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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:38.687

% Could-be-implicit typings (31)
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% Explicit typings (117)
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thf(sy_c_Map_Omap__upds_001t__Type__Oty_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_up1856409447on_val : (ty > option2118145160on_val) > list_ty > list_P561327688on_val > ty > option2118145160on_val).
thf(sy_c_Map_Omap__upds_001t__Type__Oty_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    map_up2037701830t_char : (ty > option_set_list_char) > list_ty > list_set_list_char > ty > option_set_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__Value__Oval_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_up380380464on_val : (val > option2118145160on_val) > list_val > list_P561327688on_val > val > option2118145160on_val).
thf(sy_c_Map_Omap__upds_001t__Value__Oval_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    map_up521067151t_char : (val > option_set_list_char) > list_val > list_set_list_char > val > option_set_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_Nat_Osize__class_Osize_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    size_s329991613t_char : list_exp_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    size_s2008079621t_char : list_list_char > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Type__Oty_J_J, type,
    size_s1569909163ion_ty : list_option_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Type__Oty_J, type,
    size_size_list_ty : list_ty > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
    size_size_list_val : list_val > nat).
thf(sy_c_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__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    none_set_list_char : option_set_list_char).
thf(sy_c_Option_Ooption_ONone_001t__Type__Oty, type,
    none_ty : option_ty).
thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
    none_val : option_val).
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__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_Option_Ooption_OSome_001t__Type__Oty, type,
    some_ty : ty > option_ty).
thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
    some_val : val > option_val).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    bot_bo1263509675t_char : set_list_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_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    produc713467969t_char : list_list_char > exp_list_char > produc1294284815t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_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__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J_J, type,
    produc1238538255t_char : list_char > produc1451990293t_char > produc1259892823t_char).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Type__Oty_J_001t__Product____Type__Oprod_It__Type__Oty_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    produc1730359111t_char : list_ty > produc1490933927t_char > produc1451990293t_char).
thf(sy_c_Product__Type_OPair_001t__Type__Oty_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    produc248075743t_char : ty > produc1294284815t_char > produc1490933927t_char).
thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J, type,
    collect_list_char : (list_char > $o) > set_list_char).
thf(sy_c_Set_OCollect_001t__Type__Oty, type,
    collect_ty : (ty > $o) > set_ty).
thf(sy_c_Set_OCollect_001t__Value__Oval, type,
    collect_val : (val > $o) > set_val).
thf(sy_c_Set_Oinsert_001t__List__Olist_It__String__Ochar_J, type,
    insert_list_char : list_char > set_list_char > set_list_char).
thf(sy_c_Set_Oinsert_001t__Type__Oty, type,
    insert_ty : ty > set_ty > set_ty).
thf(sy_c_Set_Oinsert_001t__Value__Oval, type,
    insert_val : val > set_val > set_val).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_TypeRel_OMethod_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    method297381284t_char : list_P1234162913t_char > list_char > list_char > list_ty > ty > produc1294284815t_char > list_char > $o).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_Type_Othis, type,
    this : list_char).
thf(sy_c_Type_Oty_OClass, type,
    class : list_char > ty).
thf(sy_c_Value_Oval_OAddr, type,
    addr : nat > val).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellType_OWT, type,
    wt : list_P1234162913t_char > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    member_exp_list_char : exp_list_char > set_exp_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__Option__Ooption_It__Type__Oty_J, type,
    member_option_ty : option_ty > set_option_ty > $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_C______, type,
    c : list_char).
thf(sy_v_D______, type,
    d : list_char).
thf(sy_v_M______, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T_H, type,
    t : ty).
thf(sy_v_T______, type,
    t2 : ty).
thf(sy_v_Ts______, type,
    ts : list_ty).
thf(sy_v_a______, type,
    a : nat > option2118145160on_val).
thf(sy_v_aa______, type,
    aa : nat).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_body______, type,
    body : exp_list_char).
thf(sy_v_fs______, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_pns______, type,
    pns : list_list_char).
thf(sy_v_vs______, type,
    vs : list_val).

