% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_199__5336124_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:56.324

% Could-be-implicit typings (27)
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thf(ty_n_t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J, type,
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thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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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__Set__Oset_It__List__Olist_It__String__Ochar_J_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,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (101)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Oconf_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_Conform_Ohconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Conform_Olconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Expr_Oexp_OCall_001t__List__Olist_It__String__Ochar_J, type,
    call_list_char : exp_list_char > list_char > list_exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Value__Oval_J_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    comp_o345283222t_char : (option_val > val) > (list_char > option_val) > list_char > val).
thf(sy_c_Fun_Ooverride__on_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
    overri1171685873on_val : (list_char > option_val) > (list_char > option_val) > set_list_char > list_char > option_val).
thf(sy_c_List_Obind_001t__Option__Ooption_It__Type__Oty_J_001t__Option__Ooption_It__Type__Oty_J, type,
    bind_o794826391ion_ty : list_option_ty > (option_ty > list_option_ty) > list_option_ty).
thf(sy_c_List_Odistinct_001t__List__Olist_It__String__Ochar_J, type,
    distinct_list_char : list_list_char > $o).
thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    cons_exp_list_char : exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_ONil_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    nil_exp_list_char : list_exp_list_char).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__String__Ochar_J, type,
    nil_list_char : list_list_char).
thf(sy_c_List_Olist_ONil_001t__Option__Ooption_It__Type__Oty_J, type,
    nil_option_ty : list_option_ty).
thf(sy_c_List_Olist_ONil_001t__Type__Oty, type,
    nil_ty : list_ty).
thf(sy_c_List_Olist_ONil_001t__Value__Oval, type,
    nil_val : list_val).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a1702871623t_char : (exp_list_char > exp_list_char > $o) > list_exp_list_char > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    list_a295513531har_ty : (exp_list_char > ty > $o) > list_exp_list_char > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    list_a2051666507t_char : (list_char > list_char > $o) > list_list_char > list_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    list_a1770748705har_ty : (list_char > ty > $o) > list_list_char > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    list_a280217834ar_val : (list_char > val > $o) > list_list_char > list_val > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Option__Ooption_It__Type__Oty_J_001t__Type__Oty, type,
    list_a1442669255_ty_ty : (option_ty > ty > $o) > list_option_ty > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a212154379t_char : (ty > exp_list_char > $o) > list_ty > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    list_a765198023ion_ty : (ty > option_ty > $o) > list_ty > list_option_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Type__Oty, type,
    list_all2_ty_ty : (ty > ty > $o) > list_ty > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Value__Oval, type,
    list_all2_ty_val : (ty > val > $o) > list_ty > list_val > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    list_a509749264ion_ty : (val > option_ty > $o) > list_val > list_option_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Type__Oty, type,
    list_all2_val_ty : (val > ty > $o) > list_val > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Value__Oval, type,
    list_all2_val_val : (val > val > $o) > list_val > list_val > $o).
thf(sy_c_List_Olist_Omap_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    map_exp_list_char_ty : (exp_list_char > ty) > list_exp_list_char > list_ty).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_list_char_ty : (list_char > ty) > list_list_char > list_ty).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_list_char_val : (list_char > val) > list_list_char > list_val).
thf(sy_c_List_Olist_Omap_001t__Option__Ooption_It__Type__Oty_J_001t__Type__Oty, type,
    map_option_ty_ty : (option_ty > ty) > list_option_ty > list_ty).
thf(sy_c_List_Olist_Omap_001t__Option__Ooption_It__Type__Oty_J_001t__Value__Oval, type,
    map_option_ty_val : (option_ty > val) > list_option_ty > list_val).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_ty_exp_list_char : (ty > exp_list_char) > list_ty > list_exp_list_char).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    map_ty_list_char : (ty > list_char) > list_ty > list_list_char).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    map_ty_option_ty : (ty > option_ty) > list_ty > list_option_ty).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Type__Oty, type,
    map_ty_ty : (ty > ty) > list_ty > list_ty).
thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Value__Oval, type,
    map_ty_val : (ty > val) > list_ty > list_val).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_va1515327237t_char : (val > exp_list_char) > list_val > list_exp_list_char).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    map_val_list_char : (val > list_char) > list_val > list_list_char).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    map_val_option_ty : (val > option_ty) > list_val > list_option_ty).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Type__Oty, type,
    map_val_ty : (val > ty) > list_val > list_ty).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Value__Oval, type,
    map_val_val : (val > val) > list_val > list_val).
thf(sy_c_List_Olist_Oset_001t__List__Olist_It__String__Ochar_J, type,
    set_list_char2 : list_list_char > set_list_char).
thf(sy_c_List_Olist__ex1_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_e560027540t_char : (exp_list_char > $o) > list_exp_list_char > $o).
thf(sy_c_List_Olist__ex1_001t__List__Olist_It__String__Ochar_J, type,
    list_ex1_list_char : (list_char > $o) > list_list_char > $o).
thf(sy_c_List_Olist__ex1_001t__Option__Ooption_It__Type__Oty_J, type,
    list_ex1_option_ty : (option_ty > $o) > list_option_ty > $o).
thf(sy_c_List_Olist__ex1_001t__Type__Oty, type,
    list_ex1_ty : (ty > $o) > list_ty > $o).
thf(sy_c_List_Olist__ex1_001t__Value__Oval, type,
    list_ex1_val : (val > $o) > list_val > $o).
thf(sy_c_List_Omap__tailrec_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    map_ta650207092har_ty : (exp_list_char > ty) > list_exp_list_char > list_ty).
thf(sy_c_List_Omap__tailrec_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ta1467130225ar_val : (list_char > val) > list_list_char > list_val).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_ta566847940t_char : (ty > exp_list_char) > list_ty > list_exp_list_char).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    map_ta795536168t_char : (ty > list_char) > list_ty > list_list_char).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Option__Ooption_It__Type__Oty_J, type,
    map_ta56519374ion_ty : (ty > option_ty) > list_ty > list_option_ty).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Type__Oty, type,
    map_tailrec_ty_ty : (ty > ty) > list_ty > list_ty).
