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thf(ty_n_t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc677445863t_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__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1109669680t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J_J, type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J_J, type,
    set_Pr1785354703ist_ty : $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__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J, type,
    produc1608520577st_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J, type,
    produc1714969711ist_ty : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J_J, type,
    set_Pr1870322241al_val : $tType).
thf(ty_n_t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    option_set_list_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J_J, type,
    set_Pr1194734255_ty_ty : $tType).
thf(ty_n_t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_exp_list_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    product_prod_val_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J, type,
    product_prod_ty_ty : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    list_list_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_list_char : $tType).
thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    set_list_char : $tType).
thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__List__Olist_It__Value__Oval_J, type,
    list_val : $tType).
thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
    list_ty : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (128)
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
    final_list_char : exp_list_char > $o).
thf(sy_c_DefAss_O_092_060D_062_001t__List__Olist_It__String__Ochar_J, type,
    d_list_char : exp_list_char > option_set_list_char > $o).
thf(sy_c_Expr_Oexp_OCall_001t__List__Olist_It__String__Ochar_J, type,
    call_list_char : exp_list_char > list_char > list_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_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
    fun_up1252458416on_val : (list_char > option_val) > list_char > option_val > list_char > option_val).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    append_exp_list_char : list_exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olex_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    lex_exp_list_char : set_Pr224372167t_char > set_Pr1932514887t_char).
thf(sy_c_List_Olex_001t__List__Olist_It__String__Ochar_J, type,
    lex_list_char : set_Pr164112643t_char > set_Pr2117892643t_char).
thf(sy_c_List_Olex_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,
    lex_Pr1119043758on_val : set_Pr1189492743on_val > set_Pr601606919on_val).
thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    lex_Pr1773567272on_val : set_Pr208351751on_val > set_Pr58336519on_val).
thf(sy_c_List_Olex_001t__Type__Oty, type,
    lex_ty : set_Pr1194734255_ty_ty > set_Pr1785354703ist_ty).
thf(sy_c_List_Olex_001t__Value__Oval, type,
    lex_val : set_Pr1870322241al_val > set_Pr723931873st_val).
thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    cons_exp_list_char : exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__String__Ochar_J, type,
    cons_list_char : list_char > list_list_char > list_list_char).
thf(sy_c_List_Olist_OCons_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,
    cons_P766091258on_val : produc1097884484on_val > list_P1873028426on_val > list_P1873028426on_val).
thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    cons_P1492043380on_val : produc335961278on_val > list_P682203204on_val > list_P682203204on_val).
thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
    cons_ty : ty > list_ty > list_ty).
thf(sy_c_List_Olist_OCons_001t__Value__Oval, type,
    cons_val : val > list_val > list_val).
thf(sy_c_List_Olist_Omap_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    map_exp_list_char_ty : (exp_list_char > ty) > list_exp_list_char > list_ty).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_li1930351204t_char : (list_char > exp_list_char) > list_list_char > list_exp_list_char).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    map_li1166989960t_char : (list_char > list_char) > list_list_char > list_list_char).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_list_char_ty : (list_char > ty) > list_list_char > list_ty).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_list_char_val : (list_char > val) > list_list_char > list_val).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_ty_exp_list_char : (ty > exp_list_char) > list_ty > list_exp_list_char).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    map_ty_list_char : (ty > list_char) > list_ty > list_list_char).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Type__Oty, type,
    map_ty_ty : (ty > ty) > list_ty > list_ty).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Value__Oval, type,
    map_ty_val : (ty > val) > list_ty > list_val).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_va1515327237t_char : (val > exp_list_char) > list_val > list_exp_list_char).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    map_val_list_char : (val > list_char) > list_val > list_list_char).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Type__Oty, type,
    map_val_ty : (val > ty) > list_val > list_ty).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Value__Oval, type,
    map_val_val : (val > val) > list_val > list_val).
thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    dom_list_char_val : (list_char > option_val) > set_list_char).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    dom_Pr269338893on_val : (produc1172664615on_val > option2118145160on_val) > set_Pr1189492743on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_Pr1335625324t_char : (produc1172664615on_val > option_set_list_char) > set_Pr1189492743on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Value__Oval, type,
    dom_Pr162898261al_val : (produc1172664615on_val > option_val) > set_Pr1189492743on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    dom_Pr2073570061on_val : (produc655058983on_val > option2118145160on_val) > set_Pr208351751on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    dom_Pr1148610668t_char : (produc655058983on_val > option_set_list_char) > set_Pr208351751on_val).
thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001t__Value__Oval, type,
    dom_Pr1128399701al_val : (produc655058983on_val > option_val) > set_Pr208351751on_val).
thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_up576607321ar_val : (list_char > option_val) > list_list_char > list_val > list_char > option_val).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    size_s329991613t_char : list_exp_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Type__Oty_J, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
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thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J, type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Value__Oval, type,
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thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    collec105960082on_val : (produc655058983on_val > $o) > set_Pr208351751on_val).
thf(sy_c_SmallStep_Oblocks, type,
    blocks : produc81045532t_char > exp_list_char).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oredp, type,
    redp : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_SmallStep_Oreds, type,
    reds : list_P1234162913t_char > set_Pr208351751on_val).
thf(sy_c_SmallStep_Oredsp, type,
    redsp : list_P1234162913t_char > list_exp_list_char > produc515445032on_val > list_exp_list_char > produc515445032on_val > $o).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
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,
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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,
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thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi1892282060t_char : set_Pr1060756575t_char > set_Pr1060756575t_char).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
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    method297381284t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > $o).
thf(sy_c_Type_Othis, type,
    this : list_char).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Value_Oval_OAddr, type,
    addr : nat > val).
thf(sy_c_WWellForm_Owwf__J__mdecl, type,
    wwf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J, type,
    member_list_char : list_char > set_list_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member1699993616t_char : produc677445863t_char > set_Pr224372167t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    member462435472t_char : produc1813212775t_char > set_Pr1932514887t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    member725442668t_char : produc1410698691t_char > set_Pr2117892643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_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_Mt__List__Olist_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_J, type,
    member321179984on_val : produc1433960743on_val > set_Pr601606919on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    member884479824on_val : produc560125991on_val > set_Pr58336519on_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__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J, type,
    member1942114840ist_ty : produc1714969711ist_ty > set_Pr1785354703ist_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J, type,
    member1382006826st_val : produc1608520577st_val > set_Pr723931873st_val > $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__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__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_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, type,
    member1392938152t_char : produc1689611007t_char > set_Pr1060756575t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    member219943760t_char : produc885582375t_char > set_Pr1314019591t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J, type,
    member2070851320_ty_ty : product_prod_ty_ty > set_Pr1194734255_ty_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    member1494223754al_val : product_prod_val_val > set_Pr1870322241al_val > $o).
thf(sy_v_C______, type,
    c : list_char).
thf(sy_v_D______, type,
    d : list_char).
thf(sy_v_M______, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T______, type,
    t : ty).
thf(sy_v_Ts______, type,
    ts : list_ty).
thf(sy_v_a______, type,
    a : nat > option2118145160on_val).
thf(sy_v_aa______, type,
    aa : nat).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_body______, type,
    body : exp_list_char).
thf(sy_v_fs______, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_pns______, type,
    pns : list_list_char).
thf(sy_v_vs______, type,
    vs : list_val).