% Relevant facts (246)
thf(fact_0_RedCall_Ohyps_I4_J, axiom,
    (((size_size_list_ty @ ts) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(4)
thf(fact_1_RedCall_Ohyps_I3_J, axiom,
    (((size_size_list_val @ vs) = (size_s2008079621t_char @ pns)))). % RedCall.hyps(3)
thf(fact_2_map__upds__twist, axiom,
    ((![A : val, As : list_val, M : val > option2118145160on_val, B : produc266837688on_val, Bs : list_P561327688on_val]: ((~ ((member_val @ A @ (set_val2 @ As)))) => ((map_up380380464on_val @ (fun_up1663496455on_val @ M @ A @ (some_P1299442195on_val @ B)) @ As @ Bs) = (fun_up1663496455on_val @ (map_up380380464on_val @ M @ As @ Bs) @ A @ (some_P1299442195on_val @ B))))))). % map_upds_twist
thf(fact_3_map__upds__twist, axiom,
    ((![A : val, As : list_val, M : val > option_set_list_char, B : set_list_char, Bs : list_set_list_char]: ((~ ((member_val @ A @ (set_val2 @ As)))) => ((map_up521067151t_char @ (fun_up705283814t_char @ M @ A @ (some_set_list_char @ B)) @ As @ Bs) = (fun_up705283814t_char @ (map_up521067151t_char @ M @ As @ Bs) @ A @ (some_set_list_char @ B))))))). % map_upds_twist
thf(fact_4_map__upds__twist, axiom,
    ((![A : val, As : list_val, M : val > option_ty, B : ty, Bs : list_ty]: ((~ ((member_val @ A @ (set_val2 @ As)))) => ((map_upds_val_ty @ (fun_up334718982ion_ty @ M @ A @ (some_ty @ B)) @ As @ Bs) = (fun_up334718982ion_ty @ (map_upds_val_ty @ M @ As @ Bs) @ A @ (some_ty @ B))))))). % map_upds_twist
thf(fact_5_map__upds__twist, axiom,
    ((![A : ty, As : list_ty, M : ty > option2118145160on_val, B : produc266837688on_val, Bs : list_P561327688on_val]: ((~ ((member_ty @ A @ (set_ty2 @ As)))) => ((map_up1856409447on_val @ (fun_up1126010942on_val @ M @ A @ (some_P1299442195on_val @ B)) @ As @ Bs) = (fun_up1126010942on_val @ (map_up1856409447on_val @ M @ As @ Bs) @ A @ (some_P1299442195on_val @ B))))))). % map_upds_twist
thf(fact_6_map__upds__twist, axiom,
    ((![A : list_char, As : list_list_char, M : list_char > option2118145160on_val, B : produc266837688on_val, Bs : list_P561327688on_val]: ((~ ((member_list_char @ A @ (set_list_char2 @ As)))) => ((map_up787232785on_val @ (fun_up1219402600on_val @ M @ A @ (some_P1299442195on_val @ B)) @ As @ Bs) = (fun_up1219402600on_val @ (map_up787232785on_val @ M @ As @ Bs) @ A @ (some_P1299442195on_val @ B))))))). % map_upds_twist
thf(fact_7_map__upds__twist, axiom,
    ((![A : ty, As : list_ty, M : ty > option_set_list_char, B : set_list_char, Bs : list_set_list_char]: ((~ ((member_ty @ A @ (set_ty2 @ As)))) => ((map_up2037701830t_char @ (fun_up1035206173t_char @ M @ A @ (some_set_list_char @ B)) @ As @ Bs) = (fun_up1035206173t_char @ (map_up2037701830t_char @ M @ As @ Bs) @ A @ (some_set_list_char @ B))))))). % map_upds_twist
thf(fact_8_map__upds__twist, axiom,
    ((![A : list_char, As : list_list_char, M : list_char > option_set_list_char, B : set_list_char, Bs : list_set_list_char]: ((~ ((member_list_char @ A @ (set_list_char2 @ As)))) => ((map_up937891184t_char @ (fun_up357931335t_char @ M @ A @ (some_set_list_char @ B)) @ As @ Bs) = (fun_up357931335t_char @ (map_up937891184t_char @ M @ As @ Bs) @ A @ (some_set_list_char @ B))))))). % map_upds_twist
thf(fact_9_map__upds__twist, axiom,
    ((![A : ty, As : list_ty, M : ty > option_ty, B : ty, Bs : list_ty]: ((~ ((member_ty @ A @ (set_ty2 @ As)))) => ((map_upds_ty_ty @ (fun_upd_ty_option_ty @ M @ A @ (some_ty @ B)) @ As @ Bs) = (fun_upd_ty_option_ty @ (map_upds_ty_ty @ M @ As @ Bs) @ A @ (some_ty @ B))))))). % map_upds_twist