thf(sy_c_List_Omap__tailrec_001t__Type__Oty_001t__Value__Oval, type,
    map_tailrec_ty_val : (ty > val) > list_ty > list_val).
thf(sy_c_List_Omap__tailrec_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_ta466610747t_char : (val > exp_list_char) > list_val > list_exp_list_char).
thf(sy_c_List_Omap__tailrec_001t__Value__Oval_001t__Option__Ooption_It__Type__Oty_J, type,
    map_ta1696661655ion_ty : (val > option_ty) > list_val > list_option_ty).
thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_up703499792har_ty : (list_char > option_ty) > list_list_char > list_ty > list_char > option_ty).
thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_up576607321ar_val : (list_char > option_val) > list_list_char > list_val > list_char > option_val).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    size_s329991613t_char : list_exp_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    size_s2008079621t_char : list_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J, type,
    size_s1569909163ion_ty : list_option_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Type__Oty_J, type,
    size_size_list_ty : list_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
    size_size_list_val : list_val > nat).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Objects_Otypeof__h, type,
    typeof_h : (nat > option2118145160on_val) > val > option_ty).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
    some_ty : ty > option_ty).
thf(sy_c_Option_Ooption_Othe_001t__Value__Oval, type,
    the_val : option_val > val).
thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc1725134254on_val : list_exp_list_char > produc515445032on_val > produc335961278on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1808722894t_char : list_list_char > produc111478616t_char > produc81045532t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc904988266on_val : list_char > (produc1257910179t_char > option_val) > produc266837688on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc1806338192t_char : list_ty > produc1109669680t_char > produc111478616t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Value__Oval_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc823987298t_char : list_val > exp_list_char > produc1109669680t_char).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    produc245869591on_val : produc335961278on_val > produc335961278on_val > produc655058983on_val).
thf(sy_c_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_Oblocks, type,
    blocks : produc81045532t_char > exp_list_char).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oreds, type,
    reds : list_P1234162913t_char > set_Pr208351751on_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_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_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_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_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_ea, type,
    ea : exp_list_char).
thf(sy_v_h, type,
    h : nat > option2118145160on_val).

% Relevant facts (244)
thf(fact_0_blocks_Osimps_I2_J, axiom,
    ((![E : exp_list_char]: ((blocks @ (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ nil_val @ E)))) = E)))). % blocks.simps(2)
thf(fact_1_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_2_map__upds__Nil1, axiom,
    ((![M : list_char > option_ty, Bs : list_ty]: ((map_up703499792har_ty @ M @ nil_list_char @ Bs) = M)))). % map_upds_Nil1
thf(fact_3_map__upds__Nil1, axiom,
    ((![M : list_char > option_val, Bs : list_val]: ((map_up576607321ar_val @ M @ nil_list_char @ Bs) = M)))). % map_upds_Nil1
thf(fact_4_map__upds__Nil2, axiom,
    ((![M : list_char > option_ty, As : list_list_char]: ((map_up703499792har_ty @ M @ As @ nil_ty) = M)))). % map_upds_Nil2
thf(fact_5_map__upds__Nil2, axiom,
    ((![M : list_char > option_val, As : list_list_char]: ((map_up576607321ar_val @ M @ As @ nil_val) = M)))). % map_upds_Nil2
thf(fact_6_list__all2__Nil, axiom,
    ((![P : ty > val > $o, Ys : list_val]: ((list_all2_ty_val @ P @ nil_ty @ Ys) = (Ys = nil_val))))). % list_all2_Nil
thf(fact_7_list__all2__Nil, axiom,
    ((![P : val > ty > $o, Ys : list_ty]: ((list_all2_val_ty @ P @ nil_val @ Ys) = (Ys = nil_ty))))). % list_all2_Nil
thf(fact_8_list__all2__Nil, axiom,
    ((![P : val > val > $o, Ys : list_val]: ((list_all2_val_val @ P @ nil_val @ Ys) = (Ys = nil_val))))). % list_all2_Nil
thf(fact_9_list__all2__Nil, axiom,
    ((![P : ty > ty > $o, Ys : list_ty]: ((list_all2_ty_ty @ P @ nil_ty @ Ys) = (Ys = nil_ty))))). % list_all2_Nil
thf(fact_10_list__all2__Nil, axiom,
    ((![P : list_char > ty > $o, Ys : list_ty]: ((list_a1770748705har_ty @ P @ nil_list_char @ Ys) = (Ys = nil_ty))))). % list_all2_Nil
thf(fact_11_list__all2__Nil, axiom,
    ((![P : list_char > val > $o, Ys : list_val]: ((list_a280217834ar_val @ P @ nil_list_char @ Ys) = (Ys = nil_val))))). % list_all2_Nil
thf(fact_12_list__all2__Nil, axiom,
    ((![P : ty > list_char > $o, Ys : list_list_char]: ((list_a1504214817t_char @ P @ nil_ty @ Ys) = (Ys = nil_list_char))))). % list_all2_Nil
thf(fact_13_list__all2__Nil, axiom,
    ((![P : val > list_char > $o, Ys : list_list_char]: ((list_a1248766058t_char @ P @ nil_val @ Ys) = (Ys = nil_list_char))))). % list_all2_Nil
thf(fact_14_list__all2__Nil, axiom,
    ((![P : list_char > list_char > $o, Ys : list_list_char]: ((list_a2051666507t_char @ P @ nil_list_char @ Ys) = (Ys = nil_list_char))))). % list_all2_Nil
thf(fact_15_list__all2__Nil, axiom,
    ((![P : ty > exp_list_char > $o, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ nil_ty @ Ys) = (Ys = nil_exp_list_char))))). % list_all2_Nil
thf(fact_16_list__all2__Nil2, axiom,
    ((![P : val > ty > $o, Xs : list_val]: ((list_all2_val_ty @ P @ Xs @ nil_ty) = (Xs = nil_val))))). % list_all2_Nil2
thf(fact_17_list__all2__Nil2, axiom,
    ((![P : ty > val > $o, Xs : list_ty]: ((list_all2_ty_val @ P @ Xs @ nil_val) = (Xs = nil_ty))))). % list_all2_Nil2
thf(fact_18_list__all2__Nil2, axiom,
    ((![P : val > val > $o, Xs : list_val]: ((list_all2_val_val @ P @ Xs @ nil_val) = (Xs = nil_val))))). % list_all2_Nil2
thf(fact_19_list__all2__Nil2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((list_all2_ty_ty @ P @ Xs @ nil_ty) = (Xs = nil_ty))))). % list_all2_Nil2