% Relevant facts (249)
thf(fact_0_RedCall_Ohyps_I4_J, axiom,
    (((size_size_list_ty @ ts) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(4)
thf(fact_1_RedCall_Ohyps_I3_J, axiom,
    (((size_size_list_val @ vs) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(3)
thf(fact_2_RedCall_Ohyps_I1_J, axiom,
    (((hp @ (produc52622304on_val @ a @ b) @ aa) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % RedCall.hyps(1)
thf(fact_3_RedCall_Ohyps_I2_J, axiom,
    ((method297381284t_char @ p @ c @ m @ ts @ t @ (produc713467969t_char @ pns @ body) @ d))). % RedCall.hyps(2)
thf(fact_4_RedCall_Oprems, axiom,
    ((d_list_char @ (call_list_char @ (val_list_char @ (addr @ aa)) @ m @ (map_va1515327237t_char @ val_list_char @ vs)) @ (some_set_list_char @ (dom_list_char_val @ b))))). % RedCall.prems
thf(fact_5_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_6_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_7_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_8_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_9_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_10_list_Oinject, axiom,
    ((![X21 : list_char, X22 : list_list_char, Y21 : list_char, Y22 : list_list_char]: (((cons_list_char @ X21 @ X22) = (cons_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_11_list_Oinject, axiom,
    ((![X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X22) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_12_list_Oinject, axiom,
    ((![X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: (((cons_val @ X21 @ X22) = (cons_val @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_13_list_Oinject, axiom,
    ((![X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X22) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_14_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_15_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_16_old_Oprod_Oinject, axiom,
    ((![A : list_ty, B : produc1109669680t_char, A2 : list_ty, B2 : produc1109669680t_char]: (((produc1806338192t_char @ A @ B) = (produc1806338192t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_17_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_18_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_19_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : exp_list_char, Y1 : list_list_char, Y2 : exp_list_char]: (((produc713467969t_char @ X1 @ X2) = (produc713467969t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_20_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_21_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1109669680t_char, Y1 : list_ty, Y2 : produc1109669680t_char]: (((produc1806338192t_char @ X1 @ X2) = (produc1806338192t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_22_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_23_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_24_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_25_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : val > ty, Ys : list_val]: (((cons_ty @ X @ Xs) = (map_val_ty @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_26_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : ty > val, Ys : list_ty]: (((cons_val @ X @ Xs) = (map_ty_val @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_27_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : val > val, Ys : list_val]: (((cons_val @ X @ Xs) = (map_val_val @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_28_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : ty > list_char, Ys : list_ty]: (((cons_list_char @ X @ Xs) = (map_ty_list_char @ F @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_ty_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_29_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : val > list_char, Ys : list_val]: (((cons_list_char @ X @ Xs) = (map_val_list_char @ F @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_val_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_30_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : list_char > ty, Ys : list_list_char]: (((cons_ty @ X @ Xs) = (map_list_char_ty @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_list_char_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_31_Cons__eq__map__conv, axiom,
    ((![X : val, Xs : list_val, F : list_char > val, Ys : list_list_char]: (((cons_val @ X @ Xs) = (map_list_char_val @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_list_char_val @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_32_Cons__eq__map__conv, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > list_char, Ys : list_list_char]: (((cons_list_char @ X @ Xs) = (map_li1166989960t_char @ F @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_li1166989960t_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_33_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : exp_list_char > ty, Ys : list_exp_list_char]: (((cons_ty @ X @ Xs) = (map_exp_list_char_ty @ F @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((X = (F @ Z))) & ((Xs = (map_exp_list_char_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_34_length__map, axiom,
    ((![F : val > exp_list_char, Xs : list_val]: ((size_s329991613t_char @ (map_va1515327237t_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_35_length__map, axiom,
    ((![F : ty > ty, Xs : list_ty]: ((size_size_list_ty @ (map_ty_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_36_length__map, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: ((size_size_list_ty @ (map_list_char_ty @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_37_length__map, axiom,
    ((![F : val > ty, Xs : list_val]: ((size_size_list_ty @ (map_val_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_38_length__map, axiom,
    ((![F : ty > list_char, Xs : list_ty]: ((size_s2008079621t_char @ (map_ty_list_char @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_39_length__map, axiom,
    ((![F : list_char > list_char, Xs : list_list_char]: ((size_s2008079621t_char @ (map_li1166989960t_char @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_40_length__map, axiom,
    ((![F : val > list_char, Xs : list_val]: ((size_s2008079621t_char @ (map_val_list_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_41_length__map, axiom,
    ((![F : ty > val, Xs : list_ty]: ((size_size_list_val @ (map_ty_val @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_42_length__map, axiom,
    ((![F : list_char > val, Xs : list_list_char]: ((size_size_list_val @ (map_list_char_val @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_43_length__map, axiom,
    ((![F : val > val, Xs : list_val]: ((size_size_list_val @ (map_val_val @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_44_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_45_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_46_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_47_neq__if__length__neq, axiom,
    ((![Xs : list_ty, Ys : list_ty]: ((~ (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_48_neq__if__length__neq, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((~ (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_49_neq__if__length__neq, axiom,
    ((![Xs : list_val, Ys : list_val]: ((~ (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_50_map__eq__imp__length__eq, axiom,
    ((![F : ty > exp_list_char, Xs : list_ty, G : val > exp_list_char, Ys : list_val]: (((map_ty_exp_list_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_51_map__eq__imp__length__eq, axiom,
