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    produc1259892823t_char : $tType).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    option2118145160on_val : $tType).
thf(ty_n_t__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__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_exp_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__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__List__Olist_It__Type__Oty_J, type,
    list_ty : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (91)
thf(sy_c_Conform_Ohconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    hconf_1244167010t_char : list_P1234162913t_char > (nat > option2118145160on_val) > $o).
thf(sy_c_Conform_Olconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    lconf_485928294t_char : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_val) > (list_char > option_ty) > $o).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
    binOp_list_char : exp_list_char > bop > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_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_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    append_exp_list_char : list_exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    cons_exp_list_char : exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
    cons_ty : ty > list_ty > list_ty).
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_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Product__Type_OPair_001_062_It__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__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    produc1725134254on_val : list_exp_list_char > produc515445032on_val > produc335961278on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2106877847on_val : produc515445032on_val > produc515445032on_val > produc744932519on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc245869591on_val : produc335961278on_val > produc335961278on_val > produc655058983on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    produc1802175319on_val : produc655058983on_val > produc655058983on_val > produc1428501223on_val).
thf(sy_c_Product__Type_Ointernal__case__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_001_Eo, type,
    produc563955725_val_o : ((nat > option2118145160on_val) > (list_char > option_val) > $o) > produc515445032on_val > $o).
thf(sy_c_Product__Type_Ointernal__case__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001_062_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_M_Eo_J, type,
    produc1326103384_val_o : (list_exp_list_char > produc515445032on_val > produc335961278on_val > $o) > produc335961278on_val > produc335961278on_val > $o).
thf(sy_c_Product__Type_Ointernal__case__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001_Eo, type,
    produc1075415231_val_o : (list_exp_list_char > produc515445032on_val > $o) > produc335961278on_val > $o).
thf(sy_c_Product__Type_Ointernal__case__prod_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001_Eo, type,
    produc463114774_val_o : (produc335961278on_val > produc335961278on_val > $o) > produc655058983on_val > $o).
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_001_062_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_M_Eo_J, type,
    produc1588213706_val_o : ((nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val > $o) > produc515445032on_val > produc515445032on_val > $o).
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_001_Eo, type,
    produc99536995_val_o : ((nat > option2118145160on_val) > (list_char > option_val) > $o) > produc515445032on_val > $o).
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,
    produc1919805778on_val : ((nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val) > produc515445032on_val > set_Pr1189492743on_val).
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__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc98852946on_val : ((nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val) > produc515445032on_val > set_Pr208351751on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_Eo, type,
    produc199145871_val_o : (exp_list_char > produc515445032on_val > $o) > produc1097884484on_val > $o).
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    produc356855678on_val : (exp_list_char > produc515445032on_val > set_Pr208351751on_val) > produc1097884484on_val > set_Pr208351751on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001_062_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_M_Eo_J, type,
    produc58203522_val_o : (list_exp_list_char > produc515445032on_val > produc335961278on_val > $o) > produc335961278on_val > produc335961278on_val > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001_Eo, type,
    produc1125182229_val_o : (list_exp_list_char > produc515445032on_val > $o) > produc335961278on_val > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_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,
    produc379229956on_val : (list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val) > produc335961278on_val > set_Pr1189492743on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc1745783812on_val : (list_exp_list_char > produc515445032on_val > set_Pr208351751on_val) > produc335961278on_val > set_Pr208351751on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_Eo, type,
    produc271780076_val_o : (produc515445032on_val > produc515445032on_val > $o) > produc744932519on_val > $o).
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    produc50362220_val_o : (produc1097884484on_val > produc1097884484on_val > $o) > produc1172664615on_val > $o).
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thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member1743964944on_val : produc1428501223on_val > set_Pr1301890247on_val > $o).
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____, type,
    t : ty).
thf(sy_v_Ts____, type,
    ts : list_ty).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    ea : exp_list_char).
thf(sy_v_esa____, type,
    esa : list_exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).

