771815on_val @ R @ (transi432893227on_val @ S)) => (ord_le1661771815on_val @ (transi432893227on_val @ R) @ (transi432893227on_val @ S)))))). % rtrancl_subset_rtrancl
thf(fact_168_rtrancl__subset__rtrancl, axiom,
    ((![R : set_Pr1368603847on_val, S : set_Pr1368603847on_val]: ((ord_le403567719on_val @ R @ (transi100378922on_val @ S)) => (ord_le403567719on_val @ (transi100378922on_val @ R) @ (transi100378922on_val @ S)))))). % rtrancl_subset_rtrancl
thf(fact_169_eval__notfree__unchanged, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, V : list_char]: ((eval @ P @ E2 @ (produc52622304on_val @ H @ L) @ E4 @ (produc52622304on_val @ H2 @ L2)) => ((~ ((member_list_char @ V @ (fv @ E2)))) => ((L2 @ V) = (L @ V))))))). % eval_notfree_unchanged
thf(fact_170_order__subst1, axiom,
    ((![A2 : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A2 @ (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C2) => ((![X3 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X3 @ Y3) => (ord_le1836582007t_char @ (F @ X3) @ (F @ Y3)))) => (ord_le1836582007t_char @ A2 @ (F @ C2)))))))). % order_subst1
thf(fact_171_order__subst2, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B2) => ((ord_le1836582007t_char @ (F @ B2) @ C2) => ((![X3 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X3 @ Y3) => (ord_le1836582007t_char @ (F @ X3) @ (F @ Y3)))) => (ord_le1836582007t_char @ (F @ A2) @ C2))))))). % order_subst2
thf(fact_172_ord__eq__le__subst, axiom,
    ((![A2 : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C2 : set_list_char]: ((A2 = (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C2) => ((![X3 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X3 @ Y3) => (ord_le1836582007t_char @ (F @ X3) @ (F @ Y3)))) => (ord_le1836582007t_char @ A2 @ (F @ C2)))))))). % ord_eq_le_subst
thf(fact_173_ord__le__eq__subst, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B2) => (((F @ B2) = C2) => ((![X3 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X3 @ Y3) => (ord_le1836582007t_char @ (F @ X3) @ (F @ Y3)))) => (ord_le1836582007t_char @ (F @ A2) @ C2))))))). % ord_le_eq_subst
thf(fact_174_eq__iff, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[X4 : set_list_char]: (^[Y5 : set_list_char]: (((ord_le1836582007t_char @ X4 @ Y5)) & ((ord_le1836582007t_char @ Y5 @ X4)))))))). % eq_iff
thf(fact_175_antisym, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ X) => (X = Y)))))). % antisym
thf(fact_176_eq__refl, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((X = Y) => (ord_le1836582007t_char @ X @ Y))))). % eq_refl
thf(fact_177_order_Otrans, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B2) => ((ord_le1836582007t_char @ B2 @ C2) => (ord_le1836582007t_char @ A2 @ C2)))))). % order.trans
thf(fact_178_antisym__conv, axiom,
    ((![Y : set_list_char, X : set_list_char]: ((ord_le1836582007t_char @ Y @ X) => ((ord_le1836582007t_char @ X @ Y) = (X = Y)))))). % antisym_conv
thf(fact_179_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[A4 : set_list_char]: (^[B4 : set_list_char]: (((ord_le1836582007t_char @ A4 @ B4)) & ((ord_le1836582007t_char @ B4 @ A4)))))))). % order_class.order.eq_iff
thf(fact_180_ord__eq__le__trans, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, C2 : set_list_char]: ((A2 = B2) => ((ord_le1836582007t_char @ B2 @ C2) => (ord_le1836582007t_char @ A2 @ C2)))))). % ord_eq_le_trans