thf(fact_10_map__upds__twist, axiom,
    ((![A : list_char, As : list_list_char, M : list_char > option_ty, B : ty, Bs : list_ty]: ((~ ((member_list_char @ A @ (set_list_char2 @ As)))) => ((map_up703499792har_ty @ (fun_up9191ion_ty @ M @ A @ (some_ty @ B)) @ As @ Bs) = (fun_up9191ion_ty @ (map_up703499792har_ty @ M @ As @ Bs) @ A @ (some_ty @ B))))))). % map_upds_twist
thf(fact_11_RedCall_Ohyps_I1_J, axiom,
    (((hp @ (produc52622304on_val @ a @ b) @ aa) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % RedCall.hyps(1)
thf(fact_12_map__fun__upd, axiom,
    ((![Y : ty, Xs : list_ty, F : ty > option2118145160on_val, V : option2118145160on_val]: ((~ ((member_ty @ Y @ (set_ty2 @ Xs)))) => ((map_ty1185747589on_val @ (fun_up1126010942on_val @ F @ Y @ V) @ Xs) = (map_ty1185747589on_val @ F @ Xs)))))). % map_fun_upd
thf(fact_13_map__fun__upd, axiom,
    ((![Y : ty, Xs : list_ty, F : ty > option_ty, V : option_ty]: ((~ ((member_ty @ Y @ (set_ty2 @ Xs)))) => ((map_ty_option_ty @ (fun_upd_ty_option_ty @ F @ Y @ V) @ Xs) = (map_ty_option_ty @ F @ Xs)))))). % map_fun_upd
thf(fact_14_map__fun__upd, axiom,
    ((![Y : ty, Xs : list_ty, F : ty > option_set_list_char, V : option_set_list_char]: ((~ ((member_ty @ Y @ (set_ty2 @ Xs)))) => ((map_ty2076285028t_char @ (fun_up1035206173t_char @ F @ Y @ V) @ Xs) = (map_ty2076285028t_char @ F @ Xs)))))). % map_fun_upd
thf(fact_15_map__fun__upd, axiom,
    ((![Y : list_char, Xs : list_list_char, F : list_char > option2118145160on_val, V : option2118145160on_val]: ((~ ((member_list_char @ Y @ (set_list_char2 @ Xs)))) => ((map_li784901935on_val @ (fun_up1219402600on_val @ F @ Y @ V) @ Xs) = (map_li784901935on_val @ F @ Xs)))))). % map_fun_upd
thf(fact_16_map__fun__upd, axiom,
    ((![Y : list_char, Xs : list_list_char, F : list_char > option_set_list_char, V : option_set_list_char]: ((~ ((member_list_char @ Y @ (set_list_char2 @ Xs)))) => ((map_li1793703182t_char @ (fun_up357931335t_char @ F @ Y @ V) @ Xs) = (map_li1793703182t_char @ F @ Xs)))))). % map_fun_upd
thf(fact_17_map__fun__upd, axiom,
    ((![Y : val, Xs : list_val, F : val > exp_list_char, V : exp_list_char]: ((~ ((member_val @ Y @ (set_val2 @ Xs)))) => ((map_va1515327237t_char @ (fun_up1707383436t_char @ F @ Y @ V) @ Xs) = (map_va1515327237t_char @ F @ Xs)))))). % map_fun_upd
thf(fact_18_map__fun__upd, axiom,
    ((![Y : list_char, Xs : list_list_char, F : list_char > option_ty, V : option_ty]: ((~ ((member_list_char @ Y @ (set_list_char2 @ Xs)))) => ((map_li427973166ion_ty @ (fun_up9191ion_ty @ F @ Y @ V) @ Xs) = (map_li427973166ion_ty @ F @ Xs)))))). % map_fun_upd
thf(fact_19_RedCall_Ohyps_I2_J, axiom,
    ((method297381284t_char @ p @ c @ m @ ts @ t2 @ (produc713467969t_char @ pns @ body) @ d))). % RedCall.hyps(2)
thf(fact_20_empty__upd__none, axiom,
    ((![X : ty]: ((fun_upd_ty_option_ty @ (^[X2 : ty]: none_ty) @ X @ none_ty) = (^[X2 : ty]: none_ty))))). % empty_upd_none
thf(fact_21_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up357931335t_char @ (^[X2 : list_char]: none_set_list_char) @ X @ none_set_list_char) = (^[X2 : list_char]: none_set_list_char))))). % empty_upd_none
thf(fact_22_empty__upd__none, axiom,
    ((![X : ty]: ((fun_up1035206173t_char @ (^[X2 : ty]: none_set_list_char) @ X @ none_set_list_char) = (^[X2 : ty]: none_set_list_char))))). % empty_upd_none