% Relevant facts (249)
thf(fact_0__092_060open_062P_ME_Mh_H_A_092_060turnstile_062_Aes_A_091_058_093_ATs_092_060close_062, axiom,
    ((wTrts @ p @ h_a @ e @ esa @ ts))). % \<open>P,E,h' \<turnstile> es [:] Ts\<close>
thf(fact_1__092_060open_062P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ANT_092_060close_062, axiom,
    ((wTrt @ p @ h_a @ e @ e_a @ nt))). % \<open>P,E,h' \<turnstile> e' : NT\<close>
thf(fact_2_wtes, axiom,
    ((wTrts @ p @ ha @ e @ esa @ ts))). % wtes
thf(fact_3_CallObj_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % CallObj.prems(2)
thf(fact_4_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % wt
thf(fact_5_exp_Oinject_I9_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, Y91 : exp_list_char, Y92 : list_char, Y93 : list_exp_list_char]: (((call_list_char @ X91 @ X92 @ X93) = (call_list_char @ Y91 @ Y92 @ Y93)) = (((X91 = Y91)) & ((((X92 = Y92)) & ((X93 = Y93))))))))). % exp.inject(9)
thf(fact_6__092_060open_062P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_092_060close_062, axiom,
    ((wTrt @ p @ ha @ e @ ea @ nt))). % \<open>P,E,h \<turnstile> e : NT\<close>
thf(fact_7_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_8_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_9_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_10_WTrtCallNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, Es : list_exp_list_char, Ts : list_ty, M : list_char, T : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))). % WTrtCallNT
thf(fact_11_CallObj_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T) => (?[T2 : ty]: ((wTrt @ p @ h_a @ E @ e_a @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % CallObj.hyps(2)
thf(fact_12_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T) => (?[U2 : ty]: ((wTrt @ p @ h_a @ E @ e_a @ U2) & (widen_917054840t_char @ p @ U2 @ T)))))))). % IH
thf(fact_13_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_14_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_15_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_16_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_17_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_18_prod_Oinject, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, Y1 : produc335961278on_val, Y2 : produc335961278on_val]: (((produc245869591on_val @ X1 @ X2) = (produc245869591on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_19_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_20_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_21_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_22_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_23_old_Oprod_Oinject, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, A2 : produc335961278on_val, B2 : produc335961278on_val]: (((produc245869591on_val @ A @ B) = (produc245869591on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_24_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_25_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_26_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ R))) = (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_27_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R))) = (^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_28_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R))) = (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_29_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X @ Y) @ R))) = (^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_30_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X @ Y) @ R))) = (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_31_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_32_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_33_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_34_surj__pair, axiom,
    ((![P2 : produc655058983on_val]: (?[X3 : produc335961278on_val, Y3 : produc335961278on_val]: (P2 = (produc245869591on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_35_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_36_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_37_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_38_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_39_prod__cases, axiom,
    ((![P : produc655058983on_val > $o, P2 : produc655058983on_val]: ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: (P @ (produc245869591on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_40_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_41_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_42_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_43_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_44_Pair__inject, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, A2 : produc335961278on_val, B2 : produc335961278on_val]: (((produc245869591on_val @ A @ B) = (produc245869591on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_45_Pair__inject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_46_prod__cases3, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (~ ((Y4 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_47_prod__cases3, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y4 = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_48_prod__cases3, axiom,
    ((![Y4 : produc655058983on_val]: (~ ((![A3 : produc335961278on_val, B3 : list_exp_list_char, C : produc515445032on_val]: (~ ((Y4 = (produc245869591on_val @ A3 @ (produc1725134254on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_49_prod__cases3, axiom,
    ((![Y4 : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y4 = (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C))))))))))). % prod_cases3
thf(fact_50_prod__cases4, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y4 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_51_prod__cases4, axiom,
    ((![Y4 : produc655058983on_val]: (~ ((![A3 : produc335961278on_val, B3 : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y4 = (produc245869591on_val @ A3 @ (produc1725134254on_val @ B3 @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_52_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_53_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_54_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_55_old_Oprod_Oinducts, axiom,
