% 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_26__5332044_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:18:42.686

% Could-be-implicit typings (19)
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,
    list_P1234162913t_char : $tType).
thf(ty_n_t__Set__Oset_It__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, type,
    set_op1111598910on_val : $tType).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    option2118145160on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    set_Pr2075231726on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    produc266837688on_val : $tType).
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Type__Oty_J_J, type,
    list_P1991792281har_ty : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
    produc1257910179t_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_list_char : $tType).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Type__Oty_J_J, type,
    set_option_ty : $tType).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J, type,
    set_option_nat : $tType).
thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $tType).
thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
    option_ty : $tType).
thf(ty_n_t__Option__Ooption_It__Nat__Onat_J, type,
    option_nat : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__Set__Oset_It__Type__Oty_J, type,
    set_ty : $tType).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (62)
thf(sy_c_Conform_Ohconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    hconf_1244167010t_char : list_P1234162913t_char > (nat > option2118145160on_val) > $o).
thf(sy_c_Conform_Ooconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    oconf_454120169t_char : list_P1234162913t_char > (nat > option2118145160on_val) > produc266837688on_val > $o).
thf(sy_c_Exceptions_Opreallocated, type,
    preallocated : (nat > option2118145160on_val) > $o).
thf(sy_c_Expr_Oexp_Onew_001t__List__Olist_It__String__Ochar_J, type,
    new_list_char : list_char > exp_list_char).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Type__Oty_J, type,
    fun_up9191ion_ty : (list_char > option_ty) > list_char > option_ty > list_char > option_ty).
thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    fun_up262443479on_val : (nat > option2118145160on_val) > nat > option2118145160on_val > nat > option2118145160on_val).
thf(sy_c_HOL_OThe_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Type__Oty_J_J, type,
    the_li2019826130har_ty : (list_P1991792281har_ty > $o) > list_P1991792281har_ty).
thf(sy_c_If_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    if_opt451925058on_val : $o > option2118145160on_val > option2118145160on_val > option2118145160on_val).
thf(sy_c_Map_Omap__le_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_le_list_char_ty : (list_char > option_ty) > (list_char > option_ty) > $o).
thf(sy_c_Map_Omap__le_001t__Nat__Onat_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    map_le931214383on_val : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Map_Omap__of_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    map_of2035691063har_ty : list_P1991792281har_ty > produc1257910179t_char > option_ty).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
thf(sy_c_Objects_Oinit__fields, type,
    init_fields : list_P1991792281har_ty > produc1257910179t_char > option_val).
thf(sy_c_Objects_Onew__Addr, type,
    new_Addr : (nat > option2118145160on_val) > option_nat).
thf(sy_c_Objects_Otypeof__h, type,
    typeof_h : (nat > option2118145160on_val) > val > option_ty).
thf(sy_c_Option_Ocombine__options_001t__Nat__Onat, type,
    combine_options_nat : (nat > nat > nat) > option_nat > option_nat > option_nat).
thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    combin1801280889on_val : (produc266837688on_val > produc266837688on_val > produc266837688on_val) > option2118145160on_val > option2118145160on_val > option2118145160on_val).
thf(sy_c_Option_Ocombine__options_001t__Type__Oty, type,
    combine_options_ty : (ty > ty > ty) > option_ty > option_ty > option_ty).
thf(sy_c_Option_Ois__none_001t__Nat__Onat, type,
    is_none_nat : option_nat > $o).
thf(sy_c_Option_Ois__none_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    is_non1389277148on_val : option2118145160on_val > $o).
thf(sy_c_Option_Ois__none_001t__Type__Oty, type,
    is_none_ty : option_ty > $o).
thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat, type,
    none_nat : option_nat).
thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    none_P1535574167on_val : option2118145160on_val).
thf(sy_c_Option_Ooption_ONone_001t__Type__Oty, type,
    none_ty : option_ty).
thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat, type,
    some_nat : nat > option_nat).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    some_P1299442195on_val : produc266837688on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_OSome_001t__Type__Oty, type,
    some_ty : ty > option_ty).
thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Nat__Onat, type,
    case_option_o_nat : $o > (nat > $o) > option_nat > $o).
thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    case_o1187854213on_val : $o > (produc266837688on_val > $o) > option2118145160on_val > $o).
thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Type__Oty, type,
    case_option_o_ty : $o > (ty > $o) > option_ty > $o).
thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat, type,
    case_o1104735357at_nat : option_nat > (nat > option_nat) > option_nat > option_nat).
thf(sy_c_Option_Ooption_Ocase__option_001t__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_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    case_o815592781on_val : option2118145160on_val > (produc266837688on_val > option2118145160on_val) > option2118145160on_val > option2118145160on_val).
thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Type__Oty_J_001t__Type__Oty, type,
    case_o105137099_ty_ty : option_ty > (ty > option_ty) > option_ty > option_ty).
thf(sy_c_Option_Ooption_Opred__option_001t__Nat__Onat, type,
    pred_option_nat : (nat > $o) > option_nat > $o).
thf(sy_c_Option_Ooption_Opred__option_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    pred_o2031621109on_val : (produc266837688on_val > $o) > option2118145160on_val > $o).
thf(sy_c_Option_Ooption_Opred__option_001t__Type__Oty, type,
    pred_option_ty : (ty > $o) > option_ty > $o).
thf(sy_c_Option_Ooption_Oset__option_001t__Nat__Onat, type,
    set_option_nat2 : option_nat > set_nat).
thf(sy_c_Option_Ooption_Oset__option_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    set_op2078752426on_val : option2118145160on_val > set_Pr2075231726on_val).
