% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_322__5337624_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:47.314

% Could-be-implicit typings (26)
thf(ty_n_t__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,
    set_Pr1368603847on_val : $tType).
thf(ty_n_t__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,
    produc1161703655on_val : $tType).
thf(ty_n_t__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,
    set_Pr1189492743on_val : $tType).
thf(ty_n_t__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,
    produc1172664615on_val : $tType).
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__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    set_Pr556513572on_val : $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__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    set_Pr723149704on_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__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr729957319t_char : $tType).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    option2118145160on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    produc442406631t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    set_Pr164112643t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1257910179t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J, type,
    produc2086909177har_ty : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_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__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (63)
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_Decl_Ois__class_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,
    is_cla1277868776t_char : list_P1234162913t_char > list_char > $o).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
    binOp_list_char : exp_list_char > bop > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCast_001t__List__Olist_It__String__Ochar_J, type,
    cast_list_char : list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCond_001t__List__Olist_It__String__Ochar_J, type,
    cond_list_char : exp_list_char > exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
    fAcc_list_char : exp_list_char > list_char > list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_OWhile_001t__List__Olist_It__String__Ochar_J, type,
    while_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    produc1304532571t_char : list_char > list_char > produc1257910179t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    produc1017542449har_ty : list_char > ty > produc2086909177har_ty).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2106877847on_val : produc515445032on_val > produc515445032on_val > produc744932519on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc395356247t_char : produc1257910179t_char > produc1257910179t_char > produc442406631t_char).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_val).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    collec768236686t_char : (produc1257910179t_char > $o) > set_Pr164112643t_char).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__List__Olist_It__String__Ochar_J, type,
    transi1879726366t_char : set_Pr164112643t_char > set_Pr164112643t_char).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    transi858104614t_char : set_Pr729957319t_char > set_Pr729957319t_char).
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_TypeRel_Ofield_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,
    field_1562896919t_char : list_P1234162913t_char > list_char > list_char > produc2086909177har_ty).
thf(sy_c_TypeRel_Ohas__field_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,
    has_fi599584195t_char : list_P1234162913t_char > list_char > list_char > ty > list_char > $o).
thf(sy_c_TypeRel_Osees__field_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,
    sees_f1424843223t_char : list_P1234162913t_char > list_char > list_char > ty > list_char > $o).
thf(sy_c_TypeRel_Osubcls1_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,
    subcls880436836t_char : list_P1234162913t_char > set_Pr164112643t_char).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_Type_OObject, type,
    object : list_char).
thf(sy_c_Type_Ois__refT, type,
    is_refT : ty > $o).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Type_Oty_ONT, type,
    nt : ty).
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__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    member803902992t_char : produc442406631t_char > set_Pr729957319t_char > $o).
thf(sy_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_v_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_F____, type,
    f : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_U____, type,
    u : ty).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    ea : exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).

% Relevant facts (191)
thf(fact_0_UsubC, axiom,
    ((widen_917054840t_char @ p @ u @ (class @ c)))). % UsubC
thf(fact_1_wte_H, axiom,
    ((wTrt @ p @ h_a @ e @ e_a @ u))). % wte'
thf(fact_2__092_060open_062U_A_061_ANT_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062F_123D_125_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    (((u = nt) => (?[T : ty]: ((wTrt @ p @ h_a @ e @ (fAcc_list_char @ e_a @ f @ d) @ T) & (widen_917054840t_char @ p @ T @ t)))))). % \<open>U = NT \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>F{D} : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_3_has, axiom,
    ((has_fi599584195t_char @ p @ c @ f @ t @ d))). % has