    ((![P : produc655058983on_val > $o, Prod : produc655058983on_val]: ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: (P @ (produc245869591on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_56_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_57_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y4 = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_58_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y4 = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_59_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y4 = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_60_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc655058983on_val]: (~ ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: (~ ((Y4 = (produc245869591on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_61_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (~ ((Y4 = (produc1725134254on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_62_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C @ D))))) => (P @ X4))))). % prod_induct4
thf(fact_63_prod__induct4, axiom,
    ((![P : produc655058983on_val > $o, X4 : produc655058983on_val]: ((![A3 : produc335961278on_val, B3 : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc245869591on_val @ A3 @ (produc1725134254on_val @ B3 @ (produc52622304on_val @ C @ D))))) => (P @ X4))))). % prod_induct4
thf(fact_64_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C)))) => (P @ X4))))). % prod_induct3
thf(fact_65_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X4))))). % prod_induct3
thf(fact_66_prod__induct3, axiom,
    ((![P : produc655058983on_val > $o, X4 : produc655058983on_val]: ((![A3 : produc335961278on_val, B3 : list_exp_list_char, C : produc515445032on_val]: (P @ (produc245869591on_val @ A3 @ (produc1725134254on_val @ B3 @ C)))) => (P @ X4))))). % prod_induct3
thf(fact_67_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X4 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C)))) => (P @ X4))))). % prod_induct3
thf(fact_68_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_69_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_70_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_71_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_72_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X4 : nat > option2118145160on_val, Y5 : list_char > option_val, Y4 : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X4) => ((member1177709994on_val @ (produc746553401on_val @ Y5 @ Y4) @ (R @ X4)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X4 @ Y5) @ (produc52622304on_val @ X4 @ Y4)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_73_same__fstI, axiom,
    ((![P : exp_list_char > $o, X4 : exp_list_char, Y5 : produc515445032on_val, Y4 : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X4) => ((member2027247312on_val @ (produc2106877847on_val @ Y5 @ Y4) @ (R @ X4)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y5) @ (produc2023458740on_val @ X4 @ Y4)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_74_same__fstI, axiom,
    ((![P : list_exp_list_char > $o, X4 : list_exp_list_char, Y5 : produc515445032on_val, Y4 : produc515445032on_val, R : list_exp_list_char > set_Pr148564103on_val]: ((P @ X4) => ((member2027247312on_val @ (produc2106877847on_val @ Y5 @ Y4) @ (R @ X4)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X4 @ Y5) @ (produc1725134254on_val @ X4 @ Y4)) @ (same_f1555812995on_val @ P @ R))))))). % same_fstI
thf(fact_75_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val, Y5 : produc1097884484on_val, Y4 : produc1097884484on_val, R : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X4) => ((member354538064on_val @ (produc1069526295on_val @ Y5 @ Y4) @ (R @ X4)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X4 @ Y5) @ (produc1069526295on_val @ X4 @ Y4)) @ (same_f962657004on_val @ P @ R))))))). % same_fstI
thf(fact_76_same__fstI, axiom,
    ((![P : produc335961278on_val > $o, X4 : produc335961278on_val, Y5 : produc335961278on_val, Y4 : produc335961278on_val, R : produc335961278on_val > set_Pr208351751on_val]: ((P @ X4) => ((member1689761872on_val @ (produc245869591on_val @ Y5 @ Y4) @ (R @ X4)) => (member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ X4 @ Y5) @ (produc245869591on_val @ X4 @ Y4)) @ (same_f1147886828on_val @ P @ R))))))). % same_fstI
thf(fact_77_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_78_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_79_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts @ P @ H @ E @ Es @ Ts) => ((hext @ H @ H2) => (wTrts @ P @ H2 @ E @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_80_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_81_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_82_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_83_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_84_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X : produc655058983on_val]: (member1689761872on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_85_Collect__cong, axiom,
    ((![P : produc655058983on_val > $o, Q : produc655058983on_val > $o]: ((![X3 : produc655058983on_val]: ((P @ X3) = (Q @ X3))) => ((collec105960082on_val @ P) = (collec105960082on_val @ Q)))))). % Collect_cong
thf(fact_86_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E)))))). % lconf_hext
thf(fact_87_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S2) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % reds_preserves_sconf
thf(fact_88_reds__preserves__lconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % reds_preserves_lconf
thf(fact_89_reds__preserves__hconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_90_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_91_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_92_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_93_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_94_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_95_redsp__reds__eq, axiom,
    ((redsp = (^[P3 : list_P1234162913t_char]: (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (^[Z : list_exp_list_char]: (^[Aa : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X @ Y) @ (produc1725134254on_val @ Z @ Aa)) @ (reds @ P3)))))))))). % redsp_reds_eq