thf(fact_23_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1219402600on_val @ (^[X2 : list_char]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X2 : list_char]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_24_empty__upd__none, axiom,
    ((![X : ty]: ((fun_up1126010942on_val @ (^[X2 : ty]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X2 : ty]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_25_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up9191ion_ty @ (^[X2 : list_char]: none_ty) @ X @ none_ty) = (^[X2 : list_char]: none_ty))))). % empty_upd_none
thf(fact_26_map__upds__apply__nontin, axiom,
    ((![X : ty, Xs : list_ty, F : ty > option_ty, Ys : list_ty]: ((~ ((member_ty @ X @ (set_ty2 @ Xs)))) => ((map_upds_ty_ty @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_27_map__upds__apply__nontin, axiom,
    ((![X : ty, Xs : list_ty, F : ty > option_set_list_char, Ys : list_set_list_char]: ((~ ((member_ty @ X @ (set_ty2 @ Xs)))) => ((map_up2037701830t_char @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_28_map__upds__apply__nontin, axiom,
    ((![X : ty, Xs : list_ty, F : ty > option2118145160on_val, Ys : list_P561327688on_val]: ((~ ((member_ty @ X @ (set_ty2 @ Xs)))) => ((map_up1856409447on_val @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_29_map__upds__apply__nontin, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > option_set_list_char, Ys : list_set_list_char]: ((~ ((member_list_char @ X @ (set_list_char2 @ Xs)))) => ((map_up937891184t_char @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_30_map__upds__apply__nontin, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > option2118145160on_val, Ys : list_P561327688on_val]: ((~ ((member_list_char @ X @ (set_list_char2 @ Xs)))) => ((map_up787232785on_val @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_31_map__upds__apply__nontin, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > option_ty, Ys : list_ty]: ((~ ((member_list_char @ X @ (set_list_char2 @ Xs)))) => ((map_up703499792har_ty @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_32_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_33_not__None__eq, axiom,
    ((![X : option_set_list_char]: ((~ ((X = none_set_list_char))) = (?[Y2 : set_list_char]: (X = (some_set_list_char @ Y2))))))). % not_None_eq
thf(fact_34_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y2 : ty]: (X = (some_ty @ Y2))))))). % not_None_eq
thf(fact_35_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_36_not__Some__eq, axiom,
    ((![X : option_set_list_char]: ((![Y2 : set_list_char]: (~ ((X = (some_set_list_char @ Y2))))) = (X = none_set_list_char))))). % not_Some_eq
thf(fact_37_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y2 : ty]: (~ ((X = (some_ty @ Y2))))) = (X = none_ty))))). % not_Some_eq
thf(fact_38_length__map, axiom,
    ((![F : val > val, Xs : list_val]: ((size_size_list_val @ (map_val_val @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_39_length__map, axiom,
    ((![F : ty > val, Xs : list_ty]: ((size_size_list_val @ (map_ty_val @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_40_length__map, axiom,
    ((![F : val > ty, Xs : list_val]: ((size_size_list_ty @ (map_val_ty @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_41_length__map, axiom,