thf(sy_c_Option_Ooption_Oset__option_001t__Type__Oty, type,
    set_option_ty2 : option_ty > set_ty).
thf(sy_c_Option_Othese_001t__Nat__Onat, type,
    these_nat : set_option_nat > set_nat).
thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    these_538817979on_val : set_op1111598910on_val > set_Pr2075231726on_val).
thf(sy_c_Option_Othese_001t__Type__Oty, type,
    these_ty : set_option_ty > set_ty).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc904988266on_val : list_char > (produc1257910179t_char > option_val) > produc266837688on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    produc1304532571t_char : list_char > list_char > produc1257910179t_char).
thf(sy_c_TypeRel_OFields_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    fields1441617180t_char : list_P1234162913t_char > list_char > list_P1991792281har_ty > $o).
thf(sy_c_TypeRel_Ofields_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    fields1811926268t_char : list_P1234162913t_char > list_char > list_P1991792281har_ty).
thf(sy_c_TypeRel_Ohas__field_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    has_fi599584195t_char : list_P1234162913t_char > list_char > list_char > ty > list_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).
thf(sy_c_member_001t__Option__Ooption_It__Nat__Onat_J, type,
    member_option_nat : option_nat > set_option_nat > $o).
thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1048249375on_val : option2118145160on_val > set_op1111598910on_val > $o).
thf(sy_c_member_001t__Option__Ooption_It__Type__Oty_J, type,
    member_option_ty : option_ty > set_option_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
thf(sy_c_member_001t__Type__Oty, type,
    member_ty : ty > set_ty > $o).
thf(sy_v_C____, type,
    c : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_FDTs____, type,
    fDTs : list_P1991792281har_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_a____, type,
    a : nat).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).

% Relevant facts (160)
thf(fact_0_RedNew_Ohyps_I1_J, axiom,
    (((new_Addr @ ha) = (some_nat @ a)))). % RedNew.hyps(1)
thf(fact_1_option_Oinject, axiom,
    ((![X2 : nat, Y2 : nat]: (((some_nat @ X2) = (some_nat @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_2_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_3_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_4_new__Addr__SomeD, axiom,
    ((![H : nat > option2118145160on_val, A : nat]: (((new_Addr @ H) = (some_nat @ A)) => ((H @ A) = none_P1535574167on_val))))). % new_Addr_SomeD
thf(fact_5_RedNew_Ohyps_I3_J, axiom,
    ((h_a = (fun_up262443479on_val @ ha @ a @ (some_P1299442195on_val @ (produc904988266on_val @ c @ (init_fields @ fDTs))))))). % RedNew.hyps(3)
thf(fact_6_RedNew_Oprems_I2_J, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % RedNew.prems(2)
thf(fact_7_combine__options__simps_I3_J, axiom,
    ((![F : nat > nat > nat, A : nat, B : nat]: ((combine_options_nat @ F @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ (F @ A @ B)))))). % combine_options_simps(3)
thf(fact_8_combine__options__simps_I3_J, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, A : produc266837688on_val, B : produc266837688on_val]: ((combin1801280889on_val @ F @ (some_P1299442195on_val @ A) @ (some_P1299442195on_val @ B)) = (some_P1299442195on_val @ (F @ A @ B)))))). % combine_options_simps(3)
thf(fact_9_combine__options__simps_I3_J, axiom,
    ((![F : ty > ty > ty, A : ty, B : ty]: ((combine_options_ty @ F @ (some_ty @ A) @ (some_ty @ B)) = (some_ty @ (F @ A @ B)))))). % combine_options_simps(3)
thf(fact_10_is__none__code_I2_J, axiom,
    ((![X : nat]: (~ ((is_none_nat @ (some_nat @ X))))))). % is_none_code(2)
thf(fact_11_is__none__code_I2_J, axiom,
    ((![X : produc266837688on_val]: (~ ((is_non1389277148on_val @ (some_P1299442195on_val @ X))))))). % is_none_code(2)
thf(fact_12_is__none__code_I2_J, axiom,
    ((![X : ty]: (~ ((is_none_ty @ (some_ty @ X))))))). % is_none_code(2)
thf(fact_13_in__these__eq, axiom,
    ((![X : nat, A2 : set_option_nat]: ((member_nat @ X @ (these_nat @ A2)) = (member_option_nat @ (some_nat @ X) @ A2))))). % in_these_eq
thf(fact_14_in__these__eq, axiom,
    ((![X : produc266837688on_val, A2 : set_op1111598910on_val]: ((member1296415951on_val @ X @ (these_538817979on_val @ A2)) = (member1048249375on_val @ (some_P1299442195on_val @ X) @ A2))))). % in_these_eq
thf(fact_15_in__these__eq, axiom,
    ((![X : ty, A2 : set_option_ty]: ((member_ty @ X @ (these_ty @ A2)) = (member_option_ty @ (some_ty @ X) @ A2))))). % in_these_eq
thf(fact_16_option_Opred__inject_I2_J, axiom,
    ((![P : nat > $o, A : nat]: ((pred_option_nat @ P @ (some_nat @ A)) = (P @ A))))). % option.pred_inject(2)
thf(fact_17_option_Opred__inject_I2_J, axiom,
    ((![P : produc266837688on_val > $o, A : produc266837688on_val]: ((pred_o2031621109on_val @ P @ (some_P1299442195on_val @ A)) = (P @ A))))). % option.pred_inject(2)