thf(fact_181_ord__le__eq__trans, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B2) => ((B2 = C2) => (ord_le1836582007t_char @ A2 @ C2)))))). % ord_le_eq_trans
thf(fact_182_order__class_Oorder_Oantisym, axiom,
    ((![A2 : set_list_char, B2 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B2) => ((ord_le1836582007t_char @ B2 @ A2) => (A2 = B2)))))). % order_class.order.antisym
thf(fact_183_order__trans, axiom,
    ((![X : set_list_char, Y : set_list_char, Z2 : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ Z2) => (ord_le1836582007t_char @ X @ Z2)))))). % order_trans
thf(fact_184_dual__order_Orefl, axiom,
    ((![A2 : set_list_char]: (ord_le1836582007t_char @ A2 @ A2)))). % dual_order.refl
thf(fact_185_dual__order_Otrans, axiom,
    ((![B2 : set_list_char, A2 : set_list_char, C2 : set_list_char]: ((ord_le1836582007t_char @ B2 @ A2) => ((ord_le1836582007t_char @ C2 @ B2) => (ord_le1836582007t_char @ C2 @ A2)))))). % dual_order.trans
thf(fact_186_dual__order_Oeq__iff, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[A4 : set_list_char]: (^[B4 : set_list_char]: (((ord_le1836582007t_char @ B4 @ A4)) & ((ord_le1836582007t_char @ A4 @ B4)))))))). % dual_order.eq_iff
thf(fact_187_dual__order_Oantisym, axiom,
    ((![B2 : set_list_char, A2 : set_list_char]: ((ord_le1836582007t_char @ B2 @ A2) => ((ord_le1836582007t_char @ A2 @ B2) => (A2 = B2)))))). % dual_order.antisym
thf(fact_188_in__mono, axiom,
    ((![A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val, X : produc1172664615on_val]: ((ord_le837504935on_val @ A5 @ B5) => ((member354538064on_val @ X @ A5) => (member354538064on_val @ X @ B5)))))). % in_mono
thf(fact_189_in__mono, axiom,
    ((![A5 : set_Pr148564103on_val, B5 : set_Pr148564103on_val, X : produc744932519on_val]: ((ord_le1661771815on_val @ A5 @ B5) => ((member2027247312on_val @ X @ A5) => (member2027247312on_val @ X @ B5)))))). % in_mono
thf(fact_190_in__mono, axiom,
    ((![A5 : set_Pr1368603847on_val, B5 : set_Pr1368603847on_val, X : produc1161703655on_val]: ((ord_le403567719on_val @ A5 @ B5) => ((member208988944on_val @ X @ A5) => (member208988944on_val @ X @ B5)))))). % in_mono
thf(fact_191_in__mono, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, X : list_char]: ((ord_le1836582007t_char @ A5 @ B5) => ((member_list_char @ X @ A5) => (member_list_char @ X @ B5)))))). % in_mono
thf(fact_192_subsetD, axiom,
    ((![A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val, C2 : produc1172664615on_val]: ((ord_le837504935on_val @ A5 @ B5) => ((member354538064on_val @ C2 @ A5) => (member354538064on_val @ C2 @ B5)))))). % subsetD
thf(fact_193_subsetD, axiom,
    ((![A5 : set_Pr148564103on_val, B5 : set_Pr148564103on_val, C2 : produc744932519on_val]: ((ord_le1661771815on_val @ A5 @ B5) => ((member2027247312on_val @ C2 @ A5) => (member2027247312on_val @ C2 @ B5)))))). % subsetD
thf(fact_194_subsetD, axiom,
    ((![A5 : set_Pr1368603847on_val, B5 : set_Pr1368603847on_val, C2 : produc1161703655on_val]: ((ord_le403567719on_val @ A5 @ B5) => ((member208988944on_val @ C2 @ A5) => (member208988944on_val @ C2 @ B5)))))). % subsetD