    ((![F : ty > ty, Xs : list_ty]: ((size_size_list_ty @ (map_ty_ty @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_42_length__map, axiom,
    ((![F : list_char > val, Xs : list_list_char]: ((size_size_list_val @ (map_list_char_val @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_43_length__map, axiom,
    ((![F : val > list_char, Xs : list_val]: ((size_s2008079621t_char @ (map_val_list_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_44_length__map, axiom,
    ((![F : ty > list_char, Xs : list_ty]: ((size_s2008079621t_char @ (map_ty_list_char @ F @ Xs)) = (size_size_list_ty @ Xs))))). % length_map
thf(fact_45_length__map, axiom,
    ((![F : list_char > ty, Xs : list_list_char]: ((size_size_list_ty @ (map_list_char_ty @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_46_length__map, axiom,
    ((![F : val > exp_list_char, Xs : list_val]: ((size_s329991613t_char @ (map_va1515327237t_char @ F @ Xs)) = (size_size_list_val @ Xs))))). % length_map
thf(fact_47_length__map, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char]: ((size_s1569909163ion_ty @ (map_li427973166ion_ty @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_48_Un__insert__left, axiom,
    ((![A : list_char, B2 : set_list_char, C : set_list_char]: ((sup_su1099679555t_char @ (insert_list_char @ A @ B2) @ C) = (insert_list_char @ A @ (sup_su1099679555t_char @ B2 @ C)))))). % Un_insert_left
thf(fact_49_Un__insert__right, axiom,
    ((![A2 : set_list_char, A : list_char, B2 : set_list_char]: ((sup_su1099679555t_char @ A2 @ (insert_list_char @ A @ B2)) = (insert_list_char @ A @ (sup_su1099679555t_char @ A2 @ B2)))))). % Un_insert_right
thf(fact_50_map__eq__conv, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char, G : list_char > option_ty]: (((map_li427973166ion_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Xs)) = (![X2 : list_char]: (((member_list_char @ X2 @ (set_list_char2 @ Xs))) => (((F @ X2) = (G @ X2))))))))). % map_eq_conv
thf(fact_51_map__eq__conv, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : val > exp_list_char]: (((map_va1515327237t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Xs)) = (![X2 : val]: (((member_val @ X2 @ (set_val2 @ Xs))) => (((F @ X2) = (G @ X2))))))))). % map_eq_conv
thf(fact_52_insert__absorb2, axiom,
    ((![X : list_char, A2 : set_list_char]: ((insert_list_char @ X @ (insert_list_char @ X @ A2)) = (insert_list_char @ X @ A2))))). % insert_absorb2
thf(fact_53_insert__iff, axiom,
    ((![A : list_char, B : list_char, A2 : set_list_char]: ((member_list_char @ A @ (insert_list_char @ B @ A2)) = (((A = B)) | ((member_list_char @ A @ A2))))))). % insert_iff
thf(fact_54_insert__iff, axiom,
    ((![A : ty, B : ty, A2 : set_ty]: ((member_ty @ A @ (insert_ty @ B @ A2)) = (((A = B)) | ((member_ty @ A @ A2))))))). % insert_iff
thf(fact_55_insert__iff, axiom,
    ((![A : val, B : val, A2 : set_val]: ((member_val @ A @ (insert_val @ B @ A2)) = (((A = B)) | ((member_val @ A @ A2))))))). % insert_iff
thf(fact_56_insertCI, axiom,
    ((![A : list_char, B2 : set_list_char, B : list_char]: (((~ ((member_list_char @ A @ B2))) => (A = B)) => (member_list_char @ A @ (insert_list_char @ B @ B2)))))). % insertCI
thf(fact_57_insertCI, axiom,
    ((![A : ty, B2 : set_ty, B : ty]: (((~ ((member_ty @ A @ B2))) => (A = B)) => (member_ty @ A @ (insert_ty @ B @ B2)))))). % insertCI
thf(fact_58_insertCI, axiom,
