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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__Type__Oty_J, type,
    list_ty : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (89)
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_OCall_001t__List__Olist_It__String__Ochar_J, type,
    call_list_char : exp_list_char > list_char > list_exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    cons_exp_list_char : exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
    cons_ty : ty > list_ty > list_ty).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a1702871623t_char : (exp_list_char > exp_list_char > $o) > list_exp_list_char > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    list_a295513531har_ty : (exp_list_char > ty > $o) > list_exp_list_char > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a212154379t_char : (ty > exp_list_char > $o) > list_ty > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Type__Oty, type,
    list_all2_ty_ty : (ty > ty > $o) > list_ty > list_ty > $o).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Order__Relation_Olinear__order__on_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,
    order_1675208697on_val : set_Pr556513572on_val > set_Pr1189492743on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_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_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_Eo_J_J, type,
    bot_bo1949275371_val_o : (nat > option2118145160on_val) > (list_char > option_val) > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_M_062_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_M_Eo_J_J, type,
    bot_bo1487430909_val_o : exp_list_char > produc515445032on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_M_Eo_J_J, type,
    bot_bo1774766339_val_o : list_exp_list_char > produc515445032on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_M_062_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_M_Eo_J_J, type,
    bot_bo1821121046char_o : list_list_char > exp_list_char > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_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_M_062_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_M_Eo_J_J, type,
    bot_bo1918180954_val_o : produc1097884484on_val > produc1097884484on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_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_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_J, type,
    bot_bo2035215066_val_o : produc335961278on_val > produc335961278on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_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_M_Eo_J, type,
    bot_bo824611882_val_o : produc1172664615on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_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_M_Eo_J, type,
    bot_bo523622954_val_o : produc655058983on_val > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    bot_bo923954676on_val : set_Pr723149704on_val).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    bot_bo1575411088on_val : set_Pr556513572on_val).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    bot_bo509638026on_val : set_Pr1511552798on_val).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    bot_bo1987439961t_char : set_Pr2063914181t_char).
thf(sy_c_Orderings_Obot__class_Obot_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,
    bot_bo1575563891on_val : set_Pr1189492743on_val).
thf(sy_c_Orderings_Obot__class_Obot_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,
    bot_bo1426907251on_val : set_Pr208351751on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc713467969t_char : list_list_char > exp_list_char > produc1294284815t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1730359111t_char : list_ty > produc1490933927t_char > produc1451990293t_char).
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thf(sy_c_member_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,
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thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_v_E____, type,
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thf(sy_v_M____, type,
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thf(sy_v_P, type,
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thf(sy_v_T____, type,
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thf(sy_v_e_Ha____, type,
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thf(sy_v_ea____, type,
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thf(sy_v_esa____, type,
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thf(sy_v_h_Ha____, type,
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thf(sy_v_ha____, type,
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thf(sy_v_l_Ha____, type,
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thf(sy_v_la____, type,
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% Relevant facts (205)
thf(fact_0_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % wt
thf(fact_1_CallObj_Oprems_I2_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (call_list_char @ ea @ m @ esa) @ t))). % CallObj.prems(2)
