% 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_112__5334550_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:20.455

% Could-be-implicit typings (43)
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__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_J_J_J_J_J_J, type,
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thf(ty_n_t__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,
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thf(ty_n_t__Option__Ooption_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_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__List__Olist_It__List__Olist_It__Value__Oval_J_J, type,
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thf(ty_n_t__Set__Oset_It__List__Olist_It__Value__Oval_J_J, type,
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thf(ty_n_t__List__Olist_It__List__Olist_It__Type__Oty_J_J, type,
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thf(ty_n_t__Set__Oset_It__List__Olist_It__Type__Oty_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__Set__Oset_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__Set__Oset_It__Type__Oty_J, type,
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thf(ty_n_t__String__Ochar, type,
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thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (107)
thf(sy_c_BigStep_Oeval, type,
    eval : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_DefAss_O_092_060D_062_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_DefAss_OhyperUn_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_If_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_If_001t__List__Olist_It__Type__Oty_J, type,
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thf(sy_c_If_001t__List__Olist_It__Value__Oval_J, type,
    if_list_val : $o > list_val > list_val > list_val).
thf(sy_c_List_Oappend_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Oappend_001t__Type__Oty, type,
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thf(sy_c_List_Oappend_001t__Value__Oval, type,
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thf(sy_c_List_Oinsert_001t__List__Olist_It__String__Ochar_J, type,
    insert_list_char : list_char > list_list_char > list_list_char).
thf(sy_c_List_Oinsert_001t__Type__Oty, type,
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thf(sy_c_List_Oinsert_001t__Value__Oval, type,
    insert_val : val > list_val > list_val).
thf(sy_c_List_Olex_001t__List__Olist_It__String__Ochar_J, type,
    lex_list_char : set_Pr164112643t_char > set_Pr2117892643t_char).
thf(sy_c_List_Olex_001t__Type__Oty, type,
    lex_ty : set_Pr1194734255_ty_ty > set_Pr1785354703ist_ty).
thf(sy_c_List_Olex_001t__Value__Oval, type,
    lex_val : set_Pr1870322241al_val > set_Pr723931873st_val).
thf(sy_c_List_Olexn_001t__List__Olist_It__String__Ochar_J, type,
    lexn_list_char : set_Pr164112643t_char > nat > set_Pr2117892643t_char).
thf(sy_c_List_Olexn_001t__Type__Oty, type,
    lexn_ty : set_Pr1194734255_ty_ty > nat > set_Pr1785354703ist_ty).
thf(sy_c_List_Olexn_001t__Value__Oval, type,
    lexn_val : set_Pr1870322241al_val > nat > set_Pr723931873st_val).
thf(sy_c_List_Olexord_001t__List__Olist_It__String__Ochar_J, type,
    lexord_list_char : set_Pr164112643t_char > set_Pr2117892643t_char).
thf(sy_c_List_Olexord_001t__Type__Oty, type,
    lexord_ty : set_Pr1194734255_ty_ty > set_Pr1785354703ist_ty).
thf(sy_c_List_Olexord_001t__Value__Oval, type,
    lexord_val : set_Pr1870322241al_val > set_Pr723931873st_val).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    cons_list_list_char : list_list_char > list_list_list_char > list_list_list_char).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__String__Ochar_J, type,
    cons_list_char : list_char > list_list_char > list_list_char).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Type__Oty_J, type,
    cons_list_ty : list_ty > list_list_ty > list_list_ty).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Value__Oval_J, type,
    cons_list_val : list_val > list_list_val > list_list_val).
thf(sy_c_List_Olist_OCons_001t__String__Ochar, type,
    cons_char : char > list_char > list_char).
thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
    cons_ty : ty > list_ty > list_ty).
thf(sy_c_List_Olist_OCons_001t__Value__Oval, type,
    cons_val : val > list_val > list_val).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    nil_list_list_char : list_list_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__List__Olist_It__Type__Oty_J, type,
    nil_list_ty : list_list_ty).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Value__Oval_J, type,
    nil_list_val : list_list_val).
thf(sy_c_List_Olist_ONil_001t__String__Ochar, type,
    nil_char : list_char).
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_Oset_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    set_list_list_char2 : list_list_list_char > set_list_list_char).
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_Oset_001t__List__Olist_It__Type__Oty_J, type,
    set_list_ty2 : list_list_ty > set_list_ty).
thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Value__Oval_J, type,
    set_list_val2 : list_list_val > set_list_val).
thf(sy_c_List_Olist_Oset_001t__Type__Oty, type,
    set_ty2 : list_ty > set_ty).
thf(sy_c_List_Olist_Oset_001t__Value__Oval, type,
    set_val2 : list_val > set_val).
thf(sy_c_List_Olistrel1_001t__List__Olist_It__String__Ochar_J, type,
    listrel1_list_char : set_Pr164112643t_char > set_Pr2117892643t_char).
thf(sy_c_List_Olistrel1_001t__Type__Oty, type,
    listrel1_ty : set_Pr1194734255_ty_ty > set_Pr1785354703ist_ty).
thf(sy_c_List_Olistrel1_001t__Value__Oval, type,
    listrel1_val : set_Pr1870322241al_val > set_Pr723931873st_val).
thf(sy_c_List_On__lists_001t__List__Olist_It__String__Ochar_J, type,
    n_lists_list_char : nat > list_list_char > list_list_list_char).
thf(sy_c_List_On__lists_001t__String__Ochar, type,
    n_lists_char : nat > list_char > list_list_char).
thf(sy_c_List_On__lists_001t__Type__Oty, type,
    n_lists_ty : nat > list_ty > list_list_ty).
thf(sy_c_List_On__lists_001t__Value__Oval, type,
    n_lists_val : nat > list_val > list_list_val).
thf(sy_c_List_Oproduct__lists_001t__List__Olist_It__String__Ochar_J, type,
    produc2062551602t_char : list_list_list_char > list_list_list_char).
thf(sy_c_List_Oproduct__lists_001t__String__Ochar, type,
    product_lists_char : list_list_char > list_list_char).
thf(sy_c_List_Oproduct__lists_001t__Type__Oty, type,
    product_lists_ty : list_list_ty > list_list_ty).
thf(sy_c_List_Oproduct__lists_001t__Value__Oval, type,
    product_lists_val : list_list_val > list_list_val).
thf(sy_c_List_Osubseqs_001t__List__Olist_It__String__Ochar_J, type,
    subseqs_list_char : list_list_char > list_list_list_char).
thf(sy_c_List_Osubseqs_001t__String__Ochar, type,
    subseqs_char : list_char > list_list_char).
thf(sy_c_List_Osubseqs_001t__Type__Oty, type,
    subseqs_ty : list_ty > list_list_ty).
thf(sy_c_List_Osubseqs_001t__Value__Oval, type,
    subseqs_val : list_val > list_list_val).
thf(sy_c_Map_Omap__upds_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    map_up354775738t_char : (list_char > option_list_char) > list_list_char > list_list_char > list_char > option_list_char).
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_Map_Omap__upds_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
    map_up436965904t_char : (ty > option_list_char) > list_ty > list_list_char > ty > option_list_char).
thf(sy_c_Map_Omap__upds_001t__Type__Oty_001t__Type__Oty, type,
    map_upds_ty_ty : (ty > option_ty) > list_ty > list_ty > ty > option_ty).
thf(sy_c_Map_Omap__upds_001t__Type__Oty_001t__Value__Oval, type,
    map_upds_ty_val : (ty > option_val) > list_ty > list_val > ty > option_val).
thf(sy_c_Map_Omap__upds_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
    map_up1545155545t_char : (val > option_list_char) > list_val > list_list_char > val > option_list_char).
thf(sy_c_Map_Omap__upds_001t__Value__Oval_001t__Type__Oty, type,
    map_upds_val_ty : (val > option_ty) > list_val > list_ty > val > option_ty).
thf(sy_c_Map_Omap__upds_001t__Value__Oval_001t__Value__Oval, type,
    map_upds_val_val : (val > option_val) > list_val > list_val > val > option_val).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    size_s1019276181t_char : list_list_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__List__Olist_It__Type__Oty_J_J, type,
    size_s1063623787ist_ty : list_list_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Value__Oval_J_J, type,
    size_s527075124st_val : list_list_val > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__String__Ochar_J, type,
    size_size_list_char : list_char > 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_Option_Ooption_OSome_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    some_set_list_char : set_list_char > option_set_list_char).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_M_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    produc1986826718t_char : (list_char > list_char > $o) > list_list_char > produc1844257764t_char).
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_001_062_It__Type__Oty_M_062_It__Type__Oty_M_Eo_J_J_001t__List__Olist_It__Type__Oty_J, type,
    produc5654152ist_ty : (ty > ty > $o) > list_ty > produc508135182ist_ty).
thf(sy_c_Product__Type_OPair_001_062_It__Value__Oval_M_062_It__Value__Oval_M_Eo_J_J_001t__List__Olist_It__Value__Oval_J, type,
    produc578411711st_val : (val > val > $o) > list_val > produc1050553413st_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    produc1181934459t_char : list_list_char > list_list_char > produc1410698691t_char).
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_001t__List__Olist_It__String__Ochar_J, type,
    produc1304532571t_char : list_char > list_char > produc1257910179t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__List__Olist_It__Type__Oty_J, type,
    produc1089615911ist_ty : list_ty > list_ty > produc1714969711ist_ty).
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__List__Olist_It__Value__Oval_J_001t__List__Olist_It__Value__Oval_J, type,
    produc180957881st_val : list_val > list_val > produc1608520577st_val).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_001t__Type__Oty, type,
    product_Pair_ty_ty : ty > ty > product_prod_ty_ty).
thf(sy_c_Product__Type_OPair_001t__Value__Oval_001t__Value__Oval, type,
    product_Pair_val_val : val > val > product_prod_val_val).
thf(sy_c_SmallStep_Oblocks, type,
    blocks : produc81045532t_char > exp_list_char).
thf(sy_c_member_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    member568250120t_char : list_list_char > set_list_list_char > $o).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J, type,
    member_list_char : list_char > set_list_char > $o).
thf(sy_c_member_001t__List__Olist_It__Type__Oty_J, type,
    member_list_ty : list_ty > set_list_ty > $o).
thf(sy_c_member_001t__List__Olist_It__Value__Oval_J, type,
    member_list_val : list_val > set_list_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J, type,
    member725442668t_char : produc1410698691t_char > set_Pr2117892643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    member89690956t_char : produc1257910179t_char > set_Pr164112643t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__List__Olist_It__Type__Oty_J_J, type,
    member1942114840ist_ty : produc1714969711ist_ty > set_Pr1785354703ist_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Value__Oval_J_Mt__List__Olist_It__Value__Oval_J_J, type,
    member1382006826st_val : produc1608520577st_val > set_Pr723931873st_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Type__Oty_Mt__Type__Oty_J, type,
    member2070851320_ty_ty : product_prod_ty_ty > set_Pr1194734255_ty_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Value__Oval_Mt__Value__Oval_J, type,
    member1494223754al_val : product_prod_val_val > set_Pr1870322241al_val > $o).
thf(sy_c_member_001t__Type__Oty, type,
    member_ty : ty > set_ty > $o).
thf(sy_c_member_001t__Value__Oval, type,
    member_val : val > set_val > $o).
thf(sy_v_A, type,
    a : option_set_list_char).
thf(sy_v_T, type,
    t : ty).
thf(sy_v_Tsa, type,
    tsa : list_ty).
thf(sy_v_V, type,
    v : list_char).
thf(sy_v_Vsa, type,
    vsa : list_list_char).
thf(sy_v_ea, type,
    ea : exp_list_char).
thf(sy_v_v, type,
    v2 : val).
thf(sy_v_vsa, type,
    vsa2 : list_val).