thf(fact_96_red__reds_OListRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_97_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_98_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P3 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (produc99536995_val_o @ (^[H4 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (((hconf_1244167010t_char @ P3 @ H4)) & ((lconf_485928294t_char @ P3 @ H4 @ L3 @ E4))))))))))). % sconf_def
thf(fact_99_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_100_split__part, axiom,
    ((![P : $o, Q : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((produc99536995_val_o @ (^[A5 : nat > option2118145160on_val]: (^[B4 : list_char > option_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc515445032on_val]: ((P) & ((produc99536995_val_o @ Q @ Ab)))))))). % split_part
thf(fact_101_split__part, axiom,
    ((![P : $o, Q : produc335961278on_val > produc335961278on_val > $o]: ((produc525028460_val_o @ (^[A5 : produc335961278on_val]: (^[B4 : produc335961278on_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc655058983on_val]: ((P) & ((produc525028460_val_o @ Q @ Ab)))))))). % split_part
thf(fact_102_split__part, axiom,
    ((![P : $o, Q : list_exp_list_char > produc515445032on_val > $o]: ((produc1125182229_val_o @ (^[A5 : list_exp_list_char]: (^[B4 : produc515445032on_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc335961278on_val]: ((P) & ((produc1125182229_val_o @ Q @ Ab)))))))). % split_part
thf(fact_103_case__prod__conv, 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_prod_conv
thf(fact_104_case__prod__conv, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, A : produc335961278on_val, B : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_105_case__prod__conv, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((produc58203522_val_o @ F @ (produc1725134254on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_106_case__prod__conv, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_107_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_108_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_109_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_110_case__prodI, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, A : produc335961278on_val, B : produc335961278on_val]: ((F @ A @ B) => (produc525028460_val_o @ F @ (produc245869591on_val @ A @ B)))))). % case_prodI
thf(fact_111_case__prodI, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((F @ A @ B) => (produc1125182229_val_o @ F @ (produc1725134254on_val @ A @ B)))))). % case_prodI
thf(fact_112_case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc50362220_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_113_case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, C2 : exp_list_char > produc515445032on_val > $o]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc199145871_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_114_case__prodI2, axiom,
    ((![P2 : produc515445032on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P2 = (produc52622304on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc99536995_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_115_case__prodI2, axiom,
    ((![P2 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > $o]: ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc525028460_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_116_case__prodI2, axiom,
    ((![P2 : produc335961278on_val, C2 : list_exp_list_char > produc515445032on_val > $o]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A3 @ B3)) => (C2 @ A3 @ B3))) => (produc1125182229_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_117_prod_Odisc__eq__case, axiom,
    ((![Prod : produc515445032on_val]: (produc99536995_val_o @ (^[Uu : nat > option2118145160on_val]: (^[Uv : list_char > option_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_118_prod_Odisc__eq__case, axiom,
    ((![Prod : produc655058983on_val]: (produc525028460_val_o @ (^[Uu : produc335961278on_val]: (^[Uv : produc335961278on_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_119_prod_Odisc__eq__case, axiom,
    ((![Prod : produc335961278on_val]: (produc1125182229_val_o @ (^[Uu : list_exp_list_char]: (^[Uv : produc515445032on_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_120_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, Prod : produc515445032on_val]: ((H @ (produc99536995_val_o @ F @ Prod)) = (produc99536995_val_o @ (^[X12 : nat > option2118145160on_val]: (^[X22 : list_char > option_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_121_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : produc335961278on_val > produc335961278on_val > $o, Prod : produc655058983on_val]: ((H @ (produc525028460_val_o @ F @ Prod)) = (produc525028460_val_o @ (^[X12 : produc335961278on_val]: (^[X22 : produc335961278on_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_122_prod_Ocase__distrib, axiom,
    ((![H : (produc335961278on_val > $o) > produc335961278on_val > $o, F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Prod : produc335961278on_val]: ((H @ (produc58203522_val_o @ F @ Prod)) = (produc58203522_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_123_prod_Ocase__distrib, axiom,
    ((![H : (produc335961278on_val > $o) > $o, F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Prod : produc335961278on_val]: ((H @ (produc58203522_val_o @ F @ Prod)) = (produc1125182229_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_124_prod_Ocase__distrib, axiom,
    ((![H : $o > produc335961278on_val > $o, F : list_exp_list_char > produc515445032on_val > $o, Prod : produc335961278on_val]: ((H @ (produc1125182229_val_o @ F @ Prod)) = (produc58203522_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_125_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : list_exp_list_char > produc515445032on_val > $o, Prod : produc335961278on_val]: ((H @ (produc1125182229_val_o @ F @ Prod)) = (produc1125182229_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_126_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S2 @ Es2 @ S3) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2 @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3))))). % redp_redsp.ListRed2