thf(fact_195_subsetD, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, C2 : list_char]: ((ord_le1836582007t_char @ A5 @ B5) => ((member_list_char @ C2 @ A5) => (member_list_char @ C2 @ B5)))))). % subsetD
thf(fact_196_equalityE, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: ((A5 = B5) => (~ (((ord_le1836582007t_char @ A5 @ B5) => (~ ((ord_le1836582007t_char @ B5 @ A5)))))))))). % equalityE
thf(fact_197_subset__eq, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![X4 : produc1172664615on_val]: (((member354538064on_val @ X4 @ A6)) => ((member354538064on_val @ X4 @ B6))))))))). % subset_eq
thf(fact_198_subset__eq, axiom,
    ((ord_le1661771815on_val = (^[A6 : set_Pr148564103on_val]: (^[B6 : set_Pr148564103on_val]: (![X4 : produc744932519on_val]: (((member2027247312on_val @ X4 @ A6)) => ((member2027247312on_val @ X4 @ B6))))))))). % subset_eq
thf(fact_199_subset__eq, axiom,
    ((ord_le403567719on_val = (^[A6 : set_Pr1368603847on_val]: (^[B6 : set_Pr1368603847on_val]: (![X4 : produc1161703655on_val]: (((member208988944on_val @ X4 @ A6)) => ((member208988944on_val @ X4 @ B6))))))))). % subset_eq
thf(fact_200_subset__eq, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (![X4 : list_char]: (((member_list_char @ X4 @ A6)) => ((member_list_char @ X4 @ B6))))))))). % subset_eq
thf(fact_201_equalityD1, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: ((A5 = B5) => (ord_le1836582007t_char @ A5 @ B5))))). % equalityD1
thf(fact_202_equalityD2, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: ((A5 = B5) => (ord_le1836582007t_char @ B5 @ A5))))). % equalityD2
thf(fact_203_subset__iff, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![T4 : produc1172664615on_val]: (((member354538064on_val @ T4 @ A6)) => ((member354538064on_val @ T4 @ B6))))))))). % subset_iff
thf(fact_204_subset__iff, axiom,
    ((ord_le1661771815on_val = (^[A6 : set_Pr148564103on_val]: (^[B6 : set_Pr148564103on_val]: (![T4 : produc744932519on_val]: (((member2027247312on_val @ T4 @ A6)) => ((member2027247312on_val @ T4 @ B6))))))))). % subset_iff
thf(fact_205_subset__iff, axiom,
    ((ord_le403567719on_val = (^[A6 : set_Pr1368603847on_val]: (^[B6 : set_Pr1368603847on_val]: (![T4 : produc1161703655on_val]: (((member208988944on_val @ T4 @ A6)) => ((member208988944on_val @ T4 @ B6))))))))). % subset_iff
thf(fact_206_subset__iff, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (![T4 : list_char]: (((member_list_char @ T4 @ A6)) => ((member_list_char @ T4 @ B6))))))))). % subset_iff
thf(fact_207_subset__refl, axiom,
    ((![A5 : set_list_char]: (ord_le1836582007t_char @ A5 @ A5)))). % subset_refl
thf(fact_208_Collect__mono, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((![X3 : list_char]: ((P @ X3) => (Q @ X3))) => (ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)))))). % Collect_mono
thf(fact_209_subset__trans, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A5 @ B5) => ((ord_le1836582007t_char @ B5 @ C4) => (ord_le1836582007t_char @ A5 @ C4)))))). % subset_trans
thf(fact_210_set__eq__subset, axiom,
    (((^[Y4 : set_list_char]: (^[Z3 : set_list_char]: (Y4 = Z3))) = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (((ord_le1836582007t_char @ A6 @ B6)) & ((ord_le1836582007t_char @ B6 @ A6)))))))). % set_eq_subset
thf(fact_211_Collect__mono__iff, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)) = (![X4 : list_char]: (((P @ X4)) => ((Q @ X4)))))))). % Collect_mono_iff
