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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:54.321

% Could-be-implicit typings (36)
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Predicate__Opred_It__Product____Type__Ounit_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__List__Olist_It__Value__Oval_J, type,
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thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (87)
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_BigStep_Ofinals_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OCall_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OTryCatch_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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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,
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thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Oappend_001t__Type__Oty, type,
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thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
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thf(sy_c_List_Olist_OCons_001t__Value__Oval, type,
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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,
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thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Omap_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Omap_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Type__Oty, type,
    map_ty_ty : (ty > ty) > list_ty > list_ty).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Objects_Ohext, type,
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thf(sy_c_Predicate_Oholds, type,
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thf(sy_c_Predicate_Opred_Oeval_001t__Product____Type__Ounit, type,
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thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc746553401on_val : (list_char > option_val) > (list_char > option_val) > produc1335728385on_val).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc240508503t_char : exp_list_char > exp_list_char > produc677445863t_char).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__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__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,
    produc1238538255t_char : list_char > produc1451990293t_char > produc1259892823t_char).
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,
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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,
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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,
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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,
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thf(sy_c_Product__Type_OPair_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_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_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__Type__Oty_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,
    produc248075743t_char : ty > produc1294284815t_char > produc1490933927t_char).
thf(sy_c_Set_OCollect_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,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec105960082on_val : (produc655058983on_val > $o) > set_Pr208351751on_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oredp, type,
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thf(sy_c_SmallStep_Oreds, type,
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thf(sy_c_State_Ohp, type,
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thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi325225921on_val : set_Pr208351751on_val > set_Pr208351751on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Transitive__Closure_Ortrancl_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,
    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_TypeRel_OMethod_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,
    method297381284t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > $o).
thf(sy_c_TypeRel_OMethod__i__i__i__i__i__i__i_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,
    method2113856933t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > pred_Product_unit).
thf(sy_c_TypeRel_Ohas__method_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,
    has_me170134744t_char : list_P1234162913t_char > list_char > list_char > $o).
thf(sy_c_TypeRel_Omethod_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,
    method667690372t_char : list_P1234162913t_char > list_char > list_char > produc1259892823t_char).
thf(sy_c_TypeRel_Owiden_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,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeRel_Owiden__i__i__i_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,
    widen_1673563217t_char : list_P1234162913t_char > ty > ty > pred_Product_unit).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Owf__config, type,
    typeSa1969945757config : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > exp_list_char > ty > $o).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Value_Oval_OAddr, type,
    addr : nat > val).
thf(sy_c_WellForm_Owf__mdecl_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_mde297024346t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellTypeRT_OWTrts, type,
    wTrts : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_Wfrec_Osame__fst_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,
    same_f1752972725on_val : ((nat > option2118145160on_val) > $o) > ((nat > option2118145160on_val) > set_Pr1104486497on_val) > set_Pr148564103on_val).
thf(sy_c_Wfrec_Osame__fst_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,
    same_f366220041on_val : (exp_list_char > $o) > (exp_list_char > set_Pr148564103on_val) > set_Pr1189492743on_val).
thf(sy_c_Wfrec_Osame__fst_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,
    same_f1555812995on_val : (list_exp_list_char > $o) > (list_exp_list_char > set_Pr148564103on_val) > set_Pr208351751on_val).
thf(sy_c_Wfrec_Osame__fst_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    same_f605082028t_char : (list_list_char > $o) > (list_list_char > set_Pr224372167t_char) > set_Pr1060756575t_char).
thf(sy_c_Wfrec_Osame__fst_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,
    same_f962657004on_val : (produc1097884484on_val > $o) > (produc1097884484on_val > set_Pr1189492743on_val) > set_Pr1368603847on_val).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1177709994on_val : produc1335728385on_val > set_Pr1104486497on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    member1699993616t_char : produc677445863t_char > set_Pr224372167t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    member1392938152t_char : produc1689611007t_char > set_Pr1060756575t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__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_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T, type,
    t : ty).