thf(fact_20_list__all2__Nil2, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty]: ((list_a1504214817t_char @ P @ Xs @ nil_list_char) = (Xs = nil_ty))))). % list_all2_Nil2
thf(fact_21_list__all2__Nil2, axiom,
    ((![P : val > list_char > $o, Xs : list_val]: ((list_a1248766058t_char @ P @ Xs @ nil_list_char) = (Xs = nil_val))))). % list_all2_Nil2
thf(fact_22_list__all2__Nil2, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char]: ((list_a1770748705har_ty @ P @ Xs @ nil_ty) = (Xs = nil_list_char))))). % list_all2_Nil2
thf(fact_23_list__all2__Nil2, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char]: ((list_a280217834ar_val @ P @ Xs @ nil_val) = (Xs = nil_list_char))))). % list_all2_Nil2
thf(fact_24_list__all2__Nil2, axiom,
    ((![P : list_char > list_char > $o, Xs : list_list_char]: ((list_a2051666507t_char @ P @ Xs @ nil_list_char) = (Xs = nil_list_char))))). % list_all2_Nil2
thf(fact_25_list__all2__Nil2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char]: ((list_a295513531har_ty @ P @ Xs @ nil_ty) = (Xs = nil_exp_list_char))))). % list_all2_Nil2
thf(fact_26_length__map, axiom,
    ((![F : ty > ty, Xs : list_ty]: ((size_size_list_ty @ (map_ty_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_27_length__map, axiom,
    ((![F : val > ty, Xs : list_val]: ((size_size_list_ty @ (map_val_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_28_length__map, axiom,
    ((![F : ty > val, Xs : list_ty]: ((size_size_list_val @ (map_ty_val @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_29_length__map, axiom,
    ((![F : val > val, Xs : list_val]: ((size_size_list_val @ (map_val_val @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_30_length__map, axiom,
    ((![F : ty > option_ty, Xs : list_ty]: ((size_s1569909163ion_ty @ (map_ty_option_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_31_length__map, axiom,
    ((![F : val > option_ty, Xs : list_val]: ((size_s1569909163ion_ty @ (map_val_option_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_32_length__map, axiom,
    ((![F : ty > list_char, Xs : list_ty]: ((size_s2008079621t_char @ (map_ty_list_char @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_33_length__map, axiom,
    ((![F : val > list_char, Xs : list_val]: ((size_s2008079621t_char @ (map_val_list_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_34_length__map, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: ((size_size_list_ty @ (map_list_char_ty @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_35_length__map, axiom,
    ((![F : list_char > val, Xs : list_list_char]: ((size_size_list_val @ (map_list_char_val @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_36_Nil__is__map__conv, axiom,
    ((![F : ty > ty, Xs : list_ty]: ((nil_ty = (map_ty_ty @ F @ Xs)) = (Xs = nil_ty))))). % Nil_is_map_conv
thf(fact_37_Nil__is__map__conv, axiom,
    ((![F : val > ty, Xs : list_val]: ((nil_ty = (map_val_ty @ F @ Xs)) = (Xs = nil_val))))). % Nil_is_map_conv
thf(fact_38_Nil__is__map__conv, axiom,
    ((![F : ty > val, Xs : list_ty]: ((nil_val = (map_ty_val @ F @ Xs)) = (Xs = nil_ty))))). % Nil_is_map_conv
thf(fact_39_Nil__is__map__conv, axiom,
    ((![F : val > val, Xs : list_val]: ((nil_val = (map_val_val @ F @ Xs)) = (Xs = nil_val))))). % Nil_is_map_conv
thf(fact_40_Nil__is__map__conv, axiom,
    ((![F : ty > list_char, Xs : list_ty]: ((nil_list_char = (map_ty_list_char @ F @ Xs)) = (Xs = nil_ty))))). % Nil_is_map_conv
thf(fact_41_Nil__is__map__conv, axiom,
    ((![F : val > list_char, Xs : list_val]: ((nil_list_char = (map_val_list_char @ F @ Xs)) = (Xs = nil_val))))). % Nil_is_map_conv
thf(fact_42_Nil__is__map__conv, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: ((nil_ty = (map_list_char_ty @ F @ Xs)) = (Xs = nil_list_char))))). % Nil_is_map_conv
thf(fact_43_Nil__is__map__conv, axiom,
    ((![F : val > option_ty, Xs : list_val]: ((nil_option_ty = (map_val_option_ty @ F @ Xs)) = (Xs = nil_val))))). % Nil_is_map_conv
thf(fact_44_Nil__is__map__conv, axiom,
    ((![F : ty > option_ty, Xs : list_ty]: ((nil_option_ty = (map_ty_option_ty @ F @ Xs)) = (Xs = nil_ty))))). % Nil_is_map_conv
thf(fact_45_Nil__is__map__conv, axiom,
    ((![F : list_char > val, Xs : list_list_char]: ((nil_val = (map_list_char_val @ F @ Xs)) = (Xs = nil_list_char))))). % Nil_is_map_conv
thf(fact_46_map__is__Nil__conv, axiom,
    ((![F : ty > ty, Xs : list_ty]: (((map_ty_ty @ F @ Xs) = nil_ty) = (Xs = nil_ty))))). % map_is_Nil_conv
thf(fact_47_map__is__Nil__conv, axiom,
    ((![F : val > ty, Xs : list_val]: (((map_val_ty @ F @ Xs) = nil_ty) = (Xs = nil_val))))). % map_is_Nil_conv
thf(fact_48_map__is__Nil__conv, axiom,
    ((![F : ty > val, Xs : list_ty]: (((map_ty_val @ F @ Xs) = nil_val) = (Xs = nil_ty))))). % map_is_Nil_conv
thf(fact_49_map__is__Nil__conv, axiom,
    ((![F : val > val, Xs : list_val]: (((map_val_val @ F @ Xs) = nil_val) = (Xs = nil_val))))). % map_is_Nil_conv
thf(fact_50_map__is__Nil__conv, axiom,
    ((![F : ty > list_char, Xs : list_ty]: (((map_ty_list_char @ F @ Xs) = nil_list_char) = (Xs = nil_ty))))). % map_is_Nil_conv
thf(fact_51_map__is__Nil__conv, axiom,
    ((![F : val > list_char, Xs : list_val]: (((map_val_list_char @ F @ Xs) = nil_list_char) = (Xs = nil_val))))). % map_is_Nil_conv
thf(fact_52_map__is__Nil__conv, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: (((map_list_char_ty @ F @ Xs) = nil_ty) = (Xs = nil_list_char))))). % map_is_Nil_conv
thf(fact_53_map__is__Nil__conv, axiom,
    ((![F : val > option_ty, Xs : list_val]: (((map_val_option_ty @ F @ Xs) = nil_option_ty) = (Xs = nil_val))))). % map_is_Nil_conv
thf(fact_54_map__is__Nil__conv, axiom,
    ((![F : ty > option_ty, Xs : list_ty]: (((map_ty_option_ty @ F @ Xs) = nil_option_ty) = (Xs = nil_ty))))). % map_is_Nil_conv
thf(fact_55_map__is__Nil__conv, axiom,
    ((![F : list_char > val, Xs : list_list_char]: (((map_list_char_val @ F @ Xs) = nil_val) = (Xs = nil_list_char))))). % map_is_Nil_conv
thf(fact_56_list_Omap__disc__iff, axiom,
    ((![F : ty > ty, A : list_ty]: (((map_ty_ty @ F @ A) = nil_ty) = (A = nil_ty))))). % list.map_disc_iff
thf(fact_57_list_Omap__disc__iff, axiom,
    ((![F : val > ty, A : list_val]: (((map_val_ty @ F @ A) = nil_ty) = (A = nil_val))))). % list.map_disc_iff
thf(fact_58_list_Omap__disc__iff, axiom,
