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thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    option2118145160on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    set_Pr2075231726on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_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_Mt__List__Olist_It__String__Ochar_J_J_J, type,
    set_Pr2090500778t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc266837688on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_I_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_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1072314740t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    set_Pr1104486497on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc1335728385on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1490933927t_char : $tType).
thf(ty_n_t__Set__Oset_I_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,
    set_Pr1986825540on_val : $tType).
thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr2117892643t_char : $tType).
thf(ty_n_t__Set__Oset_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_J, type,
    set_Pr2063914181t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    set_Pr1402464673t_char : $tType).
thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr224372167t_char : $tType).
thf(ty_n_t__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,
    produc1410698691t_char : $tType).
thf(ty_n_t__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,
    produc1294284815t_char : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc279182059t_char : $tType).
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__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1257910179t_char : $tType).
thf(ty_n_t__Set__Oset_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    set_li1111183366on_val : $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__Set__Oset_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    set_list_list_char : $tType).
thf(ty_n_t__Set__Oset_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    set_exp_list_char : $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__Option__Ooption_It__Type__Oty_J, type,
    option_ty : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__List__Olist_It__Value__Oval_J, type,
    list_val : $tType).
thf(ty_n_t__Set__Oset_It__Value__Oval_J, type,
    set_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 (187)
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_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_HOL_OThe_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,
    the_Pr958633775on_val : (produc515445032on_val > $o) > produc515445032on_val).
thf(sy_c_HOL_OThe_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,
    the_Pr506350027on_val : (produc1097884484on_val > $o) > produc1097884484on_val).
thf(sy_c_HOL_OThe_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,
    the_Pr569531848t_char : (produc1294284815t_char > $o) > produc1294284815t_char).
thf(sy_c_HOL_OThe_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,
    the_Pr1281698161on_val : (produc266837688on_val > $o) > produc266837688on_val).
thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J_J, type,
    the_Pr646501086t_char : (produc1259892823t_char > $o) > produc1259892823t_char).
thf(sy_c_HOL_OThe_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,
    the_Pr779199278on_val : (produc1172664615on_val > $o) > produc1172664615on_val).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
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_List_Olist_Oset_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    set_exp_list_char2 : list_exp_list_char > set_exp_list_char).
thf(sy_c_List_Olist_Oset_001t__Value__Oval, type,
    set_val2 : list_val > set_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,
    size_s2008079621t_char : list_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Type__Oty_J, type,
    size_size_list_ty : list_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
    size_size_list_val : list_val > nat).
thf(sy_c_Option_Ocombine__options_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,
    combin1801280889on_val : (produc266837688on_val > produc266837688on_val > produc266837688on_val) > option2118145160on_val > option2118145160on_val > option2118145160on_val).
thf(sy_c_Option_Ois__none_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,
    is_non1389277148on_val : option2118145160on_val > $o).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    some_P731082428t_char : produc1046206039t_char > option2098574493t_char).
thf(sy_c_Option_Ooption_Ocase__option_001t__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_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,
    case_o815592781on_val : option2118145160on_val > (produc266837688on_val > option2118145160on_val) > option2118145160on_val > option2118145160on_val).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc746553401on_val : (list_char > option_val) > (list_char > option_val) > produc1335728385on_val).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc69550944on_val : (list_char > option_val) > (nat > option2118145160on_val) > produc761789224on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__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, type,
    produc1392944775on_val : (nat > option2118145160on_val) > (nat > option2118145160on_val) > produc1914020559on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc797901719on_val : (produc1257910179t_char > option_val) > (produc1257910179t_char > option_val) > produc1731226791on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_001t__List__Olist_It__String__Ochar_J, type,
    produc868513902t_char : (produc1257910179t_char > option_val) > list_char > produc1072314740t_char).
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,
    produc240508503t_char : exp_list_char > exp_list_char > produc677445863t_char).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    produc210186981t_char : exp_list_char > list_list_char > produc279182059t_char).
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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_OSigma_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
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thf(sy_c_Product__Type_OSigma_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
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thf(sy_c_Product__Type_OSigma_001t__Expr__Oexp_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_Oprod_Ocase__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_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_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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    member605104934t_char : produc1294284815t_char > set_Pr2063914181t_char > $o).
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    member725442668t_char : produc1410698691t_char > set_Pr2117892643t_char > $o).
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    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_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).
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    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_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__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member197592058on_val : produc1085126737on_val > set_Pr2110063281on_val > $o).
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    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_M____, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T_H____, type,
    t : ty).
thf(sy_v_T____, type,
    t2 : ty).
thf(sy_v_Ts____, type,
    ts : list_ty).
thf(sy_v_a____, type,
    a : nat).
thf(sy_v_body____, type,
    body : exp_list_char).
thf(sy_v_fs____, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_la____, type,
    la : list_char > option_val).
thf(sy_v_pns____, type,
    pns : list_list_char).
thf(sy_v_vs____, type,
    vs : list_val).