thf(sy_v_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (243)
thf(fact_0_reds, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ s) @ (produc2023458740on_val @ e3 @ s2)) @ (transi111096263on_val @ (red @ p))))). % reds
thf(fact_1_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_2_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_3_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_4_Subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((typeSa1969945757config @ P @ E3 @ S2 @ E @ T) => (?[T2 : ty]: ((typeSa1969945757config @ P @ E3 @ S3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T))))))))). % Subject_reduction
thf(fact_5_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T3 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T3) => (conf_P93989998t_char @ P @ H @ V @ T3)))))). % conf_widen
thf(fact_6_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_7_widen_Oequation_I2_J, axiom,
    ((widen_917054840t_char = (^[X1 : list_P1234162913t_char]: (^[X2 : ty]: (^[X3 : ty]: (holds @ (widen_1673563217t_char @ X1 @ X2 @ X3)))))))). % widen.equation(2)
thf(fact_8_wf__config__def, axiom,
    ((typeSa1969945757config = (^[P2 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (^[S4 : produc515445032on_val]: (^[E5 : exp_list_char]: (^[T4 : ty]: (((typeSa1777264139_sconf @ P2 @ E4 @ S4)) & ((wTrt @ P2 @ (hp @ S4) @ E4 @ E5 @ T4))))))))))). % wf_config_def
thf(fact_9_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T) => (?[D : list_char]: (T = (class @ D))))))). % Class_widen
thf(fact_10_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_11_widen__i__i__iE, axiom,
    ((![X : list_P1234162913t_char, Xa : ty, Xb : ty, Y : product_unit]: ((eval_Product_unit @ (widen_1673563217t_char @ X @ Xa @ Xb) @ Y) => (widen_917054840t_char @ X @ Xa @ Xb))))). % widen_i_i_iE
thf(fact_12_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_13_Red__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2)))))))))). % Red_preserves_type
thf(fact_14_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3)))))))). % Red_preserves_sconf
thf(fact_15_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3))))))). % red_preserves_sconf
thf(fact_16_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((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 @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_17_rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Ax @ Ay) => ((![A : list_list_char, B : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ A @ B)) @ (transi1892282060t_char @ R)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_18_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((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 @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_19_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((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 @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_20_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : 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 @ R)) => ((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 @ R)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_21_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R)) => ((~ (((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)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_22_converse__rtranclE2, axiom,
    ((![Xa : list_list_char, Xb : exp_list_char, Za : list_list_char, Zb : exp_list_char, R : set_Pr1060756575t_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R)) => ((~ (((produc713467969t_char @ Xa @ Xb) = (produc713467969t_char @ Za @ Zb)))) => (~ ((![A : list_list_char, B : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa @ Xb) @ (produc713467969t_char @ A @ B)) @ R) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_23_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((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)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_24_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((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)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_25_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R)) => ((~ (((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)) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_26_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((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)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_27_converse__rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Bx @ By) => ((![A : list_list_char, B : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Aa @ Ba) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_28_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((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)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_29_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((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)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_30_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : 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 @ R)) => ((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)) @ R) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_31_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_32_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_33_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_34_old_Oprod_Oinject, axiom,
    ((![A2 : list_list_char, B2 : exp_list_char, A3 : list_list_char, B3 : exp_list_char]: (((produc713467969t_char @ A2 @ B2) = (produc713467969t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_35_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_36_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_37_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_38_prod_Oinject, axiom,
    ((![X12 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X12 @ X22) = (produc1069526295on_val @ Y1 @ Y2)) = (((X12 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_39_prod_Oinject, axiom,
    ((![X12 : list_list_char, X22 : exp_list_char, Y1 : list_list_char, Y2 : exp_list_char]: (((produc713467969t_char @ X12 @ X22) = (produc713467969t_char @ Y1 @ Y2)) = (((X12 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_40_prod_Oinject, axiom,
    ((![X12 : list_exp_list_char, X22 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X12 @ X22) = (produc1725134254on_val @ Y1 @ Y2)) = (((X12 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_41_prod_Oinject, axiom,