% Relevant facts (248)
thf(fact_0_prod__cases4, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (~ ((Y = (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D)))))))))))). % prod_cases4
thf(fact_1_prod__induct4, axiom,
    ((![P : produc81045532t_char > $o, X : produc81045532t_char]: ((![A : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (P @ (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_2_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_3_list_Oinject, axiom,
    ((![X21 : list_char, X22 : list_list_char, Y21 : list_char, Y22 : list_list_char]: (((cons_list_char @ X21 @ X22) = (cons_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_4_list_Oinject, axiom,
    ((![X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X22) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_5_list_Oinject, axiom,
    ((![X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: (((cons_val @ X21 @ X22) = (cons_val @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_6_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_7_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_8_prod_Oinject, axiom,
    ((![X1 : list_val, X2 : exp_list_char, Y1 : list_val, Y2 : exp_list_char]: (((produc823987298t_char @ X1 @ X2) = (produc823987298t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_9_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_10_old_Oprod_Oinject, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A2 @ B2) = (produc1808722894t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_11_old_Oprod_Oinject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_12_old_Oprod_Oinject, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char]: (((produc823987298t_char @ A2 @ B2) = (produc823987298t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_13_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_14_old_Oprod_Oinducts, axiom,
    ((![P : produc81045532t_char > $o, Prod : produc81045532t_char]: ((![A : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_15_old_Oprod_Oinducts, axiom,
    ((![P : produc111478616t_char > $o, Prod : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_16_old_Oprod_Oinducts, axiom,
    ((![P : produc1109669680t_char > $o, Prod : produc1109669680t_char]: ((![A : list_val, B : exp_list_char]: (P @ (produc823987298t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_17_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_18_old_Oprod_Oexhaust, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : produc111478616t_char]: (~ ((Y = (produc1808722894t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_19_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_20_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1109669680t_char]: (~ ((![A : list_val, B : exp_list_char]: (~ ((Y = (produc823987298t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_21_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_22_Pair__inject, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A2 @ B2) = (produc1808722894t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_23_Pair__inject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_24_Pair__inject, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char]: (((produc823987298t_char @ A2 @ B2) = (produc823987298t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_25_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_26_prod__cases, axiom,
    ((![P : produc81045532t_char > $o, P2 : produc81045532t_char]: ((![A : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_27_prod__cases, axiom,
    ((![P : produc111478616t_char > $o, P2 : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_28_prod__cases, axiom,
    ((![P : produc1109669680t_char > $o, P2 : produc1109669680t_char]: ((![A : list_val, B : exp_list_char]: (P @ (produc823987298t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_29_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_30_surj__pair, axiom,
    ((![P2 : produc81045532t_char]: (?[X3 : list_list_char, Y3 : produc111478616t_char]: (P2 = (produc1808722894t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_31_surj__pair, axiom,
    ((![P2 : produc111478616t_char]: (?[X3 : list_ty, Y3 : produc1109669680t_char]: (P2 = (produc1806338192t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_32_surj__pair, axiom,
    ((![P2 : produc1109669680t_char]: (?[X3 : list_val, Y3 : exp_list_char]: (P2 = (produc823987298t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_33_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_34_not__Cons__self2, axiom,
    ((![X : list_char, Xs : list_list_char]: (~ (((cons_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_35_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_36_not__Cons__self2, axiom,
    ((![X : val, Xs : list_val]: (~ (((cons_val @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_37_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_38_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_39_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_40_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_41_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_42_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_43_prod__induct3, axiom,
    ((![P : produc81045532t_char > $o, X : produc81045532t_char]: ((![A : list_list_char, B : list_ty, C : produc1109669680t_char]: (P @ (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_44_prod__induct3, axiom,
    ((![P : produc111478616t_char > $o, X : produc111478616t_char]: ((![A : list_ty, B : list_val, C : exp_list_char]: (P @ (produc1806338192t_char @ A @ (produc823987298t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_45_prod__cases3, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : list_ty, C : produc1109669680t_char]: (~ ((Y = (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ C))))))))))). % prod_cases3
thf(fact_46_prod__cases3, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : list_val, C : exp_list_char]: (~ ((Y = (produc1806338192t_char @ A @ (produc823987298t_char @ B @ C))))))))))). % prod_cases3
thf(fact_47_list_Oset__cases, axiom,
    ((![E : list_char, A2 : list_list_char]: ((member_list_char @ E @ (set_list_char2 @ A2)) => ((![Z2 : list_list_char]: (~ ((A2 = (cons_list_char @ E @ Z2))))) => (~ ((![Z1 : list_char, Z2 : list_list_char]: ((A2 = (cons_list_char @ Z1 @ Z2)) => (~ ((member_list_char @ E @ (set_list_char2 @ Z2))))))))))))). % list.set_cases
thf(fact_48_list_Oset__cases, axiom,
    ((![E : ty, A2 : list_ty]: ((member_ty @ E @ (set_ty2 @ A2)) => ((![Z2 : list_ty]: (~ ((A2 = (cons_ty @ E @ Z2))))) => (~ ((![Z1 : ty, Z2 : list_ty]: ((A2 = (cons_ty @ Z1 @ Z2)) => (~ ((member_ty @ E @ (set_ty2 @ Z2))))))))))))). % list.set_cases
thf(fact_49_list_Oset__cases, axiom,
    ((![E : val, A2 : list_val]: ((member_val @ E @ (set_val2 @ A2)) => ((![Z2 : list_val]: (~ ((A2 = (cons_val @ E @ Z2))))) => (~ ((![Z1 : val, Z2 : list_val]: ((A2 = (cons_val @ Z1 @ Z2)) => (~ ((member_val @ E @ (set_val2 @ Z2))))))))))))). % list.set_cases
thf(fact_50_set__ConsD, axiom,
    ((![Y : list_char, X : list_char, Xs : list_list_char]: ((member_list_char @ Y @ (set_list_char2 @ (cons_list_char @ X @ Xs))) => ((Y = X) | (member_list_char @ Y @ (set_list_char2 @ Xs))))))). % set_ConsD
thf(fact_51_set__ConsD, axiom,
    ((![Y : ty, X : ty, Xs : list_ty]: ((member_ty @ Y @ (set_ty2 @ (cons_ty @ X @ Xs))) => ((Y = X) | (member_ty @ Y @ (set_ty2 @ Xs))))))). % set_ConsD
thf(fact_52_set__ConsD, axiom,
    ((![Y : val, X : val, Xs : list_val]: ((member_val @ Y @ (set_val2 @ (cons_val @ X @ Xs))) => ((Y = X) | (member_val @ Y @ (set_val2 @ Xs))))))). % set_ConsD
thf(fact_53_list_Oset__intros_I1_J, axiom,
    ((![X21 : list_char, X22 : list_list_char]: (member_list_char @ X21 @ (set_list_char2 @ (cons_list_char @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_54_list_Oset__intros_I1_J, axiom,
    ((![X21 : ty, X22 : list_ty]: (member_ty @ X21 @ (set_ty2 @ (cons_ty @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_55_list_Oset__intros_I1_J, axiom,
    ((![X21 : val, X22 : list_val]: (member_val @ X21 @ (set_val2 @ (cons_val @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_56_list_Oset__intros_I2_J, axiom,
    ((![Y : list_char, X22 : list_list_char, X21 : list_char]: ((member_list_char @ Y @ (set_list_char2 @ X22)) => (member_list_char @ Y @ (set_list_char2 @ (cons_list_char @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_57_list_Oset__intros_I2_J, axiom,
    ((![Y : ty, X22 : list_ty, X21 : ty]: ((member_ty @ Y @ (set_ty2 @ X22)) => (member_ty @ Y @ (set_ty2 @ (cons_ty @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_58_list_Oset__intros_I2_J, axiom,
    ((![Y : val, X22 : list_val, X21 : val]: ((member_val @ Y @ (set_val2 @ X22)) => (member_val @ Y @ (set_val2 @ (cons_val @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_59_in__set__product__lists__length, axiom,
    ((![Xs : list_char, Xss : list_list_char]: ((member_list_char @ Xs @ (set_list_char2 @ (product_lists_char @ Xss))) => ((size_size_list_char @ Xs) = (size_s2008079621t_char @ Xss)))))). % in_set_product_lists_length
thf(fact_60_in__set__product__lists__length, axiom,
    ((![Xs : list_list_char, Xss : list_list_list_char]: ((member568250120t_char @ Xs @ (set_list_list_char2 @ (produc2062551602t_char @ Xss))) => ((size_s2008079621t_char @ Xs) = (size_s1019276181t_char @ Xss)))))). % in_set_product_lists_length
thf(fact_61_in__set__product__lists__length, axiom,
    ((![Xs : list_ty, Xss : list_list_ty]: ((member_list_ty @ Xs @ (set_list_ty2 @ (product_lists_ty @ Xss))) => ((size_size_list_ty @ Xs) = (size_s1063623787ist_ty @ Xss)))))). % in_set_product_lists_length
thf(fact_62_in__set__product__lists__length, axiom,
    ((![Xs : list_val, Xss : list_list_val]: ((member_list_val @ Xs @ (set_list_val2 @ (product_lists_val @ Xss))) => ((size_size_list_val @ Xs) = (size_s527075124st_val @ Xss)))))). % in_set_product_lists_length
thf(fact_63_Cons__in__lex, axiom,
    ((![X : list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ (cons_list_char @ Y @ Ys)) @ (lex_list_char @ R)) = (((((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R)) & (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys))))) | ((((X = Y)) & ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (lex_list_char @ R)))))))))). % Cons_in_lex
