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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__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 (78)
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_OFAcc_001t__List__Olist_It__String__Ochar_J, type,
    fAcc_list_char : exp_list_char > list_char > list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_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_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__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_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).
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    produc199145871_val_o : (exp_list_char > produc515445032on_val > $o) > produc1097884484on_val > $o).
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    produc848217214on_val : (exp_list_char > produc515445032on_val > set_Pr1189492743on_val) > produc1097884484on_val > set_Pr1189492743on_val).
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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).
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    produc1125182229_val_o : (list_exp_list_char > produc515445032on_val > $o) > produc335961278on_val > $o).
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    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_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_001_Eo, type,
    produc50362220_val_o : (produc1097884484on_val > produc1097884484on_val > $o) > produc1172664615on_val > $o).
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    produc493625819on_val : (produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val) > produc1172664615on_val > set_Pr1189492743on_val).
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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_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_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_1__092_060open_062_092_060And_062T_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_092_060Longrightarrow_062_A_092_060exists_062U_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_A_092_060and_062_AP_A_092_060turnstile_062_AU_A_092_060le_062_AT_092_060close_062, axiom,
    ((![T : ty]: ((wTrt @ p @ ha @ e @ ea @ T) => (?[U : ty]: ((wTrt @ p @ h_a @ e @ e_a @ U) & (widen_917054840t_char @ p @ U @ T))))))). % \<open>\<And>T. P,E,h \<turnstile> e : T \<Longrightarrow> \<exists>U. P,E,h' \<turnstile> e' : U \<and> P \<turnstile> U \<le> T\<close>
thf(fact_2_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_3_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ ea @ T) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_4_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % wt
thf(fact_5_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_6_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_7_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_8_WTrtFAccNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, F : list_char, D : list_char, T : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => (wTrt @ P @ H @ E @ (fAcc_list_char @ E2 @ F @ D) @ T))))). % WTrtFAccNT
thf(fact_9_CallObj_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % CallObj.prems(2)
thf(fact_10_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_11_ty_Odistinct_I15_J, axiom,
    ((~ ((integer = nt))))). % ty.distinct(15)
thf(fact_12_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F @ D) @ S2)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_13_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_14_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D2)))))))))))). % prod_cases4
thf(fact_15_prod__cases4, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D2)))))))))))). % prod_cases4
thf(fact_16_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_17_prod__induct4, axiom,
    ((![P : produc655058983on_val > $o, X : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_18_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_19_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_20_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_21_old_Oprod_Oinject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_22_old_Oprod_Oinject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_23_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_24_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_25_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_26_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_27_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_28_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_29_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_30_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_31_old_Oprod_Oinducts, axiom,
    ((![P : produc655058983on_val > $o, Prod : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_32_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_33_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_34_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_35_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_36_old_Oprod_Oexhaust, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : produc335961278on_val]: (~ ((Y = (produc245869591on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_38_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_39_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_40_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_41_Pair__inject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_42_Pair__inject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_43_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_44_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_45_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_46_prod__cases, axiom,
    ((![P : produc655058983on_val > $o, P2 : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_47_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_48_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_49_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_50_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_51_surj__pair, axiom,
    ((![P2 : produc655058983on_val]: (?[X3 : produc335961278on_val, Y3 : produc335961278on_val]: (P2 = (produc245869591on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_52_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_53_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_54_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_55_prod__induct3, axiom,