    ((![X12 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X12 @ X22) = (produc2023458740on_val @ Y1 @ Y2)) = (((X12 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_42_prod_Oinject, axiom,
    ((![X12 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X12 @ X22) = (produc52622304on_val @ Y1 @ Y2)) = (((X12 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_43_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R) => (member354538064on_val @ P3 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_44_r__into__rtrancl, axiom,
    ((![P3 : produc655058983on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ P3 @ R) => (member1689761872on_val @ P3 @ (transi325225921on_val @ R)))))). % r_into_rtrancl
thf(fact_45_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_46_rtrancl__idemp, axiom,
    ((![R : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R)) = (transi325225921on_val @ R))))). % rtrancl_idemp
thf(fact_47_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_48_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A : list_list_char, B : exp_list_char]: (P @ (produc713467969t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_49_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_50_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_51_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_52_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_53_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1294284815t_char]: (~ ((![A : list_list_char, B : exp_list_char]: (~ ((Y = (produc713467969t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_54_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_55_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_56_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_57_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_58_Pair__inject, axiom,
    ((![A2 : list_list_char, B2 : exp_list_char, A3 : list_list_char, B3 : exp_list_char]: (((produc713467969t_char @ A2 @ B2) = (produc713467969t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_59_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_60_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_61_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_62_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_63_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P3 : produc1294284815t_char]: ((![A : list_list_char, B : exp_list_char]: (P @ (produc713467969t_char @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_64_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P3 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_65_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_66_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_67_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_68_surj__pair, axiom,
    ((![P3 : produc1294284815t_char]: (?[X4 : list_list_char, Y3 : exp_list_char]: (P3 = (produc713467969t_char @ X4 @ Y3)))))). % surj_pair
thf(fact_69_surj__pair, axiom,
    ((![P3 : produc335961278on_val]: (?[X4 : list_exp_list_char, Y3 : produc515445032on_val]: (P3 = (produc1725134254on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_70_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X4 : exp_list_char, Y3 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_71_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P3 = (produc52622304on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_72_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_73_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_74_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_75_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_76_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_77_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_78_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_79_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, C3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C3) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C3) @ (transi325225921on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_80_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ R) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_81_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, C3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C3) @ R) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C3) @ (transi325225921on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_82_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B2) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_83_converse__rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((P @ B2) => ((![Y3 : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ R) => ((member1689761872on_val @ (produc245869591on_val @ Z @ B2) @ (transi325225921on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_84_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_85_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc335961278on_val, R : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A2 @ A2) @ (transi325225921on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_86_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_87_converse__rtranclE, axiom,
    ((![X : produc335961278on_val, Z2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Z2) @ (transi325225921on_val @ R)) => ((~ ((X = Z2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y3) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE
thf(fact_88_rtrancl_Oinducts, axiom,
    ((![X12 : produc1097884484on_val, X22 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X12 @ X22) @ (transi111096263on_val @ R)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ R) => (P @ A @ C2))))) => (P @ X12 @ X22))))))). % rtrancl.inducts
thf(fact_89_rtrancl_Oinducts, axiom,
    ((![X12 : produc335961278on_val, X22 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X12 @ X22) @ (transi325225921on_val @ R)) => ((![A : produc335961278on_val]: (P @ A @ A)) => ((![A : produc335961278on_val, B : produc335961278on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((P @ A @ B) => ((member1689761872on_val @ (produc245869591on_val @ B @ C2) @ R) => (P @ A @ C2))))) => (P @ X12 @ X22))))))). % rtrancl.inducts
thf(fact_90_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_91_rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((P @ A2) => ((![Y3 : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_92_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_93_rtrancl__trans, axiom,