thf(fact_2__092_060open_062_092_060And_062Ts_O_A_092_060lbrakk_062P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_059_AP_ME_Mh_A_092_060turnstile_062_Aes_A_091_058_093_ATs_092_060rbrakk_062_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062M_Ies_J_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    ((![Ts : list_ty]: ((wTrt2 @ p @ ha @ e @ ea @ nt) => ((wTrts2 @ p @ ha @ e @ esa @ Ts) => (?[T : ty]: ((wTrt2 @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T) & (widen_917054840t_char @ p @ T @ t)))))))). % \<open>\<And>Ts. \<lbrakk>P,E,h \<turnstile> e : NT; P,E,h \<turnstile> es [:] Ts\<rbrakk> \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>M(es) : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_3__092_060open_062_092_060And_062pns_Abody_AUs_ATs_AD_AC_O_A_092_060lbrakk_062P_ME_Mh_A_092_060turnstile_062_Ae_A_058_AClass_AC_059_AP_A_092_060turnstile_062_AC_Asees_AM_058_ATs_092_060rightarrow_062T_A_061_A_Ipns_M_Abody_J_Ain_AD_059_AP_ME_Mh_A_092_060turnstile_062_Aes_A_091_058_093_AUs_059_AP_A_092_060turnstile_062_AUs_A_091_092_060le_062_093_ATs_092_060rbrakk_062_A_092_060Longrightarrow_062_A_092_060exists_062T_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062M_Ies_J_A_058_AT_H_A_092_060and_062_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_092_060close_062, axiom,
    ((![C : list_char, Ts : list_ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Us : list_ty]: ((wTrt2 @ p @ ha @ e @ ea @ (class @ C)) => ((method297381284t_char @ p @ C @ m @ Ts @ t @ (produc713467969t_char @ Pns @ Body) @ D) => ((wTrts2 @ p @ ha @ e @ esa @ Us) => ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ Us @ Ts) => (?[T : ty]: ((wTrt2 @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T) & (widen_917054840t_char @ p @ T @ t)))))))))). % \<open>\<And>pns body Us Ts D C. \<lbrakk>P,E,h \<turnstile> e : Class C; P \<turnstile> C sees M: Ts\<rightarrow>T = (pns, body) in D; P,E,h \<turnstile> es [:] Us; P \<turnstile> Us [\<le>] Ts\<rbrakk> \<Longrightarrow> \<exists>T'. P,E,h' \<turnstile> e'\<bullet>M(es) : T' \<and> P \<turnstile> T' \<le> T\<close>
thf(fact_4_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_5_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_6_CallObj_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[T : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ T) & (widen_917054840t_char @ p @ T @ T2)))))))). % CallObj.hyps(2)
thf(fact_7_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[U : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T2)))))))). % IH
thf(fact_8_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U2 : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U2) => ((widen_917054840t_char @ P @ U2 @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_9_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_10_CallObj_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallObj.prems(1)
thf(fact_11_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, T2 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ nt) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => (wTrt2 @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))). % WTrtCallNT
thf(fact_12_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_13_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_14_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, M : list_char, Ts : list_ty, T2 : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Es : list_exp_list_char, Ts2 : list_ty]: ((wTrt2 @ P @ H @ E @ E2 @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T2 @ (produc713467969t_char @ Pns @ Body) @ D) => ((wTrts2 @ P @ H @ E @ Es @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) => (wTrt2 @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))))). % WTrtCall
thf(fact_15_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T2 : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T2) => (?[D2 : list_char]: (T2 = (class @ D2))))))). % Class_widen
thf(fact_16_sees__method__fun, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, TS : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char, TS2 : list_ty, T3 : ty, M3 : produc1294284815t_char, D3 : list_char]: ((method297381284t_char @ P @ C @ M @ TS @ T2 @ M2 @ D) => ((method297381284t_char @ P @ C @ M @ TS2 @ T3 @ M3 @ D3) => ((TS2 = TS) & ((T3 = T2) & ((M3 = M2) & (D3 = D))))))))). % sees_method_fun
thf(fact_17_sees__method__idemp, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T2 @ M2 @ D) => (method297381284t_char @ P @ D @ M @ Ts @ T2 @ M2 @ D))))). % sees_method_idemp
thf(fact_18_widen__null, axiom,
    ((![P : list_P1234162913t_char, C : list_char]: (widen_917054840t_char @ P @ nt @ (class @ C))))). % widen_null
thf(fact_19_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_20_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_21_has__method__def, axiom,
    ((has_me170134744t_char = (^[P2 : list_P1234162913t_char]: (^[C2 : list_char]: (^[M4 : list_char]: (?[Ts3 : list_ty]: (?[T4 : ty]: (?[M5 : produc1294284815t_char]: (?[X : list_char]: (method297381284t_char @ P2 @ C2 @ M4 @ Ts3 @ T4 @ M5 @ X))))))))))). % has_method_def
thf(fact_22_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_23_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : exp_list_char, Y1 : list_list_char, Y2 : exp_list_char]: (((produc713467969t_char @ X1 @ X2) = (produc713467969t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_24_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_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 : 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_27_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_28_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_29_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_30_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_31_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_32_ty_Odistinct_I19_J, axiom,
    ((![X5 : list_char]: (~ ((nt = (class @ X5))))))). % ty.distinct(19)
thf(fact_33_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_34_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X3 : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ R))) = (^[X3 : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_35_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X3 : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ R))) = (^[X3 : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_36_pred__equals__eq2, axiom,