thf(fact_4__092_060open_062_092_060And_062C_H_O_A_092_060lbrakk_062U_A_061_AClass_AC_H_059_AP_A_092_060turnstile_062_AC_H_A_092_060preceq_062_092_060_094sup_062_K_AC_092_060rbrakk_062_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062F_123D_125_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    ((![C : list_char]: ((u = (class @ C)) => ((member89690956t_char @ (produc1304532571t_char @ C @ c) @ (transi1879726366t_char @ (subcls880436836t_char @ p))) => (?[T : ty]: ((wTrt @ p @ h_a @ e @ (fAcc_list_char @ e_a @ f @ d) @ T) & (widen_917054840t_char @ p @ T @ t)))))))). % \<open>\<And>C'. \<lbrakk>U = Class C'; P \<turnstile> C' \<preceq>\<^sup>* C\<rbrakk> \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>F{D} : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_5__092_060open_062_092_060exists_062U_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_A_092_060and_062_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_092_060close_062, axiom,
    ((?[U : ty]: ((wTrt @ p @ h_a @ e @ e_a @ U) & (widen_917054840t_char @ p @ U @ (class @ c)))))). % \<open>\<exists>U. P,E,h' \<turnstile> e' : U \<and> P \<turnstile> U \<le> Class C\<close>
thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062U_O_A_092_060lbrakk_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![U : ty]: ((wTrt @ p @ h_a @ e @ e_a @ U) => (~ ((widen_917054840t_char @ p @ U @ (class @ c)))))))))). % \<open>\<And>thesis. (\<And>U. \<lbrakk>P,E,h' \<turnstile> e' : U; P \<turnstile> U \<le> Class C\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_7_FAccRed_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (fAcc_list_char @ ea @ f @ d) @ t))). % FAccRed.prems(2)
thf(fact_8_wt, axiom,
    ((wTrt @ p @ ha @ e @ (fAcc_list_char @ ea @ f @ d) @ t))). % wt
thf(fact_9_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_10_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_11_wte, axiom,
    ((wTrt @ p @ ha @ e @ ea @ (class @ c)))). % wte
thf(fact_12_WTrtFAccNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2))))). % WTrtFAccNT
thf(fact_13_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U2 : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U2) => ((widen_917054840t_char @ P @ U2 @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_14_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_15_FAccRed_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T2) => (?[T : ty]: ((wTrt @ p @ h_a @ E @ e_a @ T) & (widen_917054840t_char @ p @ T @ T2)))))))). % FAccRed.hyps(2)
thf(fact_16_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T2) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T2)))))))). % IH
thf(fact_17_FAccRed_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % FAccRed.prems(1)
thf(fact_18_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, T2 : ty]: ((widen_917054840t_char @ P @ (class @ C2) @ T2) => (?[D2 : list_char]: (T2 = (class @ D2))))))). % Class_widen
thf(fact_19_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_20_Class__widen__Class, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, D : list_char]: ((widen_917054840t_char @ P @ (class @ C2) @ (class @ D)) = (member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % Class_widen_Class
thf(fact_21_has__field__mono, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char, C : list_char]: ((has_fi599584195t_char @ P @ C2 @ F @ T2 @ D) => ((member89690956t_char @ (produc1304532571t_char @ C @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (has_fi599584195t_char @ P @ C @ F @ T2 @ D)))))). % has_field_mono
thf(fact_22_widen_Oinducts, axiom,
    ((![P : list_P1234162913t_char, X1 : ty, X2 : ty, Pa : ty > ty > $o]: ((widen_917054840t_char @ P @ X1 @ X2) => ((![T3 : ty]: (Pa @ T3 @ T3)) => ((![C3 : list_char, D2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ C3 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (Pa @ (class @ C3) @ (class @ D2)))) => ((![C3 : list_char]: (Pa @ nt @ (class @ C3))) => (Pa @ X1 @ X2)))))))). % widen.inducts
thf(fact_23_widen__Class, axiom,
    ((![P : list_P1234162913t_char, T2 : ty, C2 : list_char]: ((widen_917054840t_char @ P @ T2 @ (class @ C2)) = (((T2 = nt)) | ((?[D3 : list_char]: (((T2 = (class @ D3))) & ((member89690956t_char @ (produc1304532571t_char @ D3 @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))). % widen_Class
thf(fact_24_widen_Osimps, axiom,
    ((widen_917054840t_char = (^[P2 : list_P1234162913t_char]: (^[A1 : ty]: (^[A2 : ty]: (((?[T4 : ty]: (((A1 = T4)) & ((A2 = T4))))) | ((((?[C4 : list_char]: (?[D3 : list_char]: (((A1 = (class @ C4))) & ((((A2 = (class @ D3))) & ((member89690956t_char @ (produc1304532571t_char @ C4 @ D3) @ (transi1879726366t_char @ (subcls880436836t_char @ P2)))))))))) | ((?[C4 : list_char]: (((A1 = nt)) & ((A2 = (class @ C4))))))))))))))). % widen.simps
thf(fact_25_widen_Ocases, axiom,
    ((![P : list_P1234162913t_char, A12 : ty, A22 : ty]: ((widen_917054840t_char @ P @ A12 @ A22) => ((~ ((A22 = A12))) => ((![C3 : list_char]: ((A12 = (class @ C3)) => (![D2 : list_char]: ((A22 = (class @ D2)) => (~ ((member89690956t_char @ (produc1304532571t_char @ C3 @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))))) => (~ (((A12 = nt) => (![C3 : list_char]: (~ ((A22 = (class @ C3)))))))))))))). % widen.cases
thf(fact_26_widen__subcls, axiom,
    ((![C2 : list_char, D : list_char, P : list_P1234162913t_char]: ((member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) => (widen_917054840t_char @ P @ (class @ C2) @ (class @ D)))))). % widen_subcls
thf(fact_27_widen__null, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C2))))). % widen_null