thf(fact_18_option_Opred__inject_I2_J, axiom,
    ((![P : ty > $o, A : ty]: ((pred_option_ty @ P @ (some_ty @ A)) = (P @ A))))). % option.pred_inject(2)
thf(fact_19_elem__set, axiom,
    ((![X : nat, Xo : option_nat]: ((member_nat @ X @ (set_option_nat2 @ Xo)) = (Xo = (some_nat @ X)))))). % elem_set
thf(fact_20_elem__set, axiom,
    ((![X : produc266837688on_val, Xo : option2118145160on_val]: ((member1296415951on_val @ X @ (set_op2078752426on_val @ Xo)) = (Xo = (some_P1299442195on_val @ X)))))). % elem_set
thf(fact_21_elem__set, axiom,
    ((![X : ty, Xo : option_ty]: ((member_ty @ X @ (set_option_ty2 @ Xo)) = (Xo = (some_ty @ X)))))). % elem_set
thf(fact_22_not__Some__eq, axiom,
    ((![X : option_nat]: ((![Y : nat]: (~ ((X = (some_nat @ Y))))) = (X = none_nat))))). % not_Some_eq
thf(fact_23_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_24_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y : ty]: (~ ((X = (some_ty @ Y))))) = (X = none_ty))))). % not_Some_eq
thf(fact_25_not__None__eq, axiom,
    ((![X : option_nat]: ((~ ((X = none_nat))) = (?[Y : nat]: (X = (some_nat @ Y))))))). % not_None_eq
thf(fact_26_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y : produc266837688on_val]: (X = (some_P1299442195on_val @ Y))))))). % not_None_eq
thf(fact_27_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y : ty]: (X = (some_ty @ Y))))))). % not_None_eq
thf(fact_28_is__none__code_I1_J, axiom,
    ((is_none_ty @ none_ty))). % is_none_code(1)
thf(fact_29_is__none__code_I1_J, axiom,
    ((is_none_nat @ none_nat))). % is_none_code(1)
thf(fact_30_is__none__code_I1_J, axiom,
    ((is_non1389277148on_val @ none_P1535574167on_val))). % is_none_code(1)
thf(fact_31_combine__options__simps_I2_J, axiom,
    ((![F : ty > ty > ty, X : option_ty]: ((combine_options_ty @ F @ X @ none_ty) = X)))). % combine_options_simps(2)
thf(fact_32_combine__options__simps_I2_J, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, X : option2118145160on_val]: ((combin1801280889on_val @ F @ X @ none_P1535574167on_val) = X)))). % combine_options_simps(2)
thf(fact_33_combine__options__simps_I2_J, axiom,
    ((![F : nat > nat > nat, X : option_nat]: ((combine_options_nat @ F @ X @ none_nat) = X)))). % combine_options_simps(2)
thf(fact_34_combine__options__simps_I1_J, axiom,
    ((![F : ty > ty > ty, Y3 : option_ty]: ((combine_options_ty @ F @ none_ty @ Y3) = Y3)))). % combine_options_simps(1)
thf(fact_35_combine__options__simps_I1_J, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, Y3 : option2118145160on_val]: ((combin1801280889on_val @ F @ none_P1535574167on_val @ Y3) = Y3)))). % combine_options_simps(1)
thf(fact_36_combine__options__simps_I1_J, axiom,
    ((![F : nat > nat > nat, Y3 : option_nat]: ((combine_options_nat @ F @ none_nat @ Y3) = Y3)))). % combine_options_simps(1)
thf(fact_37_empty__upd__none, axiom,
    ((![X : nat]: ((fun_up262443479on_val @ (^[X3 : nat]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X3 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_38_RedNew_Ohyps_I2_J, axiom,
    ((fields1441617180t_char @ p @ c @ fDTs))). % RedNew.hyps(2)
thf(fact_39_is__none__simps_I1_J, axiom,
    ((is_none_ty @ none_ty))). % is_none_simps(1)
thf(fact_40_is__none__simps_I1_J, axiom,
    ((is_none_nat @ none_nat))). % is_none_simps(1)
thf(fact_41_is__none__simps_I1_J, axiom,
    ((is_non1389277148on_val @ none_P1535574167on_val))). % is_none_simps(1)
thf(fact_42_option_Opred__inject_I1_J, axiom,
    ((![P : produc266837688on_val > $o]: (pred_o2031621109on_val @ P @ none_P1535574167on_val)))). % option.pred_inject(1)
thf(fact_43_Option_Ois__none__def, axiom,
    ((is_none_ty = (^[X3 : option_ty]: (X3 = none_ty))))). % Option.is_none_def
thf(fact_44_Option_Ois__none__def, axiom,
    ((is_none_nat = (^[X3 : option_nat]: (X3 = none_nat))))). % Option.is_none_def
thf(fact_45_Option_Ois__none__def, axiom,
    ((is_non1389277148on_val = (^[X3 : option2118145160on_val]: (X3 = none_P1535574167on_val))))). % Option.is_none_def
thf(fact_46_map__upd__nonempty, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = (^[X3 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_47_combine__options__assoc, axiom,
    ((![F : ty > ty > ty, X : option_ty, Y3 : option_ty, Z : option_ty]: ((![X4 : ty, Y4 : ty, Z2 : ty]: ((F @ (F @ X4 @ Y4) @ Z2) = (F @ X4 @ (F @ Y4 @ Z2)))) => ((combine_options_ty @ F @ (combine_options_ty @ F @ X @ Y3) @ Z) = (combine_options_ty @ F @ X @ (combine_options_ty @ F @ Y3 @ Z))))))). % combine_options_assoc
thf(fact_48_combine__options__assoc, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, X : option2118145160on_val, Y3 : option2118145160on_val, Z : option2118145160on_val]: ((![X4 : produc266837688on_val, Y4 : produc266837688on_val, Z2 : produc266837688on_val]: ((F @ (F @ X4 @ Y4) @ Z2) = (F @ X4 @ (F @ Y4 @ Z2)))) => ((combin1801280889on_val @ F @ (combin1801280889on_val @ F @ X @ Y3) @ Z) = (combin1801280889on_val @ F @ X @ (combin1801280889on_val @ F @ Y3 @ Z))))))). % combine_options_assoc