    ((![X : produc335961278on_val, Y : produc335961278on_val, R : set_Pr208351751on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X @ Y) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y @ Z2) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ X @ Z2) @ (transi325225921on_val @ R))))))). % rtrancl_trans
thf(fact_94_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_95_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_96_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X5 : produc1172664615on_val]: (member354538064on_val @ X5 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_97_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X5 : produc655058983on_val]: (member1689761872on_val @ X5 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_98_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C4 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C4)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C4) @ R)))))))))))))))). % rtrancl.simps
thf(fact_99_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R)) = (((?[A5 : produc335961278on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C4 : produc335961278on_val]: (((A1 = A5)) & ((((A22 = C4)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C4) @ R)))))))))))))))). % rtrancl.simps
thf(fact_100_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_101_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_102_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_103_rtranclE, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_104_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt @ P @ H2 @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_105_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E6 @ H3 @ L3 @ E6 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E7 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_1 @ H_1 @ L_1 @ E7 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E7 @ H4 @ L4)))) => (R2 @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_106_ty_Oinject, axiom,
    ((![X52 : list_char, Y5 : list_char]: (((class @ X52) = (class @ Y5)) = (X52 = Y5))))). % ty.inject
thf(fact_107_red__preserves__hconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_108_red__preserves__lconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % red_preserves_lconf
thf(fact_109_subjects__reduction, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, Ts : list_ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrts @ P @ (hp @ S2) @ E3 @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ P @ (hp @ S3) @ E3 @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction
thf(fact_110_same__fstI, axiom,
    ((![P : list_list_char > $o, X : list_list_char, Y4 : exp_list_char, Y : exp_list_char, R2 : list_list_char > set_Pr224372167t_char]: ((P @ X) => ((member1699993616t_char @ (produc240508503t_char @ Y4 @ Y) @ (R2 @ X)) => (member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ X @ Y4) @ (produc713467969t_char @ X @ Y)) @ (same_f605082028t_char @ P @ R2))))))). % same_fstI
thf(fact_111_same__fstI, axiom,
    ((![P : list_exp_list_char > $o, X : list_exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R2 : list_exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R2 @ X)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X @ Y4) @ (produc1725134254on_val @ X @ Y)) @ (same_f1555812995on_val @ P @ R2))))))). % same_fstI
thf(fact_112_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X : nat > option2118145160on_val, Y4 : list_char > option_val, Y : list_char > option_val, R2 : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X) => ((member1177709994on_val @ (produc746553401on_val @ Y4 @ Y) @ (R2 @ X)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X @ Y4) @ (produc52622304on_val @ X @ Y)) @ (same_f1752972725on_val @ P @ R2))))))). % same_fstI
thf(fact_113_same__fstI, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R2 : exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R2 @ X)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y4) @ (produc2023458740on_val @ X @ Y)) @ (same_f366220041on_val @ P @ R2))))))). % same_fstI
thf(fact_114_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val, Y4 : produc1097884484on_val, Y : produc1097884484on_val, R2 : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Y) @ (R2 @ X)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X @ Y4) @ (produc1069526295on_val @ X @ Y)) @ (same_f962657004on_val @ P @ R2))))))). % same_fstI
thf(fact_115_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, E3 : 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 @ E3 @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_116_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, E3 : 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 @ E3 @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % reds_preserves_lconf
thf(fact_117_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S2) @ E3 @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3))))))). % reds_preserves_sconf
thf(fact_118_subjects__reduction2, axiom,
    ((![P : list_P1234162913t_char, 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, E3 : list_char > option_ty, Ts : list_ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrts @ P @ H @ E3 @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ P @ H2 @ E3 @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction2
thf(fact_119_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_120_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_121_ListReds1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_122_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_123_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_124_conf__hext, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, P : list_P1234162913t_char, V : val, T : ty]: ((hext @ H @ H2) => ((conf_P93989998t_char @ P @ H @ V @ T) => (conf_P93989998t_char @ P @ H2 @ V @ T)))))). % conf_hext
thf(fact_125_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E3) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E3)))))). % lconf_hext
thf(fact_126_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_127_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_128_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_129_ListRedsVal, axiom,