    ((![F : list_char > exp_list_char, Xs : list_list_char, G : val > exp_list_char, Ys : list_val]: (((map_li1930351204t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_52_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : ty > exp_list_char, Ys : list_ty]: (((map_va1515327237t_char @ F @ Xs) = (map_ty_exp_list_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_53_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : list_char > exp_list_char, Ys : list_list_char]: (((map_va1515327237t_char @ F @ Xs) = (map_li1930351204t_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_54_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : val > exp_list_char, Ys : list_val]: (((map_va1515327237t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_55_map__eq__Cons__conv, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_56_map__eq__Cons__conv, axiom,
    ((![F : val > ty, Xs : list_val, Y : ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_57_map__eq__Cons__conv, axiom,
    ((![F : ty > val, Xs : list_ty, Y : val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_58_map__eq__Cons__conv, axiom,
    ((![F : val > val, Xs : list_val, Y : val, Ys : list_val]: (((map_val_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_59_map__eq__Cons__conv, axiom,
    ((![F : ty > list_char, Xs : list_ty, Y : list_char, Ys : list_list_char]: (((map_ty_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_ty_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_60_map__eq__Cons__conv, axiom,
    ((![F : val > list_char, Xs : list_val, Y : list_char, Ys : list_list_char]: (((map_val_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_val_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_61_map__eq__Cons__conv, axiom,
    ((![F : list_char > ty, Xs : list_list_char, Y : ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_list_char_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_62_map__eq__Cons__conv, axiom,
    ((![F : list_char > val, Xs : list_list_char, Y : val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (cons_val @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_list_char_val @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_63_map__eq__Cons__conv, axiom,
    ((![F : list_char > list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char]: (((map_li1166989960t_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) = (?[Z : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_li1166989960t_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_64_map__eq__Cons__conv, axiom,
    ((![F : exp_list_char > ty, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: (((map_exp_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & (((((F @ Z) = Y)) & (((map_exp_list_char_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_65_map__eq__Cons__D, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z2 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_ty_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_66_map__eq__Cons__D, axiom,
    ((![F : val > ty, Xs : list_val, Y : ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z2 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_val_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_67_map__eq__Cons__D, axiom,
    ((![F : ty > val, Xs : list_ty, Y : val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z2 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_ty_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_68_map__eq__Cons__D, axiom,
    ((![F : val > val, Xs : list_val, Y : val, Ys : list_val]: (((map_val_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z2 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_val_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_69_map__eq__Cons__D, axiom,
    ((![F : ty > list_char, Xs : list_ty, Y : list_char, Ys : list_list_char]: (((map_ty_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z2 : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_ty_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_70_map__eq__Cons__D, axiom,
    ((![F : val > list_char, Xs : list_val, Y : list_char, Ys : list_list_char]: (((map_val_list_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z2 : val, Zs2 : list_val]: ((Xs = (cons_val @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_val_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_71_map__eq__Cons__D, axiom,
    ((![F : list_char > ty, Xs : list_list_char, Y : ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z2 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_list_char_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_72_map__eq__Cons__D, axiom,
    ((![F : list_char > val, Xs : list_list_char, Y : val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (cons_val @ Y @ Ys)) => (?[Z2 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_list_char_val @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_73_map__eq__Cons__D, axiom,
    ((![F : list_char > list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char]: (((map_li1166989960t_char @ F @ Xs) = (cons_list_char @ Y @ Ys)) => (?[Z2 : list_char, Zs2 : list_list_char]: ((Xs = (cons_list_char @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_li1166989960t_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_74_map__eq__Cons__D, axiom,
    ((![F : exp_list_char > ty, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: (((map_exp_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z2 : exp_list_char, Zs2 : list_exp_list_char]: ((Xs = (cons_exp_list_char @ Z2 @ Zs2)) & (((F @ Z2) = Y) & ((map_exp_list_char_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_75_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) => (?[Z2 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_ty_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_76_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : val > ty, Ys : list_val]: (((cons_ty @ X @ Xs) = (map_val_ty @ F @ Ys)) => (?[Z2 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_val_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_77_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : ty > val, Ys : list_ty]: (((cons_val @ X @ Xs) = (map_ty_val @ F @ Ys)) => (?[Z2 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_ty_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_78_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : val > val, Ys : list_val]: (((cons_val @ X @ Xs) = (map_val_val @ F @ Ys)) => (?[Z2 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_val_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_79_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : ty > list_char, Ys : list_ty]: (((cons_list_char @ X @ Xs) = (map_ty_list_char @ F @ Ys)) => (?[Z2 : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_ty_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_80_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : val > list_char, Ys : list_val]: (((cons_list_char @ X @ Xs) = (map_val_list_char @ F @ Ys)) => (?[Z2 : val, Zs2 : list_val]: ((Ys = (cons_val @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_val_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_81_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : list_char > ty, Ys : list_list_char]: (((cons_ty @ X @ Xs) = (map_list_char_ty @ F @ Ys)) => (?[Z2 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_list_char_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_82_Cons__eq__map__D, axiom,
    ((![X : val, Xs : list_val, F : list_char > val, Ys : list_list_char]: (((cons_val @ X @ Xs) = (map_list_char_val @ F @ Ys)) => (?[Z2 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_list_char_val @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_83_Cons__eq__map__D, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > list_char, Ys : list_list_char]: (((cons_list_char @ X @ Xs) = (map_li1166989960t_char @ F @ Ys)) => (?[Z2 : list_char, Zs2 : list_list_char]: ((Ys = (cons_list_char @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_li1166989960t_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_84_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : exp_list_char > ty, Ys : list_exp_list_char]: (((cons_ty @ X @ Xs) = (map_exp_list_char_ty @ F @ Ys)) => (?[Z2 : exp_list_char, Zs2 : list_exp_list_char]: ((Ys = (cons_exp_list_char @ Z2 @ Zs2)) & ((X = (F @ Z2)) & (Xs = (map_exp_list_char_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_85_list_Osimps_I9_J, axiom,