thf(fact_64_Cons__in__lex, axiom,
    ((![X : ty, Xs : list_ty, Y : ty, Ys : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) @ (lex_ty @ R)) = (((((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ R)) & (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys))))) | ((((X = Y)) & ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (lex_ty @ R)))))))))). % Cons_in_lex
thf(fact_65_Cons__in__lex, axiom,
    ((![X : val, Xs : list_val, Y : val, Ys : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) @ (lex_val @ R)) = (((((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R)) & (((size_size_list_val @ Xs) = (size_size_list_val @ Ys))))) | ((((X = Y)) & ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (lex_val @ R)))))))))). % Cons_in_lex
thf(fact_66_not__in__set__insert, axiom,
    ((![X : list_char, Xs : list_list_char]: ((~ ((member_list_char @ X @ (set_list_char2 @ Xs)))) => ((insert_list_char @ X @ Xs) = (cons_list_char @ X @ Xs)))))). % not_in_set_insert
thf(fact_67_not__in__set__insert, axiom,
    ((![X : ty, Xs : list_ty]: ((~ ((member_ty @ X @ (set_ty2 @ Xs)))) => ((insert_ty @ X @ Xs) = (cons_ty @ X @ Xs)))))). % not_in_set_insert
thf(fact_68_not__in__set__insert, axiom,
    ((![X : val, Xs : list_val]: ((~ ((member_val @ X @ (set_val2 @ Xs)))) => ((insert_val @ X @ Xs) = (cons_val @ X @ Xs)))))). % not_in_set_insert
thf(fact_69_length__n__lists__elem, axiom,
    ((![Ys : list_char, N : nat, Xs : list_char]: ((member_list_char @ Ys @ (set_list_char2 @ (n_lists_char @ N @ Xs))) => ((size_size_list_char @ Ys) = N))))). % length_n_lists_elem
thf(fact_70_length__n__lists__elem, axiom,
    ((![Ys : list_list_char, N : nat, Xs : list_list_char]: ((member568250120t_char @ Ys @ (set_list_list_char2 @ (n_lists_list_char @ N @ Xs))) => ((size_s2008079621t_char @ Ys) = N))))). % length_n_lists_elem
thf(fact_71_length__n__lists__elem, axiom,
    ((![Ys : list_ty, N : nat, Xs : list_ty]: ((member_list_ty @ Ys @ (set_list_ty2 @ (n_lists_ty @ N @ Xs))) => ((size_size_list_ty @ Ys) = N))))). % length_n_lists_elem
thf(fact_72_length__n__lists__elem, axiom,
    ((![Ys : list_val, N : nat, Xs : list_val]: ((member_list_val @ Ys @ (set_list_val2 @ (n_lists_val @ N @ Xs))) => ((size_size_list_val @ Ys) = N))))). % length_n_lists_elem
thf(fact_73_hyperUn__assoc, axiom,
    ((![A4 : option_set_list_char, B4 : option_set_list_char, C2 : option_set_list_char]: ((hyperUn_list_char @ (hyperUn_list_char @ A4 @ B4) @ C2) = (hyperUn_list_char @ A4 @ (hyperUn_list_char @ B4 @ C2)))))). % hyperUn_assoc
thf(fact_74_Cons__in__subseqsD, axiom,
    ((![Y : char, Ys : list_char, Xs : list_char]: ((member_list_char @ (cons_char @ Y @ Ys) @ (set_list_char2 @ (subseqs_char @ Xs))) => (member_list_char @ Ys @ (set_list_char2 @ (subseqs_char @ Xs))))))). % Cons_in_subseqsD
thf(fact_75_Cons__in__subseqsD, axiom,
    ((![Y : list_char, Ys : list_list_char, Xs : list_list_char]: ((member568250120t_char @ (cons_list_char @ Y @ Ys) @ (set_list_list_char2 @ (subseqs_list_char @ Xs))) => (member568250120t_char @ Ys @ (set_list_list_char2 @ (subseqs_list_char @ Xs))))))). % Cons_in_subseqsD
thf(fact_76_Cons__in__subseqsD, axiom,
    ((![Y : ty, Ys : list_ty, Xs : list_ty]: ((member_list_ty @ (cons_ty @ Y @ Ys) @ (set_list_ty2 @ (subseqs_ty @ Xs))) => (member_list_ty @ Ys @ (set_list_ty2 @ (subseqs_ty @ Xs))))))). % Cons_in_subseqsD
thf(fact_77_Cons__in__subseqsD, axiom,
    ((![Y : val, Ys : list_val, Xs : list_val]: ((member_list_val @ (cons_val @ Y @ Ys) @ (set_list_val2 @ (subseqs_val @ Xs))) => (member_list_val @ Ys @ (set_list_val2 @ (subseqs_val @ Xs))))))). % Cons_in_subseqsD
thf(fact_78_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_79_List_Oinsert__def, axiom,
    ((insert_list_char = (^[X4 : list_char]: (^[Xs3 : list_list_char]: (if_list_list_char @ (member_list_char @ X4 @ (set_list_char2 @ Xs3)) @ Xs3 @ (cons_list_char @ X4 @ Xs3))))))). % List.insert_def
thf(fact_80_List_Oinsert__def, axiom,
    ((insert_ty = (^[X4 : ty]: (^[Xs3 : list_ty]: (if_list_ty @ (member_ty @ X4 @ (set_ty2 @ Xs3)) @ Xs3 @ (cons_ty @ X4 @ Xs3))))))). % List.insert_def
thf(fact_81_List_Oinsert__def, axiom,
    ((insert_val = (^[X4 : val]: (^[Xs3 : list_val]: (if_list_val @ (member_val @ X4 @ (set_val2 @ Xs3)) @ Xs3 @ (cons_val @ X4 @ Xs3))))))). % List.insert_def
thf(fact_82_in__set__insert, axiom,
    ((![X : list_char, Xs : list_list_char]: ((member_list_char @ X @ (set_list_char2 @ Xs)) => ((insert_list_char @ X @ Xs) = Xs))))). % in_set_insert
thf(fact_83_subseqs__refl, axiom,
    ((![Xs : list_char]: (member_list_char @ Xs @ (set_list_char2 @ (subseqs_char @ Xs)))))). % subseqs_refl
thf(fact_84_map__upds__apply__nontin, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > option_val, Ys : list_val]: ((~ ((member_list_char @ X @ (set_list_char2 @ Xs)))) => ((map_up576607321ar_val @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_85_lexord__cons__cons, axiom,
    ((![A2 : list_char, X : list_list_char, B2 : list_char, Y : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ A2 @ X) @ (cons_list_char @ B2 @ Y)) @ (lexord_list_char @ R)) = (((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ R)) | ((((A2 = B2)) & ((member725442668t_char @ (produc1181934459t_char @ X @ Y) @ (lexord_list_char @ R)))))))))). % lexord_cons_cons
thf(fact_86_lexord__cons__cons, axiom,
    ((![A2 : ty, X : list_ty, B2 : ty, Y : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ A2 @ X) @ (cons_ty @ B2 @ Y)) @ (lexord_ty @ R)) = (((member2070851320_ty_ty @ (product_Pair_ty_ty @ A2 @ B2) @ R)) | ((((A2 = B2)) & ((member1942114840ist_ty @ (produc1089615911ist_ty @ X @ Y) @ (lexord_ty @ R)))))))))). % lexord_cons_cons
thf(fact_87_lexord__cons__cons, axiom,
    ((![A2 : val, X : list_val, B2 : val, Y : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ A2 @ X) @ (cons_val @ B2 @ Y)) @ (lexord_val @ R)) = (((member1494223754al_val @ (product_Pair_val_val @ A2 @ B2) @ R)) | ((((A2 = B2)) & ((member1382006826st_val @ (produc180957881st_val @ X @ Y) @ (lexord_val @ R)))))))))). % lexord_cons_cons
thf(fact_88_lexn__length, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, R : set_Pr164112643t_char, N : nat]: ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (lexn_list_char @ R @ N)) => (((size_s2008079621t_char @ Xs) = N) & ((size_s2008079621t_char @ Ys) = N)))))). % lexn_length
thf(fact_89_lexn__length, axiom,
    ((![Xs : list_ty, Ys : list_ty, R : set_Pr1194734255_ty_ty, N : nat]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (lexn_ty @ R @ N)) => (((size_size_list_ty @ Xs) = N) & ((size_size_list_ty @ Ys) = N)))))). % lexn_length
thf(fact_90_lexn__length, axiom,
    ((![Xs : list_val, Ys : list_val, R : set_Pr1870322241al_val, N : nat]: ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (lexn_val @ R @ N)) => (((size_size_list_val @ Xs) = N) & ((size_size_list_val @ Ys) = N)))))). % lexn_length
thf(fact_91_Cons__listrel1__Cons, axiom,
    ((![X : list_char, Xs : list_list_char, Y : list_char, Ys : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ (cons_list_char @ Y @ Ys)) @ (listrel1_list_char @ R)) = (((((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R)) & ((Xs = Ys)))) | ((((X = Y)) & ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (listrel1_list_char @ R)))))))))). % Cons_listrel1_Cons
thf(fact_92_Cons__listrel1__Cons, axiom,
    ((![X : ty, Xs : list_ty, Y : ty, Ys : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) @ (listrel1_ty @ R)) = (((((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ R)) & ((Xs = Ys)))) | ((((X = Y)) & ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (listrel1_ty @ R)))))))))). % Cons_listrel1_Cons
thf(fact_93_Cons__listrel1__Cons, axiom,
    ((![X : val, Xs : list_val, Y : val, Ys : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) @ (listrel1_val @ R)) = (((((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R)) & ((Xs = Ys)))) | ((((X = Y)) & ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (listrel1_val @ R)))))))))). % Cons_listrel1_Cons
thf(fact_94_lexord__lex, axiom,
    ((![X : list_list_char, Y : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ X @ Y) @ (lex_list_char @ R)) = (((member725442668t_char @ (produc1181934459t_char @ X @ Y) @ (lexord_list_char @ R))) & (((size_s2008079621t_char @ X) = (size_s2008079621t_char @ Y)))))))). % lexord_lex
thf(fact_95_lexord__lex, axiom,
    ((![X : list_ty, Y : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ X @ Y) @ (lex_ty @ R)) = (((member1942114840ist_ty @ (produc1089615911ist_ty @ X @ Y) @ (lexord_ty @ R))) & (((size_size_list_ty @ X) = (size_size_list_ty @ Y)))))))). % lexord_lex
thf(fact_96_lexord__lex, axiom,
    ((![X : list_val, Y : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ X @ Y) @ (lex_val @ R)) = (((member1382006826st_val @ (produc180957881st_val @ X @ Y) @ (lexord_val @ R))) & (((size_size_list_val @ X) = (size_size_list_val @ Y)))))))). % lexord_lex
thf(fact_97_lexord__partial__trans, axiom,
    ((![Xs : list_list_char, R : set_Pr164112643t_char, Ys : list_list_char, Zs : list_list_char]: ((![X3 : list_char, Y3 : list_char, Z : list_char]: ((member_list_char @ X3 @ (set_list_char2 @ Xs)) => ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ R) => ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z) @ R) => (member89690956t_char @ (produc1304532571t_char @ X3 @ Z) @ R))))) => ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (lexord_list_char @ R)) => ((member725442668t_char @ (produc1181934459t_char @ Ys @ Zs) @ (lexord_list_char @ R)) => (member725442668t_char @ (produc1181934459t_char @ Xs @ Zs) @ (lexord_list_char @ R)))))))). % lexord_partial_trans
thf(fact_98_listrel1I2, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, R : set_Pr164112643t_char, X : list_char]: ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (listrel1_list_char @ R)) => (member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ (cons_list_char @ X @ Ys)) @ (listrel1_list_char @ R)))))). % listrel1I2