    ((![R : set_Pr2063914181t_char, S : set_Pr2063914181t_char]: (((^[X3 : list_list_char]: (^[Y : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y) @ R))) = (^[X3 : list_list_char]: (^[Y : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_37_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X3 : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y) @ R))) = (^[X3 : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_38_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X3 : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y) @ R))) = (^[X3 : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_39_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X3 : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y) @ R))) = (^[X3 : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_40_WTrt_H__WTrts_H_Ointros_I12_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, C : list_char, M : list_char, Ts : list_ty, T2 : ty, Pns : list_list_char, Body : exp_list_char, D : list_char, Es : list_exp_list_char, Ts2 : list_ty]: ((wTrt @ P @ H @ E @ E2 @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T2 @ (produc713467969t_char @ Pns @ Body) @ D) => ((wTrts @ P @ H @ E @ Es @ Ts2) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))))). % WTrt'_WTrts'.intros(12)
thf(fact_41_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ T2) => (wTrt2 @ P @ H @ E @ E2 @ T2))))). % wt'_wt
thf(fact_42_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ E2 @ T2) => (wTrt @ P @ H @ E @ E2 @ T2))))). % wt_wt'
thf(fact_43_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_44_WTrt_H__WTrts_H_Ointros_I13_J, 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, T2 : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T2)))))). % WTrt'_WTrts'.intros(13)
thf(fact_45_wts_H__iff__wts, axiom,
    ((wTrts = wTrts2))). % wts'_iff_wts
thf(fact_46_wts__wts_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts2 @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ Es @ Ts))))). % wts_wts'
thf(fact_47_wts_H__wts, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts2 @ P @ H @ E @ Es @ Ts))))). % wts'_wts
thf(fact_48_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_49_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_50_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_51_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_52_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_53_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_54_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1294284815t_char]: (~ ((![A3 : list_list_char, B3 : exp_list_char]: (~ ((Y3 = (produc713467969t_char @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_55_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc1725134254on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_56_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_57_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_58_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D4 : list_char > option_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D4))))) => (P @ X4))))). % prod_induct4
thf(fact_59_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (P @ (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C3)))) => (P @ X4))))). % prod_induct3
thf(fact_60_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X4 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (P @ (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C3)))) => (P @ X4))))). % prod_induct3
thf(fact_61_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (P @ (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C3)))) => (P @ X4))))). % prod_induct3
thf(fact_62_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_63_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_64_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_65_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_66_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : nat > option2118145160on_val, D4 : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C3 @ D4)))))))))))). % prod_cases4
thf(fact_67_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A3 : produc1097884484on_val, B3 : exp_list_char, C3 : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A3 @ (produc2023458740on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_68_prod__cases3, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A3 : list_exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (~ ((Y3 = (produc1725134254on_val @ A3 @ (produc52622304on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_69_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A3 : exp_list_char, B3 : nat > option2118145160on_val, C3 : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A3 @ (produc52622304on_val @ B3 @ C3))))))))))). % prod_cases3
thf(fact_70_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_71_Pair__inject, axiom,
    ((![A : list_list_char, B : exp_list_char, A2 : list_list_char, B2 : exp_list_char]: (((produc713467969t_char @ A @ B) = (produc713467969t_char @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_72_Pair__inject, axiom,
    ((![A : list_exp_list_char, B : produc515445032on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = (produc1725134254on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_73_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A2 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_74_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_75_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_76_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P3 : produc1294284815t_char]: ((![A3 : list_list_char, B3 : exp_list_char]: (P @ (produc713467969t_char @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_77_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P3 : produc335961278on_val]: ((![A3 : list_exp_list_char, B3 : produc515445032on_val]: (P @ (produc1725134254on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_78_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A3 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_79_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_80_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X6 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_81_surj__pair, axiom,