thf(fact_127_old_Oprod_Ocase, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, X1 : nat > option2118145160on_val, X2 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ X1 @ X2)) = (F @ X1 @ X2))))). % old.prod.case
thf(fact_128_old_Oprod_Ocase, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, X1 : produc335961278on_val, X2 : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ X1 @ X2)) = (F @ X1 @ X2))))). % old.prod.case
thf(fact_129_old_Oprod_Ocase, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X1 : list_exp_list_char, X2 : produc515445032on_val]: ((produc58203522_val_o @ F @ (produc1725134254on_val @ X1 @ X2)) = (F @ X1 @ X2))))). % old.prod.case
thf(fact_130_old_Oprod_Ocase, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, X1 : list_exp_list_char, X2 : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ X1 @ X2)) = (F @ X1 @ X2))))). % old.prod.case
thf(fact_131_exp_Odistinct_I65_J, axiom,
    ((![X32 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X32) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_132_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_133_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_134_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_135_case__prodD, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, A : produc335961278on_val, B : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_136_case__prodD, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, A : list_exp_list_char, B : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_137_case__prodE, axiom,
    ((![C2 : produc1097884484on_val > produc1097884484on_val > $o, P2 : produc1172664615on_val]: ((produc50362220_val_o @ C2 @ P2) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_138_case__prodE, axiom,
    ((![C2 : exp_list_char > produc515445032on_val > $o, P2 : produc1097884484on_val]: ((produc199145871_val_o @ C2 @ P2) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_139_case__prodE, axiom,
    ((![C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((produc99536995_val_o @ C2 @ P2) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_140_case__prodE, axiom,
    ((![C2 : produc335961278on_val > produc335961278on_val > $o, P2 : produc655058983on_val]: ((produc525028460_val_o @ C2 @ P2) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_141_case__prodE, axiom,
    ((![C2 : list_exp_list_char > produc515445032on_val > $o, P2 : produc335961278on_val]: ((produc1125182229_val_o @ C2 @ P2) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_142_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z2 : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z2)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((Z2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_143_case__prodE2, axiom,
    ((![Q : $o > $o, P : produc335961278on_val > produc335961278on_val > $o, Z2 : produc655058983on_val]: ((Q @ (produc525028460_val_o @ P @ Z2)) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((Z2 = (produc245869591on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_144_case__prodE2, axiom,
    ((![Q : (produc335961278on_val > $o) > $o, P : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Z2 : produc335961278on_val]: ((Q @ (produc58203522_val_o @ P @ Z2)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((Z2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_145_case__prodE2, axiom,
    ((![Q : $o > $o, P : list_exp_list_char > produc515445032on_val > $o, Z2 : produc335961278on_val]: ((Q @ (produc1125182229_val_o @ P @ Z2)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((Z2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_146_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (F @ (produc52622304on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_147_case__prod__eta, axiom,
    ((![F : produc655058983on_val > $o]: ((produc525028460_val_o @ (^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (F @ (produc245869591on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_148_case__prod__eta, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o]: ((produc58203522_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (F @ (produc1725134254on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_149_case__prod__eta, axiom,
    ((![F : produc335961278on_val > $o]: ((produc1125182229_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (F @ (produc1725134254on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_150_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((F @ X3 @ Y3) = (G @ (produc52622304on_val @ X3 @ Y3)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_151_cond__case__prod__eta, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, G : produc655058983on_val > $o]: ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((F @ X3 @ Y3) = (G @ (produc245869591on_val @ X3 @ Y3)))) => ((produc525028460_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_152_cond__case__prod__eta, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, G : produc335961278on_val > produc335961278on_val > $o]: ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((F @ X3 @ Y3) = (G @ (produc1725134254on_val @ X3 @ Y3)))) => ((produc58203522_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_153_cond__case__prod__eta, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, G : produc335961278on_val > $o]: ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((F @ X3 @ Y3) = (G @ (produc1725134254on_val @ X3 @ Y3)))) => ((produc1125182229_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_154_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_155_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_156_internal__case__prod__def, axiom,
    ((produc463114774_val_o = produc525028460_val_o))). % internal_case_prod_def
thf(fact_157_internal__case__prod__def, axiom,
    ((produc1326103384_val_o = produc58203522_val_o))). % internal_case_prod_def
thf(fact_158_internal__case__prod__def, axiom,
    ((produc1075415231_val_o = produc1125182229_val_o))). % internal_case_prod_def