    ((![P : produc655058983on_val > $o, X : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_56_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_57_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_58_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_59_prod__cases3, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C))))))))))). % prod_cases3
thf(fact_60_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_61_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_62_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_63_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_64_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_65_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S2))))))). % red_preserves_sconf
thf(fact_66_exp_Odistinct_I141_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(141)
thf(fact_67_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_68_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_69_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_70_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_71_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_72_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_73_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_74_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_75_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_76_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_77_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S3 : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ R))) = (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_78_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ R))) = (^[X4 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_79_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S3 : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ R))) = (^[X4 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_80_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S3 : set_Pr208351751on_val]: (((^[X4 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X4 @ Y4) @ R))) = (^[X4 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X4 @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_81_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S3 : set_Pr1511552798on_val]: (((^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X4 @ Y4) @ R))) = (^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X4 @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_82_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_83_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_84_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_85_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_86_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_87_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S2))))))). % 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_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_91_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_92_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_93_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_94_case__prod__conv, axiom,
    ((![F2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc99536995_val_o @ F2 @ (produc52622304on_val @ A2 @ B2)) = (F2 @ A2 @ B2))))). % case_prod_conv
thf(fact_95_case__prod__conv, axiom,
    ((![F2 : produc335961278on_val > produc335961278on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((produc525028460_val_o @ F2 @ (produc245869591on_val @ A2 @ B2)) = (F2 @ A2 @ B2))))). % case_prod_conv
thf(fact_96_case__prod__conv, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc58203522_val_o @ F2 @ (produc1725134254on_val @ A2 @ B2)) = (F2 @ A2 @ B2))))). % case_prod_conv
thf(fact_97_case__prod__conv, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1125182229_val_o @ F2 @ (produc1725134254on_val @ A2 @ B2)) = (F2 @ A2 @ B2))))). % case_prod_conv
thf(fact_98_case__prodI, axiom,
    ((![F2 : produc1097884484on_val > produc1097884484on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((F2 @ A2 @ B2) => (produc50362220_val_o @ F2 @ (produc1069526295on_val @ A2 @ B2)))))). % case_prodI
thf(fact_99_case__prodI, axiom,
    ((![F2 : exp_list_char > produc515445032on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((F2 @ A2 @ B2) => (produc199145871_val_o @ F2 @ (produc2023458740on_val @ A2 @ B2)))))). % case_prodI
thf(fact_100_case__prodI, axiom,
    ((![F2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((F2 @ A2 @ B2) => (produc99536995_val_o @ F2 @ (produc52622304on_val @ A2 @ B2)))))). % case_prodI
thf(fact_101_case__prodI, axiom,
    ((![F2 : produc335961278on_val > produc335961278on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((F2 @ A2 @ B2) => (produc525028460_val_o @ F2 @ (produc245869591on_val @ A2 @ B2)))))). % case_prodI
thf(fact_102_case__prodI, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((F2 @ A2 @ B2) => (produc1125182229_val_o @ F2 @ (produc1725134254on_val @ A2 @ B2)))))). % case_prodI
thf(fact_103_case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A @ B)) => (C2 @ A @ B))) => (produc50362220_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_104_case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, C2 : exp_list_char > produc515445032on_val > $o]: ((![A : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A @ B)) => (C2 @ A @ B))) => (produc199145871_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_105_case__prodI2, axiom,
    ((![P2 : produc515445032on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A @ B)) => (C2 @ A @ B))) => (produc99536995_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_106_case__prodI2, axiom,
    ((![P2 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > $o]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P2 = (produc245869591on_val @ A @ B)) => (C2 @ A @ B))) => (produc525028460_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_107_case__prodI2, axiom,
    ((![P2 : produc335961278on_val, C2 : list_exp_list_char > produc515445032on_val > $o]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A @ B)) => (C2 @ A @ B))) => (produc1125182229_val_o @ C2 @ P2))))). % case_prodI2