% Relevant facts (238)
thf(fact_0_RedCall_Ohyps_I1_J, axiom,
    (((hp @ (produc52622304on_val @ ha @ la) @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % RedCall.hyps(1)
thf(fact_1_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_2_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_3_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_4_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_5_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_6_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_7_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_8_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_9_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_10_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_11_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_12_surj__pair, axiom,
    ((![P : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y : list_char > option_val]: (P = (produc52622304on_val @ X @ Y)))))). % surj_pair
thf(fact_13_surj__pair, axiom,
    ((![P : produc266837688on_val]: (?[X : list_char, Y : produc1257910179t_char > option_val]: (P = (produc904988266on_val @ X @ Y)))))). % surj_pair
thf(fact_14_surj__pair, axiom,
    ((![P : produc1294284815t_char]: (?[X : list_list_char, Y : exp_list_char]: (P = (produc713467969t_char @ X @ Y)))))). % surj_pair
thf(fact_15_surj__pair, axiom,
    ((![P : produc1172664615on_val]: (?[X : produc1097884484on_val, Y : produc1097884484on_val]: (P = (produc1069526295on_val @ X @ Y)))))). % surj_pair
thf(fact_16_surj__pair, axiom,
    ((![P : produc1097884484on_val]: (?[X : exp_list_char, Y : produc515445032on_val]: (P = (produc2023458740on_val @ X @ Y)))))). % surj_pair
thf(fact_17_prod__cases, axiom,
    ((![P2 : produc515445032on_val > $o, P : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P2 @ (produc52622304on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_18_prod__cases, axiom,
    ((![P2 : produc266837688on_val > $o, P : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P2 @ (produc904988266on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_19_prod__cases, axiom,
    ((![P2 : produc1294284815t_char > $o, P : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P2 @ (produc713467969t_char @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_20_prod__cases, axiom,
    ((![P2 : produc1172664615on_val > $o, P : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P2 @ (produc1069526295on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_21_prod__cases, axiom,
    ((![P2 : produc1097884484on_val > $o, P : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P2 @ (produc2023458740on_val @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_22_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_23_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_24_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_25_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_26_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_27_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_28_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_29_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_30_prod__induct3, axiom,
    ((![P2 : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (P2 @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C)))) => (P2 @ X3))))). % prod_induct3
thf(fact_31_prod__induct3, axiom,
    ((![P2 : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P2 @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P2 @ X3))))). % prod_induct3
thf(fact_32_old_Oprod_Oinducts, axiom,
    ((![P2 : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P2 @ (produc52622304on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_33_old_Oprod_Oinducts, axiom,
    ((![P2 : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (P2 @ (produc904988266on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_34_old_Oprod_Oinducts, axiom,
    ((![P2 : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P2 @ (produc713467969t_char @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_35_old_Oprod_Oinducts, axiom,
    ((![P2 : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P2 @ (produc1069526295on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_36_old_Oprod_Oinducts, axiom,
    ((![P2 : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P2 @ (produc2023458740on_val @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_38_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc266837688on_val]: (~ ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y3 = (produc904988266on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1294284815t_char]: (~ ((![A3 : list_list_char, B3 : exp_list_char]: (~ ((Y3 = (produc713467969t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_40_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_41_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_42_prod__induct4, axiom,
    ((![P2 : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P2 @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D))))) => (P2 @ X3))))). % prod_induct4
thf(fact_43_ssubst__Pair__rhs, axiom,
    ((![R : nat > option2118145160on_val, S : list_char > option_val, R2 : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R @ S) @ R2) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_44_ssubst__Pair__rhs, axiom,
    ((![R : list_char, S : produc1257910179t_char > option_val, R2 : set_Pr2075231726on_val, S2 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ R @ S) @ R2) => ((S2 = S) => (member1296415951on_val @ (produc904988266on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_45_ssubst__Pair__rhs, axiom,
    ((![R : list_list_char, S : exp_list_char, R2 : set_Pr2063914181t_char, S2 : exp_list_char]: ((member605104934t_char @ (produc713467969t_char @ R @ S) @ R2) => ((S2 = S) => (member605104934t_char @ (produc713467969t_char @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_46_ssubst__Pair__rhs, axiom,
    ((![R : produc1097884484on_val, S : produc1097884484on_val, R2 : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R @ S) @ R2) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_47_ssubst__Pair__rhs, axiom,
    ((![R : exp_list_char, S : produc515445032on_val, R2 : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R @ S) @ R2) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_48_RedCall_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % RedCall.prems(1)
thf(fact_49_curryI, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ (produc52622304on_val @ A @ B)) => (produc761261956_val_o @ F @ A @ B))))). % curryI
thf(fact_50_curryI, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((F @ (produc904988266on_val @ A @ B)) => (produc988598624_val_o @ F @ A @ B))))). % curryI
thf(fact_51_curryI, axiom,
    ((![F : produc1294284815t_char > $o, A : list_list_char, B : exp_list_char]: ((F @ (produc713467969t_char @ A @ B)) => (produc1697235145char_o @ F @ A @ B))))). % curryI
thf(fact_52_curryI, axiom,
    ((![F : produc1172664615on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((F @ (produc1069526295on_val @ A @ B)) => (produc360843917_val_o @ F @ A @ B))))). % curryI
thf(fact_53_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ (produc2023458740on_val @ A @ B)) => (produc699483184_val_o @ F @ A @ B))))). % curryI
thf(fact_54_combine__options__simps_I3_J, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, A : produc266837688on_val, B : produc266837688on_val]: ((combin1801280889on_val @ F @ (some_P1299442195on_val @ A) @ (some_P1299442195on_val @ B)) = (some_P1299442195on_val @ (F @ A @ B)))))). % combine_options_simps(3)
thf(fact_55_swap__simp, axiom,
    ((![X3 : list_char > option_val, Y3 : nat > option2118145160on_val]: ((produc1513644288on_val @ (produc69550944on_val @ X3 @ Y3)) = (produc52622304on_val @ Y3 @ X3))))). % swap_simp
thf(fact_56_swap__simp, axiom,
    ((![X3 : produc1257910179t_char > option_val, Y3 : list_char]: ((produc1890673358t_char @ (produc868513902t_char @ X3 @ Y3)) = (produc904988266on_val @ Y3 @ X3))))). % swap_simp
thf(fact_57_swap__simp, axiom,