thf(fact_28_WTrt__elim__cases_I7_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, T2 : ty]: ((wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2) => ((![C3 : list_char]: ((wTrt @ P @ H @ E @ E2 @ (class @ C3)) => (~ ((has_fi599584195t_char @ P @ C3 @ F @ T2 @ D))))) => (wTrt @ P @ H @ E @ E2 @ nt)))))). % WTrt_elim_cases(7)
thf(fact_29_WTrtFAcc, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C2 : list_char, F : list_char, T2 : ty, D : list_char]: ((wTrt @ P @ H @ E @ E2 @ (class @ C2)) => ((has_fi599584195t_char @ P @ C2 @ F @ T2 @ D) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2)))))). % WTrtFAcc
thf(fact_30_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_31_rtrancl__idemp, axiom,
    ((![R : set_Pr164112643t_char]: ((transi1879726366t_char @ (transi1879726366t_char @ R)) = (transi1879726366t_char @ R))))). % rtrancl_idemp
thf(fact_32_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_33_r__into__rtrancl, axiom,
    ((![P3 : produc1257910179t_char, R : set_Pr164112643t_char]: ((member89690956t_char @ P3 @ R) => (member89690956t_char @ P3 @ (transi1879726366t_char @ R)))))). % r_into_rtrancl
thf(fact_34_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R) => (member354538064on_val @ P3 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_35_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : list_char, Y1 : list_char, Y2 : list_char]: (((produc1304532571t_char @ X1 @ X2) = (produc1304532571t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_36_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_37_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_38_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_39_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_40_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_41_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_42_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B2)) = (((A = A3)) & ((B = B2))))))). % old.prod.inject
thf(fact_43_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_44_rtranclE, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((~ ((A = B))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_45_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((~ ((A = B))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ B) @ R)))))))))))). % rtranclE
thf(fact_46_rtrancl_Ocases, axiom,
    ((![A12 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A12 @ A22) @ (transi1879726366t_char @ R)) => ((~ ((A22 = A12))) => (~ ((![B3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A12 @ B3) @ (transi1879726366t_char @ R)) => (~ ((member89690956t_char @ (produc1304532571t_char @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_47_rtrancl_Ocases, axiom,
    ((![A12 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A12))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ B3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_48_rtrancl_Osimps, axiom,
    ((![A12 : list_char, A22 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ A12 @ A22) @ (transi1879726366t_char @ R)) = (((?[A4 : list_char]: (((A12 = A4)) & ((A22 = A4))))) | ((?[A4 : list_char]: (?[B4 : list_char]: (?[C5 : list_char]: (((A12 = A4)) & ((((A22 = C5)) & ((((member89690956t_char @ (produc1304532571t_char @ A4 @ B4) @ (transi1879726366t_char @ R))) & ((member89690956t_char @ (produc1304532571t_char @ B4 @ C5) @ R)))))))))))))))). % rtrancl.simps
thf(fact_49_rtrancl_Osimps, axiom,
    ((![A12 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ A22) @ (transi111096263on_val @ R)) = (((?[A4 : produc1097884484on_val]: (((A12 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C5 : produc1097884484on_val]: (((A12 = A4)) & ((((A22 = C5)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C5) @ R)))))))))))))))). % rtrancl.simps
thf(fact_50_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Ax @ Ay) => ((![A5 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A5 @ B3)) @ (transi858104614t_char @ R)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_51_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) => ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A5 @ B3)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_52_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) => ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A5 @ B3)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_53_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) => ((![A5 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A5 @ B3)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A5 @ B3) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_54_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A5 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A5 @ B3)) @ R) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_55_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)))) => (~ ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A5 @ B3)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_56_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)))) => (~ ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A5 @ B3)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_57_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)))) => (~ ((![A5 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A5 @ B3)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_58_converse__rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Bx @ By) => ((![A5 : list_char, B3 : list_char, Aa : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B3) @ (produc1304532571t_char @ Aa @ Ba)) @ R) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R)) => ((P @ Aa @ Ba) => (P @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_59_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) => ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B3) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_60_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) => ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B3) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_61_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) => ((![A5 : exp_list_char, B3 : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B3) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A5 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_62_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A5 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_63_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_64_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_65_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A5 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_66_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1257910179t_char]: (~ ((![A5 : list_char, B3 : list_char]: (~ ((Y3 = (produc1304532571t_char @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_67_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_68_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_69_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A5 @ B3)))))))))). % old.prod.exhaust
thf(fact_70_mem__Collect__eq, axiom,
    ((![A : produc1257910179t_char, P : produc1257910179t_char > $o]: ((member89690956t_char @ A @ (collec768236686t_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_71_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_72_Collect__mem__eq, axiom,
    ((![A6 : set_Pr164112643t_char]: ((collec768236686t_char @ (^[X : produc1257910179t_char]: (member89690956t_char @ X @ A6))) = A6)))). % Collect_mem_eq
thf(fact_73_Collect__mem__eq, axiom,
    ((![A6 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A6))) = A6)))). % Collect_mem_eq
thf(fact_74_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B3 : exp_list_char, C6 : nat > option2118145160on_val, D4 : list_char > option_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C6 @ D4))))) => (P @ X3))))). % prod_induct4
thf(fact_75_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B3 : exp_list_char, C6 : produc515445032on_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B3 @ C6)))) => (P @ X3))))). % prod_induct3
thf(fact_76_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A5 : exp_list_char, B3 : nat > option2118145160on_val, C6 : list_char > option_val]: (P @ (produc2023458740on_val @ A5 @ (produc52622304on_val @ B3 @ C6)))) => (P @ X3))))). % prod_induct3
thf(fact_77_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B3 : exp_list_char, C6 : nat > option2118145160on_val, D4 : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C6 @ D4)))))))))))). % prod_cases4
thf(fact_78_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B3 : exp_list_char, C6 : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B3 @ C6))))))))))). % prod_cases3
thf(fact_79_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B3 : nat > option2118145160on_val, C6 : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A5 @ (produc52622304on_val @ B3 @ C6))))))))))). % prod_cases3
thf(fact_80_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_81_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_82_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_83_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B2)) => (~ (((A = A3) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_84_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P3 : produc1257910179t_char]: ((![A5 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_85_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_86_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_87_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A5 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_88_surj__pair, axiom,
    ((![P3 : produc1257910179t_char]: (?[X4 : list_char, Y : list_char]: (P3 = (produc1304532571t_char @ X4 @ Y)))))). % surj_pair
thf(fact_89_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y : list_char > option_val]: (P3 = (produc52622304on_val @ X4 @ Y)))))). % surj_pair
thf(fact_90_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X4 @ Y)))))). % surj_pair
thf(fact_91_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X4 : exp_list_char, Y : produc515445032on_val]: (P3 = (produc2023458740on_val @ X4 @ Y)))))). % surj_pair
thf(fact_92_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C7 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R) => ((member89690956t_char @ (produc1304532571t_char @ B @ C7) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ A @ C7) @ (transi1879726366t_char @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_93_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C7 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B @ C7) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A @ C7) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_94_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, C7 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C7) @ R) => (member89690956t_char @ (produc1304532571t_char @ A @ C7) @ (transi1879726366t_char @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_95_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, C7 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C7) @ R) => (member354538064on_val @ (produc1069526295on_val @ A @ C7) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_96_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((P @ B) => ((![Y : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Z @ B) @ (transi1879726366t_char @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_97_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ B) => ((![Y : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_98_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R))))). % rtrancl.rtrancl_refl