    ((![P3 : produc1294284815t_char]: (?[X6 : list_list_char, Y4 : exp_list_char]: (P3 = (produc713467969t_char @ X6 @ Y4)))))). % surj_pair
thf(fact_82_surj__pair, axiom,
    ((![P3 : produc335961278on_val]: (?[X6 : list_exp_list_char, Y4 : produc515445032on_val]: (P3 = (produc1725134254on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_83_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X6 : exp_list_char, Y4 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_84_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X6 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P3 = (produc52622304on_val @ X6 @ Y4)))))). % surj_pair
thf(fact_85_singletonI, axiom,
    ((![A : produc1172664615on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ bot_bo1575563891on_val))))). % singletonI
thf(fact_86_singletonI, axiom,
    ((![A : produc655058983on_val]: (member1689761872on_val @ A @ (insert363480567on_val @ A @ bot_bo1426907251on_val))))). % singletonI
thf(fact_87_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_88_method__def2, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T2 @ M2 @ D) => ((method667690372t_char @ P @ C @ M) = (produc1238538255t_char @ D @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T2 @ M2)))))))). % method_def2
thf(fact_89_insert__iff, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A4)) = (((A = B)) | ((member354538064on_val @ A @ A4))))))). % insert_iff
thf(fact_90_insert__iff, axiom,
    ((![A : produc655058983on_val, B : produc655058983on_val, A4 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ (insert363480567on_val @ B @ A4)) = (((A = B)) | ((member1689761872on_val @ A @ A4))))))). % insert_iff
thf(fact_91_empty__iff, axiom,
    ((![C4 : produc1172664615on_val]: (~ ((member354538064on_val @ C4 @ bot_bo1575563891on_val)))))). % empty_iff
thf(fact_92_empty__iff, axiom,
    ((![C4 : produc655058983on_val]: (~ ((member1689761872on_val @ C4 @ bot_bo1426907251on_val)))))). % empty_iff
thf(fact_93_all__not__in__conv, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((![X3 : produc1172664615on_val]: (~ ((member354538064on_val @ X3 @ A4)))) = (A4 = bot_bo1575563891on_val))))). % all_not_in_conv
thf(fact_94_all__not__in__conv, axiom,
    ((![A4 : set_Pr208351751on_val]: ((![X3 : produc655058983on_val]: (~ ((member1689761872on_val @ X3 @ A4)))) = (A4 = bot_bo1426907251on_val))))). % all_not_in_conv
thf(fact_95_insertCI, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B : produc1172664615on_val]: (((~ ((member354538064on_val @ A @ B4))) => (A = B)) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B4)))))). % insertCI
thf(fact_96_insertCI, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val, B : produc655058983on_val]: (((~ ((member1689761872on_val @ A @ B4))) => (A = B)) => (member1689761872on_val @ A @ (insert363480567on_val @ B @ B4)))))). % insertCI
thf(fact_97_emptyE, axiom,
    ((![A : produc1172664615on_val]: (~ ((member354538064on_val @ A @ bot_bo1575563891on_val)))))). % emptyE
thf(fact_98_emptyE, axiom,
    ((![A : produc655058983on_val]: (~ ((member1689761872on_val @ A @ bot_bo1426907251on_val)))))). % emptyE
thf(fact_99_equals0D, axiom,
    ((![A4 : set_Pr1189492743on_val, A : produc1172664615on_val]: ((A4 = bot_bo1575563891on_val) => (~ ((member354538064on_val @ A @ A4))))))). % equals0D
thf(fact_100_equals0D, axiom,
    ((![A4 : set_Pr208351751on_val, A : produc655058983on_val]: ((A4 = bot_bo1426907251on_val) => (~ ((member1689761872on_val @ A @ A4))))))). % equals0D
thf(fact_101_equals0I, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((![Y4 : produc1172664615on_val]: (~ ((member354538064on_val @ Y4 @ A4)))) => (A4 = bot_bo1575563891on_val))))). % equals0I
thf(fact_102_equals0I, axiom,
    ((![A4 : set_Pr208351751on_val]: ((![Y4 : produc655058983on_val]: (~ ((member1689761872on_val @ Y4 @ A4)))) => (A4 = bot_bo1426907251on_val))))). % equals0I
thf(fact_103_ex__in__conv, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((?[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A4)) = (~ ((A4 = bot_bo1575563891on_val))))))). % ex_in_conv
thf(fact_104_ex__in__conv, axiom,
    ((![A4 : set_Pr208351751on_val]: ((?[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ A4)) = (~ ((A4 = bot_bo1426907251on_val))))))). % ex_in_conv
thf(fact_105_insertE, axiom,
    ((![A : produc1172664615on_val, B : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B @ A4)) => ((~ ((A = B))) => (member354538064on_val @ A @ A4)))))). % insertE
thf(fact_106_insertE, axiom,
    ((![A : produc655058983on_val, B : produc655058983on_val, A4 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ (insert363480567on_val @ B @ A4)) => ((~ ((A = B))) => (member1689761872on_val @ A @ A4)))))). % insertE
thf(fact_107_insertI1, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ B4))))). % insertI1
thf(fact_108_insertI1, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val]: (member1689761872on_val @ A @ (insert363480567on_val @ A @ B4))))). % insertI1
thf(fact_109_insertI2, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B : produc1172664615on_val]: ((member354538064on_val @ A @ B4) => (member354538064on_val @ A @ (insert1971494647on_val @ B @ B4)))))). % insertI2