    ((![X3 : exp_list_char, Y3 : list_list_char]: ((produc44907845t_char @ (produc210186981t_char @ X3 @ Y3)) = (produc713467969t_char @ Y3 @ X3))))). % swap_simp
thf(fact_58_swap__simp, axiom,
    ((![X3 : produc515445032on_val, Y3 : exp_list_char]: ((produc1741453146t_char @ (produc701409722t_char @ X3 @ Y3)) = (produc2023458740on_val @ Y3 @ X3))))). % swap_simp
thf(fact_59_swap__simp, axiom,
    ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((produc1496715648on_val @ (produc52622304on_val @ X3 @ Y3)) = (produc69550944on_val @ Y3 @ X3))))). % swap_simp
thf(fact_60_swap__simp, axiom,
    ((![X3 : list_char, Y3 : produc1257910179t_char > option_val]: ((produc1927147722on_val @ (produc904988266on_val @ X3 @ Y3)) = (produc868513902t_char @ Y3 @ X3))))). % swap_simp
thf(fact_61_swap__simp, axiom,
    ((![X3 : list_list_char, Y3 : exp_list_char]: ((produc548188833t_char @ (produc713467969t_char @ X3 @ Y3)) = (produc210186981t_char @ Y3 @ X3))))). % swap_simp
thf(fact_62_swap__simp, axiom,
    ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((produc976177847on_val @ (produc1069526295on_val @ X3 @ Y3)) = (produc1069526295on_val @ Y3 @ X3))))). % swap_simp
thf(fact_63_swap__simp, axiom,
    ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((produc916018516on_val @ (produc2023458740on_val @ X3 @ Y3)) = (produc701409722t_char @ Y3 @ X3))))). % swap_simp
thf(fact_64_is__none__code_I2_J, axiom,
    ((![X3 : produc266837688on_val]: (~ ((is_non1389277148on_val @ (some_P1299442195on_val @ X3))))))). % is_none_code(2)
thf(fact_65_is__none__simps_I2_J, axiom,
    ((![X3 : produc266837688on_val]: (~ ((is_non1389277148on_val @ (some_P1299442195on_val @ X3))))))). % is_none_simps(2)
thf(fact_66_curryD, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc761261956_val_o @ F @ A @ B) => (F @ (produc52622304on_val @ A @ B)))))). % curryD
thf(fact_67_curryD, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc988598624_val_o @ F @ A @ B) => (F @ (produc904988266on_val @ A @ B)))))). % curryD
thf(fact_68_curryD, axiom,
    ((![F : produc1294284815t_char > $o, A : list_list_char, B : exp_list_char]: ((produc1697235145char_o @ F @ A @ B) => (F @ (produc713467969t_char @ A @ B)))))). % curryD
thf(fact_69_curryD, axiom,
    ((![F : produc1172664615on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc360843917_val_o @ F @ A @ B) => (F @ (produc1069526295on_val @ A @ B)))))). % curryD
thf(fact_70_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc699483184_val_o @ F @ A @ B) => (F @ (produc2023458740on_val @ A @ B)))))). % curryD
thf(fact_71_curryE, axiom,
    ((![F : produc515445032on_val > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc761261956_val_o @ F @ A @ B) => (F @ (produc52622304on_val @ A @ B)))))). % curryE
thf(fact_72_curryE, axiom,
    ((![F : produc266837688on_val > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc988598624_val_o @ F @ A @ B) => (F @ (produc904988266on_val @ A @ B)))))). % curryE
thf(fact_73_curryE, axiom,
    ((![F : produc1294284815t_char > $o, A : list_list_char, B : exp_list_char]: ((produc1697235145char_o @ F @ A @ B) => (F @ (produc713467969t_char @ A @ B)))))). % curryE
thf(fact_74_curryE, axiom,
    ((![F : produc1172664615on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc360843917_val_o @ F @ A @ B) => (F @ (produc1069526295on_val @ A @ B)))))). % curryE
thf(fact_75_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc699483184_val_o @ F @ A @ B) => (F @ (produc2023458740on_val @ A @ B)))))). % curryE
thf(fact_76_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_77_pred__equals__eq2, axiom,
    ((![R2 : set_Pr723149704on_val, S3 : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ R2))) = (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_78_pred__equals__eq2, axiom,
    ((![R2 : set_Pr2075231726on_val, S3 : set_Pr2075231726on_val]: (((^[X4 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y4) @ R2))) = (^[X4 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X4 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_79_pred__equals__eq2, axiom,
    ((![R2 : set_Pr2063914181t_char, S3 : set_Pr2063914181t_char]: (((^[X4 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X4 @ Y4) @ R2))) = (^[X4 : list_list_char]: (^[Y4 : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X4 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_80_pred__equals__eq2, axiom,
    ((![R2 : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ R2))) = (^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_81_pred__equals__eq2, axiom,
    ((![R2 : set_Pr556513572on_val, S3 : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ R2))) = (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_82_combine__options__def, axiom,
    ((combin1801280889on_val = (^[F2 : produc266837688on_val > produc266837688on_val > produc266837688on_val]: (^[X4 : option2118145160on_val]: (^[Y4 : option2118145160on_val]: (case_o815592781on_val @ Y4 @ (^[Z : produc266837688on_val]: (case_o815592781on_val @ (some_P1299442195on_val @ Z) @ (^[Aa : produc266837688on_val]: (some_P1299442195on_val @ (F2 @ Z @ Aa))) @ Y4)) @ X4))))))). % combine_options_def
thf(fact_83_RedCall_Ohyps_I2_J, axiom,
    ((method297381284t_char @ p @ c @ m @ ts @ t2 @ (produc713467969t_char @ pns @ body) @ d))). % RedCall.hyps(2)
thf(fact_84_pair__in__swap__image, axiom,
    ((![Y3 : list_char > option_val, X3 : nat > option2118145160on_val, A4 : set_Pr723149704on_val]: ((member898386001on_val @ (produc69550944on_val @ Y3 @ X3) @ (image_214583813on_val @ produc1496715648on_val @ A4)) = (member652041809on_val @ (produc52622304on_val @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_85_pair__in__swap__image, axiom,
    ((![Y3 : produc1257910179t_char > option_val, X3 : list_char, A4 : set_Pr2075231726on_val]: ((member2101893003t_char @ (produc868513902t_char @ Y3 @ X3) @ (image_1498727091t_char @ produc1927147722on_val @ A4)) = (member1296415951on_val @ (produc904988266on_val @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_86_pair__in__swap__image, axiom,
    ((![Y3 : exp_list_char, X3 : list_list_char, A4 : set_Pr2063914181t_char]: ((member1737485826t_char @ (produc210186981t_char @ Y3 @ X3) @ (image_1472541441t_char @ produc548188833t_char @ A4)) = (member605104934t_char @ (produc713467969t_char @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_87_pair__in__swap__image, axiom,
    ((![Y3 : produc515445032on_val, X3 : exp_list_char, A4 : set_Pr556513572on_val]: ((member2023203443t_char @ (produc701409722t_char @ Y3 @ X3) @ (image_874312203t_char @ produc916018516on_val @ A4)) = (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_88_pair__in__swap__image, axiom,
    ((![Y3 : nat > option2118145160on_val, X3 : list_char > option_val, A4 : set_Pr2096385416on_val]: ((member652041809on_val @ (produc52622304on_val @ Y3 @ X3) @ (image_775878149on_val @ produc1513644288on_val @ A4)) = (member898386001on_val @ (produc69550944on_val @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_89_pair__in__swap__image, axiom,
    ((![Y3 : list_char, X3 : produc1257910179t_char > option_val, A4 : set_Pr2090500778t_char]: ((member1296415951on_val @ (produc904988266on_val @ Y3 @ X3) @ (image_1552464051on_val @ produc1890673358t_char @ A4)) = (member2101893003t_char @ (produc868513902t_char @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_90_pair__in__swap__image, axiom,
    ((![Y3 : list_list_char, X3 : exp_list_char, A4 : set_Pr1402464673t_char]: ((member605104934t_char @ (produc713467969t_char @ Y3 @ X3) @ (image_382029057t_char @ produc44907845t_char @ A4)) = (member1737485826t_char @ (produc210186981t_char @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_91_pair__in__swap__image, axiom,
    ((![Y3 : produc1097884484on_val, X3 : produc1097884484on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ X3) @ (image_1861309381on_val @ produc976177847on_val @ A4)) = (member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_92_pair__in__swap__image, axiom,