thf(fact_49_combine__options__assoc, axiom,
    ((![F : nat > nat > nat, X : option_nat, Y3 : option_nat, Z : option_nat]: ((![X4 : nat, Y4 : nat, Z2 : nat]: ((F @ (F @ X4 @ Y4) @ Z2) = (F @ X4 @ (F @ Y4 @ Z2)))) => ((combine_options_nat @ F @ (combine_options_nat @ F @ X @ Y3) @ Z) = (combine_options_nat @ F @ X @ (combine_options_nat @ F @ Y3 @ Z))))))). % combine_options_assoc
thf(fact_50_combine__options__commute, axiom,
    ((![F : ty > ty > ty, X : option_ty, Y3 : option_ty]: ((![X4 : ty, Y4 : ty]: ((F @ X4 @ Y4) = (F @ Y4 @ X4))) => ((combine_options_ty @ F @ X @ Y3) = (combine_options_ty @ F @ Y3 @ X)))))). % combine_options_commute
thf(fact_51_combine__options__commute, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, X : option2118145160on_val, Y3 : option2118145160on_val]: ((![X4 : produc266837688on_val, Y4 : produc266837688on_val]: ((F @ X4 @ Y4) = (F @ Y4 @ X4))) => ((combin1801280889on_val @ F @ X @ Y3) = (combin1801280889on_val @ F @ Y3 @ X)))))). % combine_options_commute
thf(fact_52_combine__options__commute, axiom,
    ((![F : nat > nat > nat, X : option_nat, Y3 : option_nat]: ((![X4 : nat, Y4 : nat]: ((F @ X4 @ Y4) = (F @ Y4 @ X4))) => ((combine_options_nat @ F @ X @ Y3) = (combine_options_nat @ F @ Y3 @ X)))))). % combine_options_commute
thf(fact_53_combine__options__left__commute, axiom,
    ((![F : ty > ty > ty, Y3 : option_ty, X : option_ty, Z : option_ty]: ((![X4 : ty, Y4 : ty]: ((F @ X4 @ Y4) = (F @ Y4 @ X4))) => ((![X4 : ty, Y4 : ty, Z2 : ty]: ((F @ (F @ X4 @ Y4) @ Z2) = (F @ X4 @ (F @ Y4 @ Z2)))) => ((combine_options_ty @ F @ Y3 @ (combine_options_ty @ F @ X @ Z)) = (combine_options_ty @ F @ X @ (combine_options_ty @ F @ Y3 @ Z)))))))). % combine_options_left_commute
thf(fact_54_combine__options__left__commute, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, Y3 : option2118145160on_val, X : option2118145160on_val, Z : option2118145160on_val]: ((![X4 : produc266837688on_val, Y4 : produc266837688on_val]: ((F @ X4 @ Y4) = (F @ Y4 @ X4))) => ((![X4 : produc266837688on_val, Y4 : produc266837688on_val, Z2 : produc266837688on_val]: ((F @ (F @ X4 @ Y4) @ Z2) = (F @ X4 @ (F @ Y4 @ Z2)))) => ((combin1801280889on_val @ F @ Y3 @ (combin1801280889on_val @ F @ X @ Z)) = (combin1801280889on_val @ F @ X @ (combin1801280889on_val @ F @ Y3 @ Z)))))))). % combine_options_left_commute
thf(fact_55_combine__options__left__commute, axiom,
    ((![F : nat > nat > nat, Y3 : option_nat, X : option_nat, Z : option_nat]: ((![X4 : nat, Y4 : nat]: ((F @ X4 @ Y4) = (F @ Y4 @ X4))) => ((![X4 : nat, Y4 : nat, Z2 : nat]: ((F @ (F @ X4 @ Y4) @ Z2) = (F @ X4 @ (F @ Y4 @ Z2)))) => ((combine_options_nat @ F @ Y3 @ (combine_options_nat @ F @ X @ Z)) = (combine_options_nat @ F @ X @ (combine_options_nat @ F @ Y3 @ Z)))))))). % combine_options_left_commute
thf(fact_56_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X : nat, Y3 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y3)) = (((((X = A)) & ((B = Y3)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y3)))))))))). % map_upd_Some_unfold
thf(fact_57_map__upd__triv, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_58_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y3 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y3))) => (X = Y3))))). % map_upd_eqD1
thf(fact_59_combine__options__cases, axiom,
    ((![X : option_nat, P : option_nat > option_nat > $o, Y3 : option_nat]: (((X = none_nat) => (P @ X @ Y3)) => (((Y3 = none_nat) => (P @ X @ Y3)) => ((![A3 : nat, B2 : nat]: ((X = (some_nat @ A3)) => ((Y3 = (some_nat @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_60_combine__options__cases, axiom,
    ((![X : option_nat, P : option_nat > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X = none_nat) => (P @ X @ Y3)) => (((Y3 = none_P1535574167on_val) => (P @ X @ Y3)) => ((![A3 : nat, B2 : produc266837688on_val]: ((X = (some_nat @ A3)) => ((Y3 = (some_P1299442195on_val @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_61_combine__options__cases, axiom,
    ((![X : option_nat, P : option_nat > option_ty > $o, Y3 : option_ty]: (((X = none_nat) => (P @ X @ Y3)) => (((Y3 = none_ty) => (P @ X @ Y3)) => ((![A3 : nat, B2 : ty]: ((X = (some_nat @ A3)) => ((Y3 = (some_ty @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_62_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_nat > $o, Y3 : option_nat]: (((X = none_P1535574167on_val) => (P @ X @ Y3)) => (((Y3 = none_nat) => (P @ X @ Y3)) => ((![A3 : produc266837688on_val, B2 : nat]: ((X = (some_P1299442195on_val @ A3)) => ((Y3 = (some_nat @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_63_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y3)) => (((Y3 = none_P1535574167on_val) => (P @ X @ Y3)) => ((![A3 : produc266837688on_val, B2 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A3)) => ((Y3 = (some_P1299442195on_val @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_64_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y3 : option_ty]: (((X = none_P1535574167on_val) => (P @ X @ Y3)) => (((Y3 = none_ty) => (P @ X @ Y3)) => ((![A3 : produc266837688on_val, B2 : ty]: ((X = (some_P1299442195on_val @ A3)) => ((Y3 = (some_ty @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_65_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_nat > $o, Y3 : option_nat]: (((X = none_ty) => (P @ X @ Y3)) => (((Y3 = none_nat) => (P @ X @ Y3)) => ((![A3 : ty, B2 : nat]: ((X = (some_ty @ A3)) => ((Y3 = (some_nat @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_66_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option2118145160on_val > $o, Y3 : option2118145160on_val]: (((X = none_ty) => (P @ X @ Y3)) => (((Y3 = none_P1535574167on_val) => (P @ X @ Y3)) => ((![A3 : ty, B2 : produc266837688on_val]: ((X = (some_ty @ A3)) => ((Y3 = (some_P1299442195on_val @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_67_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_ty > $o, Y3 : option_ty]: (((X = none_ty) => (P @ X @ Y3)) => (((Y3 = none_ty) => (P @ X @ Y3)) => ((![A3 : ty, B2 : ty]: ((X = (some_ty @ A3)) => ((Y3 = (some_ty @ B2)) => (P @ X @ Y3)))) => (P @ X @ Y3))))))). % combine_options_cases
thf(fact_68_split__option__all, axiom,
    (((^[P2 : option_nat > $o]: (![X5 : option_nat]: (P2 @ X5))) = (^[P3 : option_nat > $o]: (((P3 @ none_nat)) & ((![X3 : nat]: (P3 @ (some_nat @ X3))))))))). % split_option_all
thf(fact_69_split__option__all, axiom,
    (((^[P2 : option2118145160on_val > $o]: (![X5 : option2118145160on_val]: (P2 @ X5))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) & ((![X3 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X3))))))))). % split_option_all
thf(fact_70_split__option__all, axiom,
    (((^[P2 : option_ty > $o]: (![X5 : option_ty]: (P2 @ X5))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) & ((![X3 : ty]: (P3 @ (some_ty @ X3))))))))). % split_option_all
thf(fact_71_split__option__ex, axiom,
    (((^[P2 : option_nat > $o]: (?[X5 : option_nat]: (P2 @ X5))) = (^[P3 : option_nat > $o]: (((P3 @ none_nat)) | ((?[X3 : nat]: (P3 @ (some_nat @ X3))))))))). % split_option_ex
thf(fact_72_split__option__ex, axiom,
    (((^[P2 : option2118145160on_val > $o]: (?[X5 : option2118145160on_val]: (P2 @ X5))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) | ((?[X3 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X3))))))))). % split_option_ex
thf(fact_73_split__option__ex, axiom,
    (((^[P2 : option_ty > $o]: (?[X5 : option_ty]: (P2 @ X5))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) | ((?[X3 : ty]: (P3 @ (some_ty @ X3))))))))). % split_option_ex
thf(fact_74_option_Oinducts, axiom,
    ((![P : option_nat > $o, Option : option_nat]: ((P @ none_nat) => ((![X4 : nat]: (P @ (some_nat @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_75_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X4 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_76_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X4 : ty]: (P @ (some_ty @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_77_option_Oexhaust, axiom,
    ((![Y3 : option_nat]: ((~ ((Y3 = none_nat))) => (~ ((![X22 : nat]: (~ ((Y3 = (some_nat @ X22))))))))))). % option.exhaust
thf(fact_78_option_Oexhaust, axiom,
    ((![Y3 : option2118145160on_val]: ((~ ((Y3 = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y3 = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_79_option_Oexhaust, axiom,
    ((![Y3 : option_ty]: ((~ ((Y3 = none_ty))) => (~ ((![X22 : ty]: (~ ((Y3 = (some_ty @ X22))))))))))). % option.exhaust
thf(fact_80_option_OdiscI, axiom,
    ((![Option : option_nat, X2 : nat]: ((Option = (some_nat @ X2)) => (~ ((Option = none_nat))))))). % option.discI
thf(fact_81_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_82_option_OdiscI, axiom,
    ((![Option : option_ty, X2 : ty]: ((Option = (some_ty @ X2)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_83_option_Odistinct_I1_J, axiom,
    ((![X2 : nat]: (~ ((none_nat = (some_nat @ X2))))))). % option.distinct(1)
thf(fact_84_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_85_option_Odistinct_I1_J, axiom,
    ((![X2 : ty]: (~ ((none_ty = (some_ty @ X2))))))). % option.distinct(1)
thf(fact_86_option_Oset__intros, axiom,
    ((![X2 : nat]: (member_nat @ X2 @ (set_option_nat2 @ (some_nat @ X2)))))). % option.set_intros
thf(fact_87_option_Oset__intros, axiom,
    ((![X2 : produc266837688on_val]: (member1296415951on_val @ X2 @ (set_op2078752426on_val @ (some_P1299442195on_val @ X2)))))). % option.set_intros
thf(fact_88_option_Oset__intros, axiom,
    ((![X2 : ty]: (member_ty @ X2 @ (set_option_ty2 @ (some_ty @ X2)))))). % option.set_intros
thf(fact_89_option_Oset__cases, axiom,
    ((![E : nat, A : option_nat]: ((member_nat @ E @ (set_option_nat2 @ A)) => (A = (some_nat @ E)))))). % option.set_cases