thf(fact_108_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, Prod : produc515445032on_val]: ((H @ (produc99536995_val_o @ F2 @ Prod)) = (produc99536995_val_o @ (^[X12 : nat > option2118145160on_val]: (^[X22 : list_char > option_val]: (H @ (F2 @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_109_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F2 : produc335961278on_val > produc335961278on_val > $o, Prod : produc655058983on_val]: ((H @ (produc525028460_val_o @ F2 @ Prod)) = (produc525028460_val_o @ (^[X12 : produc335961278on_val]: (^[X22 : produc335961278on_val]: (H @ (F2 @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_110_prod_Ocase__distrib, axiom,
    ((![H : (produc335961278on_val > $o) > produc335961278on_val > $o, F2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Prod : produc335961278on_val]: ((H @ (produc58203522_val_o @ F2 @ Prod)) = (produc58203522_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F2 @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_111_prod_Ocase__distrib, axiom,
    ((![H : (produc335961278on_val > $o) > $o, F2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Prod : produc335961278on_val]: ((H @ (produc58203522_val_o @ F2 @ Prod)) = (produc1125182229_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F2 @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_112_prod_Ocase__distrib, axiom,
    ((![H : $o > produc335961278on_val > $o, F2 : list_exp_list_char > produc515445032on_val > $o, Prod : produc335961278on_val]: ((H @ (produc1125182229_val_o @ F2 @ Prod)) = (produc58203522_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F2 @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_113_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F2 : list_exp_list_char > produc515445032on_val > $o, Prod : produc335961278on_val]: ((H @ (produc1125182229_val_o @ F2 @ Prod)) = (produc1125182229_val_o @ (^[X12 : list_exp_list_char]: (^[X22 : produc515445032on_val]: (H @ (F2 @ X12 @ X22)))) @ Prod))))). % prod.case_distrib
thf(fact_114_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_115_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_116_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_117_old_Oprod_Ocase, axiom,
    ((![F2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, X1 : nat > option2118145160on_val, X2 : list_char > option_val]: ((produc99536995_val_o @ F2 @ (produc52622304on_val @ X1 @ X2)) = (F2 @ X1 @ X2))))). % old.prod.case
thf(fact_118_old_Oprod_Ocase, axiom,
    ((![F2 : produc335961278on_val > produc335961278on_val > $o, X1 : produc335961278on_val, X2 : produc335961278on_val]: ((produc525028460_val_o @ F2 @ (produc245869591on_val @ X1 @ X2)) = (F2 @ X1 @ X2))))). % old.prod.case
thf(fact_119_old_Oprod_Ocase, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X1 : list_exp_list_char, X2 : produc515445032on_val]: ((produc58203522_val_o @ F2 @ (produc1725134254on_val @ X1 @ X2)) = (F2 @ X1 @ X2))))). % old.prod.case
thf(fact_120_old_Oprod_Ocase, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > $o, X1 : list_exp_list_char, X2 : produc515445032on_val]: ((produc1125182229_val_o @ F2 @ (produc1725134254on_val @ X1 @ X2)) = (F2 @ X1 @ X2))))). % old.prod.case
thf(fact_121_case__prodD, axiom,
    ((![F2 : produc1097884484on_val > produc1097884484on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc50362220_val_o @ F2 @ (produc1069526295on_val @ A2 @ B2)) => (F2 @ A2 @ B2))))). % case_prodD
thf(fact_122_case__prodD, axiom,
    ((![F2 : exp_list_char > produc515445032on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc199145871_val_o @ F2 @ (produc2023458740on_val @ A2 @ B2)) => (F2 @ A2 @ B2))))). % case_prodD
thf(fact_123_case__prodD, axiom,
    ((![F2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc99536995_val_o @ F2 @ (produc52622304on_val @ A2 @ B2)) => (F2 @ A2 @ B2))))). % case_prodD
thf(fact_124_case__prodD, axiom,
    ((![F2 : produc335961278on_val > produc335961278on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((produc525028460_val_o @ F2 @ (produc245869591on_val @ A2 @ B2)) => (F2 @ A2 @ B2))))). % case_prodD
thf(fact_125_case__prodD, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1125182229_val_o @ F2 @ (produc1725134254on_val @ A2 @ B2)) => (F2 @ A2 @ B2))))). % case_prodD
thf(fact_126_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_127_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_128_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_129_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_130_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_131_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((Z = (produc52622304on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_132_case__prodE2, axiom,
    ((![Q : $o > $o, P : produc335961278on_val > produc335961278on_val > $o, Z : produc655058983on_val]: ((Q @ (produc525028460_val_o @ P @ Z)) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((Z = (produc245869591on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_133_case__prodE2, axiom,
    ((![Q : (produc335961278on_val > $o) > $o, P : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Z : produc335961278on_val]: ((Q @ (produc58203522_val_o @ P @ Z)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((Z = (produc1725134254on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_134_case__prodE2, axiom,
    ((![Q : $o > $o, P : list_exp_list_char > produc515445032on_val > $o, Z : produc335961278on_val]: ((Q @ (produc1125182229_val_o @ P @ Z)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((Z = (produc1725134254on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_135_case__prod__eta, axiom,
    ((![F2 : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X4 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (F2 @ (produc52622304on_val @ X4 @ Y4))))) = F2)))). % case_prod_eta
thf(fact_136_case__prod__eta, axiom,
    ((![F2 : produc655058983on_val > $o]: ((produc525028460_val_o @ (^[X4 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (F2 @ (produc245869591on_val @ X4 @ Y4))))) = F2)))). % case_prod_eta
thf(fact_137_case__prod__eta, axiom,
    ((![F2 : produc335961278on_val > produc335961278on_val > $o]: ((produc58203522_val_o @ (^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (F2 @ (produc1725134254on_val @ X4 @ Y4))))) = F2)))). % case_prod_eta