    ((![Y3 : exp_list_char, X3 : produc515445032on_val, A4 : set_Pr1601667242t_char]: ((member1888679917on_val @ (produc2023458740on_val @ Y3 @ X3) @ (image_381354367on_val @ produc1741453146t_char @ A4)) = (member2023203443t_char @ (produc701409722t_char @ X3 @ Y3) @ A4))))). % pair_in_swap_image
thf(fact_93_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P2 : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_94_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_95_The__split__eq, axiom,
    ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((the_Pr958633775on_val @ (produc99536995_val_o @ (^[X5 : nat > option2118145160on_val]: (^[Y5 : list_char > option_val]: (((X3 = X5)) & ((Y3 = Y5))))))) = (produc52622304on_val @ X3 @ Y3))))). % The_split_eq
thf(fact_96_The__split__eq, axiom,
    ((![X3 : list_char, Y3 : produc1257910179t_char > option_val]: ((the_Pr1281698161on_val @ (produc1336856385_val_o @ (^[X5 : list_char]: (^[Y5 : produc1257910179t_char > option_val]: (((X3 = X5)) & ((Y3 = Y5))))))) = (produc904988266on_val @ X3 @ Y3))))). % The_split_eq
thf(fact_97_The__split__eq, axiom,
    ((![X3 : list_list_char, Y3 : exp_list_char]: ((the_Pr569531848t_char @ (produc1163547050char_o @ (^[X5 : list_list_char]: (^[Y5 : exp_list_char]: (((X3 = X5)) & ((Y3 = Y5))))))) = (produc713467969t_char @ X3 @ Y3))))). % The_split_eq
thf(fact_98_The__split__eq, axiom,
    ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((the_Pr779199278on_val @ (produc50362220_val_o @ (^[X5 : produc1097884484on_val]: (^[Y5 : produc1097884484on_val]: (((X3 = X5)) & ((Y3 = Y5))))))) = (produc1069526295on_val @ X3 @ Y3))))). % The_split_eq
thf(fact_99_The__split__eq, axiom,
    ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((the_Pr506350027on_val @ (produc199145871_val_o @ (^[X5 : exp_list_char]: (^[Y5 : produc515445032on_val]: (((X3 = X5)) & ((Y3 = Y5))))))) = (produc2023458740on_val @ X3 @ Y3))))). % The_split_eq
thf(fact_100_case__prodI2, axiom,
    ((![P : produc515445032on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P = (produc52622304on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc99536995_val_o @ C2 @ P))))). % case_prodI2
thf(fact_101_case__prodI2, axiom,
    ((![P : produc266837688on_val, C2 : list_char > (produc1257910179t_char > option_val) > $o]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((P = (produc904988266on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc1336856385_val_o @ C2 @ P))))). % case_prodI2
thf(fact_102_case__prodI2, axiom,
    ((![P : produc1294284815t_char, C2 : list_list_char > exp_list_char > $o]: ((![A3 : list_list_char, B3 : exp_list_char]: ((P = (produc713467969t_char @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc1163547050char_o @ C2 @ P))))). % case_prodI2
thf(fact_103_case__prodI2, axiom,
    ((![P : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P = (produc1069526295on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc50362220_val_o @ C2 @ P))))). % case_prodI2
thf(fact_104_case__prodI2, axiom,
    ((![P : produc1097884484on_val, C2 : exp_list_char > produc515445032on_val > $o]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P = (produc2023458740on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc199145871_val_o @ C2 @ P))))). % case_prodI2
thf(fact_105_case__prodI, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ A @ B) => (produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)))))). % case_prodI
thf(fact_106_case__prodI, axiom,
    ((![F : list_char > (produc1257910179t_char > option_val) > $o, A : list_char, B : produc1257910179t_char > option_val]: ((F @ A @ B) => (produc1336856385_val_o @ F @ (produc904988266on_val @ A @ B)))))). % case_prodI
thf(fact_107_case__prodI, axiom,
    ((![F : list_list_char > exp_list_char > $o, A : list_list_char, B : exp_list_char]: ((F @ A @ B) => (produc1163547050char_o @ F @ (produc713467969t_char @ A @ B)))))). % case_prodI
thf(fact_108_case__prodI, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((F @ A @ B) => (produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)))))). % case_prodI
thf(fact_109_case__prodI, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ A @ B) => (produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)))))). % case_prodI
thf(fact_110_mem__case__prodI2, axiom,
    ((![P : produc515445032on_val, Z2 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P = (produc52622304on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc1919805778on_val @ C2 @ P)))))). % mem_case_prodI2
thf(fact_111_mem__case__prodI2, axiom,
    ((![P : produc266837688on_val, Z2 : produc1172664615on_val, C2 : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val]: ((![A3 : list_char, B3 : produc1257910179t_char > option_val]: ((P = (produc904988266on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc535686448on_val @ C2 @ P)))))). % mem_case_prodI2
thf(fact_112_mem__case__prodI2, axiom,
    ((![P : produc1294284815t_char, Z2 : produc1172664615on_val, C2 : list_list_char > exp_list_char > set_Pr1189492743on_val]: ((![A3 : list_list_char, B3 : exp_list_char]: ((P = (produc713467969t_char @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc1123062041on_val @ C2 @ P)))))). % mem_case_prodI2
thf(fact_113_mem__case__prodI2, axiom,
    ((![P : produc1172664615on_val, Z2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P = (produc1069526295on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc493625819on_val @ C2 @ P)))))). % mem_case_prodI2
thf(fact_114_mem__case__prodI2, axiom,
    ((![P : produc1097884484on_val, Z2 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P = (produc2023458740on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc848217214on_val @ C2 @ P)))))). % mem_case_prodI2
thf(fact_115_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A : nat > option2118145160on_val, B : list_char > option_val]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc1919805778on_val @ C2 @ (produc52622304on_val @ A @ B))))))). % mem_case_prodI
thf(fact_116_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val, A : list_char, B : produc1257910179t_char > option_val]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc535686448on_val @ C2 @ (produc904988266on_val @ A @ B))))))). % mem_case_prodI
thf(fact_117_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : list_list_char > exp_list_char > set_Pr1189492743on_val, A : list_list_char, B : exp_list_char]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc1123062041on_val @ C2 @ (produc713467969t_char @ A @ B))))))). % mem_case_prodI
thf(fact_118_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A : produc1097884484on_val, B : produc1097884484on_val]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc493625819on_val @ C2 @ (produc1069526295on_val @ A @ B))))))). % mem_case_prodI
thf(fact_119_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc848217214on_val @ C2 @ (produc2023458740on_val @ A @ B))))))). % mem_case_prodI
thf(fact_120_pair__imageI, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : set_Pr723149704on_val, F : (nat > option2118145160on_val) > (list_char > option_val) > produc1172664615on_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ A4) => (member354538064on_val @ (F @ A @ B) @ (image_1501783044on_val @ (produc2082459250on_val @ F) @ A4)))))). % pair_imageI
thf(fact_121_pair__imageI, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : set_Pr2075231726on_val, F : list_char > (produc1257910179t_char > option_val) > produc1172664615on_val]: ((member1296415951on_val @ (produc904988266on_val @ A @ B) @ A4) => (member354538064on_val @ (F @ A @ B) @ (image_171316520on_val @ (produc116279888on_val @ F) @ A4)))))). % pair_imageI
thf(fact_122_pair__imageI, axiom,
    ((![A : list_list_char, B : exp_list_char, A4 : set_Pr2063914181t_char, F : list_list_char > exp_list_char > produc1172664615on_val]: ((member605104934t_char @ (produc713467969t_char @ A @ B) @ A4) => (member354538064on_val @ (F @ A @ B) @ (image_200103825on_val @ (produc1728909881on_val @ F) @ A4)))))). % pair_imageI