    ((![F : ty > ty, X21 : ty, X22 : list_ty]: ((map_ty_ty @ F @ (cons_ty @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_ty_ty @ F @ X22)))))). % list.simps(9)
thf(fact_86_list_Osimps_I9_J, axiom,
    ((![F : ty > val, X21 : ty, X22 : list_ty]: ((map_ty_val @ F @ (cons_ty @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_ty_val @ F @ X22)))))). % list.simps(9)
thf(fact_87_list_Osimps_I9_J, axiom,
    ((![F : val > ty, X21 : val, X22 : list_val]: ((map_val_ty @ F @ (cons_val @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_val_ty @ F @ X22)))))). % list.simps(9)
thf(fact_88_list_Osimps_I9_J, axiom,
    ((![F : val > val, X21 : val, X22 : list_val]: ((map_val_val @ F @ (cons_val @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_val_val @ F @ X22)))))). % list.simps(9)
thf(fact_89_list_Osimps_I9_J, axiom,
    ((![F : list_char > ty, X21 : list_char, X22 : list_list_char]: ((map_list_char_ty @ F @ (cons_list_char @ X21 @ X22)) = (cons_ty @ (F @ X21) @ (map_list_char_ty @ F @ X22)))))). % list.simps(9)
thf(fact_90_list_Osimps_I9_J, axiom,
    ((![F : list_char > val, X21 : list_char, X22 : list_list_char]: ((map_list_char_val @ F @ (cons_list_char @ X21 @ X22)) = (cons_val @ (F @ X21) @ (map_list_char_val @ F @ X22)))))). % list.simps(9)
thf(fact_91_list_Osimps_I9_J, axiom,
    ((![F : ty > list_char, X21 : ty, X22 : list_ty]: ((map_ty_list_char @ F @ (cons_ty @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_ty_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_92_list_Osimps_I9_J, axiom,
    ((![F : val > list_char, X21 : val, X22 : list_val]: ((map_val_list_char @ F @ (cons_val @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_val_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_93_list_Osimps_I9_J, axiom,
    ((![F : list_char > list_char, X21 : list_char, X22 : list_list_char]: ((map_li1166989960t_char @ F @ (cons_list_char @ X21 @ X22)) = (cons_list_char @ (F @ X21) @ (map_li1166989960t_char @ F @ X22)))))). % list.simps(9)
thf(fact_94_list_Osimps_I9_J, axiom,
    ((![F : ty > exp_list_char, X21 : ty, X22 : list_ty]: ((map_ty_exp_list_char @ F @ (cons_ty @ X21 @ X22)) = (cons_exp_list_char @ (F @ X21) @ (map_ty_exp_list_char @ F @ X22)))))). % list.simps(9)
thf(fact_95_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_96_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_97_old_Oprod_Oinducts, axiom,
    ((![P : produc111478616t_char > $o, Prod : produc111478616t_char]: ((![A3 : list_ty, B3 : produc1109669680t_char]: (P @ (produc1806338192t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_98_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_99_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_100_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1294284815t_char]: (~ ((![A3 : list_list_char, B3 : exp_list_char]: (~ ((Y = (produc713467969t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_101_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_102_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A3 : list_ty, B3 : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_103_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_104_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_105_Pair__inject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_106_Pair__inject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_107_Pair__inject, axiom,
    ((![A : list_ty, B : produc1109669680t_char, A2 : list_ty, B2 : produc1109669680t_char]: (((produc1806338192t_char @ A @ B) = (produc1806338192t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_108_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_109_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_110_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P2 : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_111_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_112_prod__cases, axiom,
    ((![P : produc111478616t_char > $o, P2 : produc111478616t_char]: ((![A3 : list_ty, B3 : produc1109669680t_char]: (P @ (produc1806338192t_char @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_113_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_114_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_115_surj__pair, axiom,
    ((![P2 : produc1294284815t_char]: (?[X3 : list_list_char, Y3 : exp_list_char]: (P2 = (produc713467969t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_116_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_117_surj__pair, axiom,
    ((![P2 : produc111478616t_char]: (?[X3 : list_ty, Y3 : produc1109669680t_char]: (P2 = (produc1806338192t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_118_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_119_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_120_not__Cons__self2, axiom,
    ((![X : list_char, Xs : list_list_char]: (~ (((cons_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_121_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_122_not__Cons__self2, axiom,
    ((![X : val, Xs : list_val]: (~ (((cons_val @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_123_not__Cons__self2, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_124_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_125_prod__induct3, axiom,
    ((![P : produc111478616t_char > $o, X : produc111478616t_char]: ((![A3 : list_ty, B3 : list_val, C : exp_list_char]: (P @ (produc1806338192t_char @ A3 @ (produc823987298t_char @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_126_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_127_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_128_prod__cases3, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A3 : list_ty, B3 : list_val, C : exp_list_char]: (~ ((Y = (produc1806338192t_char @ A3 @ (produc823987298t_char @ B3 @ C))))))))))). % prod_cases3
thf(fact_129_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_130_red__reds_ORedCall, axiom,
    ((![S : produc515445032on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, P : list_P1234162913t_char, M : list_char, Ts : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Vs : list_val]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D) => (((size_size_list_val @ Vs) = (size_s2008079621t_char @ Pns)) => (((size_size_list_ty @ Ts) = (size_s2008079621t_char @ Pns)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ (addr @ A)) @ M @ (map_va1515327237t_char @ val_list_char @ Vs)) @ S) @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ (cons_list_char @ this @ Pns) @ (produc1806338192t_char @ (cons_ty @ (class @ D) @ Ts) @ (produc823987298t_char @ (cons_val @ (addr @ A) @ Vs) @ Body)))) @ S)) @ (red @ P))))))))). % red_reds.RedCall
thf(fact_131_redp__redsp_ORedCall, axiom,
    ((![S : produc515445032on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, P : list_P1234162913t_char, M : list_char, Ts : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Vs : list_val]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D) => (((size_size_list_val @ Vs) = (size_s2008079621t_char @ Pns)) => (((size_size_list_ty @ Ts) = (size_s2008079621t_char @ Pns)) => (redp @ P @ (call_list_char @ (val_list_char @ (addr @ A)) @ M @ (map_va1515327237t_char @ val_list_char @ Vs)) @ S @ (blocks @ (produc1808722894t_char @ (cons_list_char @ this @ Pns) @ (produc1806338192t_char @ (cons_ty @ (class @ D) @ Ts) @ (produc823987298t_char @ (cons_val @ (addr @ A) @ Vs) @ Body)))) @ S)))))))). % redp_redsp.RedCall