thf(fact_138_case__prod__eta, axiom,
    ((![F2 : produc335961278on_val > $o]: ((produc1125182229_val_o @ (^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (F2 @ (produc1725134254on_val @ X4 @ Y4))))) = F2)))). % case_prod_eta
thf(fact_139_cond__case__prod__eta, axiom,
    ((![F2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((F2 @ X3 @ Y3) = (G @ (produc52622304on_val @ X3 @ Y3)))) => ((produc99536995_val_o @ F2) = G))))). % cond_case_prod_eta
thf(fact_140_cond__case__prod__eta, axiom,
    ((![F2 : produc335961278on_val > produc335961278on_val > $o, G : produc655058983on_val > $o]: ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((F2 @ X3 @ Y3) = (G @ (produc245869591on_val @ X3 @ Y3)))) => ((produc525028460_val_o @ F2) = G))))). % cond_case_prod_eta
thf(fact_141_cond__case__prod__eta, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, G : produc335961278on_val > produc335961278on_val > $o]: ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((F2 @ X3 @ Y3) = (G @ (produc1725134254on_val @ X3 @ Y3)))) => ((produc58203522_val_o @ F2) = G))))). % cond_case_prod_eta
thf(fact_142_cond__case__prod__eta, axiom,
    ((![F2 : list_exp_list_char > produc515445032on_val > $o, G : produc335961278on_val > $o]: ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((F2 @ X3 @ Y3) = (G @ (produc1725134254on_val @ X3 @ Y3)))) => ((produc1125182229_val_o @ F2) = G))))). % cond_case_prod_eta
thf(fact_143_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_144_internal__case__prod__def, axiom,
    ((produc463114774_val_o = produc525028460_val_o))). % internal_case_prod_def
thf(fact_145_internal__case__prod__def, axiom,
    ((produc1326103384_val_o = produc58203522_val_o))). % internal_case_prod_def
thf(fact_146_internal__case__prod__def, axiom,
    ((produc1075415231_val_o = produc1125182229_val_o))). % internal_case_prod_def
thf(fact_147_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_148_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))) => ((![E5 : exp_list_char, H5 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H5 @ L4 @ E5 @ 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, E6 : 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 @ E6 @ H6 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E6 @ H6 @ L5)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_149_FAccReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (fAcc_list_char @ E3 @ F @ D) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_150_CallRedsObj, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_151_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_152_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_153_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) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ A @ B)) @ (transi159622442on_val @ R2)) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_154_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_155_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) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A @ B)) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_156_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)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_157_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)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_158_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)))) => (~ ((![A : produc335961278on_val, B : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ A @ B)) @ R2) => (~ ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_159_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)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_160_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)))) => (~ ((![A : list_exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A @ B)) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_161_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_162_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_163_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) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa @ Ba)) @ R2) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Aa @ Ba) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_164_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_165_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) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_166_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_167_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_168_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_169_rtrancl__idemp, axiom,
    ((![R2 : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R2)) = (transi325225921on_val @ R2))))). % rtrancl_idemp
thf(fact_170_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A @ B)) => (member354538064on_val @ Z @ (C2 @ A @ B)))) => (member354538064on_val @ Z @ (produc1919805778on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_171_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A @ B)) => (member1689761872on_val @ Z @ (C2 @ A @ B)))) => (member1689761872on_val @ Z @ (produc98852946on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_172_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A @ B)) => (member354538064on_val @ Z @ (C2 @ A @ B)))) => (member354538064on_val @ Z @ (produc493625819on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_173_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A @ B)) => (member1689761872on_val @ Z @ (C2 @ A @ B)))) => (member1689761872on_val @ Z @ (produc1067722715on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_174_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A @ B)) => (member354538064on_val @ Z @ (C2 @ A @ B)))) => (member354538064on_val @ Z @ (produc848217214on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_175_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A @ B)) => (member1689761872on_val @ Z @ (C2 @ A @ B)))) => (member1689761872on_val @ Z @ (produc356855678on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_176_mem__case__prodI2, axiom,
    ((![P2 : produc655058983on_val, Z : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P2 = (produc245869591on_val @ A @ B)) => (member354538064on_val @ Z @ (C2 @ A @ B)))) => (member354538064on_val @ Z @ (produc1705670363on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_177_mem__case__prodI2, axiom,