thf(fact_123_pair__imageI, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : set_Pr1189492743on_val, F : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ A4) => (member354538064on_val @ (F @ A @ B) @ (image_1861309381on_val @ (produc64793339on_val @ F) @ A4)))))). % pair_imageI
thf(fact_124_pair__imageI, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : set_Pr556513572on_val, F : exp_list_char > produc515445032on_val > produc1172664615on_val]: ((member1888679917on_val @ (produc2023458740on_val @ A @ B) @ A4) => (member354538064on_val @ (F @ A @ B) @ (image_34876904on_val @ (produc174283166on_val @ F) @ A4)))))). % pair_imageI
thf(fact_125_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P : produc515445032on_val]: ((member354538064on_val @ Z2 @ (produc1919805778on_val @ C2 @ P)) => (~ ((![X : nat > option2118145160on_val, Y : list_char > option_val]: ((P = (produc52622304on_val @ X @ Y)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X @ Y)))))))))))). % mem_case_prodE
thf(fact_126_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val, P : produc266837688on_val]: ((member354538064on_val @ Z2 @ (produc535686448on_val @ C2 @ P)) => (~ ((![X : list_char, Y : produc1257910179t_char > option_val]: ((P = (produc904988266on_val @ X @ Y)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X @ Y)))))))))))). % mem_case_prodE
thf(fact_127_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : list_list_char > exp_list_char > set_Pr1189492743on_val, P : produc1294284815t_char]: ((member354538064on_val @ Z2 @ (produc1123062041on_val @ C2 @ P)) => (~ ((![X : list_list_char, Y : exp_list_char]: ((P = (produc713467969t_char @ X @ Y)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X @ Y)))))))))))). % mem_case_prodE
thf(fact_128_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P : produc1172664615on_val]: ((member354538064on_val @ Z2 @ (produc493625819on_val @ C2 @ P)) => (~ ((![X : produc1097884484on_val, Y : produc1097884484on_val]: ((P = (produc1069526295on_val @ X @ Y)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X @ Y)))))))))))). % mem_case_prodE
thf(fact_129_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P : produc1097884484on_val]: ((member354538064on_val @ Z2 @ (produc848217214on_val @ C2 @ P)) => (~ ((![X : exp_list_char, Y : produc515445032on_val]: ((P = (produc2023458740on_val @ X @ Y)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X @ Y)))))))))))). % mem_case_prodE
thf(fact_130_case__prodE, axiom,
    ((![C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P : produc515445032on_val]: ((produc99536995_val_o @ C2 @ P) => (~ ((![X : nat > option2118145160on_val, Y : list_char > option_val]: ((P = (produc52622304on_val @ X @ Y)) => (~ ((C2 @ X @ Y))))))))))). % case_prodE
thf(fact_131_case__prodE, axiom,
    ((![C2 : list_char > (produc1257910179t_char > option_val) > $o, P : produc266837688on_val]: ((produc1336856385_val_o @ C2 @ P) => (~ ((![X : list_char, Y : produc1257910179t_char > option_val]: ((P = (produc904988266on_val @ X @ Y)) => (~ ((C2 @ X @ Y))))))))))). % case_prodE
thf(fact_132_case__prodE, axiom,
    ((![C2 : list_list_char > exp_list_char > $o, P : produc1294284815t_char]: ((produc1163547050char_o @ C2 @ P) => (~ ((![X : list_list_char, Y : exp_list_char]: ((P = (produc713467969t_char @ X @ Y)) => (~ ((C2 @ X @ Y))))))))))). % case_prodE
thf(fact_133_case__prodE, axiom,
    ((![C2 : produc1097884484on_val > produc1097884484on_val > $o, P : produc1172664615on_val]: ((produc50362220_val_o @ C2 @ P) => (~ ((![X : produc1097884484on_val, Y : produc1097884484on_val]: ((P = (produc1069526295on_val @ X @ Y)) => (~ ((C2 @ X @ Y))))))))))). % case_prodE
thf(fact_134_case__prodE, axiom,
    ((![C2 : exp_list_char > produc515445032on_val > $o, P : produc1097884484on_val]: ((produc199145871_val_o @ C2 @ P) => (~ ((![X : exp_list_char, Y : produc515445032on_val]: ((P = (produc2023458740on_val @ X @ Y)) => (~ ((C2 @ X @ Y))))))))))). % case_prodE
thf(fact_135_case__prodD, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_136_case__prodD, axiom,
    ((![F : list_char > (produc1257910179t_char > option_val) > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc1336856385_val_o @ F @ (produc904988266on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_137_case__prodD, axiom,
    ((![F : list_list_char > exp_list_char > $o, A : list_list_char, B : exp_list_char]: ((produc1163547050char_o @ F @ (produc713467969t_char @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_138_case__prodD, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_139_case__prodD, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_140_image__eqI, axiom,
    ((![B : produc1172664615on_val, F : produc1172664615on_val > produc1172664615on_val, X3 : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((B = (F @ X3)) => ((member354538064on_val @ X3 @ A4) => (member354538064on_val @ B @ (image_1861309381on_val @ F @ A4))))))). % image_eqI
thf(fact_141_RedCall_Ohyps_I4_J, axiom,
    (((size_size_list_ty @ ts) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(4)
thf(fact_142_rev__image__eqI, axiom,
    ((![X3 : produc1172664615on_val, A4 : set_Pr1189492743on_val, B : produc1172664615on_val, F : produc1172664615on_val > produc1172664615on_val]: ((member354538064on_val @ X3 @ A4) => ((B = (F @ X3)) => (member354538064on_val @ B @ (image_1861309381on_val @ F @ A4))))))). % rev_image_eqI
thf(fact_143_imageI, axiom,
    ((![X3 : produc1172664615on_val, A4 : set_Pr1189492743on_val, F : produc1172664615on_val > produc1172664615on_val]: ((member354538064on_val @ X3 @ A4) => (member354538064on_val @ (F @ X3) @ (image_1861309381on_val @ F @ A4)))))). % imageI
thf(fact_144_imageE, axiom,
    ((![B : produc1172664615on_val, F : produc1172664615on_val > produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ B @ (image_1861309381on_val @ F @ A4)) => (~ ((![X : produc1172664615on_val]: ((B = (F @ X)) => (~ ((member354538064on_val @ X @ A4))))))))))). % imageE
thf(fact_145_Compr__image__eq, axiom,
    ((![F : produc1172664615on_val > produc1172664615on_val, A4 : set_Pr1189492743on_val, P2 : produc1172664615on_val > $o]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (((member354538064on_val @ X4 @ (image_1861309381on_val @ F @ A4))) & ((P2 @ X4))))) = (image_1861309381on_val @ F @ (collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (((member354538064on_val @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_146_RedCall_Ohyps_I3_J, axiom,
    (((size_size_list_val @ vs) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(3)
thf(fact_147_case__prod__Pair__iden, axiom,
    ((![P : produc515445032on_val]: ((produc2088825459on_val @ produc52622304on_val @ P) = P)))). % case_prod_Pair_iden
thf(fact_148_case__prod__Pair__iden, axiom,
    ((![P : produc266837688on_val]: ((produc1336886479on_val @ produc904988266on_val @ P) = P)))). % case_prod_Pair_iden
thf(fact_149_case__prod__Pair__iden, axiom,
    ((![P : produc1294284815t_char]: ((produc202207101t_char @ produc713467969t_char @ P) = P)))). % case_prod_Pair_iden
thf(fact_150_case__prod__Pair__iden, axiom,
    ((![P : produc1172664615on_val]: ((produc64793339on_val @ produc1069526295on_val @ P) = P)))). % case_prod_Pair_iden
thf(fact_151_case__prod__Pair__iden, axiom,
    ((![P : produc1097884484on_val]: ((produc1537230907on_val @ produc2023458740on_val @ P) = P)))). % case_prod_Pair_iden
thf(fact_152_sees__method__idemp, axiom,
    ((![P2 : list_P1234162913t_char, C3 : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P2 @ C3 @ M @ Ts @ T @ M2 @ D2) => (method297381284t_char @ P2 @ D2 @ M @ Ts @ T @ M2 @ D2))))). % sees_method_idemp
thf(fact_153_SigmaI, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val, B : produc1172664615on_val, B4 : produc1172664615on_val > set_Pr1189492743on_val]: ((member354538064on_val @ A @ A4) => ((member354538064on_val @ B @ (B4 @ A)) => (member208988944on_val @ (produc564964183on_val @ A @ B) @ (produc793952520on_val @ A4 @ B4))))))). % SigmaI
thf(fact_154_SigmaI, axiom,