thf(fact_99_listrel1I2, axiom,
    ((![Xs : list_ty, Ys : list_ty, R : set_Pr1194734255_ty_ty, X : ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (listrel1_ty @ R)) => (member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ (cons_ty @ X @ Ys)) @ (listrel1_ty @ R)))))). % listrel1I2
thf(fact_100_listrel1I2, axiom,
    ((![Xs : list_val, Ys : list_val, R : set_Pr1870322241al_val, X : val]: ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (listrel1_val @ R)) => (member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ (cons_val @ X @ Ys)) @ (listrel1_val @ R)))))). % listrel1I2
thf(fact_101_listrel1__eq__len, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (listrel1_list_char @ R)) => ((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))))). % listrel1_eq_len
thf(fact_102_listrel1__eq__len, axiom,
    ((![Xs : list_ty, Ys : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (listrel1_ty @ R)) => ((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)))))). % listrel1_eq_len
thf(fact_103_listrel1__eq__len, axiom,
    ((![Xs : list_val, Ys : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (listrel1_val @ R)) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % listrel1_eq_len
thf(fact_104_Cons__listrel1E2, axiom,
    ((![Xs : list_list_char, Y : list_char, Ys : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ Xs @ (cons_list_char @ Y @ Ys)) @ (listrel1_list_char @ R)) => ((![X3 : list_char]: ((Xs = (cons_list_char @ X3 @ Ys)) => (~ ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ R))))) => (~ ((![Zs2 : list_list_char]: ((Xs = (cons_list_char @ Y @ Zs2)) => (~ ((member725442668t_char @ (produc1181934459t_char @ Zs2 @ Ys) @ (listrel1_list_char @ R))))))))))))). % Cons_listrel1E2
thf(fact_105_Cons__listrel1E2, axiom,
    ((![Xs : list_ty, Y : ty, Ys : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ (cons_ty @ Y @ Ys)) @ (listrel1_ty @ R)) => ((![X3 : ty]: ((Xs = (cons_ty @ X3 @ Ys)) => (~ ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ Y) @ R))))) => (~ ((![Zs2 : list_ty]: ((Xs = (cons_ty @ Y @ Zs2)) => (~ ((member1942114840ist_ty @ (produc1089615911ist_ty @ Zs2 @ Ys) @ (listrel1_ty @ R))))))))))))). % Cons_listrel1E2
thf(fact_106_Cons__listrel1E2, axiom,
    ((![Xs : list_val, Y : val, Ys : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ Xs @ (cons_val @ Y @ Ys)) @ (listrel1_val @ R)) => ((![X3 : val]: ((Xs = (cons_val @ X3 @ Ys)) => (~ ((member1494223754al_val @ (product_Pair_val_val @ X3 @ Y) @ R))))) => (~ ((![Zs2 : list_val]: ((Xs = (cons_val @ Y @ Zs2)) => (~ ((member1382006826st_val @ (produc180957881st_val @ Zs2 @ Ys) @ (listrel1_val @ R))))))))))))). % Cons_listrel1E2
thf(fact_107_Cons__listrel1E1, axiom,
    ((![X : list_char, Xs : list_list_char, Ys : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ Ys) @ (listrel1_list_char @ R)) => ((![Y3 : list_char]: ((Ys = (cons_list_char @ Y3 @ Xs)) => (~ ((member89690956t_char @ (produc1304532571t_char @ X @ Y3) @ R))))) => (~ ((![Zs2 : list_list_char]: ((Ys = (cons_list_char @ X @ Zs2)) => (~ ((member725442668t_char @ (produc1181934459t_char @ Xs @ Zs2) @ (listrel1_list_char @ R))))))))))))). % Cons_listrel1E1
thf(fact_108_Cons__listrel1E1, axiom,
    ((![X : ty, Xs : list_ty, Ys : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ Ys) @ (listrel1_ty @ R)) => ((![Y3 : ty]: ((Ys = (cons_ty @ Y3 @ Xs)) => (~ ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y3) @ R))))) => (~ ((![Zs2 : list_ty]: ((Ys = (cons_ty @ X @ Zs2)) => (~ ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Zs2) @ (listrel1_ty @ R))))))))))))). % Cons_listrel1E1
thf(fact_109_Cons__listrel1E1, axiom,
    ((![X : val, Xs : list_val, Ys : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ Ys) @ (listrel1_val @ R)) => ((![Y3 : val]: ((Ys = (cons_val @ Y3 @ Xs)) => (~ ((member1494223754al_val @ (product_Pair_val_val @ X @ Y3) @ R))))) => (~ ((![Zs2 : list_val]: ((Ys = (cons_val @ X @ Zs2)) => (~ ((member1382006826st_val @ (produc180957881st_val @ Xs @ Zs2) @ (listrel1_val @ R))))))))))))). % Cons_listrel1E1
thf(fact_110_listrel1I1, axiom,
    ((![X : list_char, Y : list_char, R : set_Pr164112643t_char, Xs : list_list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R) => (member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ X @ Xs) @ (cons_list_char @ Y @ Xs)) @ (listrel1_list_char @ R)))))). % listrel1I1
thf(fact_111_listrel1I1, axiom,
    ((![X : ty, Y : ty, R : set_Pr1194734255_ty_ty, Xs : list_ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ R) => (member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Xs)) @ (listrel1_ty @ R)))))). % listrel1I1
thf(fact_112_listrel1I1, axiom,
    ((![X : val, Y : val, R : set_Pr1870322241al_val, Xs : list_val]: ((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R) => (member1382006826st_val @ (produc180957881st_val @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Xs)) @ (listrel1_val @ R)))))). % listrel1I1
thf(fact_113_lexord__Nil__left, axiom,
    ((![Y : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ nil_list_char @ Y) @ (lexord_list_char @ R)) = (?[A5 : list_char]: (?[X4 : list_list_char]: (Y = (cons_list_char @ A5 @ X4)))))))). % lexord_Nil_left
thf(fact_114_lexord__Nil__left, axiom,
    ((![Y : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ nil_ty @ Y) @ (lexord_ty @ R)) = (?[A5 : ty]: (?[X4 : list_ty]: (Y = (cons_ty @ A5 @ X4)))))))). % lexord_Nil_left
thf(fact_115_lexord__Nil__left, axiom,
    ((![Y : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ nil_val @ Y) @ (lexord_val @ R)) = (?[A5 : val]: (?[X4 : list_val]: (Y = (cons_val @ A5 @ X4)))))))). % lexord_Nil_left
thf(fact_116_lexord__append__left__rightI, axiom,
    ((![A2 : list_char, B2 : list_char, R : set_Pr164112643t_char, U : list_list_char, X : list_list_char, Y : list_list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ R) => (member725442668t_char @ (produc1181934459t_char @ (append_list_char @ U @ (cons_list_char @ A2 @ X)) @ (append_list_char @ U @ (cons_list_char @ B2 @ Y))) @ (lexord_list_char @ R)))))). % lexord_append_left_rightI
thf(fact_117_lexord__append__left__rightI, axiom,
    ((![A2 : ty, B2 : ty, R : set_Pr1194734255_ty_ty, U : list_ty, X : list_ty, Y : list_ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ A2 @ B2) @ R) => (member1942114840ist_ty @ (produc1089615911ist_ty @ (append_ty @ U @ (cons_ty @ A2 @ X)) @ (append_ty @ U @ (cons_ty @ B2 @ Y))) @ (lexord_ty @ R)))))). % lexord_append_left_rightI
thf(fact_118_lexord__append__left__rightI, axiom,
    ((![A2 : val, B2 : val, R : set_Pr1870322241al_val, U : list_val, X : list_val, Y : list_val]: ((member1494223754al_val @ (product_Pair_val_val @ A2 @ B2) @ R) => (member1382006826st_val @ (produc180957881st_val @ (append_val @ U @ (cons_val @ A2 @ X)) @ (append_val @ U @ (cons_val @ B2 @ Y))) @ (lexord_val @ R)))))). % lexord_append_left_rightI
thf(fact_119_listrel1I, axiom,
    ((![X : list_char, Y : list_char, R : set_Pr164112643t_char, Xs : list_list_char, Us : list_list_char, Vs : list_list_char, Ys : list_list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R) => ((Xs = (append_list_char @ Us @ (cons_list_char @ X @ Vs))) => ((Ys = (append_list_char @ Us @ (cons_list_char @ Y @ Vs))) => (member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (listrel1_list_char @ R)))))))). % listrel1I
thf(fact_120_listrel1I, axiom,
    ((![X : ty, Y : ty, R : set_Pr1194734255_ty_ty, Xs : list_ty, Us : list_ty, Vs : list_ty, Ys : list_ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ R) => ((Xs = (append_ty @ Us @ (cons_ty @ X @ Vs))) => ((Ys = (append_ty @ Us @ (cons_ty @ Y @ Vs))) => (member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (listrel1_ty @ R)))))))). % listrel1I
thf(fact_121_listrel1I, axiom,
    ((![X : val, Y : val, R : set_Pr1870322241al_val, Xs : list_val, Us : list_val, Vs : list_val, Ys : list_val]: ((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R) => ((Xs = (append_val @ Us @ (cons_val @ X @ Vs))) => ((Ys = (append_val @ Us @ (cons_val @ Y @ Vs))) => (member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (listrel1_val @ R)))))))). % listrel1I
thf(fact_122_listrel1E, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, R : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ Xs @ Ys) @ (listrel1_list_char @ R)) => (~ ((![X3 : list_char, Y3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y3) @ R) => (![Us2 : list_list_char, Vs2 : list_list_char]: ((Xs = (append_list_char @ Us2 @ (cons_list_char @ X3 @ Vs2))) => (~ ((Ys = (append_list_char @ Us2 @ (cons_list_char @ Y3 @ Vs2))))))))))))))). % listrel1E
thf(fact_123_listrel1E, axiom,
    ((![Xs : list_ty, Ys : list_ty, R : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ Xs @ Ys) @ (listrel1_ty @ R)) => (~ ((![X3 : ty, Y3 : ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ Y3) @ R) => (![Us2 : list_ty, Vs2 : list_ty]: ((Xs = (append_ty @ Us2 @ (cons_ty @ X3 @ Vs2))) => (~ ((Ys = (append_ty @ Us2 @ (cons_ty @ Y3 @ Vs2))))))))))))))). % listrel1E
thf(fact_124_listrel1E, axiom,
    ((![Xs : list_val, Ys : list_val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (listrel1_val @ R)) => (~ ((![X3 : val, Y3 : val]: ((member1494223754al_val @ (product_Pair_val_val @ X3 @ Y3) @ R) => (![Us2 : list_val, Vs2 : list_val]: ((Xs = (append_val @ Us2 @ (cons_val @ X3 @ Vs2))) => (~ ((Ys = (append_val @ Us2 @ (cons_val @ Y3 @ Vs2))))))))))))))). % listrel1E
thf(fact_125_append__eq__append__conv, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, Us : list_list_char, Vs : list_list_char]: ((((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)) | ((size_s2008079621t_char @ Us) = (size_s2008079621t_char @ Vs))) => (((append_list_char @ Xs @ Us) = (append_list_char @ Ys @ Vs)) = (((Xs = Ys)) & ((Us = Vs)))))))). % append_eq_append_conv
thf(fact_126_append__eq__append__conv, axiom,
    ((![Xs : list_ty, Ys : list_ty, Us : list_ty, Vs : list_ty]: ((((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)) | ((size_size_list_ty @ Us) = (size_size_list_ty @ Vs))) => (((append_ty @ Xs @ Us) = (append_ty @ Ys @ Vs)) = (((Xs = Ys)) & ((Us = Vs)))))))). % append_eq_append_conv