thf(fact_132_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_133_exp_Oinject_I9_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, Y91 : exp_list_char, Y92 : list_char, Y93 : list_exp_list_char]: (((call_list_char @ X91 @ X92 @ X93) = (call_list_char @ Y91 @ Y92 @ Y93)) = (((X91 = Y91)) & ((((X92 = Y92)) & ((X93 = Y93))))))))). % exp.inject(9)
thf(fact_134_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_135__092_060D_062_Osimps_I3_J, axiom,
    ((![V : val, A4 : option_set_list_char]: (d_list_char @ (val_list_char @ V) @ A4)))). % \<D>.simps(3)
thf(fact_136_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_137_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_138_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_139_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_140_domI, axiom,
    ((![M2 : produc1172664615on_val > option_set_list_char, A : produc1172664615on_val, B : set_list_char]: (((M2 @ A) = (some_set_list_char @ B)) => (member354538064on_val @ A @ (dom_Pr1335625324t_char @ M2)))))). % domI
thf(fact_141_domI, axiom,
    ((![M2 : produc655058983on_val > option_set_list_char, A : produc655058983on_val, B : set_list_char]: (((M2 @ A) = (some_set_list_char @ B)) => (member1689761872on_val @ A @ (dom_Pr1148610668t_char @ M2)))))). % domI
thf(fact_142_domI, axiom,
    ((![M2 : produc1172664615on_val > option2118145160on_val, A : produc1172664615on_val, B : produc266837688on_val]: (((M2 @ A) = (some_P1299442195on_val @ B)) => (member354538064on_val @ A @ (dom_Pr269338893on_val @ M2)))))). % domI
thf(fact_143_domI, axiom,
    ((![M2 : produc655058983on_val > option2118145160on_val, A : produc655058983on_val, B : produc266837688on_val]: (((M2 @ A) = (some_P1299442195on_val @ B)) => (member1689761872on_val @ A @ (dom_Pr2073570061on_val @ M2)))))). % domI
thf(fact_144_domI, axiom,
    ((![M2 : list_char > option_val, A : list_char, B : val]: (((M2 @ A) = (some_val @ B)) => (member_list_char @ A @ (dom_list_char_val @ M2)))))). % domI
thf(fact_145_domI, axiom,
    ((![M2 : produc1172664615on_val > option_val, A : produc1172664615on_val, B : val]: (((M2 @ A) = (some_val @ B)) => (member354538064on_val @ A @ (dom_Pr162898261al_val @ M2)))))). % domI
thf(fact_146_domI, axiom,
    ((![M2 : produc655058983on_val > option_val, A : produc655058983on_val, B : val]: (((M2 @ A) = (some_val @ B)) => (member1689761872on_val @ A @ (dom_Pr1128399701al_val @ M2)))))). % domI
thf(fact_147_domD, axiom,
    ((![A : produc1172664615on_val, M2 : produc1172664615on_val > option_set_list_char]: ((member354538064on_val @ A @ (dom_Pr1335625324t_char @ M2)) => (?[B3 : set_list_char]: ((M2 @ A) = (some_set_list_char @ B3))))))). % domD
thf(fact_148_domD, axiom,
    ((![A : produc655058983on_val, M2 : produc655058983on_val > option_set_list_char]: ((member1689761872on_val @ A @ (dom_Pr1148610668t_char @ M2)) => (?[B3 : set_list_char]: ((M2 @ A) = (some_set_list_char @ B3))))))). % domD
thf(fact_149_domD, axiom,
    ((![A : produc1172664615on_val, M2 : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A @ (dom_Pr269338893on_val @ M2)) => (?[B3 : produc266837688on_val]: ((M2 @ A) = (some_P1299442195on_val @ B3))))))). % domD
thf(fact_150_domD, axiom,
    ((![A : produc655058983on_val, M2 : produc655058983on_val > option2118145160on_val]: ((member1689761872on_val @ A @ (dom_Pr2073570061on_val @ M2)) => (?[B3 : produc266837688on_val]: ((M2 @ A) = (some_P1299442195on_val @ B3))))))). % domD
thf(fact_151_domD, axiom,
    ((![A : list_char, M2 : list_char > option_val]: ((member_list_char @ A @ (dom_list_char_val @ M2)) => (?[B3 : val]: ((M2 @ A) = (some_val @ B3))))))). % domD
thf(fact_152_domD, axiom,
    ((![A : produc1172664615on_val, M2 : produc1172664615on_val > option_val]: ((member354538064on_val @ A @ (dom_Pr162898261al_val @ M2)) => (?[B3 : val]: ((M2 @ A) = (some_val @ B3))))))). % domD
thf(fact_153_domD, axiom,
    ((![A : produc655058983on_val, M2 : produc655058983on_val > option_val]: ((member1689761872on_val @ A @ (dom_Pr1128399701al_val @ M2)) => (?[B3 : val]: ((M2 @ A) = (some_val @ B3))))))). % domD
thf(fact_154_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (^[Z : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y4) @ (produc2023458740on_val @ Z @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_155_redp__redsp_OCallObj, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, M : list_char, Es : list_exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (call_list_char @ E @ M @ Es) @ S @ (call_list_char @ E2 @ M @ Es) @ S2))))). % redp_redsp.CallObj
thf(fact_156_red__reds_OCallObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_157_exp_Odistinct_I65_J, axiom,
    ((![X32 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X32) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_158_red__reds_ORedFAcc, axiom,
    ((![S : produc515445032on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, F2 : list_char, D : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F2 @ D)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F2 @ D) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_159_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_160_redp__redsp_ORedFAcc, axiom,
    ((![S : produc515445032on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val, F2 : list_char, D : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F2 @ D)) = (some_val @ V)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F2 @ D) @ S @ (val_list_char @ V) @ S)))))). % redp_redsp.RedFAcc
thf(fact_161_blocksFinal, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((final_list_char @ E) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L))) @ (transi111096263on_val @ (red @ P))))))))). % blocksFinal
thf(fact_162_redp__redsp_OCallParams, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, V : val, M : list_char]: ((redsp @ P @ Es @ S @ Es2 @ S2) => (redp @ P @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2))))). % redp_redsp.CallParams
thf(fact_163_red__lcl__incr, axiom,
    ((![E : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E2 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_0) @ (dom_list_char_val @ L_1)))))). % red_lcl_incr
thf(fact_164_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_165_redsp__reds__eq, axiom,
    ((redsp = (^[P3 : list_P1234162913t_char]: (^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (^[Z : list_exp_list_char]: (^[Aa : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X4 @ Y4) @ (produc1725134254on_val @ Z @ Aa)) @ (reds @ P3)))))))))). % redsp_reds_eq
thf(fact_166_FAccReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_167_redp__redsp_OFAccRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, F2 : list_char, D : list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (fAcc_list_char @ E @ F2 @ D) @ S @ (fAcc_list_char @ E2 @ F2 @ D) @ S2))))). % redp_redsp.FAccRed
thf(fact_168_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_169_exp_Odistinct_I141_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(141)
thf(fact_170__092_060D_062_Osimps_I7_J, axiom,
    ((![E : exp_list_char, F2 : list_char, D : list_char, A4 : option_set_list_char]: ((d_list_char @ (fAcc_list_char @ E @ F2 @ D) @ A4) = (d_list_char @ E @ A4))))). % \<D>.simps(7)
thf(fact_171_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_172_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S @ Es2 @ S2) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2))))). % redp_redsp.ListRed2
thf(fact_173_redp__redsp_OListRed1, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, Es : list_exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redsp @ P @ (cons_exp_list_char @ E @ Es) @ S @ (cons_exp_list_char @ E2 @ Es) @ S2))))). % redp_redsp.ListRed1