    ((![A : nat > option2118145160on_val, A4 : set_na1254475949on_val, B : list_char > option_val, B4 : (nat > option2118145160on_val) > set_li1111183366on_val]: ((member1749232398on_val @ A @ A4) => ((member301160679on_val @ B @ (B4 @ A)) => (member652041809on_val @ (produc52622304on_val @ A @ B) @ (produc2106061969on_val @ A4 @ B4))))))). % SigmaI
thf(fact_155_SigmaI, axiom,
    ((![A : list_char, A4 : set_list_char, B : produc1257910179t_char > option_val, B4 : list_char > set_Pr1986825540on_val]: ((member_list_char @ A @ A4) => ((member1336971789on_val @ B @ (B4 @ A)) => (member1296415951on_val @ (produc904988266on_val @ A @ B) @ (produc58497785on_val @ A4 @ B4))))))). % SigmaI
thf(fact_156_SigmaI, axiom,
    ((![A : list_list_char, A4 : set_list_list_char, B : exp_list_char, B4 : list_list_char > set_exp_list_char]: ((member568250120t_char @ A @ A4) => ((member_exp_list_char @ B @ (B4 @ A)) => (member605104934t_char @ (produc713467969t_char @ A @ B) @ (produc277084624t_char @ A4 @ B4))))))). % SigmaI
thf(fact_157_SigmaI, axiom,
    ((![A : produc1097884484on_val, A4 : set_Pr556513572on_val, B : produc1097884484on_val, B4 : produc1097884484on_val > set_Pr556513572on_val]: ((member1888679917on_val @ A @ A4) => ((member1888679917on_val @ B @ (B4 @ A)) => (member354538064on_val @ (produc1069526295on_val @ A @ B) @ (produc2080530888on_val @ A4 @ B4))))))). % SigmaI
thf(fact_158_SigmaI, axiom,
    ((![A : exp_list_char, A4 : set_exp_list_char, B : produc515445032on_val, B4 : exp_list_char > set_Pr723149704on_val]: ((member_exp_list_char @ A @ A4) => ((member652041809on_val @ B @ (B4 @ A)) => (member1888679917on_val @ (produc2023458740on_val @ A @ B) @ (produc1610804197on_val @ A4 @ B4))))))). % SigmaI
thf(fact_159_mem__Sigma__iff, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A4 : set_Pr1189492743on_val, B4 : produc1172664615on_val > set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ A @ B) @ (produc793952520on_val @ A4 @ B4)) = (((member354538064on_val @ A @ A4)) & ((member354538064on_val @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_160_mem__Sigma__iff, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : set_na1254475949on_val, B4 : (nat > option2118145160on_val) > set_li1111183366on_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ (produc2106061969on_val @ A4 @ B4)) = (((member1749232398on_val @ A @ A4)) & ((member301160679on_val @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_161_mem__Sigma__iff, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : set_list_char, B4 : list_char > set_Pr1986825540on_val]: ((member1296415951on_val @ (produc904988266on_val @ A @ B) @ (produc58497785on_val @ A4 @ B4)) = (((member_list_char @ A @ A4)) & ((member1336971789on_val @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_162_mem__Sigma__iff, axiom,
    ((![A : list_list_char, B : exp_list_char, A4 : set_list_list_char, B4 : list_list_char > set_exp_list_char]: ((member605104934t_char @ (produc713467969t_char @ A @ B) @ (produc277084624t_char @ A4 @ B4)) = (((member568250120t_char @ A @ A4)) & ((member_exp_list_char @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_163_mem__Sigma__iff, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : set_Pr556513572on_val, B4 : produc1097884484on_val > set_Pr556513572on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (produc2080530888on_val @ A4 @ B4)) = (((member1888679917on_val @ A @ A4)) & ((member1888679917on_val @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_164_mem__Sigma__iff, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : set_exp_list_char, B4 : exp_list_char > set_Pr723149704on_val]: ((member1888679917on_val @ (produc2023458740on_val @ A @ B) @ (produc1610804197on_val @ A4 @ B4)) = (((member_exp_list_char @ A @ A4)) & ((member652041809on_val @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_165_in__inv__image, axiom,
    ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val, R : set_Pr1189492743on_val, F : produc1097884484on_val > produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ (inv_im130641106on_val @ R @ F)) = (member354538064on_val @ (produc1069526295on_val @ (F @ X3) @ (F @ Y3)) @ R))))). % in_inv_image
thf(fact_166_SigmaE, axiom,
    ((![C2 : produc1161703655on_val, A4 : set_Pr1189492743on_val, B4 : produc1172664615on_val > set_Pr1189492743on_val]: ((member208988944on_val @ C2 @ (produc793952520on_val @ A4 @ B4)) => (~ ((![X : produc1172664615on_val]: ((member354538064on_val @ X @ A4) => (![Y : produc1172664615on_val]: ((member354538064on_val @ Y @ (B4 @ X)) => (~ ((C2 = (produc564964183on_val @ X @ Y)))))))))))))). % SigmaE
thf(fact_167_SigmaE, axiom,
    ((![C2 : produc515445032on_val, A4 : set_na1254475949on_val, B4 : (nat > option2118145160on_val) > set_li1111183366on_val]: ((member652041809on_val @ C2 @ (produc2106061969on_val @ A4 @ B4)) => (~ ((![X : nat > option2118145160on_val]: ((member1749232398on_val @ X @ A4) => (![Y : list_char > option_val]: ((member301160679on_val @ Y @ (B4 @ X)) => (~ ((C2 = (produc52622304on_val @ X @ Y)))))))))))))). % SigmaE
thf(fact_168_SigmaE, axiom,
    ((![C2 : produc266837688on_val, A4 : set_list_char, B4 : list_char > set_Pr1986825540on_val]: ((member1296415951on_val @ C2 @ (produc58497785on_val @ A4 @ B4)) => (~ ((![X : list_char]: ((member_list_char @ X @ A4) => (![Y : produc1257910179t_char > option_val]: ((member1336971789on_val @ Y @ (B4 @ X)) => (~ ((C2 = (produc904988266on_val @ X @ Y)))))))))))))). % SigmaE
thf(fact_169_SigmaE, axiom,
    ((![C2 : produc1294284815t_char, A4 : set_list_list_char, B4 : list_list_char > set_exp_list_char]: ((member605104934t_char @ C2 @ (produc277084624t_char @ A4 @ B4)) => (~ ((![X : list_list_char]: ((member568250120t_char @ X @ A4) => (![Y : exp_list_char]: ((member_exp_list_char @ Y @ (B4 @ X)) => (~ ((C2 = (produc713467969t_char @ X @ Y)))))))))))))). % SigmaE
thf(fact_170_SigmaE, axiom,
    ((![C2 : produc1172664615on_val, A4 : set_Pr556513572on_val, B4 : produc1097884484on_val > set_Pr556513572on_val]: ((member354538064on_val @ C2 @ (produc2080530888on_val @ A4 @ B4)) => (~ ((![X : produc1097884484on_val]: ((member1888679917on_val @ X @ A4) => (![Y : produc1097884484on_val]: ((member1888679917on_val @ Y @ (B4 @ X)) => (~ ((C2 = (produc1069526295on_val @ X @ Y)))))))))))))). % SigmaE
thf(fact_171_SigmaE, axiom,
    ((![C2 : produc1097884484on_val, A4 : set_exp_list_char, B4 : exp_list_char > set_Pr723149704on_val]: ((member1888679917on_val @ C2 @ (produc1610804197on_val @ A4 @ B4)) => (~ ((![X : exp_list_char]: ((member_exp_list_char @ X @ A4) => (![Y : produc515445032on_val]: ((member652041809on_val @ Y @ (B4 @ X)) => (~ ((C2 = (produc2023458740on_val @ X @ Y)))))))))))))). % SigmaE
thf(fact_172_SigmaD1, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : set_na1254475949on_val, B4 : (nat > option2118145160on_val) > set_li1111183366on_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ (produc2106061969on_val @ A4 @ B4)) => (member1749232398on_val @ A @ A4))))). % SigmaD1
thf(fact_173_SigmaD1, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : set_list_char, B4 : list_char > set_Pr1986825540on_val]: ((member1296415951on_val @ (produc904988266on_val @ A @ B) @ (produc58497785on_val @ A4 @ B4)) => (member_list_char @ A @ A4))))). % SigmaD1
thf(fact_174_SigmaD1, axiom,
    ((![A : list_list_char, B : exp_list_char, A4 : set_list_list_char, B4 : list_list_char > set_exp_list_char]: ((member605104934t_char @ (produc713467969t_char @ A @ B) @ (produc277084624t_char @ A4 @ B4)) => (member568250120t_char @ A @ A4))))). % SigmaD1
thf(fact_175_SigmaD1, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : set_Pr556513572on_val, B4 : produc1097884484on_val > set_Pr556513572on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (produc2080530888on_val @ A4 @ B4)) => (member1888679917on_val @ A @ A4))))). % SigmaD1
thf(fact_176_SigmaD1, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : set_exp_list_char, B4 : exp_list_char > set_Pr723149704on_val]: ((member1888679917on_val @ (produc2023458740on_val @ A @ B) @ (produc1610804197on_val @ A4 @ B4)) => (member_exp_list_char @ A @ A4))))). % SigmaD1