thf(fact_127_append__eq__append__conv, axiom,
    ((![Xs : list_val, Ys : list_val, Us : list_val, Vs : list_val]: ((((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) | ((size_size_list_val @ Us) = (size_size_list_val @ Vs))) => (((append_val @ Xs @ Us) = (append_val @ Ys @ Vs)) = (((Xs = Ys)) & ((Us = Vs)))))))). % append_eq_append_conv
thf(fact_128_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_129_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_130_append1__eq__conv, axiom,
    ((![Xs : list_list_char, X : list_char, Ys : list_list_char, Y : list_char]: (((append_list_char @ Xs @ (cons_list_char @ X @ nil_list_char)) = (append_list_char @ Ys @ (cons_list_char @ Y @ nil_list_char))) = (((Xs = Ys)) & ((X = Y))))))). % append1_eq_conv
thf(fact_131_append1__eq__conv, axiom,
    ((![Xs : list_ty, X : ty, Ys : list_ty, Y : ty]: (((append_ty @ Xs @ (cons_ty @ X @ nil_ty)) = (append_ty @ Ys @ (cons_ty @ Y @ nil_ty))) = (((Xs = Ys)) & ((X = Y))))))). % append1_eq_conv
thf(fact_132_append1__eq__conv, axiom,
    ((![Xs : list_val, X : val, Ys : list_val, Y : val]: (((append_val @ Xs @ (cons_val @ X @ nil_val)) = (append_val @ Ys @ (cons_val @ Y @ nil_val))) = (((Xs = Ys)) & ((X = Y))))))). % append1_eq_conv
thf(fact_133_fun__upds__append2__drop, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, M : list_char > option_list_char, Zs : list_list_char]: (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)) => ((map_up354775738t_char @ M @ Xs @ (append_list_char @ Ys @ Zs)) = (map_up354775738t_char @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_134_fun__upds__append2__drop, axiom,
    ((![Xs : list_list_char, Ys : list_ty, M : list_char > option_ty, Zs : list_ty]: (((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)) => ((map_up703499792har_ty @ M @ Xs @ (append_ty @ Ys @ Zs)) = (map_up703499792har_ty @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_135_fun__upds__append2__drop, axiom,
    ((![Xs : list_list_char, Ys : list_val, M : list_char > option_val, Zs : list_val]: (((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)) => ((map_up576607321ar_val @ M @ Xs @ (append_val @ Ys @ Zs)) = (map_up576607321ar_val @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_136_fun__upds__append2__drop, axiom,
    ((![Xs : list_ty, Ys : list_list_char, M : ty > option_list_char, Zs : list_list_char]: (((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)) => ((map_up436965904t_char @ M @ Xs @ (append_list_char @ Ys @ Zs)) = (map_up436965904t_char @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_137_fun__upds__append2__drop, axiom,
    ((![Xs : list_ty, Ys : list_ty, M : ty > option_ty, Zs : list_ty]: (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)) => ((map_upds_ty_ty @ M @ Xs @ (append_ty @ Ys @ Zs)) = (map_upds_ty_ty @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_138_fun__upds__append2__drop, axiom,
    ((![Xs : list_ty, Ys : list_val, M : ty > option_val, Zs : list_val]: (((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)) => ((map_upds_ty_val @ M @ Xs @ (append_val @ Ys @ Zs)) = (map_upds_ty_val @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_139_fun__upds__append2__drop, axiom,
    ((![Xs : list_val, Ys : list_list_char, M : val > option_list_char, Zs : list_list_char]: (((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)) => ((map_up1545155545t_char @ M @ Xs @ (append_list_char @ Ys @ Zs)) = (map_up1545155545t_char @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_140_fun__upds__append2__drop, axiom,
    ((![Xs : list_val, Ys : list_ty, M : val > option_ty, Zs : list_ty]: (((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)) => ((map_upds_val_ty @ M @ Xs @ (append_ty @ Ys @ Zs)) = (map_upds_val_ty @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_141_fun__upds__append2__drop, axiom,
    ((![Xs : list_val, Ys : list_val, M : val > option_val, Zs : list_val]: (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) => ((map_upds_val_val @ M @ Xs @ (append_val @ Ys @ Zs)) = (map_upds_val_val @ M @ Xs @ Ys)))))). % fun_upds_append2_drop
thf(fact_142_fun__upds__append__drop, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, M : list_char > option_list_char, Zs : list_list_char]: (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)) => ((map_up354775738t_char @ M @ (append_list_char @ Xs @ Zs) @ Ys) = (map_up354775738t_char @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_143_fun__upds__append__drop, axiom,
    ((![Xs : list_list_char, Ys : list_ty, M : list_char > option_ty, Zs : list_list_char]: (((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)) => ((map_up703499792har_ty @ M @ (append_list_char @ Xs @ Zs) @ Ys) = (map_up703499792har_ty @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_144_fun__upds__append__drop, axiom,
    ((![Xs : list_list_char, Ys : list_val, M : list_char > option_val, Zs : list_list_char]: (((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)) => ((map_up576607321ar_val @ M @ (append_list_char @ Xs @ Zs) @ Ys) = (map_up576607321ar_val @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_145_fun__upds__append__drop, axiom,
    ((![Xs : list_ty, Ys : list_list_char, M : ty > option_list_char, Zs : list_ty]: (((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)) => ((map_up436965904t_char @ M @ (append_ty @ Xs @ Zs) @ Ys) = (map_up436965904t_char @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_146_fun__upds__append__drop, axiom,
    ((![Xs : list_ty, Ys : list_ty, M : ty > option_ty, Zs : list_ty]: (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)) => ((map_upds_ty_ty @ M @ (append_ty @ Xs @ Zs) @ Ys) = (map_upds_ty_ty @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_147_fun__upds__append__drop, axiom,
    ((![Xs : list_ty, Ys : list_val, M : ty > option_val, Zs : list_ty]: (((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)) => ((map_upds_ty_val @ M @ (append_ty @ Xs @ Zs) @ Ys) = (map_upds_ty_val @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_148_fun__upds__append__drop, axiom,
    ((![Xs : list_val, Ys : list_list_char, M : val > option_list_char, Zs : list_val]: (((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)) => ((map_up1545155545t_char @ M @ (append_val @ Xs @ Zs) @ Ys) = (map_up1545155545t_char @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_149_fun__upds__append__drop, axiom,
    ((![Xs : list_val, Ys : list_ty, M : val > option_ty, Zs : list_val]: (((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)) => ((map_upds_val_ty @ M @ (append_val @ Xs @ Zs) @ Ys) = (map_upds_val_ty @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_150_fun__upds__append__drop, axiom,
    ((![Xs : list_val, Ys : list_val, M : val > option_val, Zs : list_val]: (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) => ((map_upds_val_val @ M @ (append_val @ Xs @ Zs) @ Ys) = (map_upds_val_val @ M @ Xs @ Ys)))))). % fun_upds_append_drop
thf(fact_151_insert__Nil, axiom,
    ((![X : list_char]: ((insert_list_char @ X @ nil_list_char) = (cons_list_char @ X @ nil_list_char))))). % insert_Nil
thf(fact_152_insert__Nil, axiom,
    ((![X : ty]: ((insert_ty @ X @ nil_ty) = (cons_ty @ X @ nil_ty))))). % insert_Nil
thf(fact_153_insert__Nil, axiom,
    ((![X : val]: ((insert_val @ X @ nil_val) = (cons_val @ X @ nil_val))))). % insert_Nil
thf(fact_154_rev__induct, axiom,
    ((![P : list_list_char > $o, Xs : list_list_char]: ((P @ nil_list_char) => ((![X3 : list_char, Xs2 : list_list_char]: ((P @ Xs2) => (P @ (append_list_char @ Xs2 @ (cons_list_char @ X3 @ nil_list_char))))) => (P @ Xs)))))). % rev_induct
thf(fact_155_rev__induct, axiom,
    ((![P : list_ty > $o, Xs : list_ty]: ((P @ nil_ty) => ((![X3 : ty, Xs2 : list_ty]: ((P @ Xs2) => (P @ (append_ty @ Xs2 @ (cons_ty @ X3 @ nil_ty))))) => (P @ Xs)))))). % rev_induct
thf(fact_156_rev__induct, axiom,
    ((![P : list_val > $o, Xs : list_val]: ((P @ nil_val) => ((![X3 : val, Xs2 : list_val]: ((P @ Xs2) => (P @ (append_val @ Xs2 @ (cons_val @ X3 @ nil_val))))) => (P @ Xs)))))). % rev_induct
thf(fact_157_rev__exhaust, axiom,
    ((![Xs : list_list_char]: ((~ ((Xs = nil_list_char))) => (~ ((![Ys2 : list_list_char, Y3 : list_char]: (~ ((Xs = (append_list_char @ Ys2 @ (cons_list_char @ Y3 @ nil_list_char)))))))))))). % rev_exhaust
thf(fact_158_rev__exhaust, axiom,
    ((![Xs : list_ty]: ((~ ((Xs = nil_ty))) => (~ ((![Ys2 : list_ty, Y3 : ty]: (~ ((Xs = (append_ty @ Ys2 @ (cons_ty @ Y3 @ nil_ty)))))))))))). % rev_exhaust
thf(fact_159_rev__exhaust, axiom,
    ((![Xs : list_val]: ((~ ((Xs = nil_val))) => (~ ((![Ys2 : list_val, Y3 : val]: (~ ((Xs = (append_val @ Ys2 @ (cons_val @ Y3 @ nil_val)))))))))))). % rev_exhaust
thf(fact_160_Cons__eq__append__conv, axiom,
    ((![X : list_char, Xs : list_list_char, Ys : list_list_char, Zs : list_list_char]: (((cons_list_char @ X @ Xs) = (append_list_char @ Ys @ Zs)) = (((((Ys = nil_list_char)) & (((cons_list_char @ X @ Xs) = Zs)))) | ((?[Ys3 : list_list_char]: ((((cons_list_char @ X @ Ys3) = Ys)) & ((Xs = (append_list_char @ Ys3 @ Zs))))))))))). % Cons_eq_append_conv
thf(fact_161_Cons__eq__append__conv, axiom,
    ((![X : ty, Xs : list_ty, Ys : list_ty, Zs : list_ty]: (((cons_ty @ X @ Xs) = (append_ty @ Ys @ Zs)) = (((((Ys = nil_ty)) & (((cons_ty @ X @ Xs) = Zs)))) | ((?[Ys3 : list_ty]: ((((cons_ty @ X @ Ys3) = Ys)) & ((Xs = (append_ty @ Ys3 @ Zs))))))))))). % Cons_eq_append_conv
thf(fact_162_Cons__eq__append__conv, axiom,
    ((![X : val, Xs : list_val, Ys : list_val, Zs : list_val]: (((cons_val @ X @ Xs) = (append_val @ Ys @ Zs)) = (((((Ys = nil_val)) & (((cons_val @ X @ Xs) = Zs)))) | ((?[Ys3 : list_val]: ((((cons_val @ X @ Ys3) = Ys)) & ((Xs = (append_val @ Ys3 @ Zs))))))))))). % Cons_eq_append_conv
thf(fact_163_append__eq__Cons__conv, axiom,
    ((![Ys : list_list_char, Zs : list_list_char, X : list_char, Xs : list_list_char]: (((append_list_char @ Ys @ Zs) = (cons_list_char @ X @ Xs)) = (((((Ys = nil_list_char)) & ((Zs = (cons_list_char @ X @ Xs))))) | ((?[Ys3 : list_list_char]: (((Ys = (cons_list_char @ X @ Ys3))) & (((append_list_char @ Ys3 @ Zs) = Xs)))))))))). % append_eq_Cons_conv