thf(fact_90_option_Oset__cases, axiom,
    ((![E : produc266837688on_val, A : option2118145160on_val]: ((member1296415951on_val @ E @ (set_op2078752426on_val @ A)) => (A = (some_P1299442195on_val @ E)))))). % option.set_cases
thf(fact_91_option_Oset__cases, axiom,
    ((![E : ty, A : option_ty]: ((member_ty @ E @ (set_option_ty2 @ A)) => (A = (some_ty @ E)))))). % option.set_cases
thf(fact_92_ospec, axiom,
    ((![A2 : option_nat, P : nat > $o, X : nat]: ((![X4 : nat]: ((member_nat @ X4 @ (set_option_nat2 @ A2)) => (P @ X4))) => ((A2 = (some_nat @ X)) => (P @ X)))))). % ospec
thf(fact_93_ospec, axiom,
    ((![A2 : option2118145160on_val, P : produc266837688on_val > $o, X : produc266837688on_val]: ((![X4 : produc266837688on_val]: ((member1296415951on_val @ X4 @ (set_op2078752426on_val @ A2)) => (P @ X4))) => ((A2 = (some_P1299442195on_val @ X)) => (P @ X)))))). % ospec
thf(fact_94_ospec, axiom,
    ((![A2 : option_ty, P : ty > $o, X : ty]: ((![X4 : ty]: ((member_ty @ X4 @ (set_option_ty2 @ A2)) => (P @ X4))) => ((A2 = (some_ty @ X)) => (P @ X)))))). % ospec
thf(fact_95_is__none__simps_I2_J, axiom,
    ((![X : nat]: (~ ((is_none_nat @ (some_nat @ X))))))). % is_none_simps(2)
thf(fact_96_is__none__simps_I2_J, axiom,
    ((![X : produc266837688on_val]: (~ ((is_non1389277148on_val @ (some_P1299442195on_val @ X))))))). % is_none_simps(2)
thf(fact_97_is__none__simps_I2_J, axiom,
    ((![X : ty]: (~ ((is_none_ty @ (some_ty @ X))))))). % is_none_simps(2)
thf(fact_98_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y3) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_99_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_100_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X3 : nat]: (^[Y : option2118145160on_val]: (^[Z3 : nat]: (if_opt451925058on_val @ (Z3 = X3) @ Y @ (F2 @ Z3))))))))). % fun_upd_apply
thf(fact_101_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_102_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A4 @ B3)) = (((A = A4)) & ((B = B3))))))). % old.prod.inject
thf(fact_103_RedNew_Oprems_I1_J, axiom,
    ((wTrt @ p @ ha @ e @ (new_list_char @ c) @ t))). % RedNew.prems(1)
thf(fact_104_hconf__new, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = none_P1535574167on_val) => ((oconf_454120169t_char @ P @ H @ Obj) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_105_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: (((H @ A) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_106_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => ((oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C @ Fs2)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))))))). % hconf_upd_obj
thf(fact_107_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))))). % hext_upd_obj
thf(fact_108_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_109_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_110_oconf__init__fields, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, H : nat > option2118145160on_val]: ((fields1441617180t_char @ P @ C @ FDTs) => (oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C @ (init_fields @ FDTs))))))). % oconf_init_fields
thf(fact_111_hconfD, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P @ H @ Obj)))))). % hconfD
thf(fact_112_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs3))))))))). % hext_objD
thf(fact_113_hext__def, axiom,
    ((hext = (^[H4 : nat > option2118145160on_val]: (^[H5 : nat > option2118145160on_val]: (![A5 : nat]: (![C2 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H4 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H5 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs5)))))))))))))). % hext_def
thf(fact_114_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A3 : nat, C3 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))))) => (hext @ H @ H2))))). % hextI
thf(fact_115_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A3 : list_char, B2 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B2))) => (P @ Prod))))). % old.prod.inducts
thf(fact_116_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc266837688on_val]: (~ ((![A3 : list_char, B2 : produc1257910179t_char > option_val]: (~ ((Y3 = (produc904988266on_val @ A3 @ B2)))))))))). % old.prod.exhaust
thf(fact_117_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A4 @ B3)) => (~ (((A = A4) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_118_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P4 : produc266837688on_val]: ((![A3 : list_char, B2 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A3 @ B2))) => (P @ P4))))). % prod_cases
thf(fact_119_surj__pair, axiom,
    ((![P4 : produc266837688on_val]: (?[X4 : list_char, Y4 : produc1257910179t_char > option_val]: (P4 = (produc904988266on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_120_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y3) = F) = ((F @ X) = Y3))))). % fun_upd_idem_iff
thf(fact_121_fun__upd__twist, axiom,