    ((![P2 : produc655058983on_val, Z : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P2 = (produc245869591on_val @ A @ B)) => (member1689761872on_val @ Z @ (C2 @ A @ B)))) => (member1689761872on_val @ Z @ (produc1707441371on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_178_mem__case__prodI2, axiom,
    ((![P2 : produc335961278on_val, Z : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A @ B)) => (member354538064on_val @ Z @ (C2 @ A @ B)))) => (member354538064on_val @ Z @ (produc379229956on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_179_mem__case__prodI2, axiom,
    ((![P2 : produc335961278on_val, Z : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A @ B)) => (member1689761872on_val @ Z @ (C2 @ A @ B)))) => (member1689761872on_val @ Z @ (produc1745783812on_val @ C2 @ P2)))))). % mem_case_prodI2
thf(fact_180_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((member354538064on_val @ Z @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z @ (produc1919805778on_val @ C2 @ (produc52622304on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_181_mem__case__prodI, axiom,
    ((![Z : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((member1689761872on_val @ Z @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z @ (produc98852946on_val @ C2 @ (produc52622304on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_182_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((member354538064on_val @ Z @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z @ (produc493625819on_val @ C2 @ (produc1069526295on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_183_mem__case__prodI, axiom,
    ((![Z : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((member1689761872on_val @ Z @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z @ (produc1067722715on_val @ C2 @ (produc1069526295on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_184_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A2 : exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z @ (produc848217214on_val @ C2 @ (produc2023458740on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_185_mem__case__prodI, axiom,
    ((![Z : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, A2 : exp_list_char, B2 : produc515445032on_val]: ((member1689761872on_val @ Z @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z @ (produc356855678on_val @ C2 @ (produc2023458740on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_186_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((member354538064on_val @ Z @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z @ (produc1705670363on_val @ C2 @ (produc245869591on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_187_mem__case__prodI, axiom,
    ((![Z : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((member1689761872on_val @ Z @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z @ (produc1707441371on_val @ C2 @ (produc245869591on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_188_mem__case__prodI, axiom,
    ((![Z : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z @ (produc379229956on_val @ C2 @ (produc1725134254on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_189_mem__case__prodI, axiom,
    ((![Z : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((member1689761872on_val @ Z @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z @ (produc1745783812on_val @ C2 @ (produc1725134254on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_190_case__prodI2_H, axiom,
    ((![P2 : produc335961278on_val, C2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = P2) => (C2 @ A @ B @ X))) => (produc58203522_val_o @ C2 @ P2 @ X))))). % case_prodI2'
thf(fact_191_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P2 : produc515445032on_val]: ((member354538064on_val @ Z @ (produc1919805778on_val @ C2 @ P2)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_192_mem__case__prodE, axiom,
    ((![Z : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, P2 : produc515445032on_val]: ((member1689761872on_val @ Z @ (produc98852946on_val @ C2 @ P2)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_193_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P2 : produc1172664615on_val]: ((member354538064on_val @ Z @ (produc493625819on_val @ C2 @ P2)) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_194_mem__case__prodE, axiom,
    ((![Z : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, P2 : produc1172664615on_val]: ((member1689761872on_val @ Z @ (produc1067722715on_val @ C2 @ P2)) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_195_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc1097884484on_val]: ((member354538064on_val @ Z @ (produc848217214on_val @ C2 @ P2)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_196_mem__case__prodE, axiom,
    ((![Z : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, P2 : produc1097884484on_val]: ((member1689761872on_val @ Z @ (produc356855678on_val @ C2 @ P2)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_197_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val, P2 : produc655058983on_val]: ((member354538064on_val @ Z @ (produc1705670363on_val @ C2 @ P2)) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_198_mem__case__prodE, axiom,
    ((![Z : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val, P2 : produc655058983on_val]: ((member1689761872on_val @ Z @ (produc1707441371on_val @ C2 @ P2)) => (~ ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_199_mem__case__prodE, axiom,
    ((![Z : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc335961278on_val]: ((member354538064on_val @ Z @ (produc379229956on_val @ C2 @ P2)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((member354538064on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_200_mem__case__prodE, axiom,
    ((![Z : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, P2 : produc335961278on_val]: ((member1689761872on_val @ Z @ (produc1745783812on_val @ C2 @ P2)) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((member1689761872on_val @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_201_case__prodE_H, axiom,
    ((![C2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, P2 : produc335961278on_val, Z : produc335961278on_val]: ((produc58203522_val_o @ C2 @ P2 @ Z) => (~ ((![X3 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3 @ Z))))))))))). % case_prodE'