thf(fact_164_append__eq__Cons__conv, axiom,
    ((![Ys : list_ty, Zs : list_ty, X : ty, Xs : list_ty]: (((append_ty @ Ys @ Zs) = (cons_ty @ X @ Xs)) = (((((Ys = nil_ty)) & ((Zs = (cons_ty @ X @ Xs))))) | ((?[Ys3 : list_ty]: (((Ys = (cons_ty @ X @ Ys3))) & (((append_ty @ Ys3 @ Zs) = Xs)))))))))). % append_eq_Cons_conv
thf(fact_165_append__eq__Cons__conv, axiom,
    ((![Ys : list_val, Zs : list_val, X : val, Xs : list_val]: (((append_val @ Ys @ Zs) = (cons_val @ X @ Xs)) = (((((Ys = nil_val)) & ((Zs = (cons_val @ X @ Xs))))) | ((?[Ys3 : list_val]: (((Ys = (cons_val @ X @ Ys3))) & (((append_val @ Ys3 @ Zs) = Xs)))))))))). % append_eq_Cons_conv
thf(fact_166_rev__nonempty__induct, axiom,
    ((![Xs : list_list_char, P : list_list_char > $o]: ((~ ((Xs = nil_list_char))) => ((![X3 : list_char]: (P @ (cons_list_char @ X3 @ nil_list_char))) => ((![X3 : list_char, Xs2 : list_list_char]: ((~ ((Xs2 = nil_list_char))) => ((P @ Xs2) => (P @ (append_list_char @ Xs2 @ (cons_list_char @ X3 @ nil_list_char)))))) => (P @ Xs))))))). % rev_nonempty_induct
thf(fact_167_rev__nonempty__induct, axiom,
    ((![Xs : list_ty, P : list_ty > $o]: ((~ ((Xs = nil_ty))) => ((![X3 : ty]: (P @ (cons_ty @ X3 @ nil_ty))) => ((![X3 : ty, Xs2 : list_ty]: ((~ ((Xs2 = nil_ty))) => ((P @ Xs2) => (P @ (append_ty @ Xs2 @ (cons_ty @ X3 @ nil_ty)))))) => (P @ Xs))))))). % rev_nonempty_induct
thf(fact_168_rev__nonempty__induct, axiom,
    ((![Xs : list_val, P : list_val > $o]: ((~ ((Xs = nil_val))) => ((![X3 : val]: (P @ (cons_val @ X3 @ nil_val))) => ((![X3 : val, Xs2 : list_val]: ((~ ((Xs2 = nil_val))) => ((P @ Xs2) => (P @ (append_val @ Xs2 @ (cons_val @ X3 @ nil_val)))))) => (P @ Xs))))))). % rev_nonempty_induct
thf(fact_169_same__length__different, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((~ ((Xs = Ys))) => (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)) => (?[Pre : list_list_char, X3 : list_char, Xs4 : list_list_char, Y3 : list_char, Ys4 : list_list_char]: ((~ ((X3 = Y3))) & ((Xs = (append_list_char @ Pre @ (append_list_char @ (cons_list_char @ X3 @ nil_list_char) @ Xs4))) & (Ys = (append_list_char @ Pre @ (append_list_char @ (cons_list_char @ Y3 @ nil_list_char) @ Ys4))))))))))). % same_length_different
thf(fact_170_same__length__different, axiom,
    ((![Xs : list_ty, Ys : list_ty]: ((~ ((Xs = Ys))) => (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)) => (?[Pre : list_ty, X3 : ty, Xs4 : list_ty, Y3 : ty, Ys4 : list_ty]: ((~ ((X3 = Y3))) & ((Xs = (append_ty @ Pre @ (append_ty @ (cons_ty @ X3 @ nil_ty) @ Xs4))) & (Ys = (append_ty @ Pre @ (append_ty @ (cons_ty @ Y3 @ nil_ty) @ Ys4))))))))))). % same_length_different
thf(fact_171_same__length__different, axiom,
    ((![Xs : list_val, Ys : list_val]: ((~ ((Xs = Ys))) => (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) => (?[Pre : list_val, X3 : val, Xs4 : list_val, Y3 : val, Ys4 : list_val]: ((~ ((X3 = Y3))) & ((Xs = (append_val @ Pre @ (append_val @ (cons_val @ X3 @ nil_val) @ Xs4))) & (Ys = (append_val @ Pre @ (append_val @ (cons_val @ Y3 @ nil_val) @ Ys4))))))))))). % same_length_different
thf(fact_172_transpose_Ocases, axiom,
    ((![X : list_list_list_char]: ((~ ((X = nil_list_list_char))) => ((![Xss2 : list_list_list_char]: (~ ((X = (cons_list_list_char @ nil_list_char @ Xss2))))) => (~ ((![X3 : list_char, Xs2 : list_list_char, Xss2 : list_list_list_char]: (~ ((X = (cons_list_list_char @ (cons_list_char @ X3 @ Xs2) @ Xss2)))))))))))). % transpose.cases
thf(fact_173_transpose_Ocases, axiom,
    ((![X : list_list_ty]: ((~ ((X = nil_list_ty))) => ((![Xss2 : list_list_ty]: (~ ((X = (cons_list_ty @ nil_ty @ Xss2))))) => (~ ((![X3 : ty, Xs2 : list_ty, Xss2 : list_list_ty]: (~ ((X = (cons_list_ty @ (cons_ty @ X3 @ Xs2) @ Xss2)))))))))))). % transpose.cases
thf(fact_174_transpose_Ocases, axiom,
    ((![X : list_list_val]: ((~ ((X = nil_list_val))) => ((![Xss2 : list_list_val]: (~ ((X = (cons_list_val @ nil_val @ Xss2))))) => (~ ((![X3 : val, Xs2 : list_val, Xss2 : list_list_val]: (~ ((X = (cons_list_val @ (cons_val @ X3 @ Xs2) @ Xss2)))))))))))). % transpose.cases
thf(fact_175_transpose_Ocases, axiom,
    ((![X : list_list_char]: ((~ ((X = nil_list_char))) => ((![Xss2 : list_list_char]: (~ ((X = (cons_list_char @ nil_char @ Xss2))))) => (~ ((![X3 : char, Xs2 : list_char, Xss2 : list_list_char]: (~ ((X = (cons_list_char @ (cons_char @ X3 @ Xs2) @ Xss2)))))))))))). % transpose.cases
thf(fact_176_Cons__eq__appendI, axiom,
    ((![X : list_char, Xs1 : list_list_char, Ys : list_list_char, Xs : list_list_char, Zs : list_list_char]: (((cons_list_char @ X @ Xs1) = Ys) => ((Xs = (append_list_char @ Xs1 @ Zs)) => ((cons_list_char @ X @ Xs) = (append_list_char @ Ys @ Zs))))))). % Cons_eq_appendI
thf(fact_177_Cons__eq__appendI, axiom,
    ((![X : ty, Xs1 : list_ty, Ys : list_ty, Xs : list_ty, Zs : list_ty]: (((cons_ty @ X @ Xs1) = Ys) => ((Xs = (append_ty @ Xs1 @ Zs)) => ((cons_ty @ X @ Xs) = (append_ty @ Ys @ Zs))))))). % Cons_eq_appendI
thf(fact_178_Cons__eq__appendI, axiom,
    ((![X : val, Xs1 : list_val, Ys : list_val, Xs : list_val, Zs : list_val]: (((cons_val @ X @ Xs1) = Ys) => ((Xs = (append_val @ Xs1 @ Zs)) => ((cons_val @ X @ Xs) = (append_val @ Ys @ Zs))))))). % Cons_eq_appendI
thf(fact_179_append__Cons, axiom,
    ((![X : list_char, Xs : list_list_char, Ys : list_list_char]: ((append_list_char @ (cons_list_char @ X @ Xs) @ Ys) = (cons_list_char @ X @ (append_list_char @ Xs @ Ys)))))). % append_Cons
thf(fact_180_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_181_append__Cons, axiom,
    ((![X : val, Xs : list_val, Ys : list_val]: ((append_val @ (cons_val @ X @ Xs) @ Ys) = (cons_val @ X @ (append_val @ Xs @ Ys)))))). % append_Cons
thf(fact_182_list_Odistinct_I1_J, axiom,
    ((![X21 : list_char, X22 : list_list_char]: (~ ((nil_list_char = (cons_list_char @ X21 @ X22))))))). % list.distinct(1)
thf(fact_183_list_Odistinct_I1_J, axiom,
    ((![X21 : ty, X22 : list_ty]: (~ ((nil_ty = (cons_ty @ X21 @ X22))))))). % list.distinct(1)
thf(fact_184_list_Odistinct_I1_J, axiom,
    ((![X21 : val, X22 : list_val]: (~ ((nil_val = (cons_val @ X21 @ X22))))))). % list.distinct(1)
thf(fact_185_list_OdiscI, axiom,
    ((![List : list_list_char, X21 : list_char, X22 : list_list_char]: ((List = (cons_list_char @ X21 @ X22)) => (~ ((List = nil_list_char))))))). % list.discI
thf(fact_186_list_OdiscI, axiom,
    ((![List : list_ty, X21 : ty, X22 : list_ty]: ((List = (cons_ty @ X21 @ X22)) => (~ ((List = nil_ty))))))). % list.discI
thf(fact_187_list_OdiscI, axiom,
    ((![List : list_val, X21 : val, X22 : list_val]: ((List = (cons_val @ X21 @ X22)) => (~ ((List = nil_val))))))). % list.discI
thf(fact_188_list_Oexhaust, axiom,
    ((![Y : list_list_char]: ((~ ((Y = nil_list_char))) => (~ ((![X212 : list_char, X222 : list_list_char]: (~ ((Y = (cons_list_char @ X212 @ X222))))))))))). % list.exhaust
thf(fact_189_list_Oexhaust, axiom,
    ((![Y : list_ty]: ((~ ((Y = nil_ty))) => (~ ((![X212 : ty, X222 : list_ty]: (~ ((Y = (cons_ty @ X212 @ X222))))))))))). % list.exhaust
thf(fact_190_list_Oexhaust, axiom,
    ((![Y : list_val]: ((~ ((Y = nil_val))) => (~ ((![X212 : val, X222 : list_val]: (~ ((Y = (cons_val @ X212 @ X222))))))))))). % list.exhaust
thf(fact_191_list_Oinducts, axiom,
    ((![P : list_list_char > $o, List : list_list_char]: ((P @ nil_list_char) => ((![X12 : list_char, X23 : list_list_char]: ((P @ X23) => (P @ (cons_list_char @ X12 @ X23)))) => (P @ List)))))). % list.inducts
thf(fact_192_list_Oinducts, axiom,
    ((![P : list_ty > $o, List : list_ty]: ((P @ nil_ty) => ((![X12 : ty, X23 : list_ty]: ((P @ X23) => (P @ (cons_ty @ X12 @ X23)))) => (P @ List)))))). % list.inducts
thf(fact_193_list_Oinducts, axiom,
    ((![P : list_val > $o, List : list_val]: ((P @ nil_val) => ((![X12 : val, X23 : list_val]: ((P @ X23) => (P @ (cons_val @ X12 @ X23)))) => (P @ List)))))). % list.inducts
thf(fact_194_neq__Nil__conv, axiom,
    ((![Xs : list_list_char]: ((~ ((Xs = nil_list_char))) = (?[Y4 : list_char]: (?[Ys5 : list_list_char]: (Xs = (cons_list_char @ Y4 @ Ys5)))))))). % neq_Nil_conv
thf(fact_195_neq__Nil__conv, axiom,
    ((![Xs : list_ty]: ((~ ((Xs = nil_ty))) = (?[Y4 : ty]: (?[Ys5 : list_ty]: (Xs = (cons_ty @ Y4 @ Ys5)))))))). % neq_Nil_conv
thf(fact_196_neq__Nil__conv, axiom,
    ((![Xs : list_val]: ((~ ((Xs = nil_val))) = (?[Y4 : val]: (?[Ys5 : list_val]: (Xs = (cons_val @ Y4 @ Ys5)))))))). % neq_Nil_conv
thf(fact_197_list__induct2_H, axiom,
    ((![P : list_list_char > list_list_char > $o, Xs : list_list_char, Ys : list_list_char]: ((P @ nil_list_char @ nil_list_char) => ((![X3 : list_char, Xs2 : list_list_char]: (P @ (cons_list_char @ X3 @ Xs2) @ nil_list_char)) => ((![Y3 : list_char, Ys2 : list_list_char]: (P @ nil_list_char @ (cons_list_char @ Y3 @ Ys2))) => ((![X3 : list_char, Xs2 : list_list_char, Y3 : list_char, Ys2 : list_list_char]: ((P @ Xs2 @ Ys2) => (P @ (cons_list_char @ X3 @ Xs2) @ (cons_list_char @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_198_list__induct2_H, axiom,
    ((![P : list_list_char > list_ty > $o, Xs : list_list_char, Ys : list_ty]: ((P @ nil_list_char @ nil_ty) => ((![X3 : list_char, Xs2 : list_list_char]: (P @ (cons_list_char @ X3 @ Xs2) @ nil_ty)) => ((![Y3 : ty, Ys2 : list_ty]: (P @ nil_list_char @ (cons_ty @ Y3 @ Ys2))) => ((![X3 : list_char, Xs2 : list_list_char, Y3 : ty, Ys2 : list_ty]: ((P @ Xs2 @ Ys2) => (P @ (cons_list_char @ X3 @ Xs2) @ (cons_ty @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_199_list__induct2_H, axiom,
    ((![P : list_list_char > list_val > $o, Xs : list_list_char, Ys : list_val]: ((P @ nil_list_char @ nil_val) => ((![X3 : list_char, Xs2 : list_list_char]: (P @ (cons_list_char @ X3 @ Xs2) @ nil_val)) => ((![Y3 : val, Ys2 : list_val]: (P @ nil_list_char @ (cons_val @ Y3 @ Ys2))) => ((![X3 : list_char, Xs2 : list_list_char, Y3 : val, Ys2 : list_val]: ((P @ Xs2 @ Ys2) => (P @ (cons_list_char @ X3 @ Xs2) @ (cons_val @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_200_list__induct2_H, axiom,