thf(fact_177_SigmaD2, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : set_na1254475949on_val, B4 : (nat > option2118145160on_val) > set_li1111183366on_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ (produc2106061969on_val @ A4 @ B4)) => (member301160679on_val @ B @ (B4 @ A)))))). % SigmaD2
thf(fact_178_SigmaD2, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : set_list_char, B4 : list_char > set_Pr1986825540on_val]: ((member1296415951on_val @ (produc904988266on_val @ A @ B) @ (produc58497785on_val @ A4 @ B4)) => (member1336971789on_val @ B @ (B4 @ A)))))). % SigmaD2
thf(fact_179_SigmaD2, axiom,
    ((![A : list_list_char, B : exp_list_char, A4 : set_list_list_char, B4 : list_list_char > set_exp_list_char]: ((member605104934t_char @ (produc713467969t_char @ A @ B) @ (produc277084624t_char @ A4 @ B4)) => (member_exp_list_char @ B @ (B4 @ A)))))). % SigmaD2
thf(fact_180_SigmaD2, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : set_Pr556513572on_val, B4 : produc1097884484on_val > set_Pr556513572on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (produc2080530888on_val @ A4 @ B4)) => (member1888679917on_val @ B @ (B4 @ A)))))). % SigmaD2
thf(fact_181_SigmaD2, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : set_exp_list_char, B4 : exp_list_char > set_Pr723149704on_val]: ((member1888679917on_val @ (produc2023458740on_val @ A @ B) @ (produc1610804197on_val @ A4 @ B4)) => (member652041809on_val @ B @ (B4 @ A)))))). % SigmaD2
thf(fact_182_SigmaE2, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A4 : set_Pr1189492743on_val, B4 : produc1172664615on_val > set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ A @ B) @ (produc793952520on_val @ A4 @ B4)) => (~ (((member354538064on_val @ A @ A4) => (~ ((member354538064on_val @ B @ (B4 @ A))))))))))). % SigmaE2
thf(fact_183_SigmaE2, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : set_na1254475949on_val, B4 : (nat > option2118145160on_val) > set_li1111183366on_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ (produc2106061969on_val @ A4 @ B4)) => (~ (((member1749232398on_val @ A @ A4) => (~ ((member301160679on_val @ B @ (B4 @ A))))))))))). % SigmaE2
thf(fact_184_SigmaE2, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : set_list_char, B4 : list_char > set_Pr1986825540on_val]: ((member1296415951on_val @ (produc904988266on_val @ A @ B) @ (produc58497785on_val @ A4 @ B4)) => (~ (((member_list_char @ A @ A4) => (~ ((member1336971789on_val @ B @ (B4 @ A))))))))))). % SigmaE2
thf(fact_185_SigmaE2, axiom,
    ((![A : list_list_char, B : exp_list_char, A4 : set_list_list_char, B4 : list_list_char > set_exp_list_char]: ((member605104934t_char @ (produc713467969t_char @ A @ B) @ (produc277084624t_char @ A4 @ B4)) => (~ (((member568250120t_char @ A @ A4) => (~ ((member_exp_list_char @ B @ (B4 @ A))))))))))). % SigmaE2
thf(fact_186_SigmaE2, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : set_Pr556513572on_val, B4 : produc1097884484on_val > set_Pr556513572on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (produc2080530888on_val @ A4 @ B4)) => (~ (((member1888679917on_val @ A @ A4) => (~ ((member1888679917on_val @ B @ (B4 @ A))))))))))). % SigmaE2
thf(fact_187_SigmaE2, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : set_exp_list_char, B4 : exp_list_char > set_Pr723149704on_val]: ((member1888679917on_val @ (produc2023458740on_val @ A @ B) @ (produc1610804197on_val @ A4 @ B4)) => (~ (((member_exp_list_char @ A @ A4) => (~ ((member652041809on_val @ B @ (B4 @ A))))))))))). % SigmaE2
thf(fact_188_swap__product, axiom,
    ((![A4 : set_li1111183366on_val, B4 : set_na1254475949on_val]: ((image_775878149on_val @ (produc702841587on_val @ (^[I : list_char > option_val]: (^[J : nat > option2118145160on_val]: (produc52622304on_val @ J @ I)))) @ (produc2122990609on_val @ A4 @ (^[Uu : list_char > option_val]: B4))) = (produc2106061969on_val @ B4 @ (^[Uu : nat > option2118145160on_val]: A4)))))). % swap_product
thf(fact_189_swap__product, axiom,
    ((![A4 : set_Pr1986825540on_val, B4 : set_list_char]: ((image_1552464051on_val @ (produc1270390995on_val @ (^[I : produc1257910179t_char > option_val]: (^[J : list_char]: (produc904988266on_val @ J @ I)))) @ (produc22023421t_char @ A4 @ (^[Uu : produc1257910179t_char > option_val]: B4))) = (produc58497785on_val @ B4 @ (^[Uu : list_char]: A4)))))). % swap_product
thf(fact_190_swap__product, axiom,
    ((![A4 : set_exp_list_char, B4 : set_list_list_char]: ((image_382029057t_char @ (produc1007951905t_char @ (^[I : exp_list_char]: (^[J : list_list_char]: (produc713467969t_char @ J @ I)))) @ (produc1921287284t_char @ A4 @ (^[Uu : exp_list_char]: B4))) = (produc277084624t_char @ B4 @ (^[Uu : list_list_char]: A4)))))). % swap_product
thf(fact_191_swap__product, axiom,
    ((![A4 : set_Pr556513572on_val, B4 : set_Pr556513572on_val]: ((image_1861309381on_val @ (produc64793339on_val @ (^[I : produc1097884484on_val]: (^[J : produc1097884484on_val]: (produc1069526295on_val @ J @ I)))) @ (produc2080530888on_val @ A4 @ (^[Uu : produc1097884484on_val]: B4))) = (produc2080530888on_val @ B4 @ (^[Uu : produc1097884484on_val]: A4)))))). % swap_product
thf(fact_192_swap__product, axiom,
    ((![A4 : set_Pr723149704on_val, B4 : set_exp_list_char]: ((image_381354367on_val @ (produc357444277on_val @ (^[I : produc515445032on_val]: (^[J : exp_list_char]: (produc2023458740on_val @ J @ I)))) @ (produc288755179t_char @ A4 @ (^[Uu : produc515445032on_val]: B4))) = (produc1610804197on_val @ B4 @ (^[Uu : exp_list_char]: A4)))))). % swap_product
thf(fact_193_sees__method__fun, axiom,
    ((![P2 : list_P1234162913t_char, C3 : list_char, M : list_char, TS : list_ty, T : ty, M2 : produc1294284815t_char, D2 : list_char, TS2 : list_ty, T2 : ty, M3 : produc1294284815t_char, D3 : list_char]: ((method297381284t_char @ P2 @ C3 @ M @ TS @ T @ M2 @ D2) => ((method297381284t_char @ P2 @ C3 @ M @ TS2 @ T2 @ M3 @ D3) => ((TS2 = TS) & ((T2 = T) & ((M3 = M2) & (D3 = D2))))))))). % sees_method_fun
thf(fact_194_has__method__def, axiom,
    ((has_me170134744t_char = (^[P3 : list_P1234162913t_char]: (^[C4 : list_char]: (^[M4 : list_char]: (?[Ts2 : list_ty]: (?[T3 : ty]: (?[M5 : produc1294284815t_char]: (?[X6 : list_char]: (method297381284t_char @ P3 @ C4 @ M4 @ Ts2 @ T3 @ M5 @ X6))))))))))). % has_method_def
thf(fact_195_method__def2, axiom,
    ((![P2 : list_P1234162913t_char, C3 : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D2 : list_char]: ((method297381284t_char @ P2 @ C3 @ M @ Ts @ T @ M2 @ D2) => ((method667690372t_char @ P2 @ C3 @ M) = (produc1238538255t_char @ D2 @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2)))))))). % method_def2
thf(fact_196_method__def, axiom,
    ((method667690372t_char = (^[P3 : list_P1234162913t_char]: (^[C4 : list_char]: (^[M4 : list_char]: (the_Pr646501086t_char @ (produc995854452char_o @ (^[D4 : list_char]: (produc182021412char_o @ (^[Ts2 : list_ty]: (produc1433497764char_o @ (^[T3 : ty]: (^[M5 : produc1294284815t_char]: (method297381284t_char @ P3 @ C4 @ M4 @ Ts2 @ T3 @ M5 @ D4))))))))))))))). % method_def
thf(fact_197_sees__wf__mdecl, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P2 : list_P1234162913t_char, C3 : list_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D2 : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P2) => ((method297381284t_char @ P2 @ C3 @ M @ Ts @ T @ M2 @ D2) => (wf_mde297024346t_char @ Wf_md @ P2 @ D2 @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2))))))))). % sees_wf_mdecl
thf(fact_198_Method__code, axiom,
    ((![P2 : list_P1234162913t_char, C3 : list_char, Mm : list_char > option2098574493t_char, M : list_char, Ts : list_ty, T : ty, M2 : produc1294284815t_char, D2 : list_char]: ((method527166639t_char @ P2 @ C3 @ Mm) => (((Mm @ M) = (some_P731082428t_char @ (produc1514622991t_char @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M2)) @ D2))) => (method297381284t_char @ P2 @ C3 @ M @ Ts @ T @ M2 @ D2)))))). % Method_code
thf(fact_199_Method__def, axiom,