thf(fact_99_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_100_converse__rtranclE, axiom,
    ((![X3 : list_char, Z2 : list_char, R : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Z2) @ (transi1879726366t_char @ R)) => ((~ ((X3 = Z2))) => (~ ((![Y : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ R) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y @ Z2) @ (transi1879726366t_char @ R))))))))))))). % converse_rtranclE
thf(fact_101_converse__rtranclE, axiom,
    ((![X3 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X3 = Z2))) => (~ ((![Y : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_102_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R)) => ((![A5 : list_char]: (P @ A5 @ A5)) => ((![A5 : list_char, B3 : list_char, C6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A5 @ B3) @ (transi1879726366t_char @ R)) => ((P @ A5 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C6) @ R) => (P @ A5 @ C6))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_103_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)) => ((![A5 : produc1097884484on_val]: (P @ A5 @ A5)) => ((![A5 : produc1097884484on_val, B3 : produc1097884484on_val, C6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A5 @ B3) @ (transi111096263on_val @ R)) => ((P @ A5 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C6) @ R) => (P @ A5 @ C6))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_104_rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R)) => ((P @ A) => ((![Y : list_char, Z : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ Y) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_105_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A) => ((![Y : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ R) => ((P @ Y) => (P @ Z))))) => (P @ B))))))). % rtrancl_induct
thf(fact_106_rtrancl__trans, axiom,
    ((![X3 : list_char, Y3 : list_char, R : set_Pr164112643t_char, Z2 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ (transi1879726366t_char @ R)) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z2) @ (transi1879726366t_char @ R)) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Z2) @ (transi1879726366t_char @ R))))))). % rtrancl_trans
thf(fact_107_rtrancl__trans, axiom,
    ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X3 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_108_FAccRed_Ohyps_I1_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % FAccRed.hyps(1)
thf(fact_109_pred__equals__eq2, axiom,
    ((![R2 : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y4) @ R2))) = (^[X : list_char]: (^[Y4 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_110_pred__equals__eq2, axiom,
    ((![R2 : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ R2))) = (^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_111_pred__equals__eq2, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R2))) = (^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_112_pred__equals__eq2, axiom,
    ((![R2 : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ R2))) = (^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_113_sees__field__decl__above, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char]: ((sees_f1424843223t_char @ P @ C2 @ F @ T2 @ D) => (member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))))))). % sees_field_decl_above
thf(fact_114_is__refT__def, axiom,
    ((is_refT = (^[T4 : ty]: (((T4 = nt)) | ((?[C4 : list_char]: (T4 = (class @ C4))))))))). % is_refT_def
thf(fact_115_refTE, axiom,
    ((![T2 : ty]: ((is_refT @ T2) => ((~ ((T2 = nt))) => (~ ((![C3 : list_char]: (~ ((T2 = (class @ C3)))))))))))). % refTE
thf(fact_116_sees__field__idemp, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char]: ((sees_f1424843223t_char @ P @ C2 @ F @ T2 @ D) => (sees_f1424843223t_char @ P @ D @ F @ T2 @ D))))). % sees_field_idemp
thf(fact_117_sees__field__fun, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char, T5 : ty, D5 : list_char]: ((sees_f1424843223t_char @ P @ C2 @ F @ T2 @ D) => ((sees_f1424843223t_char @ P @ C2 @ F @ T5 @ D5) => ((T5 = T2) & (D5 = D))))))). % sees_field_fun
thf(fact_118_has__visible__field, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char]: ((sees_f1424843223t_char @ P @ C2 @ F @ T2 @ D) => (has_fi599584195t_char @ P @ C2 @ F @ T2 @ D))))). % has_visible_field
thf(fact_119_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F @ D) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_120_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F @ D) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_121_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : 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 @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E4 @ H3 @ L3 @ E4 @ 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, E5 : 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 @ E5 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L4)))) => (R2 @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_122_field__def2, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, F : list_char, T2 : ty, D : list_char]: ((sees_f1424843223t_char @ P @ C2 @ F @ T2 @ D) => ((field_1562896919t_char @ P @ C2 @ F) = (produc1017542449har_ty @ D @ T2)))))). % field_def2