    ((![P : list_ty > list_list_char > $o, Xs : list_ty, Ys : list_list_char]: ((P @ nil_ty @ nil_list_char) => ((![X3 : ty, Xs2 : list_ty]: (P @ (cons_ty @ X3 @ Xs2) @ nil_list_char)) => ((![Y3 : list_char, Ys2 : list_list_char]: (P @ nil_ty @ (cons_list_char @ Y3 @ Ys2))) => ((![X3 : ty, Xs2 : list_ty, Y3 : list_char, Ys2 : list_list_char]: ((P @ Xs2 @ Ys2) => (P @ (cons_ty @ X3 @ Xs2) @ (cons_list_char @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_201_list__induct2_H, axiom,
    ((![P : list_ty > list_ty > $o, Xs : list_ty, Ys : list_ty]: ((P @ nil_ty @ nil_ty) => ((![X3 : ty, Xs2 : list_ty]: (P @ (cons_ty @ X3 @ Xs2) @ nil_ty)) => ((![Y3 : ty, Ys2 : list_ty]: (P @ nil_ty @ (cons_ty @ Y3 @ Ys2))) => ((![X3 : ty, Xs2 : list_ty, Y3 : ty, Ys2 : list_ty]: ((P @ Xs2 @ Ys2) => (P @ (cons_ty @ X3 @ Xs2) @ (cons_ty @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_202_list__induct2_H, axiom,
    ((![P : list_ty > list_val > $o, Xs : list_ty, Ys : list_val]: ((P @ nil_ty @ nil_val) => ((![X3 : ty, Xs2 : list_ty]: (P @ (cons_ty @ X3 @ Xs2) @ nil_val)) => ((![Y3 : val, Ys2 : list_val]: (P @ nil_ty @ (cons_val @ Y3 @ Ys2))) => ((![X3 : ty, Xs2 : list_ty, Y3 : val, Ys2 : list_val]: ((P @ Xs2 @ Ys2) => (P @ (cons_ty @ X3 @ Xs2) @ (cons_val @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_203_list__induct2_H, axiom,
    ((![P : list_val > list_list_char > $o, Xs : list_val, Ys : list_list_char]: ((P @ nil_val @ nil_list_char) => ((![X3 : val, Xs2 : list_val]: (P @ (cons_val @ X3 @ Xs2) @ nil_list_char)) => ((![Y3 : list_char, Ys2 : list_list_char]: (P @ nil_val @ (cons_list_char @ Y3 @ Ys2))) => ((![X3 : val, Xs2 : list_val, Y3 : list_char, Ys2 : list_list_char]: ((P @ Xs2 @ Ys2) => (P @ (cons_val @ X3 @ Xs2) @ (cons_list_char @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_204_list__induct2_H, axiom,
    ((![P : list_val > list_ty > $o, Xs : list_val, Ys : list_ty]: ((P @ nil_val @ nil_ty) => ((![X3 : val, Xs2 : list_val]: (P @ (cons_val @ X3 @ Xs2) @ nil_ty)) => ((![Y3 : ty, Ys2 : list_ty]: (P @ nil_val @ (cons_ty @ Y3 @ Ys2))) => ((![X3 : val, Xs2 : list_val, Y3 : ty, Ys2 : list_ty]: ((P @ Xs2 @ Ys2) => (P @ (cons_val @ X3 @ Xs2) @ (cons_ty @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_205_list__induct2_H, axiom,
    ((![P : list_val > list_val > $o, Xs : list_val, Ys : list_val]: ((P @ nil_val @ nil_val) => ((![X3 : val, Xs2 : list_val]: (P @ (cons_val @ X3 @ Xs2) @ nil_val)) => ((![Y3 : val, Ys2 : list_val]: (P @ nil_val @ (cons_val @ Y3 @ Ys2))) => ((![X3 : val, Xs2 : list_val, Y3 : val, Ys2 : list_val]: ((P @ Xs2 @ Ys2) => (P @ (cons_val @ X3 @ Xs2) @ (cons_val @ Y3 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_206_splice_Oinduct, axiom,
    ((![P : list_list_char > list_list_char > $o, A0 : list_list_char, A1 : list_list_char]: ((![X_1 : list_list_char]: (P @ nil_list_char @ X_1)) => ((![X3 : list_char, Xs2 : list_list_char, Ys2 : list_list_char]: ((P @ Ys2 @ Xs2) => (P @ (cons_list_char @ X3 @ Xs2) @ Ys2))) => (P @ A0 @ A1)))))). % splice.induct
thf(fact_207_splice_Oinduct, axiom,
    ((![P : list_ty > list_ty > $o, A0 : list_ty, A1 : list_ty]: ((![X_1 : list_ty]: (P @ nil_ty @ X_1)) => ((![X3 : ty, Xs2 : list_ty, Ys2 : list_ty]: ((P @ Ys2 @ Xs2) => (P @ (cons_ty @ X3 @ Xs2) @ Ys2))) => (P @ A0 @ A1)))))). % splice.induct
thf(fact_208_splice_Oinduct, axiom,
    ((![P : list_val > list_val > $o, A0 : list_val, A1 : list_val]: ((![X_1 : list_val]: (P @ nil_val @ X_1)) => ((![X3 : val, Xs2 : list_val, Ys2 : list_val]: ((P @ Ys2 @ Xs2) => (P @ (cons_val @ X3 @ Xs2) @ Ys2))) => (P @ A0 @ A1)))))). % splice.induct
thf(fact_209_induct__list012, axiom,
    ((![P : list_list_char > $o, Xs : list_list_char]: ((P @ nil_list_char) => ((![X3 : list_char]: (P @ (cons_list_char @ X3 @ nil_list_char))) => ((![X3 : list_char, Y3 : list_char, Zs2 : list_list_char]: ((P @ Zs2) => ((P @ (cons_list_char @ Y3 @ Zs2)) => (P @ (cons_list_char @ X3 @ (cons_list_char @ Y3 @ Zs2)))))) => (P @ Xs))))))). % induct_list012
thf(fact_210_induct__list012, axiom,
    ((![P : list_ty > $o, Xs : list_ty]: ((P @ nil_ty) => ((![X3 : ty]: (P @ (cons_ty @ X3 @ nil_ty))) => ((![X3 : ty, Y3 : ty, Zs2 : list_ty]: ((P @ Zs2) => ((P @ (cons_ty @ Y3 @ Zs2)) => (P @ (cons_ty @ X3 @ (cons_ty @ Y3 @ Zs2)))))) => (P @ Xs))))))). % induct_list012
thf(fact_211_induct__list012, axiom,
    ((![P : list_val > $o, Xs : list_val]: ((P @ nil_val) => ((![X3 : val]: (P @ (cons_val @ X3 @ nil_val))) => ((![X3 : val, Y3 : val, Zs2 : list_val]: ((P @ Zs2) => ((P @ (cons_val @ Y3 @ Zs2)) => (P @ (cons_val @ X3 @ (cons_val @ Y3 @ Zs2)))))) => (P @ Xs))))))). % induct_list012
thf(fact_212_shuffles_Oinduct, axiom,
    ((![P : list_list_char > list_list_char > $o, A0 : list_list_char, A1 : list_list_char]: ((![X_1 : list_list_char]: (P @ nil_list_char @ X_1)) => ((![Xs2 : list_list_char]: (P @ Xs2 @ nil_list_char)) => ((![X3 : list_char, Xs2 : list_list_char, Y3 : list_char, Ys2 : list_list_char]: ((P @ Xs2 @ (cons_list_char @ Y3 @ Ys2)) => ((P @ (cons_list_char @ X3 @ Xs2) @ Ys2) => (P @ (cons_list_char @ X3 @ Xs2) @ (cons_list_char @ Y3 @ Ys2))))) => (P @ A0 @ A1))))))). % shuffles.induct
thf(fact_213_shuffles_Oinduct, axiom,
    ((![P : list_ty > list_ty > $o, A0 : list_ty, A1 : list_ty]: ((![X_1 : list_ty]: (P @ nil_ty @ X_1)) => ((![Xs2 : list_ty]: (P @ Xs2 @ nil_ty)) => ((![X3 : ty, Xs2 : list_ty, Y3 : ty, Ys2 : list_ty]: ((P @ Xs2 @ (cons_ty @ Y3 @ Ys2)) => ((P @ (cons_ty @ X3 @ Xs2) @ Ys2) => (P @ (cons_ty @ X3 @ Xs2) @ (cons_ty @ Y3 @ Ys2))))) => (P @ A0 @ A1))))))). % shuffles.induct
thf(fact_214_shuffles_Oinduct, axiom,
    ((![P : list_val > list_val > $o, A0 : list_val, A1 : list_val]: ((![X_1 : list_val]: (P @ nil_val @ X_1)) => ((![Xs2 : list_val]: (P @ Xs2 @ nil_val)) => ((![X3 : val, Xs2 : list_val, Y3 : val, Ys2 : list_val]: ((P @ Xs2 @ (cons_val @ Y3 @ Ys2)) => ((P @ (cons_val @ X3 @ Xs2) @ Ys2) => (P @ (cons_val @ X3 @ Xs2) @ (cons_val @ Y3 @ Ys2))))) => (P @ A0 @ A1))))))). % shuffles.induct
thf(fact_215_remdups__adj_Ocases, axiom,
    ((![X : list_list_char]: ((~ ((X = nil_list_char))) => ((![X3 : list_char]: (~ ((X = (cons_list_char @ X3 @ nil_list_char))))) => (~ ((![X3 : list_char, Y3 : list_char, Xs2 : list_list_char]: (~ ((X = (cons_list_char @ X3 @ (cons_list_char @ Y3 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_216_remdups__adj_Ocases, axiom,
    ((![X : list_ty]: ((~ ((X = nil_ty))) => ((![X3 : ty]: (~ ((X = (cons_ty @ X3 @ nil_ty))))) => (~ ((![X3 : ty, Y3 : ty, Xs2 : list_ty]: (~ ((X = (cons_ty @ X3 @ (cons_ty @ Y3 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_217_remdups__adj_Ocases, axiom,
    ((![X : list_val]: ((~ ((X = nil_val))) => ((![X3 : val]: (~ ((X = (cons_val @ X3 @ nil_val))))) => (~ ((![X3 : val, Y3 : val, Xs2 : list_val]: (~ ((X = (cons_val @ X3 @ (cons_val @ Y3 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_218_sorted__wrt_Oinduct, axiom,
    ((![P : (list_char > list_char > $o) > list_list_char > $o, A0 : list_char > list_char > $o, A1 : list_list_char]: ((![P3 : list_char > list_char > $o]: (P @ P3 @ nil_list_char)) => ((![P3 : list_char > list_char > $o, X3 : list_char, Ys2 : list_list_char]: ((P @ P3 @ Ys2) => (P @ P3 @ (cons_list_char @ X3 @ Ys2)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_219_sorted__wrt_Oinduct, axiom,
    ((![P : (ty > ty > $o) > list_ty > $o, A0 : ty > ty > $o, A1 : list_ty]: ((![P3 : ty > ty > $o]: (P @ P3 @ nil_ty)) => ((![P3 : ty > ty > $o, X3 : ty, Ys2 : list_ty]: ((P @ P3 @ Ys2) => (P @ P3 @ (cons_ty @ X3 @ Ys2)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_220_sorted__wrt_Oinduct, axiom,
    ((![P : (val > val > $o) > list_val > $o, A0 : val > val > $o, A1 : list_val]: ((![P3 : val > val > $o]: (P @ P3 @ nil_val)) => ((![P3 : val > val > $o, X3 : val, Ys2 : list_val]: ((P @ P3 @ Ys2) => (P @ P3 @ (cons_val @ X3 @ Ys2)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_221_remdups__adj_Oinduct, axiom,
    ((![P : list_list_char > $o, A0 : list_list_char]: ((P @ nil_list_char) => ((![X3 : list_char]: (P @ (cons_list_char @ X3 @ nil_list_char))) => ((![X3 : list_char, Y3 : list_char, Xs2 : list_list_char]: (((X3 = Y3) => (P @ (cons_list_char @ X3 @ Xs2))) => (((~ ((X3 = Y3))) => (P @ (cons_list_char @ Y3 @ Xs2))) => (P @ (cons_list_char @ X3 @ (cons_list_char @ Y3 @ Xs2)))))) => (P @ A0))))))). % remdups_adj.induct
thf(fact_222_remdups__adj_Oinduct, axiom,
    ((![P : list_ty > $o, A0 : list_ty]: ((P @ nil_ty) => ((![X3 : ty]: (P @ (cons_ty @ X3 @ nil_ty))) => ((![X3 : ty, Y3 : ty, Xs2 : list_ty]: (((X3 = Y3) => (P @ (cons_ty @ X3 @ Xs2))) => (((~ ((X3 = Y3))) => (P @ (cons_ty @ Y3 @ Xs2))) => (P @ (cons_ty @ X3 @ (cons_ty @ Y3 @ Xs2)))))) => (P @ A0))))))). % remdups_adj.induct
thf(fact_223_remdups__adj_Oinduct, axiom,
    ((![P : list_val > $o, A0 : list_val]: ((P @ nil_val) => ((![X3 : val]: (P @ (cons_val @ X3 @ nil_val))) => ((![X3 : val, Y3 : val, Xs2 : list_val]: (((X3 = Y3) => (P @ (cons_val @ X3 @ Xs2))) => (((~ ((X3 = Y3))) => (P @ (cons_val @ Y3 @ Xs2))) => (P @ (cons_val @ X3 @ (cons_val @ Y3 @ Xs2)))))) => (P @ A0))))))). % remdups_adj.induct
thf(fact_224_successively_Oinduct, axiom,
    ((![P : (list_char > list_char > $o) > list_list_char > $o, A0 : list_char > list_char > $o, A1 : list_list_char]: ((![P3 : list_char > list_char > $o]: (P @ P3 @ nil_list_char)) => ((![P3 : list_char > list_char > $o, X3 : list_char]: (P @ P3 @ (cons_list_char @ X3 @ nil_list_char))) => ((![P3 : list_char > list_char > $o, X3 : list_char, Y3 : list_char, Xs2 : list_list_char]: ((P @ P3 @ (cons_list_char @ Y3 @ Xs2)) => (P @ P3 @ (cons_list_char @ X3 @ (cons_list_char @ Y3 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_225_successively_Oinduct, axiom,
    ((![P : (ty > ty > $o) > list_ty > $o, A0 : ty > ty > $o, A1 : list_ty]: ((![P3 : ty > ty > $o]: (P @ P3 @ nil_ty)) => ((![P3 : ty > ty > $o, X3 : ty]: (P @ P3 @ (cons_ty @ X3 @ nil_ty))) => ((![P3 : ty > ty > $o, X3 : ty, Y3 : ty, Xs2 : list_ty]: ((P @ P3 @ (cons_ty @ Y3 @ Xs2)) => (P @ P3 @ (cons_ty @ X3 @ (cons_ty @ Y3 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_226_successively_Oinduct, axiom,