    ((![A : nat, C4 : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D : option2118145160on_val]: ((~ ((A = C4))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C4 @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C4 @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_122_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y3 : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y3 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_123_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y3 @ X) = Y3)))). % fun_upd_same
thf(fact_124_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val]: (((F @ X) = Y3) => ((fun_up262443479on_val @ F @ X @ Y3) = F))))). % fun_upd_idem
thf(fact_125_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y3 : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y3) = (fun_up262443479on_val @ G @ X @ Z)) => (Y3 = Z))))). % fun_upd_eqD
thf(fact_126_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A5 : nat]: (^[B4 : option2118145160on_val]: (^[X3 : nat]: (if_opt451925058on_val @ (X3 = A5) @ B4 @ (F2 @ X3))))))))). % fun_upd_def
thf(fact_127_exp_Oinject_I1_J, axiom,
    ((![X1 : list_char, Y1 : list_char]: (((new_list_char @ X1) = (new_list_char @ Y1)) = (X1 = Y1))))). % exp.inject(1)
thf(fact_128_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E2 : list_char > option_ty, E : exp_list_char, T2 : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E2 @ E @ T2) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E2 @ E @ T2)))))). % WTrt_hext_mono
thf(fact_129_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P3 : list_P1234162913t_char]: (^[H4 : nat > option2118145160on_val]: (((![A5 : nat]: (![Obj2 : produc266837688on_val]: ((((H4 @ A5) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P3 @ H4 @ Obj2)))))) & ((preallocated @ H4)))))))). % hconf_def
thf(fact_130_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X3 : list_char]: (^[Y : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X3 @ Y) @ R))) = (^[X3 : list_char]: (^[Y : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X3 @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_131_preallocated__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: ((preallocated @ H) => (((H @ A) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X)))))))). % preallocated_new
thf(fact_132_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2))))))))). % preallocated_upd_obj
thf(fact_133_preallocated__hext, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((preallocated @ H) => ((hext @ H @ H2) => (preallocated @ H2)))))). % preallocated_hext
thf(fact_134_has__fields__fun, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, FDTs2 : list_P1991792281har_ty]: ((fields1441617180t_char @ P @ C @ FDTs) => ((fields1441617180t_char @ P @ C @ FDTs2) => (FDTs2 = FDTs)))))). % has_fields_fun
thf(fact_135_map__le__imp__upd__le, axiom,
    ((![M1 : nat > option2118145160on_val, M2 : nat > option2118145160on_val, X : nat, Y3 : produc266837688on_val]: ((map_le931214383on_val @ M1 @ M2) => (map_le931214383on_val @ (fun_up262443479on_val @ M1 @ X @ none_P1535574167on_val) @ (fun_up262443479on_val @ M2 @ X @ (some_P1299442195on_val @ Y3))))))). % map_le_imp_upd_le
thf(fact_136_map__le__imp__upd__le, axiom,
    ((![M1 : list_char > option_ty, M2 : list_char > option_ty, X : list_char, Y3 : ty]: ((map_le_list_char_ty @ M1 @ M2) => (map_le_list_char_ty @ (fun_up9191ion_ty @ M1 @ X @ none_ty) @ (fun_up9191ion_ty @ M2 @ X @ (some_ty @ Y3))))))). % map_le_imp_upd_le
thf(fact_137_WTrt__env__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E2 : list_char > option_ty, E : exp_list_char, T2 : ty, E3 : list_char > option_ty]: ((wTrt @ P @ H @ E2 @ E @ T2) => ((map_le_list_char_ty @ E2 @ E3) => (wTrt @ P @ H @ E3 @ E @ T2)))))). % WTrt_env_mono
thf(fact_138_map__le__upd, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty, A : list_char, B : option_ty]: ((map_le_list_char_ty @ F @ G) => (map_le_list_char_ty @ (fun_up9191ion_ty @ F @ A @ B) @ (fun_up9191ion_ty @ G @ A @ B)))))). % map_le_upd
thf(fact_139_map__le__upd, axiom,
    ((![F : nat > option2118145160on_val, G : nat > option2118145160on_val, A : nat, B : option2118145160on_val]: ((map_le931214383on_val @ F @ G) => (map_le931214383on_val @ (fun_up262443479on_val @ F @ A @ B) @ (fun_up262443479on_val @ G @ A @ B)))))). % map_le_upd
thf(fact_140_map__le__empty, axiom,
    ((![G : list_char > option_ty]: (map_le_list_char_ty @ (^[X3 : list_char]: none_ty) @ G)))). % map_le_empty
thf(fact_141_map__le__refl, axiom,
    ((![F : list_char > option_ty]: (map_le_list_char_ty @ F @ F)))). % map_le_refl
thf(fact_142_map__le__trans, axiom,
    ((![M1 : list_char > option_ty, M2 : list_char > option_ty, M3 : list_char > option_ty]: ((map_le_list_char_ty @ M1 @ M2) => ((map_le_list_char_ty @ M2 @ M3) => (map_le_list_char_ty @ M1 @ M3)))))). % map_le_trans