thf(fact_212_WT__fv, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T : ty]: ((wt @ P @ E @ E2 @ T) => (ord_le1836582007t_char @ (fv @ E2) @ (dom_list_char_ty @ E)))))). % WT_fv
thf(fact_213_Reds__dom__lcl, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (ord_le1836582007t_char @ (dom_list_char_val @ L2) @ (sup_su1099679555t_char @ (dom_list_char_val @ L) @ (fv @ E2)))))))). % Reds_dom_lcl
thf(fact_214_eval__restrict__lcl, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, W : set_list_char]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ (produc52622304on_val @ H @ L) @ E4 @ (produc52622304on_val @ H2 @ L2)) => ((ord_le1836582007t_char @ (fv @ E2) @ W) => (eval @ P @ E2 @ (produc52622304on_val @ H @ (restri1468981139ar_val @ L @ W)) @ E4 @ (produc52622304on_val @ H2 @ (restri1468981139ar_val @ L2 @ W))))))))). % eval_restrict_lcl
thf(fact_215_Red__dom__lcl, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L2) @ (sup_su1099679555t_char @ (dom_list_char_val @ L) @ (fv @ E2))))))). % Red_dom_lcl
thf(fact_216_UnCI, axiom,
    ((![C2 : produc1172664615on_val, B5 : set_Pr1189492743on_val, A5 : set_Pr1189492743on_val]: (((~ ((member354538064on_val @ C2 @ B5))) => (member354538064on_val @ C2 @ A5)) => (member354538064on_val @ C2 @ (sup_su886787547on_val @ A5 @ B5)))))). % UnCI
thf(fact_217_UnCI, axiom,
    ((![C2 : produc744932519on_val, B5 : set_Pr148564103on_val, A5 : set_Pr148564103on_val]: (((~ ((member2027247312on_val @ C2 @ B5))) => (member2027247312on_val @ C2 @ A5)) => (member2027247312on_val @ C2 @ (sup_su499610203on_val @ A5 @ B5)))))). % UnCI
thf(fact_218_UnCI, axiom,
    ((![C2 : produc1161703655on_val, B5 : set_Pr1368603847on_val, A5 : set_Pr1368603847on_val]: (((~ ((member208988944on_val @ C2 @ B5))) => (member208988944on_val @ C2 @ A5)) => (member208988944on_val @ C2 @ (sup_su2093213339on_val @ A5 @ B5)))))). % UnCI
thf(fact_219_UnCI, axiom,
    ((![C2 : list_char, B5 : set_list_char, A5 : set_list_char]: (((~ ((member_list_char @ C2 @ B5))) => (member_list_char @ C2 @ A5)) => (member_list_char @ C2 @ (sup_su1099679555t_char @ A5 @ B5)))))). % UnCI
thf(fact_220_Un__iff, axiom,
    ((![C2 : produc1172664615on_val, A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((member354538064on_val @ C2 @ (sup_su886787547on_val @ A5 @ B5)) = (((member354538064on_val @ C2 @ A5)) | ((member354538064on_val @ C2 @ B5))))))). % Un_iff
thf(fact_221_Un__iff, axiom,
    ((![C2 : produc744932519on_val, A5 : set_Pr148564103on_val, B5 : set_Pr148564103on_val]: ((member2027247312on_val @ C2 @ (sup_su499610203on_val @ A5 @ B5)) = (((member2027247312on_val @ C2 @ A5)) | ((member2027247312on_val @ C2 @ B5))))))). % Un_iff
thf(fact_222_Un__iff, axiom,
    ((![C2 : produc1161703655on_val, A5 : set_Pr1368603847on_val, B5 : set_Pr1368603847on_val]: ((member208988944on_val @ C2 @ (sup_su2093213339on_val @ A5 @ B5)) = (((member208988944on_val @ C2 @ A5)) | ((member208988944on_val @ C2 @ B5))))))). % Un_iff
thf(fact_223_Un__iff, axiom,
    ((![C2 : list_char, A5 : set_list_char, B5 : set_list_char]: ((member_list_char @ C2 @ (sup_su1099679555t_char @ A5 @ B5)) = (((member_list_char @ C2 @ A5)) | ((member_list_char @ C2 @ B5))))))). % Un_iff
thf(fact_224_restrict__in, axiom,