thf(fact_202_case__prodD_H, axiom,
    ((![R : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val, C2 : produc335961278on_val]: ((produc58203522_val_o @ R @ (produc1725134254on_val @ A2 @ B2) @ C2) => (R @ A2 @ B2 @ C2))))). % case_prodD'
thf(fact_203_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_204_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C2) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C2) @ (transi325225921on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_205_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_206_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C2) @ R2) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C2) @ (transi325225921on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_207_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_208_converse__rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ B2) => ((![Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ Z2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_209_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_210_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc335961278on_val, R2 : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A2 @ A2) @ (transi325225921on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_211_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_212_converse__rtranclE, axiom,
    ((![X : produc335961278on_val, Z : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y3) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_213_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_214_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X2) @ (transi325225921on_val @ R2)) => ((![A : produc335961278on_val]: (P @ A @ A)) => ((![A : produc335961278on_val, B : produc335961278on_val, C : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ A @ B) => ((member1689761872on_val @ (produc245869591on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_215_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_216_rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ A2) => ((![Y3 : produc335961278on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ R2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_217_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_218_rtrancl__trans, axiom,
    ((![X : produc335961278on_val, Y : produc335961278on_val, R2 : set_Pr208351751on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ X @ Z) @ (transi325225921on_val @ R2))))))). % rtrancl_trans
thf(fact_219_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) = (((?[A5 : produc335961278on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C3 : produc335961278on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R2))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_220_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_221_ListReds1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_222_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_223_redsp__reds__eq, axiom,
    ((redsp = (^[P3 : list_P1234162913t_char]: (^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (^[Z3 : list_exp_list_char]: (^[Aa2 : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X4 @ Y4) @ (produc1725134254on_val @ Z3 @ Aa2)) @ (reds @ P3)))))))))). % redsp_reds_eq
thf(fact_224_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S @ Es2 @ S2) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2))))). % redp_redsp.ListRed2
thf(fact_225_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_226_ListReds2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_227_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)) => ((![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.cases
thf(fact_228_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)) = (((?[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.simps
thf(fact_229_reds__def, axiom,
    ((reds = (^[P3 : list_P1234162913t_char]: (collec105960082on_val @ (produc525028460_val_o @ (produc58203522_val_o @ (^[X4 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (produc1125182229_val_o @ (redsp @ P3 @ X4 @ Y4))))))))))). % reds_def
thf(fact_230_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_231_red__reds_OListRed1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S2)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_232_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_233_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_234_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_235_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_236_ThrowReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_237_red__reds_OCallThrowObj, axiom,
    ((![E2 : exp_list_char, M : list_char, Es : list_exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E2) @ M @ Es) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_238_red__reds_OFAccThrow, axiom,
    ((![E2 : exp_list_char, F : list_char, D : list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E2) @ F @ D) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_239_CallRedsThrowObj, axiom,
    ((![E2 : exp_list_char, S0 : produc515445032on_val, A2 : 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 @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
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, A2 : 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 @ A2) @ 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 @ A2) @ 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, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S2)) @ (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, S : 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) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P)))))). % red_reds.CallThrowParams
thf(fact_244_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E3) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_245_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_246_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_247_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E2 : exp_list_char, S : 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)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_248_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrt @ p @ h_a @ e @ e_a @ nt))).