thf(fact_110_insertI2, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val, B : produc655058983on_val]: ((member1689761872on_val @ A @ B4) => (member1689761872on_val @ A @ (insert363480567on_val @ B @ B4)))))). % insertI2
thf(fact_111_Set_Oset__insert, axiom,
    ((![X4 : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ X4 @ A4) => (~ ((![B5 : set_Pr1189492743on_val]: ((A4 = (insert1971494647on_val @ X4 @ B5)) => (member354538064on_val @ X4 @ B5))))))))). % Set.set_insert
thf(fact_112_Set_Oset__insert, axiom,
    ((![X4 : produc655058983on_val, A4 : set_Pr208351751on_val]: ((member1689761872on_val @ X4 @ A4) => (~ ((![B5 : set_Pr208351751on_val]: ((A4 = (insert363480567on_val @ X4 @ B5)) => (member1689761872on_val @ X4 @ B5))))))))). % Set.set_insert
thf(fact_113_insert__ident, axiom,
    ((![X4 : produc1172664615on_val, A4 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X4 @ A4))) => ((~ ((member354538064on_val @ X4 @ B4))) => (((insert1971494647on_val @ X4 @ A4) = (insert1971494647on_val @ X4 @ B4)) = (A4 = B4))))))). % insert_ident
thf(fact_114_insert__ident, axiom,
    ((![X4 : produc655058983on_val, A4 : set_Pr208351751on_val, B4 : set_Pr208351751on_val]: ((~ ((member1689761872on_val @ X4 @ A4))) => ((~ ((member1689761872on_val @ X4 @ B4))) => (((insert363480567on_val @ X4 @ A4) = (insert363480567on_val @ X4 @ B4)) = (A4 = B4))))))). % insert_ident
thf(fact_115_insert__absorb, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A4) => ((insert1971494647on_val @ A @ A4) = A4))))). % insert_absorb
thf(fact_116_insert__absorb, axiom,
    ((![A : produc655058983on_val, A4 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ A4) => ((insert363480567on_val @ A @ A4) = A4))))). % insert_absorb
thf(fact_117_insert__eq__iff, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val, B : produc1172664615on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ A @ A4))) => ((~ ((member354538064on_val @ B @ B4))) => (((insert1971494647on_val @ A @ A4) = (insert1971494647on_val @ B @ B4)) = (((((A = B)) => ((A4 = B4)))) & ((((~ ((A = B)))) => ((?[C2 : set_Pr1189492743on_val]: (((A4 = (insert1971494647on_val @ B @ C2))) & ((((~ ((member354538064on_val @ B @ C2)))) & ((((B4 = (insert1971494647on_val @ A @ C2))) & ((~ ((member354538064on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_118_insert__eq__iff, axiom,
    ((![A : produc655058983on_val, A4 : set_Pr208351751on_val, B : produc655058983on_val, B4 : set_Pr208351751on_val]: ((~ ((member1689761872on_val @ A @ A4))) => ((~ ((member1689761872on_val @ B @ B4))) => (((insert363480567on_val @ A @ A4) = (insert363480567on_val @ B @ B4)) = (((((A = B)) => ((A4 = B4)))) & ((((~ ((A = B)))) => ((?[C2 : set_Pr208351751on_val]: (((A4 = (insert363480567on_val @ B @ C2))) & ((((~ ((member1689761872on_val @ B @ C2)))) & ((((B4 = (insert363480567on_val @ A @ C2))) & ((~ ((member1689761872on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_119_mk__disjoint__insert, axiom,
    ((![A : produc1172664615on_val, A4 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A4) => (?[B5 : set_Pr1189492743on_val]: ((A4 = (insert1971494647on_val @ A @ B5)) & (~ ((member354538064on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_120_mk__disjoint__insert, axiom,
    ((![A : produc655058983on_val, A4 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ A4) => (?[B5 : set_Pr208351751on_val]: ((A4 = (insert363480567on_val @ A @ B5)) & (~ ((member1689761872on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_121_insert__compr, axiom,
    ((insert1971494647on_val = (^[A5 : produc1172664615on_val]: (^[B6 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((X3 = A5)) | ((member354538064on_val @ X3 @ B6)))))))))). % insert_compr
thf(fact_122_insert__compr, axiom,
    ((insert363480567on_val = (^[A5 : produc655058983on_val]: (^[B6 : set_Pr208351751on_val]: (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((X3 = A5)) | ((member1689761872on_val @ X3 @ B6)))))))))). % insert_compr
thf(fact_123_singletonD, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) => (B = A))))). % singletonD
thf(fact_124_singletonD, axiom,
    ((![B : produc655058983on_val, A : produc655058983on_val]: ((member1689761872on_val @ B @ (insert363480567on_val @ A @ bot_bo1426907251on_val)) => (B = A))))). % singletonD
thf(fact_125_singleton__iff, axiom,
    ((![B : produc1172664615on_val, A : produc1172664615on_val]: ((member354538064on_val @ B @ (insert1971494647on_val @ A @ bot_bo1575563891on_val)) = (B = A))))). % singleton_iff
thf(fact_126_singleton__iff, axiom,
    ((![B : produc655058983on_val, A : produc655058983on_val]: ((member1689761872on_val @ B @ (insert363480567on_val @ A @ bot_bo1426907251on_val)) = (B = A))))). % singleton_iff
thf(fact_127_sees__wf__mdecl, axiom,
    ((![Wf_md : list_P1234162913t_char > list_char > produc1259892823t_char > $o, P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T2 : ty, M2 : produc1294284815t_char, D : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts @ T2 @ M2 @ D) => (wf_mde297024346t_char @ Wf_md @ P @ D @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T2 @ M2))))))))). % sees_wf_mdecl
thf(fact_128_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_129_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_130_bot__empty__eq, axiom,
    ((bot_bo824611882_val_o = (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ bot_bo1575563891on_val))))). % bot_empty_eq
thf(fact_131_bot__empty__eq, axiom,
    ((bot_bo523622954_val_o = (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ bot_bo1426907251on_val))))). % bot_empty_eq
thf(fact_132_bot__empty__eq2, axiom,
    ((bot_bo2035215066_val_o = (^[X3 : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ bot_bo1426907251on_val)))))). % bot_empty_eq2