thf(fact_174_CallRedsObj, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_175_red__reds_OFAccRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F2 : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F2 @ D) @ S2)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_176_FAccRedsVal, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A : nat, S2 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char, Fs : produc1257910179t_char > option_val, F2 : list_char, D : list_char, V : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S2)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (((Fs @ (produc1304532571t_char @ F2 @ D)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E @ F2 @ D) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_177_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E3 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E3 @ H3 @ L3 @ E3 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val, E4 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_12 @ L_12))) @ (red @ P)) => ((R @ E_1 @ H_12 @ L_12 @ E4 @ H4 @ L4) => (R @ E_0 @ H_02 @ L_02 @ E4 @ H4 @ L4)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_178_redsp_Osimps, axiom,
    ((redsp = (^[P3 : list_P1234162913t_char]: (^[A1 : list_exp_list_char]: (^[A22 : produc515445032on_val]: (^[A32 : list_exp_list_char]: (^[A42 : produc515445032on_val]: (((?[E5 : exp_list_char]: (?[S3 : produc515445032on_val]: (?[E6 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E5 @ Es3))) & ((((A22 = S3)) & ((((A32 = (cons_exp_list_char @ E6 @ Es3))) & ((((A42 = S4)) & ((redp @ P3 @ E5 @ S3 @ E6 @ S4))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S3 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[V2 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3))) & ((((A22 = S3)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A42 = S4)) & ((redsp @ P3 @ Es3 @ S3 @ Es4 @ S4)))))))))))))))))))))))). % redsp.simps
thf(fact_179_redsp_Ocases, axiom,
    ((![P : list_P1234162913t_char, A12 : list_exp_list_char, A23 : produc515445032on_val, A33 : list_exp_list_char, A43 : produc515445032on_val]: ((redsp @ P @ A12 @ A23 @ A33 @ A43) => ((![E3 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S6 : produc515445032on_val, Es5 : list_exp_list_char]: ((A12 = (cons_exp_list_char @ E3 @ Es5)) => ((A23 = S5) => ((A33 = (cons_exp_list_char @ E4 @ Es5)) => ((A43 = S6) => (~ ((redp @ P @ E3 @ S5 @ E4 @ S6)))))))) => (~ ((![Es5 : list_exp_list_char, S5 : produc515445032on_val, Es6 : list_exp_list_char, S6 : produc515445032on_val, V3 : val]: ((A12 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5)) => ((A23 = S5) => ((A33 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6)) => ((A43 = S6) => (~ ((redsp @ P @ Es5 @ S5 @ Es6 @ S6))))))))))))))). % redsp.cases
thf(fact_180_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_181_reds_Osimps, axiom,
    ((![A12 : list_exp_list_char, A23 : produc515445032on_val, A33 : list_exp_list_char, A43 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A12 @ A23) @ (produc1725134254on_val @ A33 @ A43)) @ (reds @ P)) = (((?[E5 : exp_list_char]: (?[S3 : produc515445032on_val]: (?[E6 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A12 = (cons_exp_list_char @ E5 @ Es3))) & ((((A23 = S3)) & ((((A33 = (cons_exp_list_char @ E6 @ Es3))) & ((((A43 = S4)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E5 @ S3) @ (produc2023458740on_val @ E6 @ S4)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S3 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[V2 : val]: (((A12 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3))) & ((((A23 = S3)) & ((((A33 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A43 = S4)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S3) @ (produc1725134254on_val @ Es4 @ S4)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_182_reds_Ocases, axiom,
    ((![A12 : list_exp_list_char, A23 : produc515445032on_val, A33 : list_exp_list_char, A43 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A12 @ A23) @ (produc1725134254on_val @ A33 @ A43)) @ (reds @ P)) => ((![E3 : exp_list_char, S5 : produc515445032on_val, E4 : exp_list_char, S6 : produc515445032on_val, Es5 : list_exp_list_char]: ((A12 = (cons_exp_list_char @ E3 @ Es5)) => ((A23 = S5) => ((A33 = (cons_exp_list_char @ E4 @ Es5)) => ((A43 = S6) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S5) @ (produc2023458740on_val @ E4 @ S6)) @ (red @ P))))))))) => (~ ((![Es5 : list_exp_list_char, S5 : produc515445032on_val, Es6 : list_exp_list_char, S6 : produc515445032on_val, V3 : val]: ((A12 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5)) => ((A23 = S5) => ((A33 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6)) => ((A43 = S6) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S5) @ (produc1725134254on_val @ Es6 @ S6)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_183_rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R2 : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_list_char, B3 : exp_list_char, Aa2 : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ A3 @ B3)) @ (transi1892282060t_char @ R2)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_184_rtrancl__induct2, axiom,
    ((![Ax : list_ty, Ay : produc1109669680t_char, Bx : list_ty, By : produc1109669680t_char, R2 : set_Pr1314019591t_char, P : list_ty > produc1109669680t_char > $o]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Ax @ Ay) @ (produc1806338192t_char @ Bx @ By)) @ (transi311435739t_char @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_ty, B3 : produc1109669680t_char, Aa2 : list_ty, Ba : produc1109669680t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Ax @ Ay) @ (produc1806338192t_char @ A3 @ B3)) @ (transi311435739t_char @ R2)) => ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A3 @ B3) @ (produc1806338192t_char @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_185_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : 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 @ R2)) => ((P @ Ax @ Ay) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_186_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_187_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_exp_list_char, B3 : produc515445032on_val, Aa2 : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A3 @ B3)) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_188_converse__rtranclE2, axiom,
    ((![Xa : list_list_char, Xb : exp_list_char, Za : list_list_char, Zb : exp_list_char, R2 : set_Pr1060756575t_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R2)) => ((~ (((produc713467969t_char @ Xa @ Xb) = (produc713467969t_char @ Za @ Zb)))) => (~ ((![A3 : list_list_char, B3 : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ A3 @ B3)) @ R2) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_189_converse__rtranclE2, axiom,
    ((![Xa : list_ty, Xb : produc1109669680t_char, Za : list_ty, Zb : produc1109669680t_char, R2 : set_Pr1314019591t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Xa @ Xb) @ (produc1806338192t_char @ Za @ Zb)) @ (transi311435739t_char @ R2)) => ((~ (((produc1806338192t_char @ Xa @ Xb) = (produc1806338192t_char @ Za @ Zb)))) => (~ ((![A3 : list_ty, B3 : produc1109669680t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Xa @ Xb) @ (produc1806338192t_char @ A3 @ B3)) @ R2) => (~ ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A3 @ B3) @ (produc1806338192t_char @ Za @ Zb)) @ (transi311435739t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_190_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_191_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_192_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A3 @ B3)) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_193_converse__rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R2 : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R2)) => ((P @ Bx @ By) => ((![A3 : list_list_char, B3 : exp_list_char, Aa2 : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A3 @ B3) @ (produc713467969t_char @ Aa2 @ Ba)) @ R2) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Aa2 @ Ba) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_194_converse__rtrancl__induct2, axiom,