    ((![P : (val > val > $o) > list_val > $o, A0 : val > val > $o, A1 : list_val]: ((![P3 : val > val > $o]: (P @ P3 @ nil_val)) => ((![P3 : val > val > $o, X3 : val]: (P @ P3 @ (cons_val @ X3 @ nil_val))) => ((![P3 : val > val > $o, X3 : val, Y3 : val, Xs2 : list_val]: ((P @ P3 @ (cons_val @ Y3 @ Xs2)) => (P @ P3 @ (cons_val @ X3 @ (cons_val @ Y3 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_227_list__nonempty__induct, axiom,
    ((![Xs : list_list_char, P : list_list_char > $o]: ((~ ((Xs = nil_list_char))) => ((![X3 : list_char]: (P @ (cons_list_char @ X3 @ nil_list_char))) => ((![X3 : list_char, Xs2 : list_list_char]: ((~ ((Xs2 = nil_list_char))) => ((P @ Xs2) => (P @ (cons_list_char @ X3 @ Xs2))))) => (P @ Xs))))))). % list_nonempty_induct
thf(fact_228_list__nonempty__induct, axiom,
    ((![Xs : list_ty, P : list_ty > $o]: ((~ ((Xs = nil_ty))) => ((![X3 : ty]: (P @ (cons_ty @ X3 @ nil_ty))) => ((![X3 : ty, Xs2 : list_ty]: ((~ ((Xs2 = nil_ty))) => ((P @ Xs2) => (P @ (cons_ty @ X3 @ Xs2))))) => (P @ Xs))))))). % list_nonempty_induct
thf(fact_229_list__nonempty__induct, axiom,
    ((![Xs : list_val, P : list_val > $o]: ((~ ((Xs = nil_val))) => ((![X3 : val]: (P @ (cons_val @ X3 @ nil_val))) => ((![X3 : val, Xs2 : list_val]: ((~ ((Xs2 = nil_val))) => ((P @ Xs2) => (P @ (cons_val @ X3 @ Xs2))))) => (P @ Xs))))))). % list_nonempty_induct
thf(fact_230_map__tailrec__rev_Oinduct, axiom,
    ((![P : (list_char > list_char) > list_list_char > list_list_char > $o, A0 : list_char > list_char, A1 : list_list_char, A22 : list_list_char]: ((![F2 : list_char > list_char, X_1 : list_list_char]: (P @ F2 @ nil_list_char @ X_1)) => ((![F2 : list_char > list_char, A : list_char, As2 : list_list_char, Bs2 : list_list_char]: ((P @ F2 @ As2 @ (cons_list_char @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_list_char @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_231_map__tailrec__rev_Oinduct, axiom,
    ((![P : (ty > list_char) > list_ty > list_list_char > $o, A0 : ty > list_char, A1 : list_ty, A22 : list_list_char]: ((![F2 : ty > list_char, X_1 : list_list_char]: (P @ F2 @ nil_ty @ X_1)) => ((![F2 : ty > list_char, A : ty, As2 : list_ty, Bs2 : list_list_char]: ((P @ F2 @ As2 @ (cons_list_char @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_ty @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_232_map__tailrec__rev_Oinduct, axiom,
    ((![P : (val > list_char) > list_val > list_list_char > $o, A0 : val > list_char, A1 : list_val, A22 : list_list_char]: ((![F2 : val > list_char, X_1 : list_list_char]: (P @ F2 @ nil_val @ X_1)) => ((![F2 : val > list_char, A : val, As2 : list_val, Bs2 : list_list_char]: ((P @ F2 @ As2 @ (cons_list_char @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_val @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_233_map__tailrec__rev_Oinduct, axiom,
    ((![P : (list_char > ty) > list_list_char > list_ty > $o, A0 : list_char > ty, A1 : list_list_char, A22 : list_ty]: ((![F2 : list_char > ty, X_1 : list_ty]: (P @ F2 @ nil_list_char @ X_1)) => ((![F2 : list_char > ty, A : list_char, As2 : list_list_char, Bs2 : list_ty]: ((P @ F2 @ As2 @ (cons_ty @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_list_char @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_234_map__tailrec__rev_Oinduct, axiom,
    ((![P : (ty > ty) > list_ty > list_ty > $o, A0 : ty > ty, A1 : list_ty, A22 : list_ty]: ((![F2 : ty > ty, X_1 : list_ty]: (P @ F2 @ nil_ty @ X_1)) => ((![F2 : ty > ty, A : ty, As2 : list_ty, Bs2 : list_ty]: ((P @ F2 @ As2 @ (cons_ty @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_ty @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_235_map__tailrec__rev_Oinduct, axiom,
    ((![P : (val > ty) > list_val > list_ty > $o, A0 : val > ty, A1 : list_val, A22 : list_ty]: ((![F2 : val > ty, X_1 : list_ty]: (P @ F2 @ nil_val @ X_1)) => ((![F2 : val > ty, A : val, As2 : list_val, Bs2 : list_ty]: ((P @ F2 @ As2 @ (cons_ty @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_val @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_236_map__tailrec__rev_Oinduct, axiom,
    ((![P : (list_char > val) > list_list_char > list_val > $o, A0 : list_char > val, A1 : list_list_char, A22 : list_val]: ((![F2 : list_char > val, X_1 : list_val]: (P @ F2 @ nil_list_char @ X_1)) => ((![F2 : list_char > val, A : list_char, As2 : list_list_char, Bs2 : list_val]: ((P @ F2 @ As2 @ (cons_val @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_list_char @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_237_map__tailrec__rev_Oinduct, axiom,
    ((![P : (ty > val) > list_ty > list_val > $o, A0 : ty > val, A1 : list_ty, A22 : list_val]: ((![F2 : ty > val, X_1 : list_val]: (P @ F2 @ nil_ty @ X_1)) => ((![F2 : ty > val, A : ty, As2 : list_ty, Bs2 : list_val]: ((P @ F2 @ As2 @ (cons_val @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_ty @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_238_map__tailrec__rev_Oinduct, axiom,
    ((![P : (val > val) > list_val > list_val > $o, A0 : val > val, A1 : list_val, A22 : list_val]: ((![F2 : val > val, X_1 : list_val]: (P @ F2 @ nil_val @ X_1)) => ((![F2 : val > val, A : val, As2 : list_val, Bs2 : list_val]: ((P @ F2 @ As2 @ (cons_val @ (F2 @ A) @ Bs2)) => (P @ F2 @ (cons_val @ A @ As2) @ Bs2))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_239_successively_Ocases, axiom,
    ((![X : produc1844257764t_char]: ((![P3 : list_char > list_char > $o]: (~ ((X = (produc1986826718t_char @ P3 @ nil_list_char))))) => ((![P3 : list_char > list_char > $o, X3 : list_char]: (~ ((X = (produc1986826718t_char @ P3 @ (cons_list_char @ X3 @ nil_list_char)))))) => (~ ((![P3 : list_char > list_char > $o, X3 : list_char, Y3 : list_char, Xs2 : list_list_char]: (~ ((X = (produc1986826718t_char @ P3 @ (cons_list_char @ X3 @ (cons_list_char @ Y3 @ Xs2)))))))))))))). % successively.cases
thf(fact_240_successively_Ocases, axiom,
    ((![X : produc508135182ist_ty]: ((![P3 : ty > ty > $o]: (~ ((X = (produc5654152ist_ty @ P3 @ nil_ty))))) => ((![P3 : ty > ty > $o, X3 : ty]: (~ ((X = (produc5654152ist_ty @ P3 @ (cons_ty @ X3 @ nil_ty)))))) => (~ ((![P3 : ty > ty > $o, X3 : ty, Y3 : ty, Xs2 : list_ty]: (~ ((X = (produc5654152ist_ty @ P3 @ (cons_ty @ X3 @ (cons_ty @ Y3 @ Xs2)))))))))))))). % successively.cases
thf(fact_241_successively_Ocases, axiom,
    ((![X : produc1050553413st_val]: ((![P3 : val > val > $o]: (~ ((X = (produc578411711st_val @ P3 @ nil_val))))) => ((![P3 : val > val > $o, X3 : val]: (~ ((X = (produc578411711st_val @ P3 @ (cons_val @ X3 @ nil_val)))))) => (~ ((![P3 : val > val > $o, X3 : val, Y3 : val, Xs2 : list_val]: (~ ((X = (produc578411711st_val @ P3 @ (cons_val @ X3 @ (cons_val @ Y3 @ Xs2)))))))))))))). % successively.cases
thf(fact_242_sorted__wrt_Ocases, axiom,
    ((![X : produc1844257764t_char]: ((![P3 : list_char > list_char > $o]: (~ ((X = (produc1986826718t_char @ P3 @ nil_list_char))))) => (~ ((![P3 : list_char > list_char > $o, X3 : list_char, Ys2 : list_list_char]: (~ ((X = (produc1986826718t_char @ P3 @ (cons_list_char @ X3 @ Ys2)))))))))))). % sorted_wrt.cases
thf(fact_243_sorted__wrt_Ocases, axiom,
    ((![X : produc508135182ist_ty]: ((![P3 : ty > ty > $o]: (~ ((X = (produc5654152ist_ty @ P3 @ nil_ty))))) => (~ ((![P3 : ty > ty > $o, X3 : ty, Ys2 : list_ty]: (~ ((X = (produc5654152ist_ty @ P3 @ (cons_ty @ X3 @ Ys2)))))))))))). % sorted_wrt.cases
thf(fact_244_sorted__wrt_Ocases, axiom,
    ((![X : produc1050553413st_val]: ((![P3 : val > val > $o]: (~ ((X = (produc578411711st_val @ P3 @ nil_val))))) => (~ ((![P3 : val > val > $o, X3 : val, Ys2 : list_val]: (~ ((X = (produc578411711st_val @ P3 @ (cons_val @ X3 @ Ys2)))))))))))). % sorted_wrt.cases
thf(fact_245_subseqs_Osimps_I1_J, axiom,
    (((subseqs_char @ nil_char) = (cons_list_char @ nil_char @ nil_list_char)))). % subseqs.simps(1)
thf(fact_246_product__lists_Osimps_I1_J, axiom,
    (((product_lists_char @ nil_list_char) = (cons_list_char @ nil_char @ nil_list_char)))). % product_lists.simps(1)
thf(fact_247_snoc__listrel1__snoc__iff, axiom,
    ((![Xs : list_val, X : val, Ys : list_val, Y : val, R : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (append_val @ Xs @ (cons_val @ X @ nil_val)) @ (append_val @ Ys @ (cons_val @ Y @ nil_val))) @ (listrel1_val @ R)) = (((((member1382006826st_val @ (produc180957881st_val @ Xs @ Ys) @ (listrel1_val @ R))) & ((X = Y)))) | ((((Xs = Ys)) & ((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ R))))))))). % snoc_listrel1_snoc_iff

% Helper facts (7)
thf(help_If_2_1_If_001t__List__Olist_It__Type__Oty_J_T, axiom,
    ((![X : list_ty, Y : list_ty]: ((if_list_ty @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__List__Olist_It__Type__Oty_J_T, axiom,
    ((![X : list_ty, Y : list_ty]: ((if_list_ty @ $true @ X @ Y) = X)))).
thf(help_If_2_1_If_001t__List__Olist_It__Value__Oval_J_T, axiom,
    ((![X : list_val, Y : list_val]: ((if_list_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__List__Olist_It__Value__Oval_J_T, axiom,
    ((![X : list_val, Y : list_val]: ((if_list_val @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_T, axiom,
    ((![X : list_list_char, Y : list_list_char]: ((if_list_list_char @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_T, axiom,
    ((![X : list_list_char, Y : list_list_char]: ((if_list_list_char @ $true @ X @ Y) = X)))).

% Conjectures (4)
thf(conj_0, hypothesis,
    ((![A6 : option_set_list_char]: (((size_s2008079621t_char @ vsa) = (size_size_list_ty @ tsa)) => (((size_size_list_val @ vsa2) = (size_size_list_ty @ tsa)) => ((d_list_char @ (blocks @ (produc1808722894t_char @ vsa @ (produc1806338192t_char @ tsa @ (produc823987298t_char @ vsa2 @ ea)))) @ A6) = (d_list_char @ ea @ (hyperUn_list_char @ A6 @ (some_set_list_char @ (set_list_char2 @ vsa)))))))))).
thf(conj_1, hypothesis,
    (((size_s2008079621t_char @ (cons_list_char @ v @ vsa)) = (size_size_list_ty @ (cons_ty @ t @ tsa))))).
thf(conj_2, hypothesis,
    (((size_size_list_val @ (cons_val @ v2 @ vsa2)) = (size_size_list_ty @ (cons_ty @ t @ tsa))))).
thf(conj_3, conjecture,
    (((d_list_char @ (blocks @ (produc1808722894t_char @ (cons_list_char @ v @ vsa) @ (produc1806338192t_char @ (cons_ty @ t @ tsa) @ (produc823987298t_char @ (cons_val @ v2 @ vsa2) @ ea)))) @ a) = (d_list_char @ ea @ (hyperUn_list_char @ a @ (some_set_list_char @ (set_list_char2 @ (cons_list_char @ v @ vsa)))))))).