thf(fact_133_bot__empty__eq2, axiom,
    ((bot_bo1918180954_val_o = (^[X3 : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ bot_bo1575563891on_val)))))). % bot_empty_eq2
thf(fact_134_bot__empty__eq2, axiom,
    ((bot_bo1821121046char_o = (^[X3 : list_list_char]: (^[Y : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X3 @ Y) @ bot_bo1987439961t_char)))))). % bot_empty_eq2
thf(fact_135_bot__empty__eq2, axiom,
    ((bot_bo1774766339_val_o = (^[X3 : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y) @ bot_bo509638026on_val)))))). % bot_empty_eq2
thf(fact_136_bot__empty__eq2, axiom,
    ((bot_bo1487430909_val_o = (^[X3 : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y) @ bot_bo1575411088on_val)))))). % bot_empty_eq2
thf(fact_137_bot__empty__eq2, axiom,
    ((bot_bo1949275371_val_o = (^[X3 : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y) @ bot_bo923954676on_val)))))). % bot_empty_eq2
thf(fact_138_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E2 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_139_is__singletonI_H, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((~ ((A4 = bot_bo1575563891on_val))) => ((![X6 : produc1172664615on_val, Y4 : produc1172664615on_val]: ((member354538064on_val @ X6 @ A4) => ((member354538064on_val @ Y4 @ A4) => (X6 = Y4)))) => (is_sin1880980507on_val @ A4)))))). % is_singletonI'
thf(fact_140_is__singletonI_H, axiom,
    ((![A4 : set_Pr208351751on_val]: ((~ ((A4 = bot_bo1426907251on_val))) => ((![X6 : produc655058983on_val, Y4 : produc655058983on_val]: ((member1689761872on_val @ X6 @ A4) => ((member1689761872on_val @ Y4 @ A4) => (X6 = Y4)))) => (is_sin412639003on_val @ A4)))))). % is_singletonI'
thf(fact_141_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_142_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((wTrts2 @ P @ (hp @ S2) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % reds_preserves_sconf
thf(fact_143_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_144_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]: ((wTrts2 @ P @ H @ E @ Es @ Ts) => ((hext @ H @ H2) => (wTrts2 @ P @ H2 @ E @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_145_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, H2 : nat > option2118145160on_val]: ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((hext @ H @ H2) => (wTrt2 @ P @ H2 @ E @ E2 @ T2)))))). % WTrt_hext_mono
thf(fact_146_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)) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_147_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)) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % reds_preserves_lconf
thf(fact_148_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_149_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_150_redsp__reds__eq, axiom,
    ((redsp = (^[P2 : list_P1234162913t_char]: (^[X3 : list_exp_list_char]: (^[Y : produc515445032on_val]: (^[Z : list_exp_list_char]: (^[Aa : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X3 @ Y) @ (produc1725134254on_val @ Z @ Aa)) @ (reds @ P2)))))))))). % redsp_reds_eq
thf(fact_151_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_152_exp_Odistinct_I65_J, axiom,
    ((![X32 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X32) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_153_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)) => ((![E4 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S5 : produc515445032on_val, Es3 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E4 @ Es3)) => ((A22 = S4) => ((A32 = (cons_exp_list_char @ E5 @ Es3)) => ((A42 = S5) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S4) @ (produc2023458740on_val @ E5 @ 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_154_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)) = (((?[E6 : exp_list_char]: (?[S6 : produc515445032on_val]: (?[E7 : exp_list_char]: (?[S7 : produc515445032on_val]: (?[Es5 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E6 @ Es5))) & ((((A22 = S6)) & ((((A32 = (cons_exp_list_char @ E7 @ Es5))) & ((((A42 = S7)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E6 @ S6) @ (produc2023458740on_val @ E7 @ 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_155_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S2 @ Es2 @ S3) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2 @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3))))). % redp_redsp.ListRed2
thf(fact_156_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_157_red__reds_OListRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_158_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1702871623t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_159_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : ty, Y22 : list_ty]: ((list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a295513531har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_160_list_Orel__inject_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, X22 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a212154379t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_161_list_Orel__inject_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_162_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, Y21 : exp_list_char, X22 : list_exp_list_char, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a1702871623t_char @ R @ X22 @ Y22) => (list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_163_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, Y21 : ty, X22 : list_exp_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a295513531har_ty @ R @ X22 @ Y22) => (list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_164_list_Orel__intros_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X22 : list_ty, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a212154379t_char @ R @ X22 @ Y22) => (list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_165_list_Orel__intros_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_ty_ty @ R @ X22 @ Y22) => (list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_166_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X4 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X4 @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((widen_917054840t_char @ P @ X4 @ Z)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_167_list__all2__eq, axiom,