    ((![F : ty > val, A : list_ty]: (((map_ty_val @ F @ A) = nil_val) = (A = nil_ty))))). % list.map_disc_iff
thf(fact_59_list_Omap__disc__iff, axiom,
    ((![F : val > val, A : list_val]: (((map_val_val @ F @ A) = nil_val) = (A = nil_val))))). % list.map_disc_iff
thf(fact_60_list_Omap__disc__iff, axiom,
    ((![F : ty > list_char, A : list_ty]: (((map_ty_list_char @ F @ A) = nil_list_char) = (A = nil_ty))))). % list.map_disc_iff
thf(fact_61_list_Omap__disc__iff, axiom,
    ((![F : val > list_char, A : list_val]: (((map_val_list_char @ F @ A) = nil_list_char) = (A = nil_val))))). % list.map_disc_iff
thf(fact_62_list_Omap__disc__iff, axiom,
    ((![F : list_char > ty, A : list_list_char]: (((map_list_char_ty @ F @ A) = nil_ty) = (A = nil_list_char))))). % list.map_disc_iff
thf(fact_63_list_Omap__disc__iff, axiom,
    ((![F : val > option_ty, A : list_val]: (((map_val_option_ty @ F @ A) = nil_option_ty) = (A = nil_val))))). % list.map_disc_iff
thf(fact_64_list_Omap__disc__iff, axiom,
    ((![F : ty > option_ty, A : list_ty]: (((map_ty_option_ty @ F @ A) = nil_option_ty) = (A = nil_ty))))). % list.map_disc_iff
thf(fact_65_list_Omap__disc__iff, axiom,
    ((![F : list_char > val, A : list_list_char]: (((map_list_char_val @ F @ A) = nil_val) = (A = nil_list_char))))). % list.map_disc_iff
thf(fact_66_prod__cases4, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A2 : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (~ ((Y = (produc1808722894t_char @ A2 @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D)))))))))))). % prod_cases4
thf(fact_67_old_Oprod_Oinject, axiom,
    ((![A : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A @ B2) = (produc1808722894t_char @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_68_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A @ B2) = (produc1725134254on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_69_old_Oprod_Oinject, axiom,
    ((![A : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A @ B2) = (produc1806338192t_char @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_70_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_71_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_72_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : produc111478616t_char, Y1 : list_list_char, Y2 : produc111478616t_char]: (((produc1808722894t_char @ X1 @ X2) = (produc1808722894t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_73_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_74_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1109669680t_char, Y1 : list_ty, Y2 : produc1109669680t_char]: (((produc1806338192t_char @ X1 @ X2) = (produc1806338192t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_75_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_76_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_77_old_Oprod_Oinducts, axiom,
    ((![P : produc81045532t_char > $o, Prod : produc81045532t_char]: ((![A2 : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_78_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A2 : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_79_old_Oprod_Oinducts, axiom,
    ((![P : produc111478616t_char > $o, Prod : produc111478616t_char]: ((![A2 : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_80_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_81_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_82_old_Oprod_Oexhaust, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A2 : list_list_char, B : produc111478616t_char]: (~ ((Y = (produc1808722894t_char @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_83_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A2 : list_exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_84_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A2 : list_ty, B : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_85_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_86_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A2 @ B)))))))))). % old.prod.exhaust
thf(fact_87_Pair__inject, axiom,
    ((![A : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A @ B2) = (produc1808722894t_char @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_88_Pair__inject, axiom,
    ((![A : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A @ B2) = (produc1725134254on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_89_Pair__inject, axiom,
    ((![A : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A @ B2) = (produc1806338192t_char @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_90_Pair__inject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_91_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_92_prod__cases, axiom,
    ((![P : produc81045532t_char > $o, P2 : produc81045532t_char]: ((![A2 : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_93_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A2 : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_94_prod__cases, axiom,
    ((![P : produc111478616t_char > $o, P2 : produc111478616t_char]: ((![A2 : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_95_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A2 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_96_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B))) => (P @ P2))))). % prod_cases
thf(fact_97_surj__pair, axiom,
    ((![P2 : produc81045532t_char]: (?[X : list_list_char, Y3 : produc111478616t_char]: (P2 = (produc1808722894t_char @ X @ Y3)))))). % surj_pair
thf(fact_98_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X @ Y3)))))). % surj_pair
thf(fact_99_surj__pair, axiom,
    ((![P2 : produc111478616t_char]: (?[X : list_ty, Y3 : produc1109669680t_char]: (P2 = (produc1806338192t_char @ X @ Y3)))))). % surj_pair
thf(fact_100_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X @ Y3)))))). % surj_pair
thf(fact_101_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X @ Y3)))))). % surj_pair
thf(fact_102_neq__if__length__neq, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((~ (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_103_neq__if__length__neq, axiom,
    ((![Xs : list_ty, Ys : list_ty]: ((~ (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_104_neq__if__length__neq, axiom,
    ((![Xs : list_val, Ys : list_val]: ((~ (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_105_neq__if__length__neq, axiom,