    ((![X : list_char, A5 : set_list_char, M : list_char > option_val]: ((member_list_char @ X @ A5) => ((restri1468981139ar_val @ M @ A5 @ X) = (M @ X)))))). % restrict_in
thf(fact_225_Un__subset__iff, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ (sup_su1099679555t_char @ A5 @ B5) @ C4) = (((ord_le1836582007t_char @ A5 @ C4)) & ((ord_le1836582007t_char @ B5 @ C4))))))). % Un_subset_iff
thf(fact_226_subset__Un__eq, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: ((sup_su1099679555t_char @ A6 @ B6) = B6)))))). % subset_Un_eq
thf(fact_227_subset__UnE, axiom,
    ((![C4 : set_list_char, A5 : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ C4 @ (sup_su1099679555t_char @ A5 @ B5)) => (~ ((![A7 : set_list_char]: ((ord_le1836582007t_char @ A7 @ A5) => (![B7 : set_list_char]: ((ord_le1836582007t_char @ B7 @ B5) => (~ ((C4 = (sup_su1099679555t_char @ A7 @ B7)))))))))))))). % subset_UnE
thf(fact_228_Un__absorb2, axiom,
    ((![B5 : set_list_char, A5 : set_list_char]: ((ord_le1836582007t_char @ B5 @ A5) => ((sup_su1099679555t_char @ A5 @ B5) = A5))))). % Un_absorb2
thf(fact_229_Un__absorb1, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ A5 @ B5) => ((sup_su1099679555t_char @ A5 @ B5) = B5))))). % Un_absorb1
thf(fact_230_Un__upper2, axiom,
    ((![B5 : set_list_char, A5 : set_list_char]: (ord_le1836582007t_char @ B5 @ (sup_su1099679555t_char @ A5 @ B5))))). % Un_upper2
thf(fact_231_Un__upper1, axiom,
    ((![A5 : set_list_char, B5 : set_list_char]: (ord_le1836582007t_char @ A5 @ (sup_su1099679555t_char @ A5 @ B5))))). % Un_upper1
thf(fact_232_Un__least, axiom,
    ((![A5 : set_list_char, C4 : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ A5 @ C4) => ((ord_le1836582007t_char @ B5 @ C4) => (ord_le1836582007t_char @ (sup_su1099679555t_char @ A5 @ B5) @ C4)))))). % Un_least
thf(fact_233_Un__mono, axiom,
    ((![A5 : set_list_char, C4 : set_list_char, B5 : set_list_char, D2 : set_list_char]: ((ord_le1836582007t_char @ A5 @ C4) => ((ord_le1836582007t_char @ B5 @ D2) => (ord_le1836582007t_char @ (sup_su1099679555t_char @ A5 @ B5) @ (sup_su1099679555t_char @ C4 @ D2))))))). % Un_mono
thf(fact_234_UnE, axiom,
    ((![C2 : produc1172664615on_val, A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((member354538064on_val @ C2 @ (sup_su886787547on_val @ A5 @ B5)) => ((~ ((member354538064on_val @ C2 @ A5))) => (member354538064on_val @ C2 @ B5)))))). % UnE
thf(fact_235_UnE, axiom,
    ((![C2 : produc744932519on_val, A5 : set_Pr148564103on_val, B5 : set_Pr148564103on_val]: ((member2027247312on_val @ C2 @ (sup_su499610203on_val @ A5 @ B5)) => ((~ ((member2027247312on_val @ C2 @ A5))) => (member2027247312on_val @ C2 @ B5)))))). % UnE
thf(fact_236_UnE, axiom,
    ((![C2 : produc1161703655on_val, A5 : set_Pr1368603847on_val, B5 : set_Pr1368603847on_val]: ((member208988944on_val @ C2 @ (sup_su2093213339on_val @ A5 @ B5)) => ((~ ((member208988944on_val @ C2 @ A5))) => (member208988944on_val @ C2 @ B5)))))). % UnE
thf(fact_237_UnE, axiom,
    ((![C2 : list_char, A5 : set_list_char, B5 : set_list_char]: ((member_list_char @ C2 @ (sup_su1099679555t_char @ A5 @ B5)) => ((~ ((member_list_char @ C2 @ A5))) => (member_list_char @ C2 @ B5)))))). % UnE
thf(fact_238_UnI1, axiom,