    (((^[Y6 : list_ty]: (^[Z2 : list_ty]: (Y6 = Z2))) = (list_all2_ty_ty @ (^[Y6 : ty]: (^[Z2 : ty]: (Y6 = Z2))))))). % list_all2_eq
thf(fact_168_list__all2__mono, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty, Q : ty > ty > $o]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_169_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X6 : ty]: (P @ X6 @ X6)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_170_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > ty > $o, P32 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A3 : ty, B3 : ty, C3 : ty]: ((P1 @ A3 @ B3) => ((P22 @ B3 @ C3) => (P32 @ A3 @ C3)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P32 @ As @ Cs))))))). % list_all2_trans
thf(fact_171_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y6 : ty]: (^[Z2 : ty]: (Y6 = Z2)))) = (^[Y6 : list_ty]: (^[Z2 : list_ty]: (Y6 = Z2)))))). % list.rel_eq
thf(fact_172_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X6 : ty, Y4 : ty]: ((P @ X6 @ Y4) => ((Q @ Y4 @ X6) => (X6 = Y4)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_173_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X4 : list_ty]: ((![X6 : ty]: (Ra @ X6 @ X6)) => (list_all2_ty_ty @ Ra @ X4 @ X4))))). % list.rel_refl
thf(fact_174_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt2 @ P @ H @ E @ E2 @ T2) => ((wTrts2 @ P @ H @ E @ Es @ Ts) => (wTrts2 @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T2 @ Ts))))))). % WTrtCons
thf(fact_175_WTrt_H__WTrts_H_Ointros_I15_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E @ E2 @ T2) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T2 @ Ts))))))). % WTrt'_WTrts'.intros(15)
thf(fact_176_list__all2__Cons2, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ Xs @ (cons_exp_list_char @ Y3 @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_a1702871623t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_177_list__all2__Cons2, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ (cons_exp_list_char @ Y3 @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_178_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y3 : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y3 @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_179_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y3 : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y3 @ Ys)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y3)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_180_list__all2__Cons1, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X4 : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X4 @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X4 @ Z)) & ((list_a1702871623t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_181_list__all2__Cons1, axiom,
    ((![P : exp_list_char > ty > $o, X4 : exp_list_char, Xs : list_exp_list_char, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X4 @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X4 @ Z)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_182_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X4 : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X4 @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X4 @ Z)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_183_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X4 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X4 @ Xs) @ Ys) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X4 @ Z)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_184_list__all2__Cons, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X4 : exp_list_char, Xs : list_exp_list_char, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X4 @ Xs) @ (cons_exp_list_char @ Y3 @ Ys)) = (((P @ X4 @ Y3)) & ((list_a1702871623t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_185_list__all2__Cons, axiom,
    ((![P : exp_list_char > ty > $o, X4 : exp_list_char, Xs : list_exp_list_char, Y3 : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X4 @ Xs) @ (cons_ty @ Y3 @ Ys)) = (((P @ X4 @ Y3)) & ((list_a295513531har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_186_list__all2__Cons, axiom,
    ((![P : ty > exp_list_char > $o, X4 : ty, Xs : list_ty, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X4 @ Xs) @ (cons_exp_list_char @ Y3 @ Ys)) = (((P @ X4 @ Y3)) & ((list_a212154379t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_187_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X4 : ty, Xs : list_ty, Y3 : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X4 @ Xs) @ (cons_ty @ Y3 @ Ys)) = (((P @ X4 @ Y3)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_188_total__on__singleton, axiom,
    ((![X4 : produc1097884484on_val]: (total_472666312on_val @ (insert161294612on_val @ X4 @ bot_bo1575411088on_val) @ (insert1971494647on_val @ (produc1069526295on_val @ X4 @ X4) @ bot_bo1575563891on_val))))). % total_on_singleton
thf(fact_189_total__on__def, axiom,
    ((total_1812707394on_val = (^[A6 : set_Pr1511552798on_val]: (^[R2 : set_Pr208351751on_val]: (![X3 : produc335961278on_val]: (((member184158439on_val @ X3 @ A6)) => ((![Y : produc335961278on_val]: (((member184158439on_val @ Y @ A6)) => ((((~ ((X3 = Y)))) => ((((member1689761872on_val @ (produc245869591on_val @ X3 @ Y) @ R2)) | ((member1689761872on_val @ (produc245869591on_val @ Y @ X3) @ R2)))))))))))))))). % total_on_def