thf(fact_159_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E5 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E6 : exp_list_char]: (?[S5 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E5 @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ E6 @ Es3))) & ((((A42 = S5)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E5 @ S4) @ (produc2023458740on_val @ E6 @ S5)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S5 : produc515445032on_val]: (?[V2 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A42 = S5)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_160_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E7 : exp_list_char, S6 : produc515445032on_val, E8 : exp_list_char, S7 : produc515445032on_val, Es5 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E7 @ Es5)) => ((A22 = S6) => ((A32 = (cons_exp_list_char @ E8 @ Es5)) => ((A42 = S7) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E7 @ S6) @ (produc2023458740on_val @ E8 @ S7)) @ (red @ P))))))))) => (~ ((![Es5 : list_exp_list_char, S6 : produc515445032on_val, Es6 : list_exp_list_char, S7 : produc515445032on_val, V3 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5)) => ((A22 = S6) => ((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6)) => ((A42 = S7) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S6) @ (produc1725134254on_val @ Es6 @ S7)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_161_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E7 : exp_list_char, H5 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E7 @ H5 @ L4 @ E7 @ H5 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E8 : exp_list_char, H6 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E8 @ H6 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E8 @ H6 @ L5)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_162_CallRedsObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_163_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_164_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_165_converse__rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R2 : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : produc335961278on_val, B3 : produc335961278on_val, Aa2 : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A3 @ B3) @ (produc245869591on_val @ Aa2 @ Ba)) @ R2) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Aa2 @ Ba) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_166_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_167_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Bx @ By) => ((![A3 : list_exp_list_char, B3 : produc515445032on_val, Aa2 : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Aa2 @ Ba)) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa2 @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A3 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_168_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A3 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_169_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A3 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_170_converse__rtranclE2, axiom,
    ((![Xa : produc335961278on_val, Xb : produc335961278on_val, Za : produc335961278on_val, Zb : produc335961278on_val, R2 : set_Pr1301890247on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2)) => ((~ (((produc245869591on_val @ Xa @ Xb) = (produc245869591on_val @ Za @ Zb)))) => (~ ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ A3 @ B3)) @ R2) => (~ ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A3 @ B3) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_171_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A3 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_172_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A3 @ B3)) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_173_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A3 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A3 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_174_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A3 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A3 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_175_rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R2 : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : produc335961278on_val, B3 : produc335961278on_val, Aa2 : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ A3 @ B3)) @ (transi159622442on_val @ R2)) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A3 @ B3) @ (produc245869591on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_176_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A3 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A3 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_177_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Ax @ Ay) => ((![A3 : list_exp_list_char, B3 : produc515445032on_val, Aa2 : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A3 @ B3)) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A3 @ B3) @ (produc1725134254on_val @ Aa2 @ Ba)) @ R2) => ((P @ A3 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_178_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_179_rtrancl__idemp, axiom,
    ((![R2 : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R2)) = (transi325225921on_val @ R2))))). % rtrancl_idemp
thf(fact_180_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_181_r__into__rtrancl, axiom,
    ((![P2 : produc655058983on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ P2 @ R2) => (member1689761872on_val @ P2 @ (transi325225921on_val @ R2)))))). % r_into_rtrancl
thf(fact_182_mem__case__prodI2, axiom,