    ((![E : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_130_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts @ P @ H @ E3 @ Es @ Ts) => ((hext @ H @ H2) => (wTrts @ P @ H2 @ E3 @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_131_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_132_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_133_ListReds2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_134_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E5 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E8 : 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 @ E8 @ Es3))) & ((((A42 = S5)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E5 @ S4) @ (produc2023458740on_val @ E8 @ S5)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S5 : produc515445032on_val]: (?[V2 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A42 = S5)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_135_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)) => ((![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.cases
thf(fact_136_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E3 @ E @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E3 @ E @ T)))))). % WTrt_hext_mono
thf(fact_137_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_138_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_139_list_Oinject, axiom,
    ((![X21 : exp_list_char, X222 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X222) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X222 = Y22))))))). % list.inject
thf(fact_140_list_Oinject, axiom,
    ((![X21 : ty, X222 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X222) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X222 = Y22))))))). % list.inject
thf(fact_141_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_142_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((widen_917054840t_char @ P @ X @ Z3)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_143_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_144_red__reds_OCallObj, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_145_not__Cons__self2, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_146_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_147_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X : list_ty]: ((![X4 : ty]: (Ra @ X4 @ X4)) => (list_all2_ty_ty @ Ra @ X @ X))))). % list.rel_refl
thf(fact_148_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X4 : ty, Y3 : ty]: ((P @ X4 @ Y3) => ((Q @ Y3 @ X4) => (X4 = Y3)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_149_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y6 : ty]: (^[Z4 : ty]: (Y6 = Z4)))) = (^[Y6 : list_ty]: (^[Z4 : list_ty]: (Y6 = Z4)))))). % list.rel_eq
thf(fact_150_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]: ((![A : ty, B : ty, C2 : ty]: ((P1 @ A @ B) => ((P22 @ B @ C2) => (P32 @ A @ C2)))) => ((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_151_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X4 : ty]: (P @ X4 @ X4)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_152_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_153_list__all2__eq, axiom,
    (((^[Y6 : list_ty]: (^[Z4 : list_ty]: (Y6 = Z4))) = (list_all2_ty_ty @ (^[Y6 : ty]: (^[Z4 : ty]: (Y6 = Z4))))))). % list_all2_eq
thf(fact_154_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E3 @ E @ T) => ((wTrts @ P @ H @ E3 @ Es @ Ts) => (wTrts @ P @ H @ E3 @ (cons_exp_list_char @ E @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_155_CallRedsObj, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_156_list_Orel__inject_I2_J, axiom,
    ((![R2 : exp_list_char > exp_list_char > $o, X21 : exp_list_char, X222 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a1702871623t_char @ R2 @ (cons_exp_list_char @ X21 @ X222) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_a1702871623t_char @ R2 @ X222 @ Y22))))))). % list.rel_inject(2)
thf(fact_157_list_Orel__inject_I2_J, axiom,
    ((![R2 : exp_list_char > ty > $o, X21 : exp_list_char, X222 : list_exp_list_char, Y21 : ty, Y22 : list_ty]: ((list_a295513531har_ty @ R2 @ (cons_exp_list_char @ X21 @ X222) @ (cons_ty @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_a295513531har_ty @ R2 @ X222 @ Y22))))))). % list.rel_inject(2)
thf(fact_158_list_Orel__inject_I2_J, axiom,
    ((![R2 : ty > exp_list_char > $o, X21 : ty, X222 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R2 @ (cons_ty @ X21 @ X222) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_a212154379t_char @ R2 @ X222 @ Y22))))))). % list.rel_inject(2)
thf(fact_159_list_Orel__inject_I2_J, axiom,
    ((![R2 : ty > ty > $o, X21 : ty, X222 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R2 @ (cons_ty @ X21 @ X222) @ (cons_ty @ Y21 @ Y22)) = (((R2 @ X21 @ Y21)) & ((list_all2_ty_ty @ R2 @ X222 @ Y22))))))). % list.rel_inject(2)
thf(fact_160_list_Orel__intros_I2_J, axiom,
    ((![R2 : exp_list_char > exp_list_char > $o, X21 : exp_list_char, Y21 : exp_list_char, X222 : list_exp_list_char, Y22 : list_exp_list_char]: ((R2 @ X21 @ Y21) => ((list_a1702871623t_char @ R2 @ X222 @ Y22) => (list_a1702871623t_char @ R2 @ (cons_exp_list_char @ X21 @ X222) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_161_list_Orel__intros_I2_J, axiom,
    ((![R2 : exp_list_char > ty > $o, X21 : exp_list_char, Y21 : ty, X222 : list_exp_list_char, Y22 : list_ty]: ((R2 @ X21 @ Y21) => ((list_a295513531har_ty @ R2 @ X222 @ Y22) => (list_a295513531har_ty @ R2 @ (cons_exp_list_char @ X21 @ X222) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_162_list_Orel__intros_I2_J, axiom,
    ((![R2 : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X222 : list_ty, Y22 : list_exp_list_char]: ((R2 @ X21 @ Y21) => ((list_a212154379t_char @ R2 @ X222 @ Y22) => (list_a212154379t_char @ R2 @ (cons_ty @ X21 @ X222) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_163_list_Orel__intros_I2_J, axiom,
    ((![R2 : ty > ty > $o, X21 : ty, Y21 : ty, X222 : list_ty, Y22 : list_ty]: ((R2 @ X21 @ Y21) => ((list_all2_ty_ty @ R2 @ X222 @ Y22) => (list_all2_ty_ty @ R2 @ (cons_ty @ X21 @ X222) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_164_list__all2__Cons, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X : exp_list_char, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1702871623t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_165_list__all2__Cons, axiom,
    ((![P : exp_list_char > ty > $o, X : exp_list_char, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a295513531har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_166_list__all2__Cons, axiom,
    ((![P : ty > exp_list_char > $o, X : ty, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a212154379t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_167_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_168_list__all2__Cons1, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X @ Xs) @ Ys) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ X @ Z3)) & ((list_a1702871623t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_169_list__all2__Cons1, axiom,