thf(fact_190_total__on__def, axiom,
    ((total_472666312on_val = (^[A6 : set_Pr556513572on_val]: (^[R2 : set_Pr1189492743on_val]: (![X3 : produc1097884484on_val]: (((member1888679917on_val @ X3 @ A6)) => ((![Y : produc1097884484on_val]: (((member1888679917on_val @ Y @ A6)) => ((((~ ((X3 = Y)))) => ((((member354538064on_val @ (produc1069526295on_val @ X3 @ Y) @ R2)) | ((member354538064on_val @ (produc1069526295on_val @ Y @ X3) @ R2)))))))))))))))). % total_on_def
thf(fact_191_total__onI, axiom,
    ((![A4 : set_Pr1511552798on_val, R3 : set_Pr208351751on_val]: ((![X6 : produc335961278on_val, Y4 : produc335961278on_val]: ((member184158439on_val @ X6 @ A4) => ((member184158439on_val @ Y4 @ A4) => ((~ ((X6 = Y4))) => ((member1689761872on_val @ (produc245869591on_val @ X6 @ Y4) @ R3) | (member1689761872on_val @ (produc245869591on_val @ Y4 @ X6) @ R3)))))) => (total_1812707394on_val @ A4 @ R3))))). % total_onI
thf(fact_192_total__onI, axiom,
    ((![A4 : set_Pr1189492743on_val, R3 : set_Pr1368603847on_val]: ((![X6 : produc1172664615on_val, Y4 : produc1172664615on_val]: ((member354538064on_val @ X6 @ A4) => ((member354538064on_val @ Y4 @ A4) => ((~ ((X6 = Y4))) => ((member208988944on_val @ (produc564964183on_val @ X6 @ Y4) @ R3) | (member208988944on_val @ (produc564964183on_val @ Y4 @ X6) @ R3)))))) => (total_40304811on_val @ A4 @ R3))))). % total_onI
thf(fact_193_total__onI, axiom,
    ((![A4 : set_Pr208351751on_val, R3 : set_Pr1301890247on_val]: ((![X6 : produc655058983on_val, Y4 : produc655058983on_val]: ((member1689761872on_val @ X6 @ A4) => ((member1689761872on_val @ Y4 @ A4) => ((~ ((X6 = Y4))) => ((member1743964944on_val @ (produc1802175319on_val @ X6 @ Y4) @ R3) | (member1743964944on_val @ (produc1802175319on_val @ Y4 @ X6) @ R3)))))) => (total_1939788715on_val @ A4 @ R3))))). % total_onI
thf(fact_194_total__onI, axiom,
    ((![A4 : set_Pr556513572on_val, R3 : set_Pr1189492743on_val]: ((![X6 : produc1097884484on_val, Y4 : produc1097884484on_val]: ((member1888679917on_val @ X6 @ A4) => ((member1888679917on_val @ Y4 @ A4) => ((~ ((X6 = Y4))) => ((member354538064on_val @ (produc1069526295on_val @ X6 @ Y4) @ R3) | (member354538064on_val @ (produc1069526295on_val @ Y4 @ X6) @ R3)))))) => (total_472666312on_val @ A4 @ R3))))). % total_onI
thf(fact_195_refl__on__singleton, axiom,
    ((![X4 : produc1097884484on_val]: (refl_o1242125251on_val @ (insert161294612on_val @ X4 @ bot_bo1575411088on_val) @ (insert1971494647on_val @ (produc1069526295on_val @ X4 @ X4) @ bot_bo1575563891on_val))))). % refl_on_singleton
thf(fact_196_linear__order__on__singleton, axiom,
    ((![X4 : produc1097884484on_val]: (order_1675208697on_val @ (insert161294612on_val @ X4 @ bot_bo1575411088on_val) @ (insert1971494647on_val @ (produc1069526295on_val @ X4 @ X4) @ bot_bo1575563891on_val))))). % linear_order_on_singleton
thf(fact_197_refl__on__domain, axiom,
    ((![A4 : set_Pr1189492743on_val, R3 : set_Pr1368603847on_val, A : produc1172664615on_val, B : produc1172664615on_val]: ((refl_o852224294on_val @ A4 @ R3) => ((member208988944on_val @ (produc564964183on_val @ A @ B) @ R3) => ((member354538064on_val @ A @ A4) & (member354538064on_val @ B @ A4))))))). % refl_on_domain
thf(fact_198_refl__on__domain, axiom,
    ((![A4 : set_Pr208351751on_val, R3 : set_Pr1301890247on_val, A : produc655058983on_val, B : produc655058983on_val]: ((refl_o709265702on_val @ A4 @ R3) => ((member1743964944on_val @ (produc1802175319on_val @ A @ B) @ R3) => ((member1689761872on_val @ A @ A4) & (member1689761872on_val @ B @ A4))))))). % refl_on_domain
thf(fact_199_refl__on__domain, axiom,
    ((![A4 : set_Pr1511552798on_val, R3 : set_Pr208351751on_val, A : produc335961278on_val, B : produc335961278on_val]: ((refl_o729121213on_val @ A4 @ R3) => ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ R3) => ((member184158439on_val @ A @ A4) & (member184158439on_val @ B @ A4))))))). % refl_on_domain
thf(fact_200_refl__on__domain, axiom,
    ((![A4 : set_Pr556513572on_val, R3 : set_Pr1189492743on_val, A : produc1097884484on_val, B : produc1097884484on_val]: ((refl_o1242125251on_val @ A4 @ R3) => ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R3) => ((member1888679917on_val @ A @ A4) & (member1888679917on_val @ B @ A4))))))). % refl_on_domain
thf(fact_201_refl__onD, axiom,
    ((![A4 : set_Pr1511552798on_val, R3 : set_Pr208351751on_val, A : produc335961278on_val]: ((refl_o729121213on_val @ A4 @ R3) => ((member184158439on_val @ A @ A4) => (member1689761872on_val @ (produc245869591on_val @ A @ A) @ R3)))))). % refl_onD
thf(fact_202_refl__onD, axiom,
    ((![A4 : set_Pr1189492743on_val, R3 : set_Pr1368603847on_val, A : produc1172664615on_val]: ((refl_o852224294on_val @ A4 @ R3) => ((member354538064on_val @ A @ A4) => (member208988944on_val @ (produc564964183on_val @ A @ A) @ R3)))))). % refl_onD
thf(fact_203_refl__onD, axiom,
    ((![A4 : set_Pr208351751on_val, R3 : set_Pr1301890247on_val, A : produc655058983on_val]: ((refl_o709265702on_val @ A4 @ R3) => ((member1689761872on_val @ A @ A4) => (member1743964944on_val @ (produc1802175319on_val @ A @ A) @ R3)))))). % refl_onD
thf(fact_204_refl__onD, axiom,
    ((![A4 : set_Pr556513572on_val, R3 : set_Pr1189492743on_val, A : produc1097884484on_val]: ((refl_o1242125251on_val @ A4 @ R3) => ((member1888679917on_val @ A @ A4) => (member354538064on_val @ (produc1069526295on_val @ A @ A) @ R3)))))). % refl_onD

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T5 : ty]: ((wTrt2 @ p @ h_a @ e @ (call_list_char @ e_a @ m @ esa) @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