    ((![Xs : list_exp_list_char, Ys : list_exp_list_char]: ((~ (((size_s329991613t_char @ Xs) = (size_s329991613t_char @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_106_neq__if__length__neq, axiom,
    ((![Xs : list_option_ty, Ys : list_option_ty]: ((~ (((size_s1569909163ion_ty @ Xs) = (size_s1569909163ion_ty @ Ys)))) => (~ ((Xs = Ys))))))). % neq_if_length_neq
thf(fact_107_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_108_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_109_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_110_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_exp_list_char]: ((size_s329991613t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_111_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_option_ty]: ((size_s1569909163ion_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_112_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X3 : list_ty]: ((![X : ty]: (Ra @ X @ X)) => (list_all2_ty_ty @ Ra @ X3 @ X3))))). % list.rel_refl
thf(fact_113_list_Orel__refl, axiom,
    ((![Ra : exp_list_char > exp_list_char > $o, X3 : list_exp_list_char]: ((![X : exp_list_char]: (Ra @ X @ X)) => (list_a1702871623t_char @ Ra @ X3 @ X3))))). % list.rel_refl
thf(fact_114_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X : ty, Y3 : ty]: ((P @ X @ Y3) => ((Q @ Y3 @ X) => (X = Y3)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_115_list__all2__antisym, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Q : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((![X : exp_list_char, Y3 : exp_list_char]: ((P @ X @ Y3) => ((Q @ Y3 @ X) => (X = Y3)))) => ((list_a1702871623t_char @ P @ Xs @ Ys) => ((list_a1702871623t_char @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_116_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y4 : ty]: (^[Z : ty]: (Y4 = Z)))) = (^[Y4 : list_ty]: (^[Z : list_ty]: (Y4 = Z)))))). % list.rel_eq
thf(fact_117_list_Orel__eq, axiom,
    (((list_a1702871623t_char @ (^[Y4 : exp_list_char]: (^[Z : exp_list_char]: (Y4 = Z)))) = (^[Y4 : list_exp_list_char]: (^[Z : list_exp_list_char]: (Y4 = Z)))))). % list.rel_eq
thf(fact_118_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A2 : ty, B : ty, C : ty]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_119_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > val > $o, P3 : ty > val > $o, As : list_ty, Bs : list_ty, Cs : list_val]: ((![A2 : ty, B : ty, C : val]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_val @ P22 @ Bs @ Cs) => (list_all2_ty_val @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_120_list__all2__trans, axiom,
    ((![P1 : ty > val > $o, P22 : val > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_val, Cs : list_ty]: ((![A2 : ty, B : val, C : ty]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_val @ P1 @ As @ Bs) => ((list_all2_val_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_121_list__all2__trans, axiom,
    ((![P1 : ty > val > $o, P22 : val > val > $o, P3 : ty > val > $o, As : list_ty, Bs : list_val, Cs : list_val]: ((![A2 : ty, B : val, C : val]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_val @ P1 @ As @ Bs) => ((list_all2_val_val @ P22 @ Bs @ Cs) => (list_all2_ty_val @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_122_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > list_char > $o, P3 : ty > list_char > $o, As : list_ty, Bs : list_ty, Cs : list_list_char]: ((![A2 : ty, B : ty, C : list_char]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_a1504214817t_char @ P22 @ Bs @ Cs) => (list_a1504214817t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_123_list__all2__trans, axiom,
    ((![P1 : ty > val > $o, P22 : val > list_char > $o, P3 : ty > list_char > $o, As : list_ty, Bs : list_val, Cs : list_list_char]: ((![A2 : ty, B : val, C : list_char]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_val @ P1 @ As @ Bs) => ((list_a1248766058t_char @ P22 @ Bs @ Cs) => (list_a1504214817t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_124_list__all2__trans, axiom,
    ((![P1 : ty > list_char > $o, P22 : list_char > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_list_char, Cs : list_ty]: ((![A2 : ty, B : list_char, C : ty]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_a1504214817t_char @ P1 @ As @ Bs) => ((list_a1770748705har_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_125_list__all2__trans, axiom,
    ((![P1 : ty > list_char > $o, P22 : list_char > val > $o, P3 : ty > val > $o, As : list_ty, Bs : list_list_char, Cs : list_val]: ((![A2 : ty, B : list_char, C : val]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_a1504214817t_char @ P1 @ As @ Bs) => ((list_a280217834ar_val @ P22 @ Bs @ Cs) => (list_all2_ty_val @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_126_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > exp_list_char > $o, P3 : ty > exp_list_char > $o, As : list_ty, Bs : list_ty, Cs : list_exp_list_char]: ((![A2 : ty, B : ty, C : exp_list_char]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_a212154379t_char @ P22 @ Bs @ Cs) => (list_a212154379t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_127_list__all2__trans, axiom,
    ((![P1 : exp_list_char > ty > $o, P22 : ty > ty > $o, P3 : exp_list_char > ty > $o, As : list_exp_list_char, Bs : list_ty, Cs : list_ty]: ((![A2 : exp_list_char, B : ty, C : ty]: ((P1 @ A2 @ B) => ((P22 @ B @ C) => (P3 @ A2 @ C)))) => ((list_a295513531har_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P22 @ Bs @ Cs) => (list_a295513531har_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_128_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X : ty]: (P @ X @ X)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_129_list__all2__refl, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char]: ((![X : exp_list_char]: (P @ X @ X)) => (list_a1702871623t_char @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_130_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_131_list__all2__mono, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Ys : list_exp_list_char, Q : exp_list_char > exp_list_char > $o]: ((list_a1702871623t_char @ P @ Xs @ Ys) => ((![Xs2 : exp_list_char, Ys2 : exp_list_char]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a1702871623t_char @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_132_list__all2__mono, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Ys : list_ty, Q : exp_list_char > ty > $o]: ((list_a295513531har_ty @ P @ Xs @ Ys) => ((![Xs2 : exp_list_char, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a295513531har_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_133_list__all2__mono, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Ys : list_val, Q : ty > val > $o]: ((list_all2_ty_val @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : val]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_val @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_134_list__all2__mono, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Ys : list_list_char, Q : ty > list_char > $o]: ((list_a1504214817t_char @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : list_char]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a1504214817t_char @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_135_list__all2__mono, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Ys : list_exp_list_char, Q : ty > exp_list_char > $o]: ((list_a212154379t_char @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : exp_list_char]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a212154379t_char @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_136_list__all2__eq, axiom,
    (((^[Y4 : list_ty]: (^[Z : list_ty]: (Y4 = Z))) = (list_all2_ty_ty @ (^[Y4 : ty]: (^[Z : ty]: (Y4 = Z))))))). % list_all2_eq
thf(fact_137_list__all2__eq, axiom,
    (((^[Y4 : list_exp_list_char]: (^[Z : list_exp_list_char]: (Y4 = Z))) = (list_a1702871623t_char @ (^[Y4 : exp_list_char]: (^[Z : exp_list_char]: (Y4 = Z))))))). % list_all2_eq
thf(fact_138_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_139_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_140_prod__induct3, axiom,
    ((![P : produc81045532t_char > $o, X3 : produc81045532t_char]: ((![A2 : list_list_char, B : list_ty, C : produc1109669680t_char]: (P @ (produc1808722894t_char @ A2 @ (produc1806338192t_char @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_141_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X3 : produc335961278on_val]: ((![A2 : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A2 @ (produc52622304on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_142_prod__induct3, axiom,
    ((![P : produc111478616t_char > $o, X3 : produc111478616t_char]: ((![A2 : list_ty, B : list_val, C : exp_list_char]: (P @ (produc1806338192t_char @ A2 @ (produc823987298t_char @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_143_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_144_prod__cases3, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A2 : list_list_char, B : list_ty, C : produc1109669680t_char]: (~ ((Y = (produc1808722894t_char @ A2 @ (produc1806338192t_char @ B @ C))))))))))). % prod_cases3
thf(fact_145_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A2 : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A2 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_146_prod__cases3, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A2 : list_ty, B : list_val, C : exp_list_char]: (~ ((Y = (produc1806338192t_char @ A2 @ (produc823987298t_char @ B @ C))))))))))). % prod_cases3
thf(fact_147_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A2 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_148_list_Osimps_I8_J, axiom,
    ((![F : val > ty]: ((map_val_ty @ F @ nil_val) = nil_ty)))). % list.simps(8)
thf(fact_149_list_Osimps_I8_J, axiom,
    ((![F : val > val]: ((map_val_val @ F @ nil_val) = nil_val)))). % list.simps(8)
thf(fact_150_list_Osimps_I8_J, axiom,
    ((![F : ty > val]: ((map_ty_val @ F @ nil_ty) = nil_val)))). % list.simps(8)
thf(fact_151_list_Osimps_I8_J, axiom,
    ((![F : ty > ty]: ((map_ty_ty @ F @ nil_ty) = nil_ty)))). % list.simps(8)
thf(fact_152_list_Osimps_I8_J, axiom,
    ((![F : list_char > ty]: ((map_list_char_ty @ F @ nil_list_char) = nil_ty)))). % list.simps(8)
thf(fact_153_list_Osimps_I8_J, axiom,
    ((![F : val > list_char]: ((map_val_list_char @ F @ nil_val) = nil_list_char)))). % list.simps(8)
thf(fact_154_list_Osimps_I8_J, axiom,
    ((![F : option_ty > ty]: ((map_option_ty_ty @ F @ nil_option_ty) = nil_ty)))). % list.simps(8)
thf(fact_155_list_Osimps_I8_J, axiom,
    ((![F : option_ty > val]: ((map_option_ty_val @ F @ nil_option_ty) = nil_val)))). % list.simps(8)
thf(fact_156_list_Osimps_I8_J, axiom,
    ((![F : val > option_ty]: ((map_val_option_ty @ F @ nil_val) = nil_option_ty)))). % list.simps(8)
thf(fact_157_list_Osimps_I8_J, axiom,
    ((![F : ty > option_ty]: ((map_ty_option_ty @ F @ nil_ty) = nil_option_ty)))). % list.simps(8)
thf(fact_158_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : ty > val, Ys : list_ty]: (((map_ty_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_159_map__eq__imp__length__eq, axiom,
    ((![F : ty > ty, Xs : list_ty, G : ty > ty, Ys : list_ty]: (((map_ty_ty @ F @ Xs) = (map_ty_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_160_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : val > val, Ys : list_val]: (((map_ty_val @ F @ Xs) = (map_val_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_161_map__eq__imp__length__eq, axiom,
    ((![F : ty > ty, Xs : list_ty, G : val > ty, Ys : list_val]: (((map_ty_ty @ F @ Xs) = (map_val_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_162_map__eq__imp__length__eq, axiom,
    ((![F : val > val, Xs : list_val, G : ty > val, Ys : list_ty]: (((map_val_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_163_map__eq__imp__length__eq, axiom,
    ((![F : val > ty, Xs : list_val, G : ty > ty, Ys : list_ty]: (((map_val_ty @ F @ Xs) = (map_ty_ty @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_164_map__eq__imp__length__eq, axiom,
    ((![F : list_char > ty, Xs : list_list_char, G : ty > ty, Ys : list_ty]: (((map_list_char_ty @ F @ Xs) = (map_ty_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_165_map__eq__imp__length__eq, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : ty > val, Ys : list_ty]: (((map_list_char_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_166_map__eq__imp__length__eq, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : val > val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (map_val_val @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_167_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : list_char > val, Ys : list_list_char]: (((map_ty_val @ F @ Xs) = (map_list_char_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_168_list_Octr__transfer_I1_J, axiom,