    ((method297381284t_char = (^[P3 : list_P1234162913t_char]: (^[C4 : list_char]: (^[M4 : list_char]: (^[Ts2 : list_ty]: (^[T3 : ty]: (^[M5 : produc1294284815t_char]: (^[D4 : list_char]: (?[Mm2 : list_char > option2098574493t_char]: (((method527166639t_char @ P3 @ C4 @ Mm2)) & (((Mm2 @ M4) = (some_P731082428t_char @ (produc1514622991t_char @ (produc1730359111t_char @ Ts2 @ (produc248075743t_char @ T3 @ M5)) @ D4)))))))))))))))). % Method_def
thf(fact_200_member__product, axiom,
    ((![X3 : produc1172664615on_val, A4 : set_Pr556513572on_val, B4 : set_Pr556513572on_val]: ((member354538064on_val @ X3 @ (produc1808404178on_val @ A4 @ B4)) = (member354538064on_val @ X3 @ (produc2080530888on_val @ A4 @ (^[Uu : produc1097884484on_val]: B4))))))). % member_product
thf(fact_201_same__fstI, axiom,
    ((![P2 : (nat > option2118145160on_val) > $o, X3 : nat > option2118145160on_val, Y6 : list_char > option_val, Y3 : list_char > option_val, R2 : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P2 @ X3) => ((member1177709994on_val @ (produc746553401on_val @ Y6 @ Y3) @ (R2 @ X3)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X3 @ Y6) @ (produc52622304on_val @ X3 @ Y3)) @ (same_f1752972725on_val @ P2 @ R2))))))). % same_fstI
thf(fact_202_same__fstI, axiom,
    ((![P2 : list_char > $o, X3 : list_char, Y6 : produc1257910179t_char > option_val, Y3 : produc1257910179t_char > option_val, R2 : list_char > set_Pr227219079on_val]: ((P2 @ X3) => ((member548035792on_val @ (produc797901719on_val @ Y6 @ Y3) @ (R2 @ X3)) => (member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ X3 @ Y6) @ (produc904988266on_val @ X3 @ Y3)) @ (same_f2003279573on_val @ P2 @ R2))))))). % same_fstI
thf(fact_203_same__fstI, axiom,
    ((![P2 : list_list_char > $o, X3 : list_list_char, Y6 : exp_list_char, Y3 : exp_list_char, R2 : list_list_char > set_Pr224372167t_char]: ((P2 @ X3) => ((member1699993616t_char @ (produc240508503t_char @ Y6 @ Y3) @ (R2 @ X3)) => (member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ X3 @ Y6) @ (produc713467969t_char @ X3 @ Y3)) @ (same_f605082028t_char @ P2 @ R2))))))). % same_fstI
thf(fact_204_same__fstI, axiom,
    ((![P2 : exp_list_char > $o, X3 : exp_list_char, Y6 : produc515445032on_val, Y3 : produc515445032on_val, R2 : exp_list_char > set_Pr148564103on_val]: ((P2 @ X3) => ((member2027247312on_val @ (produc2106877847on_val @ Y6 @ Y3) @ (R2 @ X3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X3 @ Y6) @ (produc2023458740on_val @ X3 @ Y3)) @ (same_f366220041on_val @ P2 @ R2))))))). % same_fstI
thf(fact_205_same__fstI, axiom,
    ((![P2 : produc1097884484on_val > $o, X3 : produc1097884484on_val, Y6 : produc1097884484on_val, Y3 : produc1097884484on_val, R2 : produc1097884484on_val > set_Pr1189492743on_val]: ((P2 @ X3) => ((member354538064on_val @ (produc1069526295on_val @ Y6 @ Y3) @ (R2 @ X3)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X3 @ Y6) @ (produc1069526295on_val @ X3 @ Y3)) @ (same_f962657004on_val @ P2 @ R2))))))). % same_fstI
thf(fact_206_lex__prod__def, axiom,
    ((lex_pr186272047on_val = (^[Ra : set_Pr1189492743on_val]: (^[Rb : set_Pr1189492743on_val]: (collec608254290on_val @ (produc669005100_val_o @ (produc791746242_val_o @ (^[A5 : produc1097884484on_val]: (^[B5 : produc1097884484on_val]: (produc50362220_val_o @ (^[A6 : produc1097884484on_val]: (^[B6 : produc1097884484on_val]: (((member354538064on_val @ (produc1069526295on_val @ A5 @ A6) @ Ra)) | ((((A5 = A6)) & ((member354538064on_val @ (produc1069526295on_val @ B5 @ B6) @ Rb)))))))))))))))))). % lex_prod_def
thf(fact_207_RedCall_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ (val_list_char @ (addr @ a)) @ m @ (map_va1515327237t_char @ val_list_char @ vs)) @ t))). % RedCall.prems(2)
thf(fact_208_in__lex__prod, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val, R : set_Pr1465729071on_val, S : set_Pr1104486497on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ A2 @ B2)) @ (lex_pr683585528on_val @ R @ S)) = (((member78096504on_val @ (produc1392944775on_val @ A @ A2) @ R)) | ((((A = A2)) & ((member1177709994on_val @ (produc746553401on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_209_in__lex__prod, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A2 : list_char, B2 : produc1257910179t_char > option_val, R : set_Pr164112643t_char, S : set_Pr227219079on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A @ B) @ (produc904988266on_val @ A2 @ B2)) @ (lex_pr1753065554on_val @ R @ S)) = (((member89690956t_char @ (produc1304532571t_char @ A @ A2) @ R)) | ((((A = A2)) & ((member548035792on_val @ (produc797901719on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_210_in__lex__prod, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char, R : set_Pr2117892643t_char, S : set_Pr224372167t_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ A2 @ B2)) @ (lex_pr1444053545t_char @ R @ S)) = (((member725442668t_char @ (produc1181934459t_char @ A @ A2) @ R)) | ((((A = A2)) & ((member1699993616t_char @ (produc240508503t_char @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_211_in__lex__prod, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ A2 @ B2)) @ (lex_pr186272047on_val @ R @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A @ A2) @ R)) | ((((A = A2)) & ((member354538064on_val @ (produc1069526295on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_212_in__lex__prod, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val, R : set_Pr224372167t_char, S : set_Pr148564103on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ A2 @ B2)) @ (lex_pr1764546508on_val @ R @ S)) = (((member1699993616t_char @ (produc240508503t_char @ A @ A2) @ R)) | ((((A = A2)) & ((member2027247312on_val @ (produc2106877847on_val @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_213_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_214_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_215_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_216_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_217_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_218_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_219_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_220_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_221_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_222_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_223_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_224_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_225_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_226_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_227_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_228_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_229_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_230_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_231_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_232_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_233_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_234_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P2 : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P2)) => ((wTrt @ P2 @ (hp @ S) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P2 @ E3 @ S) => (typeSa1777264139_sconf @ P2 @ E3 @ S2))))))). % red_preserves_sconf
thf(fact_235_list_Oset__map, axiom,
    ((![F : val > exp_list_char, V : list_val]: ((set_exp_list_char2 @ (map_va1515327237t_char @ F @ V)) = (image_926780676t_char @ F @ (set_val2 @ V)))))). % list.set_map
thf(fact_236_image__set, axiom,
    ((![F : val > exp_list_char, Xs : list_val]: ((image_926780676t_char @ F @ (set_val2 @ Xs)) = (set_exp_list_char2 @ (map_va1515327237t_char @ F @ Xs)))))). % image_set
thf(fact_237_Ball__def, axiom,
    ((ball_P459159249on_val = (^[A7 : set_Pr1189492743on_val]: (^[P3 : produc1172664615on_val > $o]: (![X4 : produc1172664615on_val]: (((member354538064on_val @ X4 @ A7)) => ((P3 @ X4))))))))). % Ball_def

% Conjectures (1)
thf(conj_0, conjecture,
    (((hp @ (produc52622304on_val @ ha @ la) @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))).