    ((![P : exp_list_char > ty > $o, X : exp_list_char, Xs : list_exp_list_char, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X @ Xs) @ Ys) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((P @ X @ Z3)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_170_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ X @ Z3)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_171_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((P @ X @ Z3)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_172_list__all2__Cons2, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_a1702871623t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_173_list__all2__Cons2, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_174_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_175_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z3 @ Zs))) & ((((P @ Z3 @ Y)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_176_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, C : list_char, M : list_char, Ts : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D3 : list_char, Es : list_exp_list_char, Ts3 : list_ty]: ((wTrt @ P @ H @ E3 @ E @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D3) => ((wTrts @ P @ H @ E3 @ Es @ Ts3) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts) => (wTrt @ P @ H @ E3 @ (call_list_char @ E @ M @ Es) @ T)))))))). % WTrtCall
thf(fact_177_CallRedsThrowObj, axiom,
    ((![E : 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 @ E @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_178_TryRedsVal, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, V : val, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_179_exp_Odistinct_I77_J, axiom,
    ((![X32 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X32) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_180_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_181_confs__Cons2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z3 : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z3 @ Zs))) & ((((conf_P93989998t_char @ P @ H @ Z3 @ Y)) & ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Zs @ Ys))))))))))). % confs_Cons2
thf(fact_182_sees__method__idemp, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M4 : produc1294284815t_char, D3 : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T @ M4 @ D3) => (method297381284t_char @ P @ D3 @ M @ Ts @ T @ M4 @ D3))))). % sees_method_idemp
thf(fact_183_sees__method__fun, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, TS : list_ty, T : ty, M4 : produc1294284815t_char, D3 : list_char, TS2 : list_ty, T3 : ty, M5 : produc1294284815t_char, D4 : list_char]: ((method297381284t_char @ P @ C @ M @ TS @ T @ M4 @ D3) => ((method297381284t_char @ P @ C @ M @ TS2 @ T3 @ M5 @ D4) => ((TS2 = TS) & ((T3 = T) & ((M5 = M4) & (D4 = D3))))))))). % sees_method_fun
thf(fact_184_confs__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts : list_ty, H2 : nat > option2118145160on_val]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts) => ((hext @ H @ H2) => (list_all2_val_ty @ (conf_P93989998t_char @ P @ H2) @ Vs @ Ts)))))). % confs_hext
thf(fact_185_red__reds_OTryRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V4 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.TryRed
thf(fact_186_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_187_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_188_confs__widens, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts : list_ty, Ts3 : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) => (list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts3)))))). % confs_widens
thf(fact_189_red__reds_ORedTry, axiom,
    ((![V : val, C : list_char, V4 : list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ (val_list_char @ V) @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P))))). % red_reds.RedTry
thf(fact_190_TryReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2) @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C @ V4 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % TryReds
thf(fact_191_ThrowReds, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_192_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_193_red__reds_OCallThrowObj, axiom,
    ((![E : exp_list_char, M : list_char, Es : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_194_has__method__def, axiom,
    ((has_me170134744t_char = (^[P2 : list_P1234162913t_char]: (^[C5 : list_char]: (^[M6 : list_char]: (?[Ts4 : list_ty]: (?[T4 : ty]: (?[M7 : produc1294284815t_char]: (?[X6 : list_char]: (method297381284t_char @ P2 @ C5 @ M6 @ Ts4 @ T4 @ M7 @ X6))))))))))). % has_method_def
thf(fact_195_method__def2, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M : list_char, Ts : list_ty, T : ty, M4 : produc1294284815t_char, D3 : list_char]: ((method297381284t_char @ P @ C @ M @ Ts @ T @ M4 @ D3) => ((method667690372t_char @ P @ C @ M) = (produc1238538255t_char @ D3 @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M4)))))))). % method_def2
thf(fact_196_Method_Oequation_I3_J, axiom,
    ((method297381284t_char = (^[X1 : list_P1234162913t_char]: (^[X2 : list_char]: (^[X3 : list_char]: (^[X42 : list_ty]: (^[X53 : ty]: (^[X62 : produc1294284815t_char]: (^[X7 : list_char]: (holds @ (method2113856933t_char @ X1 @ X2 @ X3 @ X42 @ X53 @ X62 @ X7)))))))))))). % Method.equation(3)
thf(fact_197_Method__i__i__i__i__i__i__iE, axiom,
    ((![X : list_P1234162913t_char, Xa : list_char, Xb : list_char, Xc : list_ty, Xd : ty, Xe : produc1294284815t_char, Xf : list_char, Y : product_unit]: ((eval_Product_unit @ (method2113856933t_char @ X @ Xa @ Xb @ Xc @ Xd @ Xe @ Xf) @ Y) => (method297381284t_char @ X @ Xa @ Xb @ Xc @ Xd @ Xe @ Xf))))). % Method_i_i_i_i_i_i_iE
thf(fact_198_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, T : ty, M4 : produc1294284815t_char, D3 : list_char]: ((wf_pro1229751607t_char @ Wf_md @ P) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ M4 @ D3) => (wf_mde297024346t_char @ Wf_md @ P @ D3 @ (produc1238538255t_char @ M @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T @ M4))))))))). % sees_wf_mdecl
thf(fact_199_CallRedsThrowParams, axiom,