    ((![R : val > ty > $o]: (list_all2_val_ty @ R @ nil_val @ nil_ty)))). % list.ctr_transfer(1)
thf(fact_169_list_Octr__transfer_I1_J, axiom,
    ((![R : val > val > $o]: (list_all2_val_val @ R @ nil_val @ nil_val)))). % list.ctr_transfer(1)
thf(fact_170_list_Octr__transfer_I1_J, axiom,
    ((![R : ty > ty > $o]: (list_all2_ty_ty @ R @ nil_ty @ nil_ty)))). % list.ctr_transfer(1)
thf(fact_171_list_Octr__transfer_I1_J, axiom,
    ((![R : ty > val > $o]: (list_all2_ty_val @ R @ nil_ty @ nil_val)))). % list.ctr_transfer(1)
thf(fact_172_list_Octr__transfer_I1_J, axiom,
    ((![R : list_char > ty > $o]: (list_a1770748705har_ty @ R @ nil_list_char @ nil_ty)))). % list.ctr_transfer(1)
thf(fact_173_list_Octr__transfer_I1_J, axiom,
    ((![R : list_char > val > $o]: (list_a280217834ar_val @ R @ nil_list_char @ nil_val)))). % list.ctr_transfer(1)
thf(fact_174_list_Octr__transfer_I1_J, axiom,
    ((![R : ty > option_ty > $o]: (list_a765198023ion_ty @ R @ nil_ty @ nil_option_ty)))). % list.ctr_transfer(1)
thf(fact_175_list_Octr__transfer_I1_J, axiom,
    ((![R : val > list_char > $o]: (list_a1248766058t_char @ R @ nil_val @ nil_list_char)))). % list.ctr_transfer(1)
thf(fact_176_list_Octr__transfer_I1_J, axiom,
    ((![R : val > option_ty > $o]: (list_a509749264ion_ty @ R @ nil_val @ nil_option_ty)))). % list.ctr_transfer(1)
thf(fact_177_list_Octr__transfer_I1_J, axiom,
    ((![R : option_ty > ty > $o]: (list_a1442669255_ty_ty @ R @ nil_option_ty @ nil_ty)))). % list.ctr_transfer(1)
thf(fact_178_list__all2__lengthD, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_179_list__all2__lengthD, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_180_list__all2__lengthD, axiom,
    ((![P : val > ty > $o, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_181_list__all2__lengthD, axiom,
    ((![P : val > val > $o, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_182_list__all2__lengthD, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % list_all2_lengthD
thf(fact_183_list__all2__lengthD, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ P @ Xs @ Ys) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % list_all2_lengthD
thf(fact_184_list__all2__lengthD, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_185_list__all2__lengthD, axiom,
    ((![P : ty > option_ty > $o, Xs : list_ty, Ys : list_option_ty]: ((list_a765198023ion_ty @ P @ Xs @ Ys) => ((size_size_list_ty @ Xs) = (size_s1569909163ion_ty @ Ys)))))). % list_all2_lengthD
thf(fact_186_list__all2__lengthD, axiom,
    ((![P : val > list_char > $o, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % list_all2_lengthD
thf(fact_187_list__all2__lengthD, axiom,
    ((![P : val > option_ty > $o, Xs : list_val, Ys : list_option_ty]: ((list_a509749264ion_ty @ P @ Xs @ Ys) => ((size_size_list_val @ Xs) = (size_s1569909163ion_ty @ Ys)))))). % list_all2_lengthD
thf(fact_188_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_189_prod__induct4, axiom,
    ((![P : produc81045532t_char > $o, X3 : produc81045532t_char]: ((![A2 : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (P @ (produc1808722894t_char @ A2 @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D))))) => (P @ X3))))). % prod_induct4
thf(fact_190_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_191_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_192_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_193_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_194_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_195_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_196_confs__conv__map, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts2 : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts2) = (?[Ts3 : list_ty]: ((((map_val_option_ty @ (typeof_h @ H) @ Vs) = (map_ty_option_ty @ some_ty @ Ts3))) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts2)))))))). % confs_conv_map
thf(fact_197_blocksEval, axiom,
    ((![Ps : list_list_char, Ts : list_ty, Vs : list_val, 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]: (((size_s2008079621t_char @ Ps) = (size_size_list_ty @ Ts)) => (((size_s2008079621t_char @ Ps) = (size_size_list_val @ Vs)) => ((eval @ P @ (blocks @ (produc1808722894t_char @ Ps @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (?[L3 : list_char > option_val]: (eval @ P @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Ps @ Vs)) @ E2 @ (produc52622304on_val @ H2 @ L3))))))))). % blocksEval
thf(fact_198_map__eq__map__tailrec, axiom,
    ((map_val_option_ty = map_ta1696661655ion_ty))). % map_eq_map_tailrec
thf(fact_199_map__eq__map__tailrec, axiom,
    ((map_ty_option_ty = map_ta56519374ion_ty))). % map_eq_map_tailrec
thf(fact_200_map__eq__map__tailrec, axiom,
    ((map_va1515327237t_char = map_ta466610747t_char))). % map_eq_map_tailrec
thf(fact_201_map__eq__map__tailrec, axiom,
    ((map_list_char_val = map_ta1467130225ar_val))). % map_eq_map_tailrec
thf(fact_202_map__eq__map__tailrec, axiom,
    ((map_exp_list_char_ty = map_ta650207092har_ty))). % map_eq_map_tailrec
thf(fact_203_map__eq__map__tailrec, axiom,
    ((map_ty_val = map_tailrec_ty_val))). % map_eq_map_tailrec
thf(fact_204_map__eq__map__tailrec, axiom,
    ((map_ty_list_char = map_ta795536168t_char))). % map_eq_map_tailrec
thf(fact_205_map__eq__map__tailrec, axiom,
    ((map_ty_exp_list_char = map_ta566847940t_char))). % map_eq_map_tailrec
thf(fact_206_map__eq__map__tailrec, axiom,
    ((map_ty_ty = map_tailrec_ty_ty))). % map_eq_map_tailrec
thf(fact_207_list__ex1__simps_I1_J, axiom,
    ((![P : list_char > $o]: (~ ((list_ex1_list_char @ P @ nil_list_char)))))). % list_ex1_simps(1)
thf(fact_208_list__ex1__simps_I1_J, axiom,
    ((![P : ty > $o]: (~ ((list_ex1_ty @ P @ nil_ty)))))). % list_ex1_simps(1)
thf(fact_209_list__ex1__simps_I1_J, axiom,
    ((![P : val > $o]: (~ ((list_ex1_val @ P @ nil_val)))))). % list_ex1_simps(1)
thf(fact_210_list__ex1__simps_I1_J, axiom,
    ((![P : exp_list_char > $o]: (~ ((list_e560027540t_char @ P @ nil_exp_list_char)))))). % list_ex1_simps(1)