    ((![P2 : 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]: ((P2 = (produc52622304on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc1919805778on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_183_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z2 : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: ((P2 = (produc52622304on_val @ A3 @ B3)) => (member1689761872on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member1689761872on_val @ Z2 @ (produc98852946on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_184_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc493625819on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_185_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z2 : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A3 @ B3)) => (member1689761872on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member1689761872on_val @ Z2 @ (produc1067722715on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_186_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z2 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc848217214on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_187_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z2 : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A3 @ B3)) => (member1689761872on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member1689761872on_val @ Z2 @ (produc356855678on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_188_mem__case__prodI2, axiom,
    ((![P2 : produc655058983on_val, Z2 : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val]: ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc1705670363on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_189_mem__case__prodI2, axiom,
    ((![P2 : produc655058983on_val, Z2 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val]: ((![A3 : produc335961278on_val, B3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ A3 @ B3)) => (member1689761872on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member1689761872on_val @ Z2 @ (produc1707441371on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_190_mem__case__prodI2, axiom,
    ((![P2 : produc335961278on_val, Z2 : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A3 @ B3)) => (member354538064on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member354538064on_val @ Z2 @ (produc379229956on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_191_mem__case__prodI2, axiom,
    ((![P2 : produc335961278on_val, Z2 : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A3 @ B3)) => (member1689761872on_val @ Z2 @ (C2 @ A3 @ B3)))) => (member1689761872on_val @ Z2 @ (produc1745783812on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_192_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_193_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, A : nat > option2118145160on_val, B : list_char > option_val]: ((member1689761872on_val @ Z2 @ (C2 @ A @ B)) => (member1689761872on_val @ Z2 @ (produc98852946on_val @ C2 @ (produc52622304on_val @ A @ B))))))). % mem_case_prodI
thf(fact_194_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_195_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, A : produc1097884484on_val, B : produc1097884484on_val]: ((member1689761872on_val @ Z2 @ (C2 @ A @ B)) => (member1689761872on_val @ Z2 @ (produc1067722715on_val @ C2 @ (produc1069526295on_val @ A @ B))))))). % mem_case_prodI
thf(fact_196_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_197_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, A : exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ Z2 @ (C2 @ A @ B)) => (member1689761872on_val @ Z2 @ (produc356855678on_val @ C2 @ (produc2023458740on_val @ A @ B))))))). % mem_case_prodI
thf(fact_198_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val, A : produc335961278on_val, B : produc335961278on_val]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc1705670363on_val @ C2 @ (produc245869591on_val @ A @ B))))))). % mem_case_prodI
thf(fact_199_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val, A : produc335961278on_val, B : produc335961278on_val]: ((member1689761872on_val @ Z2 @ (C2 @ A @ B)) => (member1689761872on_val @ Z2 @ (produc1707441371on_val @ C2 @ (produc245869591on_val @ A @ B))))))). % mem_case_prodI
thf(fact_200_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A : list_exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ Z2 @ (C2 @ A @ B)) => (member354538064on_val @ Z2 @ (produc379229956on_val @ C2 @ (produc1725134254on_val @ A @ B))))))). % mem_case_prodI
thf(fact_201_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, A : list_exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ Z2 @ (C2 @ A @ B)) => (member1689761872on_val @ Z2 @ (produc1745783812on_val @ C2 @ (produc1725134254on_val @ A @ B))))))). % mem_case_prodI
thf(fact_202_case__prodI2_H, axiom,
    ((![P2 : produc335961278on_val, C2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X4 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A3 @ B3) = P2) => (C2 @ A3 @ B3 @ X4))) => (produc58203522_val_o @ C2 @ P2 @ X4))))). % case_prodI2'
thf(fact_203_reds__def, axiom,
    ((reds = (^[P3 : list_P1234162913t_char]: (collec105960082on_val @ (produc525028460_val_o @ (produc58203522_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (produc1125182229_val_o @ (redsp @ P3 @ X @ Y))))))))))). % reds_def
thf(fact_204_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P2 : produc515445032on_val]: ((member354538064on_val @ Z2 @ (produc1919805778on_val @ C2 @ P2)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_205_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, P2 : produc515445032on_val]: ((member1689761872on_val @ Z2 @ (produc98852946on_val @ C2 @ P2)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_206_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P2 : produc1172664615on_val]: ((member354538064on_val @ Z2 @ (produc493625819on_val @ C2 @ P2)) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_207_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, P2 : produc1172664615on_val]: ((member1689761872on_val @ Z2 @ (produc1067722715on_val @ C2 @ P2)) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_208_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc1097884484on_val]: ((member354538064on_val @ Z2 @ (produc848217214on_val @ C2 @ P2)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_209_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, P2 : produc1097884484on_val]: ((member1689761872on_val @ Z2 @ (produc356855678on_val @ C2 @ P2)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_210_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val, P2 : produc655058983on_val]: ((member354538064on_val @ Z2 @ (produc1705670363on_val @ C2 @ P2)) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_211_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val, P2 : produc655058983on_val]: ((member1689761872on_val @ Z2 @ (produc1707441371on_val @ C2 @ P2)) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_212_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc335961278on_val]: ((member354538064on_val @ Z2 @ (produc379229956on_val @ C2 @ P2)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_213_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, P2 : produc335961278on_val]: ((member1689761872on_val @ Z2 @ (produc1745783812on_val @ C2 @ P2)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_214_case__prodE_H, axiom,