    ((![Ax : list_ty, Ay : produc1109669680t_char, Bx : list_ty, By : produc1109669680t_char, R2 : set_Pr1314019591t_char, P : list_ty > produc1109669680t_char > $o]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Ax @ Ay) @ (produc1806338192t_char @ Bx @ By)) @ (transi311435739t_char @ R2)) => ((P @ Bx @ By) => ((![A3 : list_ty, B3 : produc1109669680t_char, Aa2 : list_ty, Ba : produc1109669680t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A3 @ B3) @ (produc1806338192t_char @ Aa2 @ Ba)) @ R2) => ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Aa2 @ Ba) @ (produc1806338192t_char @ Bx @ By)) @ (transi311435739t_char @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_195_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : 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 @ R2)) => ((P @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_196_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_197_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_exp_list_char, B3 : produc515445032on_val, Aa2 : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Aa2 @ Ba)) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa2 @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_198_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_199_rtrancl__idemp, axiom,
    ((![R2 : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R2)) = (transi325225921on_val @ R2))))). % rtrancl_idemp
thf(fact_200_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_201_r__into__rtrancl, axiom,
    ((![P2 : produc655058983on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ P2 @ R2) => (member1689761872on_val @ P2 @ (transi325225921on_val @ R2)))))). % r_into_rtrancl
thf(fact_202_ListReds2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_203_rtranclE, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_204_rtranclE, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((~ ((A = B))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ Y3) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ B) @ R2)))))))))))). % rtranclE
thf(fact_205_rtrancl_Ocases, axiom,
    ((![A12 : produc1097884484on_val, A23 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ A23) @ (transi111096263on_val @ R2)) => ((~ ((A23 = A12))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A23) @ R2)))))))))))). % rtrancl.cases
thf(fact_206_rtrancl_Ocases, axiom,
    ((![A12 : produc335961278on_val, A23 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A12 @ A23) @ (transi325225921on_val @ R2)) => ((~ ((A23 = A12))) => (~ ((![B3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A12 @ B3) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B3 @ A23) @ R2)))))))))))). % rtrancl.cases
thf(fact_207_rtrancl_Osimps, axiom,
    ((![A12 : produc1097884484on_val, A23 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A12 @ A23) @ (transi111096263on_val @ R2)) = (((?[A5 : produc1097884484on_val]: (((A12 = A5)) & ((A23 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A12 = A5)) & ((((A23 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_208_rtrancl_Osimps, axiom,
    ((![A12 : produc335961278on_val, A23 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A12 @ A23) @ (transi325225921on_val @ R2)) = (((?[A5 : produc335961278on_val]: (((A12 = A5)) & ((A23 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C3 : produc335961278on_val]: (((A12 = A5)) & ((((A23 = C3)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R2))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_209_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z3) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_210_rtrancl__trans, axiom,
    ((![X : produc335961278on_val, Y : produc335961278on_val, R2 : set_Pr208351751on_val, Z3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z3) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ X @ Z3) @ (transi325225921on_val @ R2))))))). % rtrancl_trans
thf(fact_211_rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_212_rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ A) => ((![Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ Y3) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B))))))). % rtrancl_induct
thf(fact_213_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A3 : produc1097884484on_val]: (P @ A3 @ A3)) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A3 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A3 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_214_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X2) @ (transi325225921on_val @ R2)) => ((![A3 : produc335961278on_val]: (P @ A3 @ A3)) => ((![A3 : produc335961278on_val, B3 : produc335961278on_val, C : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A3 @ B3) @ (transi325225921on_val @ R2)) => ((P @ A3 @ B3) => ((member1689761872on_val @ (produc245869591on_val @ B3 @ C) @ R2) => (P @ A3 @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_215_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z3 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z3) @ (transi111096263on_val @ R2)) => ((~ ((X = Z3))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_216_converse__rtranclE, axiom,
    ((![X : produc335961278on_val, Z3 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Z3) @ (transi325225921on_val @ R2)) => ((~ ((X = Z3))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y3) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z3) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_217_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_218_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc335961278on_val, R2 : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A @ A) @ (transi325225921on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_219_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_220_converse__rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ B) => ((![Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ Z2 @ B) @ (transi325225921on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_221_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C4) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_222_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, C4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ B @ C4) @ R2) => (member1689761872on_val @ (produc245869591on_val @ A @ C4) @ (transi325225921on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_223_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C4) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C4) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_224_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, C4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ B @ C4) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ A @ C4) @ (transi325225921on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_225_ListReds1, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_226_ListRedsVal, axiom,
    ((![E : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_227_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_228_subset__antisym, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ A4 @ B5) => ((ord_le1836582007t_char @ B5 @ A4) => (A4 = B5)))))). % subset_antisym