    ((![E : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A2 : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A2) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_200_Cons__eq__map__conv, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, F : val > exp_list_char, Ys : list_val]: (((cons_exp_list_char @ X @ Xs) = (map_va1515327237t_char @ F @ Ys)) = (?[Z3 : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z3 @ Zs))) & ((((X = (F @ Z3))) & ((Xs = (map_va1515327237t_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_201_Cons__eq__map__conv, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, F : exp_list_char > exp_list_char, Ys : list_exp_list_char]: (((cons_exp_list_char @ X @ Xs) = (map_ex886010884t_char @ F @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z3 @ Zs))) & ((((X = (F @ Z3))) & ((Xs = (map_ex886010884t_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_202_Cons__eq__map__conv, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, F : ty > exp_list_char, Ys : list_ty]: (((cons_exp_list_char @ X @ Xs) = (map_ty_exp_list_char @ F @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((X = (F @ Z3))) & ((Xs = (map_ty_exp_list_char @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_203_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : exp_list_char > ty, Ys : list_exp_list_char]: (((cons_ty @ X @ Xs) = (map_exp_list_char_ty @ F @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z3 @ Zs))) & ((((X = (F @ Z3))) & ((Xs = (map_exp_list_char_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_204_Cons__eq__map__conv, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z3 @ Zs))) & ((((X = (F @ Z3))) & ((Xs = (map_ty_ty @ F @ Zs)))))))))))). % Cons_eq_map_conv
thf(fact_205_list__all2__appendI, axiom,
    ((![P : exp_list_char > exp_list_char > $o, A2 : list_exp_list_char, B2 : list_exp_list_char, C3 : list_exp_list_char, D5 : list_exp_list_char]: ((list_a1702871623t_char @ P @ A2 @ B2) => ((list_a1702871623t_char @ P @ C3 @ D5) => (list_a1702871623t_char @ P @ (append_exp_list_char @ A2 @ C3) @ (append_exp_list_char @ B2 @ D5))))))). % list_all2_appendI
thf(fact_206_list__all2__appendI, axiom,
    ((![P : ty > ty > $o, A2 : list_ty, B2 : list_ty, C3 : list_ty, D5 : list_ty]: ((list_all2_ty_ty @ P @ A2 @ B2) => ((list_all2_ty_ty @ P @ C3 @ D5) => (list_all2_ty_ty @ P @ (append_ty @ A2 @ C3) @ (append_ty @ B2 @ D5))))))). % list_all2_appendI
thf(fact_207_list_Osimps_I9_J, axiom,
    ((![F : val > exp_list_char, X21 : val, X222 : list_val]: ((map_va1515327237t_char @ F @ (cons_val @ X21 @ X222)) = (cons_exp_list_char @ (F @ X21) @ (map_va1515327237t_char @ F @ X222)))))). % list.simps(9)
thf(fact_208_list_Osimps_I9_J, axiom,
    ((![F : exp_list_char > exp_list_char, X21 : exp_list_char, X222 : list_exp_list_char]: ((map_ex886010884t_char @ F @ (cons_exp_list_char @ X21 @ X222)) = (cons_exp_list_char @ (F @ X21) @ (map_ex886010884t_char @ F @ X222)))))). % list.simps(9)
thf(fact_209_list_Osimps_I9_J, axiom,
    ((![F : exp_list_char > ty, X21 : exp_list_char, X222 : list_exp_list_char]: ((map_exp_list_char_ty @ F @ (cons_exp_list_char @ X21 @ X222)) = (cons_ty @ (F @ X21) @ (map_exp_list_char_ty @ F @ X222)))))). % list.simps(9)
thf(fact_210_list_Osimps_I9_J, axiom,
    ((![F : ty > exp_list_char, X21 : ty, X222 : list_ty]: ((map_ty_exp_list_char @ F @ (cons_ty @ X21 @ X222)) = (cons_exp_list_char @ (F @ X21) @ (map_ty_exp_list_char @ F @ X222)))))). % list.simps(9)
thf(fact_211_list_Osimps_I9_J, axiom,
    ((![F : ty > ty, X21 : ty, X222 : list_ty]: ((map_ty_ty @ F @ (cons_ty @ X21 @ X222)) = (cons_ty @ (F @ X21) @ (map_ty_ty @ F @ X222)))))). % list.simps(9)
thf(fact_212_Cons__eq__map__D, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, F : val > exp_list_char, Ys : list_val]: (((cons_exp_list_char @ X @ Xs) = (map_va1515327237t_char @ F @ Ys)) => (?[Z : val, Zs2 : list_val]: ((Ys = (cons_val @ Z @ Zs2)) & ((X = (F @ Z)) & (Xs = (map_va1515327237t_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_213_Cons__eq__map__D, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, F : exp_list_char > exp_list_char, Ys : list_exp_list_char]: (((cons_exp_list_char @ X @ Xs) = (map_ex886010884t_char @ F @ Ys)) => (?[Z : exp_list_char, Zs2 : list_exp_list_char]: ((Ys = (cons_exp_list_char @ Z @ Zs2)) & ((X = (F @ Z)) & (Xs = (map_ex886010884t_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_214_Cons__eq__map__D, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, F : ty > exp_list_char, Ys : list_ty]: (((cons_exp_list_char @ X @ Xs) = (map_ty_exp_list_char @ F @ Ys)) => (?[Z : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z @ Zs2)) & ((X = (F @ Z)) & (Xs = (map_ty_exp_list_char @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_215_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : exp_list_char > ty, Ys : list_exp_list_char]: (((cons_ty @ X @ Xs) = (map_exp_list_char_ty @ F @ Ys)) => (?[Z : exp_list_char, Zs2 : list_exp_list_char]: ((Ys = (cons_exp_list_char @ Z @ Zs2)) & ((X = (F @ Z)) & (Xs = (map_exp_list_char_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_216_Cons__eq__map__D, axiom,
    ((![X : ty, Xs : list_ty, F : ty > ty, Ys : list_ty]: (((cons_ty @ X @ Xs) = (map_ty_ty @ F @ Ys)) => (?[Z : ty, Zs2 : list_ty]: ((Ys = (cons_ty @ Z @ Zs2)) & ((X = (F @ Z)) & (Xs = (map_ty_ty @ F @ Zs2))))))))). % Cons_eq_map_D
thf(fact_217_map__eq__Cons__D, axiom,
    ((![F : val > exp_list_char, Xs : list_val, Y : exp_list_char, Ys : list_exp_list_char]: (((map_va1515327237t_char @ F @ Xs) = (cons_exp_list_char @ Y @ Ys)) => (?[Z : val, Zs2 : list_val]: ((Xs = (cons_val @ Z @ Zs2)) & (((F @ Z) = Y) & ((map_va1515327237t_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_218_map__eq__Cons__D, axiom,
    ((![F : exp_list_char > exp_list_char, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: (((map_ex886010884t_char @ F @ Xs) = (cons_exp_list_char @ Y @ Ys)) => (?[Z : exp_list_char, Zs2 : list_exp_list_char]: ((Xs = (cons_exp_list_char @ Z @ Zs2)) & (((F @ Z) = Y) & ((map_ex886010884t_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_219_map__eq__Cons__D, axiom,
    ((![F : ty > exp_list_char, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: (((map_ty_exp_list_char @ F @ Xs) = (cons_exp_list_char @ Y @ Ys)) => (?[Z : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z @ Zs2)) & (((F @ Z) = Y) & ((map_ty_exp_list_char @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_220_map__eq__Cons__D, axiom,