    ((![C2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, P2 : produc335961278on_val, Z2 : produc335961278on_val]: ((produc58203522_val_o @ C2 @ P2 @ Z2) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3 @ Z2))))))))))). % case_prodE'
thf(fact_215_case__prodD_H, axiom,
    ((![R : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, A : list_exp_list_char, B : produc515445032on_val, C2 : produc335961278on_val]: ((produc58203522_val_o @ R @ (produc1725134254on_val @ A @ B) @ C2) => (R @ A @ B @ C2))))). % case_prodD'
thf(fact_216_ListReds2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_217_same__fst__def, axiom,
    ((same_f1752972725on_val = (^[P3 : (nat > option2118145160on_val) > $o]: (^[R3 : (nat > option2118145160on_val) > set_Pr1104486497on_val]: (collec1161811218on_val @ (produc271780076_val_o @ (produc1588213706_val_o @ (^[X5 : nat > option2118145160on_val]: (^[Y6 : list_char > option_val]: (produc99536995_val_o @ (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (((X5 = X)) & ((((P3 @ X)) & ((member1177709994on_val @ (produc746553401on_val @ Y6 @ Y) @ (R3 @ X))))))))))))))))))). % same_fst_def
thf(fact_218_same__fst__def, axiom,
    ((same_f1147886828on_val = (^[P3 : produc335961278on_val > $o]: (^[R3 : produc335961278on_val > set_Pr208351751on_val]: (collec1570633042on_val @ (produc7931180_val_o @ (produc870903746_val_o @ (^[X5 : produc335961278on_val]: (^[Y6 : produc335961278on_val]: (produc525028460_val_o @ (^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (((X5 = X)) & ((((P3 @ X)) & ((member1689761872on_val @ (produc245869591on_val @ Y6 @ Y) @ (R3 @ X))))))))))))))))))). % same_fst_def
thf(fact_219_same__fst__def, axiom,
    ((same_f1555812995on_val = (^[P3 : list_exp_list_char > $o]: (^[R3 : list_exp_list_char > set_Pr148564103on_val]: (collec105960082on_val @ (produc525028460_val_o @ (produc58203522_val_o @ (^[X5 : list_exp_list_char]: (^[Y6 : produc515445032on_val]: (produc1125182229_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (((X5 = X)) & ((((P3 @ X)) & ((member2027247312on_val @ (produc2106877847on_val @ Y6 @ Y) @ (R3 @ X))))))))))))))))))). % same_fst_def
thf(fact_220_ListReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_221_ListRedsVal, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_222_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_223_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_224_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ B @ C2) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ A @ C2) @ (transi325225921on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_225_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C2) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_226_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ B @ C2) @ R2) => (member1689761872on_val @ (produc245869591on_val @ A @ C2) @ (transi325225921on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_227_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_228_converse__rtrancl__induct, axiom,
    ((![A : produc335961278on_val, B : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ B) => ((![Y3 : produc335961278on_val, Z3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z3) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ Z3 @ B) @ (transi325225921on_val @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_229_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_230_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc335961278on_val, R2 : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A @ A) @ (transi325225921on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_231_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R2)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_232_converse__rtranclE, axiom,
    ((![X4 : produc335961278on_val, Z2 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Z2) @ (transi325225921on_val @ R2)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Y3) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_233_CallRedsThrowObj, axiom,
    ((![E2 : exp_list_char, S0 : produc515445032on_val, A : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_234_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_235_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_236_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_237_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_238_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_239_red__reds_OCallThrowObj, axiom,
    ((![E2 : exp_list_char, M : list_char, Es : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E2) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_240_CallRedsThrowParams, axiom,
    ((![E2 : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_241_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_242_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_243_red__reds_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E2 : exp_list_char, Es2 : list_exp_list_char, V : val, M : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E2) @ Es2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P)))))). % red_reds.CallThrowParams
thf(fact_244_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E3) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_245_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_246_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_247_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_248_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T3 : ty]: ((wTrt @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T3) & (widen_917054840t_char @ p @ T3 @ t))))).