thf(fact_229_subsetI, axiom,
    ((![A4 : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((![X3 : produc1172664615on_val]: ((member354538064on_val @ X3 @ A4) => (member354538064on_val @ X3 @ B5))) => (ord_le837504935on_val @ A4 @ B5))))). % subsetI
thf(fact_230_subsetI, axiom,
    ((![A4 : set_Pr208351751on_val, B5 : set_Pr208351751on_val]: ((![X3 : produc655058983on_val]: ((member1689761872on_val @ X3 @ A4) => (member1689761872on_val @ X3 @ B5))) => (ord_le1331145127on_val @ A4 @ B5))))). % subsetI
thf(fact_231_subsetI, axiom,
    ((![A4 : set_list_char, B5 : set_list_char]: ((![X3 : list_char]: ((member_list_char @ X3 @ A4) => (member_list_char @ X3 @ B5))) => (ord_le1836582007t_char @ A4 @ B5))))). % subsetI
thf(fact_232_order__refl, axiom,
    ((![X : set_list_char]: (ord_le1836582007t_char @ X @ X)))). % order_refl
thf(fact_233_Cons__in__lex, axiom,
    ((![X : produc1097884484on_val, Xs : list_P1873028426on_val, Y : produc1097884484on_val, Ys : list_P1873028426on_val, R2 : set_Pr1189492743on_val]: ((member321179984on_val @ (produc2055752471on_val @ (cons_P766091258on_val @ X @ Xs) @ (cons_P766091258on_val @ Y @ Ys)) @ (lex_Pr1119043758on_val @ R2)) = (((((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R2)) & (((size_s2061184438on_val @ Xs) = (size_s2061184438on_val @ Ys))))) | ((((X = Y)) & ((member321179984on_val @ (produc2055752471on_val @ Xs @ Ys) @ (lex_Pr1119043758on_val @ R2)))))))))). % Cons_in_lex
thf(fact_234_Cons__in__lex, axiom,
    ((![X : produc335961278on_val, Xs : list_P682203204on_val, Y : produc335961278on_val, Ys : list_P682203204on_val, R2 : set_Pr208351751on_val]: ((member884479824on_val @ (produc234842647on_val @ (cons_P1492043380on_val @ X @ Xs) @ (cons_P1492043380on_val @ Y @ Ys)) @ (lex_Pr1773567272on_val @ R2)) = (((((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ R2)) & (((size_s975927984on_val @ Xs) = (size_s975927984on_val @ Ys))))) | ((((X = Y)) & ((member884479824on_val @ (produc234842647on_val @ Xs @ Ys) @ (lex_Pr1773567272on_val @ R2)))))))))). % Cons_in_lex
thf(fact_235_Cons__in__lex, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char, R2 : set_Pr224372167t_char]: ((member462435472t_char @ (produc1721801175t_char @ (cons_exp_list_char @ X @ Xs) @ (cons_exp_list_char @ Y @ Ys)) @ (lex_exp_list_char @ R2)) = (((((member1699993616t_char @ (produc240508503t_char @ X @ Y) @ R2)) & (((size_s329991613t_char @ Xs) = (size_s329991613t_char @ Ys))))) | ((((X = Y)) & ((member462435472t_char @ (produc1721801175t_char @ Xs @ Ys) @ (lex_exp_list_char @ R2)))))))))). % Cons_in_lex
thf(fact_236_Cons__in__lex, axiom,
    ((![X : ty, Xs : list_ty, Y : ty, Ys : list_ty, R2 : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) @ (lex_ty @ R2)) = (((((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ R2)) & (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys))))) | ((((X = Y)) & ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (lex_ty @ R2)))))))))). % Cons_in_lex
thf(fact_237_Cons__in__lex, axiom,
    ((![X : list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char, R2 : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ (cons_list_char @ Y @ Ys)) @ (lex_list_char @ R2)) = (((((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R2)) & (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys))))) | ((((X = Y)) & ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (lex_list_char @ R2)))))))))). % Cons_in_lex
thf(fact_238_Cons__in__lex, axiom,
    ((![X : val, Xs : list_val, Y : val, Ys : list_val, R2 : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) @ (lex_val @ R2)) = (((((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R2)) & (((size_size_list_val @ Xs) = (size_size_list_val @ Ys))))) | ((((X = Y)) & ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (lex_val @ R2)))))))))). % Cons_in_lex
thf(fact_239_rtrancl__mono, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R2 @ S) => (ord_le837504935on_val @ (transi111096263on_val @ R2) @ (transi111096263on_val @ S)))))). % rtrancl_mono
thf(fact_240_rtrancl__mono, axiom,
    ((![R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: ((ord_le1331145127on_val @ R2 @ S) => (ord_le1331145127on_val @ (transi325225921on_val @ R2) @ (transi325225921on_val @ S)))))). % rtrancl_mono
thf(fact_241_rtrancl__subset, axiom,
    ((![R : set_Pr1189492743on_val, S7 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R @ S7) => ((ord_le837504935on_val @ S7 @ (transi111096263on_val @ R)) => ((transi111096263on_val @ S7) = (transi111096263on_val @ R))))))). % rtrancl_subset
thf(fact_242_rtrancl__subset, axiom,
    ((![R : set_Pr208351751on_val, S7 : set_Pr208351751on_val]: ((ord_le1331145127on_val @ R @ S7) => ((ord_le1331145127on_val @ S7 @ (transi325225921on_val @ R)) => ((transi325225921on_val @ S7) = (transi325225921on_val @ R))))))). % rtrancl_subset
thf(fact_243_rtrancl__subset__rtrancl, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R2 @ (transi111096263on_val @ S)) => (ord_le837504935on_val @ (transi111096263on_val @ R2) @ (transi111096263on_val @ S)))))). % rtrancl_subset_rtrancl
thf(fact_244_rtrancl__subset__rtrancl, axiom,
    ((![R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: ((ord_le1331145127on_val @ R2 @ (transi325225921on_val @ S)) => (ord_le1331145127on_val @ (transi325225921on_val @ R2) @ (transi325225921on_val @ S)))))). % rtrancl_subset_rtrancl
thf(fact_245_less__eq__set__def, axiom,
    ((ord_le1331145127on_val = (^[A6 : set_Pr208351751on_val]: (^[B6 : set_Pr208351751on_val]: (ord_le1839507958_val_o @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A6)) @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ B6)))))))). % less_eq_set_def
thf(fact_246_less__eq__set__def, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (ord_le1945897678char_o @ (^[X4 : list_char]: (member_list_char @ X4 @ A6)) @ (^[X4 : list_char]: (member_list_char @ X4 @ B6)))))))). % less_eq_set_def
thf(fact_247_CallRedsFinal, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, Es : list_exp_list_char, Vs : list_val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C2 : list_char, Fs : produc1257910179t_char > option_val, M : list_char, Ts : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, L_22 : list_char > option_val, Ef : exp_list_char, H_3 : nat > option2118145160on_val, L_3 : list_char > option_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (map_va1515327237t_char @ val_list_char @ Vs) @ (produc52622304on_val @ H_2 @ L_2))) @ (transi325225921on_val @ (reds @ P))) => (((H_2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => ((method297381284t_char @ P @ C2 @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D) => (((size_size_list_val @ Vs) = (size_s2008079621t_char @ Pns)) => ((L_22 = (map_up576607321ar_val @ (fun_up1252458416on_val @ (^[X4 : list_char]: none_val) @ this @ (some_val @ (addr @ A))) @ Pns @ Vs)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Body @ (produc52622304on_val @ H_2 @ L_22)) @ (produc2023458740on_val @ Ef @ (produc52622304on_val @ H_3 @ L_3))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ Ef) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S_0) @ (produc2023458740on_val @ Ef @ (produc52622304on_val @ H_3 @ L_2))) @ (transi111096263on_val @ (red @ P))))))))))))))). % CallRedsFinal
thf(fact_248_CallRedsThrowParams, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams

% Conjectures (1)
thf(conj_0, conjecture,
    ((d_list_char @ (blocks @ (produc1808722894t_char @ (cons_list_char @ this @ pns) @ (produc1806338192t_char @ (cons_ty @ (class @ d) @ ts) @ (produc823987298t_char @ (cons_val @ (addr @ aa) @ vs) @ body)))) @ (some_set_list_char @ (dom_list_char_val @ b))))).