    ((![A : val, B2 : set_val, B : val]: (((~ ((member_val @ A @ B2))) => (A = B)) => (member_val @ A @ (insert_val @ B @ B2)))))). % insertCI
thf(fact_59_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_60_option_Oinject, axiom,
    ((![X22 : set_list_char, Y22 : set_list_char]: (((some_set_list_char @ X22) = (some_set_list_char @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_61_option_Oinject, axiom,
    ((![X22 : ty, Y22 : ty]: (((some_ty @ X22) = (some_ty @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_62_Un__iff, axiom,
    ((![C2 : ty, A2 : set_ty, B2 : set_ty]: ((member_ty @ C2 @ (sup_sup_set_ty @ A2 @ B2)) = (((member_ty @ C2 @ A2)) | ((member_ty @ C2 @ B2))))))). % Un_iff
thf(fact_63_Un__iff, axiom,
    ((![C2 : val, A2 : set_val, B2 : set_val]: ((member_val @ C2 @ (sup_sup_set_val @ A2 @ B2)) = (((member_val @ C2 @ A2)) | ((member_val @ C2 @ B2))))))). % Un_iff
thf(fact_64_Un__iff, axiom,
    ((![C2 : list_char, A2 : set_list_char, B2 : set_list_char]: ((member_list_char @ C2 @ (sup_su1099679555t_char @ A2 @ B2)) = (((member_list_char @ C2 @ A2)) | ((member_list_char @ C2 @ B2))))))). % Un_iff
thf(fact_65_UnCI, axiom,
    ((![C2 : ty, B2 : set_ty, A2 : set_ty]: (((~ ((member_ty @ C2 @ B2))) => (member_ty @ C2 @ A2)) => (member_ty @ C2 @ (sup_sup_set_ty @ A2 @ B2)))))). % UnCI
thf(fact_66_UnCI, axiom,
    ((![C2 : val, B2 : set_val, A2 : set_val]: (((~ ((member_val @ C2 @ B2))) => (member_val @ C2 @ A2)) => (member_val @ C2 @ (sup_sup_set_val @ A2 @ B2)))))). % UnCI
thf(fact_67_UnCI, axiom,
    ((![C2 : list_char, B2 : set_list_char, A2 : set_list_char]: (((~ ((member_list_char @ C2 @ B2))) => (member_list_char @ C2 @ A2)) => (member_list_char @ C2 @ (sup_su1099679555t_char @ A2 @ B2)))))). % UnCI
thf(fact_68_mk__disjoint__insert, axiom,
    ((![A : list_char, A2 : set_list_char]: ((member_list_char @ A @ A2) => (?[B3 : set_list_char]: ((A2 = (insert_list_char @ A @ B3)) & (~ ((member_list_char @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_69_mk__disjoint__insert, axiom,
    ((![A : ty, A2 : set_ty]: ((member_ty @ A @ A2) => (?[B3 : set_ty]: ((A2 = (insert_ty @ A @ B3)) & (~ ((member_ty @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_70_mk__disjoint__insert, axiom,
    ((![A : val, A2 : set_val]: ((member_val @ A @ A2) => (?[B3 : set_val]: ((A2 = (insert_val @ A @ B3)) & (~ ((member_val @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_71_insert__commute, axiom,
    ((![X : list_char, Y : list_char, A2 : set_list_char]: ((insert_list_char @ X @ (insert_list_char @ Y @ A2)) = (insert_list_char @ Y @ (insert_list_char @ X @ A2)))))). % insert_commute
thf(fact_72_insert__eq__iff, axiom,
    ((![A : list_char, A2 : set_list_char, B : list_char, B2 : set_list_char]: ((~ ((member_list_char @ A @ A2))) => ((~ ((member_list_char @ B @ B2))) => (((insert_list_char @ A @ A2) = (insert_list_char @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C3 : set_list_char]: (((A2 = (insert_list_char @ B @ C3))) & ((((~ ((member_list_char @ B @ C3)))) & ((((B2 = (insert_list_char @ A @ C3))) & ((~ ((member_list_char @ A @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_73_insert__eq__iff, axiom,
    ((![A : ty, A2 : set_ty, B : ty, B2 : set_ty]: ((~ ((member_ty @ A @ A2))) => ((~ ((member_ty @ B @ B2))) => (((insert_ty @ A @ A2) = (insert_ty @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C3 : set_ty]: (((A2 = (insert_ty @ B @ C3))) & ((((~ ((member_ty @ B @ C3)))) & ((((B2 = (insert_ty @ A @ C3))) & ((~ ((member_ty @ A @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_74_insert__eq__iff, axiom,