    ((![C2 : produc1172664615on_val, A5 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((member354538064on_val @ C2 @ A5) => (member354538064on_val @ C2 @ (sup_su886787547on_val @ A5 @ B5)))))). % UnI1
thf(fact_239_UnI1, axiom,
    ((![C2 : produc744932519on_val, A5 : set_Pr148564103on_val, B5 : set_Pr148564103on_val]: ((member2027247312on_val @ C2 @ A5) => (member2027247312on_val @ C2 @ (sup_su499610203on_val @ A5 @ B5)))))). % UnI1
thf(fact_240_UnI1, axiom,
    ((![C2 : produc1161703655on_val, A5 : set_Pr1368603847on_val, B5 : set_Pr1368603847on_val]: ((member208988944on_val @ C2 @ A5) => (member208988944on_val @ C2 @ (sup_su2093213339on_val @ A5 @ B5)))))). % UnI1
thf(fact_241_UnI1, axiom,
    ((![C2 : list_char, A5 : set_list_char, B5 : set_list_char]: ((member_list_char @ C2 @ A5) => (member_list_char @ C2 @ (sup_su1099679555t_char @ A5 @ B5)))))). % UnI1
thf(fact_242_UnI2, axiom,
    ((![C2 : produc1172664615on_val, B5 : set_Pr1189492743on_val, A5 : set_Pr1189492743on_val]: ((member354538064on_val @ C2 @ B5) => (member354538064on_val @ C2 @ (sup_su886787547on_val @ A5 @ B5)))))). % UnI2
thf(fact_243_UnI2, axiom,
    ((![C2 : produc744932519on_val, B5 : set_Pr148564103on_val, A5 : set_Pr148564103on_val]: ((member2027247312on_val @ C2 @ B5) => (member2027247312on_val @ C2 @ (sup_su499610203on_val @ A5 @ B5)))))). % UnI2
thf(fact_244_UnI2, axiom,
    ((![C2 : produc1161703655on_val, B5 : set_Pr1368603847on_val, A5 : set_Pr1368603847on_val]: ((member208988944on_val @ C2 @ B5) => (member208988944on_val @ C2 @ (sup_su2093213339on_val @ A5 @ B5)))))). % UnI2
thf(fact_245_UnI2, axiom,
    ((![C2 : list_char, B5 : set_list_char, A5 : set_list_char]: ((member_list_char @ C2 @ B5) => (member_list_char @ C2 @ (sup_su1099679555t_char @ A5 @ B5)))))). % UnI2
thf(fact_246_bex__Un, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, P : list_char > $o]: ((?[X4 : list_char]: (((member_list_char @ X4 @ (sup_su1099679555t_char @ A5 @ B5))) & ((P @ X4)))) = (((?[X4 : list_char]: (((member_list_char @ X4 @ A5)) & ((P @ X4))))) | ((?[X4 : list_char]: (((member_list_char @ X4 @ B5)) & ((P @ X4)))))))))). % bex_Un
thf(fact_247_ball__Un, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, P : list_char > $o]: ((![X4 : list_char]: (((member_list_char @ X4 @ (sup_su1099679555t_char @ A5 @ B5))) => ((P @ X4)))) = (((![X4 : list_char]: (((member_list_char @ X4 @ A5)) => ((P @ X4))))) & ((![X4 : list_char]: (((member_list_char @ X4 @ B5)) => ((P @ X4)))))))))). % ball_Un
thf(fact_248_Un__assoc, axiom,
    ((![A5 : set_list_char, B5 : set_list_char, C4 : set_list_char]: ((sup_su1099679555t_char @ (sup_su1099679555t_char @ A5 @ B5) @ C4) = (sup_su1099679555t_char @ A5 @ (sup_su1099679555t_char @ B5 @ C4)))))). % Un_assoc

% Conjectures (11)
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, S7 : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e3 @ s2) @ (produc2023458740on_val @ E9 @ S7)) @ (red @ p))))))).
thf(conj_6, hypothesis,
    ((typeSa1969945757config @ p @ e @ s @ e2 @ t))).
thf(conj_7, hypothesis,
    ((typeSa1969945757config @ p @ e @ s2 @ e3 @ t2))).
thf(conj_8, hypothesis,
    ((widen_917054840t_char @ p @ t2 @ t))).
thf(conj_9, hypothesis,
    ((d_list_char @ e3 @ (some_set_list_char @ (dom_list_char_val @ (lcl @ s2)))))).
thf(conj_10, conjecture,
    ((final_list_char @ e3))).