thf(fact_143_map__le__antisym, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F @ G) => ((map_le_list_char_ty @ G @ F) => (F = G)))))). % map_le_antisym
thf(fact_144_upd__None__map__le, axiom,
    ((![F : list_char > option_ty, X : list_char]: (map_le_list_char_ty @ (fun_up9191ion_ty @ F @ X @ none_ty) @ F)))). % upd_None_map_le
thf(fact_145_upd__None__map__le, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: (map_le931214383on_val @ (fun_up262443479on_val @ F @ X @ none_P1535574167on_val) @ F)))). % upd_None_map_le
thf(fact_146_fields__def2, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty]: ((fields1441617180t_char @ P @ C @ FDTs) => ((fields1811926268t_char @ P @ C) = FDTs))))). % fields_def2
thf(fact_147_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, V : val, T2 : ty]: ((hext @ H @ H2) => (((typeof_h @ H @ V) = (some_ty @ T2)) => ((typeof_h @ H2 @ V) = (some_ty @ T2))))))). % hext_typeof_mono
thf(fact_148_typeof__lit__typeof, axiom,
    ((![V : val, T2 : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X3 : nat]: none_P1535574167on_val) @ V) = (some_ty @ T2)) => ((typeof_h @ H @ V) = (some_ty @ T2)))))). % typeof_lit_typeof
thf(fact_149_has__field__def, axiom,
    ((has_fi599584195t_char = (^[P3 : list_P1234162913t_char]: (^[C2 : list_char]: (^[F3 : list_char]: (^[T3 : ty]: (^[D2 : list_char]: (?[FDTs3 : list_P1991792281har_ty]: (((fields1441617180t_char @ P3 @ C2 @ FDTs3)) & (((map_of2035691063har_ty @ FDTs3 @ (produc1304532571t_char @ F3 @ D2)) = (some_ty @ T3))))))))))))). % has_field_def
thf(fact_150_has__field__code, axiom,
    ((![P : list_P1234162913t_char, C : list_char, FDTs : list_P1991792281har_ty, F4 : list_char, D3 : list_char, T2 : ty]: ((fields1441617180t_char @ P @ C @ FDTs) => (((map_of2035691063har_ty @ FDTs @ (produc1304532571t_char @ F4 @ D3)) = (some_ty @ T2)) => (has_fi599584195t_char @ P @ C @ F4 @ T2 @ D3)))))). % has_field_code
thf(fact_151_combine__options__def, axiom,
    ((combine_options_ty = (^[F2 : ty > ty > ty]: (^[X3 : option_ty]: (^[Y : option_ty]: (case_o105137099_ty_ty @ Y @ (^[Z3 : ty]: (case_o105137099_ty_ty @ (some_ty @ Z3) @ (^[Aa : ty]: (some_ty @ (F2 @ Z3 @ Aa))) @ Y)) @ X3))))))). % combine_options_def
thf(fact_152_combine__options__def, axiom,
    ((combin1801280889on_val = (^[F2 : produc266837688on_val > produc266837688on_val > produc266837688on_val]: (^[X3 : option2118145160on_val]: (^[Y : option2118145160on_val]: (case_o815592781on_val @ Y @ (^[Z3 : produc266837688on_val]: (case_o815592781on_val @ (some_P1299442195on_val @ Z3) @ (^[Aa : produc266837688on_val]: (some_P1299442195on_val @ (F2 @ Z3 @ Aa))) @ Y)) @ X3))))))). % combine_options_def
thf(fact_153_combine__options__def, axiom,
    ((combine_options_nat = (^[F2 : nat > nat > nat]: (^[X3 : option_nat]: (^[Y : option_nat]: (case_o1104735357at_nat @ Y @ (^[Z3 : nat]: (case_o1104735357at_nat @ (some_nat @ Z3) @ (^[Aa : nat]: (some_nat @ (F2 @ Z3 @ Aa))) @ Y)) @ X3))))))). % combine_options_def
thf(fact_154_fields__def, axiom,
    ((fields1811926268t_char = (^[P3 : list_P1234162913t_char]: (^[C2 : list_char]: (the_li2019826130har_ty @ (fields1441617180t_char @ P3 @ C2))))))). % fields_def
thf(fact_155_option_Odisc__eq__case_I1_J, axiom,
    ((![Option : option2118145160on_val]: ((Option = none_P1535574167on_val) = (case_o1187854213on_val @ $true @ (^[Uu : produc266837688on_val]: $false) @ Option))))). % option.disc_eq_case(1)
thf(fact_156_option_Odisc__eq__case_I2_J, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) = (case_o1187854213on_val @ $false @ (^[Uu : produc266837688on_val]: $true) @ Option))))). % option.disc_eq_case(2)
thf(fact_157_case__optionE, axiom,
    ((![P : $o, Q : nat > $o, X : option_nat]: ((case_option_o_nat @ P @ Q @ X) => (((X = none_nat) => (~ (P))) => (~ ((![Y4 : nat]: ((X = (some_nat @ Y4)) => (~ ((Q @ Y4)))))))))))). % case_optionE
thf(fact_158_case__optionE, axiom,
    ((![P : $o, Q : produc266837688on_val > $o, X : option2118145160on_val]: ((case_o1187854213on_val @ P @ Q @ X) => (((X = none_P1535574167on_val) => (~ (P))) => (~ ((![Y4 : produc266837688on_val]: ((X = (some_P1299442195on_val @ Y4)) => (~ ((Q @ Y4)))))))))))). % case_optionE
thf(fact_159_case__optionE, axiom,
    ((![P : $o, Q : ty > $o, X : option_ty]: ((case_option_o_ty @ P @ Q @ X) => (((X = none_ty) => (~ (P))) => (~ ((![Y4 : ty]: ((X = (some_ty @ Y4)) => (~ ((Q @ Y4)))))))))))). % case_optionE

% Helper facts (3)
thf(help_If_3_1_If_001t__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_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__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_T, axiom,
    ((![X : option2118145160on_val, Y3 : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__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_T, axiom,
    ((![X : option2118145160on_val, Y3 : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y3) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    (((new_Addr @ ha) = (some_nat @ a)))).