    ((![F : exp_list_char > ty, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: (((map_exp_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z : exp_list_char, Zs2 : list_exp_list_char]: ((Xs = (cons_exp_list_char @ Z @ Zs2)) & (((F @ Z) = Y) & ((map_exp_list_char_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_221_map__eq__Cons__D, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) => (?[Z : ty, Zs2 : list_ty]: ((Xs = (cons_ty @ Z @ Zs2)) & (((F @ Z) = Y) & ((map_ty_ty @ F @ Zs2) = Ys)))))))). % map_eq_Cons_D
thf(fact_222_Cons__eq__appendI, axiom,
    ((![X : exp_list_char, Xs1 : list_exp_list_char, Ys : list_exp_list_char, Xs : list_exp_list_char, Zs3 : list_exp_list_char]: (((cons_exp_list_char @ X @ Xs1) = Ys) => ((Xs = (append_exp_list_char @ Xs1 @ Zs3)) => ((cons_exp_list_char @ X @ Xs) = (append_exp_list_char @ Ys @ Zs3))))))). % Cons_eq_appendI
thf(fact_223_Cons__eq__appendI, axiom,
    ((![X : ty, Xs1 : list_ty, Ys : list_ty, Xs : list_ty, Zs3 : list_ty]: (((cons_ty @ X @ Xs1) = Ys) => ((Xs = (append_ty @ Xs1 @ Zs3)) => ((cons_ty @ X @ Xs) = (append_ty @ Ys @ Zs3))))))). % Cons_eq_appendI
thf(fact_224_map__eq__Cons__conv, axiom,
    ((![F : val > exp_list_char, Xs : list_val, Y : exp_list_char, Ys : list_exp_list_char]: (((map_va1515327237t_char @ F @ Xs) = (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z3 @ Zs))) & (((((F @ Z3) = Y)) & (((map_va1515327237t_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_225_map__eq__Cons__conv, axiom,
    ((![F : exp_list_char > exp_list_char, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: (((map_ex886010884t_char @ F @ Xs) = (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z3 @ Zs))) & (((((F @ Z3) = Y)) & (((map_ex886010884t_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_226_map__eq__Cons__conv, axiom,
    ((![F : ty > exp_list_char, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: (((map_ty_exp_list_char @ F @ Xs) = (cons_exp_list_char @ Y @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z3 @ Zs))) & (((((F @ Z3) = Y)) & (((map_ty_exp_list_char @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_227_map__eq__Cons__conv, axiom,
    ((![F : exp_list_char > ty, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: (((map_exp_list_char_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z3 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z3 @ Zs))) & (((((F @ Z3) = Y)) & (((map_exp_list_char_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_228_map__eq__Cons__conv, axiom,
    ((![F : ty > ty, Xs : list_ty, Y : ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (cons_ty @ Y @ Ys)) = (?[Z3 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z3 @ Zs))) & (((((F @ Z3) = Y)) & (((map_ty_ty @ F @ Zs) = Ys))))))))))). % map_eq_Cons_conv
thf(fact_229_append__Cons, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((append_exp_list_char @ (cons_exp_list_char @ X @ Xs) @ Ys) = (cons_exp_list_char @ X @ (append_exp_list_char @ Xs @ Ys)))))). % append_Cons
thf(fact_230_append__Cons, axiom,
    ((![X : ty, Xs : list_ty, Ys : list_ty]: ((append_ty @ (cons_ty @ X @ Xs) @ Ys) = (cons_ty @ X @ (append_ty @ Xs @ Ys)))))). % append_Cons
thf(fact_231_red__reds_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E : exp_list_char, Es2 : list_exp_list_char, V : val, M : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E) @ Es2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E) @ S2)) @ (red @ P)))))). % red_reds.CallThrowParams
thf(fact_232_finals__app__map, axiom,
    ((![Vs : list_val, Es : list_exp_list_char]: ((finals_list_char @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ Es)) = (finals_list_char @ Es))))). % finals_app_map
thf(fact_233_redp__redsp_OCallThrowParams, axiom,
    ((![Es : list_exp_list_char, Vs : list_val, E : exp_list_char, Es2 : list_exp_list_char, P : list_P1234162913t_char, V : val, M : list_char, S2 : produc515445032on_val]: ((Es = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs) @ (cons_exp_list_char @ (throw_list_char @ E) @ Es2))) => (redp @ P @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2 @ (throw_list_char @ E) @ S2))))). % redp_redsp.CallThrowParams
thf(fact_234_redp__redsp_OCallObj, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, M : list_char, Es : list_exp_list_char]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (call_list_char @ E @ M @ Es) @ S2 @ (call_list_char @ E2 @ M @ Es) @ S3))))). % redp_redsp.CallObj
thf(fact_235_redp__redsp_ORedTry, axiom,
    ((![P : list_P1234162913t_char, V : val, C : list_char, V4 : list_char, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (tryCatch_list_char @ (val_list_char @ V) @ C @ V4 @ E_2) @ S2 @ (val_list_char @ V) @ S2)))). % redp_redsp.RedTry
thf(fact_236_redp__redsp_OTryRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, C : list_char, V4 : list_char, E_2 : exp_list_char]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (tryCatch_list_char @ E @ C @ V4 @ E_2) @ S2 @ (tryCatch_list_char @ E2 @ C @ V4 @ E_2) @ S3))))). % redp_redsp.TryRed
thf(fact_237_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((redp @ P @ E @ S2 @ E2 @ S3) => (redp @ P @ (throw_list_char @ E) @ S2 @ (throw_list_char @ E2) @ S3))))). % redp_redsp.ThrowRed
thf(fact_238_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E)) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.ThrowThrow
thf(fact_239_redp__redsp_OCallThrowObj, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, M : list_char, Es : list_exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (call_list_char @ (throw_list_char @ E) @ M @ Es) @ S2 @ (throw_list_char @ E) @ S2)))). % redp_redsp.CallThrowObj
thf(fact_240_not__finals__ConsI, axiom,
    ((![E : exp_list_char, Es : list_exp_list_char]: ((~ ((final_list_char @ E))) => (~ ((finals_list_char @ (cons_exp_list_char @ E @ Es)))))))). % not_finals_ConsI
thf(fact_241_finals__def, axiom,
    ((finals_list_char = (^[Es3 : list_exp_list_char]: (((?[Vs2 : list_val]: (Es3 = (map_va1515327237t_char @ val_list_char @ Vs2)))) | ((?[Vs2 : list_val]: (?[A5 : nat]: (?[Es4 : list_exp_list_char]: (Es3 = (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs2) @ (cons_exp_list_char @ (throw_list_char @ (val_list_char @ (addr @ A5))) @ Es4)))))))))))). % finals_def
thf(fact_242_final__def, axiom,
    ((final_list_char = (^[E5 : exp_list_char]: (((?[V2 : val]: (E5 = (val_list_char @ V2)))) | ((?[A5 : nat]: (E5 = (throw_list_char @ (val_list_char @ (addr @ A5))))))))))). % final_def

% Conjectures (2)
thf(conj_0, hypothesis,
    ((typeSa1969945757config @ p @ e @ s @ e2 @ t))).
thf(conj_1, conjecture,
    ((?[T5 : ty]: ((typeSa1969945757config @ p @ e @ s2 @ e3 @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