thf(fact_211_list__ex1__simps_I1_J, axiom,
    ((![P : option_ty > $o]: (~ ((list_ex1_option_ty @ P @ nil_option_ty)))))). % list_ex1_simps(1)
thf(fact_212_bind__simps_I1_J, axiom,
    ((![F : option_ty > list_option_ty]: ((bind_o794826391ion_ty @ nil_option_ty @ F) = nil_option_ty)))). % bind_simps(1)
thf(fact_213_blocksFinal, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((final_list_char @ E) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L))) @ (transi111096263on_val @ (red @ P))))))))). % blocksFinal
thf(fact_214_WTrts__Val, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Vs : list_val, Ts : list_ty]: ((wTrts @ P @ H @ E3 @ (map_va1515327237t_char @ val_list_char @ Vs) @ Ts) = ((map_val_option_ty @ (typeof_h @ H) @ Vs) = (map_ty_option_ty @ some_ty @ Ts)))))). % WTrts_Val
thf(fact_215_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_216_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, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E4 @ H3 @ L4 @ E4 @ H3 @ L4)) => ((![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, E5 : exp_list_char, H4 : nat > option2118145160on_val, L5 : 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)) => ((R @ E_1 @ H_1 @ L_1 @ E5 @ H4 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L5)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_217_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_218_WTrtNil, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty]: (wTrts @ P @ H @ E3 @ nil_exp_list_char @ nil_ty)))). % WTrtNil
thf(fact_219_WTrts__same__length, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrts @ P @ H @ E3 @ Es @ Ts) => ((size_s329991613t_char @ Es) = (size_size_list_ty @ Ts)))))). % WTrts_same_length
thf(fact_220_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_221_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_222_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V : val, T : ty, P : list_P1234162913t_char, E3 : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T)) => (wTrt @ P @ H @ E3 @ (val_list_char @ V) @ T))))). % WTrtVal
thf(fact_223_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, V : val, T : ty]: ((hext @ H @ H2) => (((typeof_h @ H @ V) = (some_ty @ T)) => ((typeof_h @ H2 @ V) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_224_eval__hext, 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]: ((eval @ P @ E @ (produc52622304on_val @ H @ L) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (hext @ H @ H2))))). % eval_hext
thf(fact_225_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_226_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_227_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C2 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs2))))))))). % hext_objD
thf(fact_228_hext__def, axiom,
    ((hext = (^[H6 : nat > option2118145160on_val]: (^[H7 : nat > option2118145160on_val]: (![A5 : nat]: (![C3 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H6 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H7 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs4)))))))))))))). % hext_def
thf(fact_229_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A2 : nat, C4 : list_char, Fs5 : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs6)))))) => (hext @ H @ H2))))). % hextI
thf(fact_230_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E2 @ S3) => (~ (((E2 = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_231_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S2 @ (val_list_char @ V) @ S2)))). % Val
thf(fact_232_eval__final, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ E @ S2 @ E2 @ S3) => (final_list_char @ E2))))). % eval_final
thf(fact_233_eval__finalId, axiom,
    ((![E : exp_list_char, P : list_P1234162913t_char, S2 : produc515445032on_val]: ((final_list_char @ E) => (eval @ P @ E @ S2 @ E @ S2))))). % eval_finalId
thf(fact_234_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_235_blocksRedsFinal, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, 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, L6 : list_char > option_val]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((distinct_list_char @ Vs2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Vs2 @ Vs))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E2) => ((L6 = (overri1171685873on_val @ L2 @ L @ (set_list_char2 @ Vs2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L6))) @ (transi111096263on_val @ (red @ P)))))))))))). % blocksRedsFinal
thf(fact_236_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_237_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_238_blocksReds, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, 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]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((distinct_list_char @ Vs2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Vs2 @ Vs))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ (map_list_char_val @ (comp_o345283222t_char @ the_val @ L2) @ Vs2) @ E2)))) @ (produc52622304on_val @ H2 @ (overri1171685873on_val @ L2 @ L @ (set_list_char2 @ Vs2))))) @ (transi111096263on_val @ (red @ P)))))))))). % blocksReds
thf(fact_239_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_240_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_241_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_242_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_243_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M2 : 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) @ M2 @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M2 @ Es2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams

% Conjectures (3)
thf(conj_0, hypothesis,
    (((size_s2008079621t_char @ nil_list_char) = (size_size_list_ty @ nil_ty)))).
thf(conj_1, hypothesis,
    (((size_size_list_val @ nil_val) = (size_size_list_ty @ nil_ty)))).
thf(conj_2, conjecture,
    (((wTrt @ p @ h @ e @ (blocks @ (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ nil_val @ ea)))) @ t) = (((wTrt @ p @ h @ (map_up703499792har_ty @ e @ nil_list_char @ nil_ty) @ ea @ t)) & ((?[Ts4 : list_ty]: ((((map_val_option_ty @ (typeof_h @ h) @ nil_val) = (map_ty_option_ty @ some_ty @ Ts4))) & ((list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts4 @ nil_ty))))))))).