thf(fact_123_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_124_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_125_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_126_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_127_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_128_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_129_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : 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 @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_130_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_131_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_132_exp_Odistinct_I151_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X14 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (throw_list_char @ X14))))))). % exp.distinct(151)
thf(fact_133_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T2) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T2)))))). % WTrt_hext_mono
thf(fact_134_WTrtThrow, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T_r : ty, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T_r) => ((is_refT @ T_r) => (wTrt @ P @ H @ E @ (throw_list_char @ E2) @ T2)))))). % WTrtThrow
thf(fact_135_WTrt__elim__cases_I4_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ (throw_list_char @ E2) @ T2) => (~ ((![T_r2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T_r2) => (~ ((is_refT @ T_r2))))))))))). % WTrt_elim_cases(4)
thf(fact_136_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_137_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_138_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_139_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_140_red__reds_OFAccThrow, axiom,
    ((![E2 : exp_list_char, F : list_char, D : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E2) @ F @ D) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_141_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E)))))). % lconf_hext
thf(fact_142_WhileRedsThrow, axiom,
    ((![B : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C7 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B @ C7) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_143_CastRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_144_exp_Oinject_I2_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, Y21 : list_char, Y22 : exp_list_char]: (((cast_list_char @ X21 @ X22) = (cast_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % exp.inject(2)
thf(fact_145_exp_Oinject_I13_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, Y131 : exp_list_char, Y132 : exp_list_char]: (((while_list_char @ X131 @ X132) = (while_list_char @ Y131 @ Y132)) = (((X131 = Y131)) & ((X132 = Y132))))))). % exp.inject(13)
thf(fact_146_exp_Odistinct_I205_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X14 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (throw_list_char @ X14))))))). % exp.distinct(205)
thf(fact_147_exp_Odistinct_I51_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X14 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (throw_list_char @ X14))))))). % exp.distinct(51)
thf(fact_148_exp_Odistinct_I49_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (while_list_char @ X131 @ X132))))))). % exp.distinct(49)
thf(fact_149_exp_Odistinct_I37_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((cast_list_char @ X21 @ X22) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(37)
thf(fact_150_exp_Odistinct_I149_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (while_list_char @ X131 @ X132))))))). % exp.distinct(149)
thf(fact_151_red__reds_OCastRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E3) @ S3)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_152_red__reds_OCastThrow, axiom,
    ((![C2 : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_153_CastReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_154_WTrtCast, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, C2 : list_char]: ((wTrt @ P @ H @ E @ E2 @ T2) => ((is_refT @ T2) => ((is_cla1277868776t_char @ P @ C2) => (wTrt @ P @ H @ E @ (cast_list_char @ C2 @ E2) @ (class @ C2)))))))). % WTrtCast
thf(fact_155_WTrt__elim__cases_I6_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, D : list_char, E2 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ (cast_list_char @ D @ E2) @ T2) => (~ (((T2 = (class @ D)) => (![T3 : ty]: ((wTrt @ P @ H @ E @ E2 @ T3) => ((is_refT @ T3) => (~ ((is_cla1277868776t_char @ P @ D))))))))))))). % WTrt_elim_cases(6)
thf(fact_156_CondRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondRedsThrow
thf(fact_157_exp_Oinject_I12_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, Y121 : exp_list_char, Y122 : exp_list_char, Y123 : exp_list_char]: (((cond_list_char @ X121 @ X122 @ X123) = (cond_list_char @ Y121 @ Y122 @ Y123)) = (((X121 = Y121)) & ((((X122 = Y122)) & ((X123 = Y123))))))))). % exp.inject(12)
thf(fact_158_exp_Odistinct_I201_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X14 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (throw_list_char @ X14))))))). % exp.distinct(201)
thf(fact_159_exp_Odistinct_I47_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(47)
thf(fact_160_exp_Odistinct_I199_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (while_list_char @ X131 @ X132))))))). % exp.distinct(199)
thf(fact_161_exp_Odistinct_I147_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(147)
thf(fact_162_red__reds_OCondRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E3 @ E_12 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.CondRed
thf(fact_163_red__reds_OCondThrow, axiom,
    ((![E2 : exp_list_char, E_12 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (throw_list_char @ E2) @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CondThrow
thf(fact_164_CondReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_12 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_12 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E3 @ E_12 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondReds
thf(fact_165_WTCast, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, D : list_char, C2 : list_char]: ((wt @ P @ E @ E2 @ (class @ D)) => ((is_cla1277868776t_char @ P @ C2) => (((member89690956t_char @ (produc1304532571t_char @ C2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) | (member89690956t_char @ (produc1304532571t_char @ D @ C2) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))) => (wt @ P @ E @ (cast_list_char @ C2 @ E2) @ (class @ C2)))))))). % WTCast
thf(fact_166_WT__elim__cases_I6_J, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, D : list_char, E2 : exp_list_char, T2 : ty]: ((wt @ P @ E @ (cast_list_char @ D @ E2) @ T2) => (~ (((T2 = (class @ D)) => (![D2 : list_char]: ((wt @ P @ E @ E2 @ (class @ D2)) => ((is_cla1277868776t_char @ P @ D) => (~ (((member89690956t_char @ (produc1304532571t_char @ D @ D2) @ (transi1879726366t_char @ (subcls880436836t_char @ P))) | (member89690956t_char @ (produc1304532571t_char @ D2 @ D) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))))))))))). % WT_elim_cases(6)
thf(fact_167_WT__elim__cases_I7_J, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, A : exp_list_char, F : list_char, D : list_char, T2 : ty]: ((wt @ P @ E @ (fAcc_list_char @ A @ F @ D) @ T2) => (~ ((![C3 : list_char]: ((wt @ P @ E @ A @ (class @ C3)) => (~ ((sees_f1424843223t_char @ P @ C3 @ F @ T2 @ D))))))))))). % WT_elim_cases(7)
thf(fact_168_WTFAcc, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, C2 : list_char, F : list_char, T2 : ty, D : list_char]: ((wt @ P @ E @ E2 @ (class @ C2)) => ((sees_f1424843223t_char @ P @ C2 @ F @ T2 @ D) => (wt @ P @ E @ (fAcc_list_char @ E2 @ F @ D) @ T2)))))). % WTFAcc
thf(fact_169_WT__implies__WTrt, axiom,
    ((![P : list_P1234162913t_char, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, H : nat > option2118145160on_val]: ((wt @ P @ E @ E2 @ T2) => (wTrt @ P @ H @ E @ E2 @ T2))))). % WT_implies_WTrt
thf(fact_170_subcls__C__Object, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o]: ((is_cla1277868776t_char @ P @ C2) => ((wf_pro1229751607t_char @ Wf_md @ P) => (member89690956t_char @ (produc1304532571t_char @ C2 @ object) @ (transi1879726366t_char @ (subcls880436836t_char @ P)))))))). % subcls_C_Object
thf(fact_171_BinOpRedsThrow1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_172_exp_Oinject_I4_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (((binOp_list_char @ X41 @ X42 @ X43) = (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((X41 = Y41)) & ((((X42 = Y42)) & ((X43 = Y43))))))))). % exp.inject(4)
thf(fact_173_exp_Odistinct_I93_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(93)
thf(fact_174_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)
thf(fact_175_exp_Odistinct_I83_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(83)
thf(fact_176_is__class__Object, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => (is_cla1277868776t_char @ P @ object))))). % is_class_Object
thf(fact_177_exp_Odistinct_I95_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (while_list_char @ X131 @ X132))))))). % exp.distinct(95)
thf(fact_178_exp_Odistinct_I31_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(31)
thf(fact_179_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_180_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_181_subcls1__induct, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C2 : list_char, Q : list_char > $o]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((is_cla1277868776t_char @ P @ C2) => ((Q @ object) => ((![C3 : list_char, D2 : list_char]: ((~ ((C3 = object))) => ((member89690956t_char @ (produc1304532571t_char @ C3 @ D2) @ (subcls880436836t_char @ P)) => ((is_cla1277868776t_char @ P @ D2) => ((Q @ D2) => (Q @ C3)))))) => (Q @ C2)))))))). % subcls1_induct
thf(fact_182_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_183_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_184_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_185_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_186_exp_Odistinct_I55_J, axiom,
    ((![X32 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X32) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_187_exp_Odistinct_I29_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X32 : val]: (~ (((cast_list_char @ X21 @ X22) = (val_list_char @ X32))))))). % exp.distinct(29)
thf(fact_188_exp_Odistinct_I73_J, axiom,
    ((![X32 : val, X131 : exp_list_char, X132 : exp_list_char]: (~ (((val_list_char @ X32) = (while_list_char @ X131 @ X132))))))). % exp.distinct(73)
thf(fact_189_exp_Odistinct_I61_J, axiom,
    ((![X32 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X32) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_190_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T6 : ty]: ((wTrt @ p @ h_a @ e @ (fAcc_list_char @ e_a @ f @ d) @ T6) & (widen_917054840t_char @ p @ T6 @ t))))).