    ((![A : val, A2 : set_val, B : val, B2 : set_val]: ((~ ((member_val @ A @ A2))) => ((~ ((member_val @ B @ B2))) => (((insert_val @ A @ A2) = (insert_val @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C3 : set_val]: (((A2 = (insert_val @ B @ C3))) & ((((~ ((member_val @ B @ C3)))) & ((((B2 = (insert_val @ A @ C3))) & ((~ ((member_val @ A @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_75_insert__absorb, axiom,
    ((![A : list_char, A2 : set_list_char]: ((member_list_char @ A @ A2) => ((insert_list_char @ A @ A2) = A2))))). % insert_absorb
thf(fact_76_insert__absorb, axiom,
    ((![A : ty, A2 : set_ty]: ((member_ty @ A @ A2) => ((insert_ty @ A @ A2) = A2))))). % insert_absorb
thf(fact_77_insert__absorb, axiom,
    ((![A : val, A2 : set_val]: ((member_val @ A @ A2) => ((insert_val @ A @ A2) = A2))))). % insert_absorb
thf(fact_78_insert__ident, axiom,
    ((![X : list_char, A2 : set_list_char, B2 : set_list_char]: ((~ ((member_list_char @ X @ A2))) => ((~ ((member_list_char @ X @ B2))) => (((insert_list_char @ X @ A2) = (insert_list_char @ X @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_79_insert__ident, axiom,
    ((![X : ty, A2 : set_ty, B2 : set_ty]: ((~ ((member_ty @ X @ A2))) => ((~ ((member_ty @ X @ B2))) => (((insert_ty @ X @ A2) = (insert_ty @ X @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_80_insert__ident, axiom,
    ((![X : val, A2 : set_val, B2 : set_val]: ((~ ((member_val @ X @ A2))) => ((~ ((member_val @ X @ B2))) => (((insert_val @ X @ A2) = (insert_val @ X @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_81_Set_Oset__insert, axiom,
    ((![X : list_char, A2 : set_list_char]: ((member_list_char @ X @ A2) => (~ ((![B3 : set_list_char]: ((A2 = (insert_list_char @ X @ B3)) => (member_list_char @ X @ B3))))))))). % Set.set_insert
thf(fact_82_Set_Oset__insert, axiom,
    ((![X : ty, A2 : set_ty]: ((member_ty @ X @ A2) => (~ ((![B3 : set_ty]: ((A2 = (insert_ty @ X @ B3)) => (member_ty @ X @ B3))))))))). % Set.set_insert
thf(fact_83_Set_Oset__insert, axiom,
    ((![X : val, A2 : set_val]: ((member_val @ X @ A2) => (~ ((![B3 : set_val]: ((A2 = (insert_val @ X @ B3)) => (member_val @ X @ B3))))))))). % Set.set_insert
thf(fact_84_insertI2, axiom,
    ((![A : list_char, B2 : set_list_char, B : list_char]: ((member_list_char @ A @ B2) => (member_list_char @ A @ (insert_list_char @ B @ B2)))))). % insertI2
thf(fact_85_insertI2, axiom,
    ((![A : ty, B2 : set_ty, B : ty]: ((member_ty @ A @ B2) => (member_ty @ A @ (insert_ty @ B @ B2)))))). % insertI2
thf(fact_86_insertI2, axiom,
    ((![A : val, B2 : set_val, B : val]: ((member_val @ A @ B2) => (member_val @ A @ (insert_val @ B @ B2)))))). % insertI2
thf(fact_87_insertI1, axiom,
    ((![A : list_char, B2 : set_list_char]: (member_list_char @ A @ (insert_list_char @ A @ B2))))). % insertI1
thf(fact_88_insertI1, axiom,
    ((![A : ty, B2 : set_ty]: (member_ty @ A @ (insert_ty @ A @ B2))))). % insertI1
thf(fact_89_insertI1, axiom,
    ((![A : val, B2 : set_val]: (member_val @ A @ (insert_val @ A @ B2))))). % insertI1
thf(fact_90_insertE, axiom,
    ((![A : list_char, B : list_char, A2 : set_list_char]: ((member_list_char @ A @ (insert_list_char @ B @ A2)) => ((~ ((A = B))) => (member_list_char @ A @ A2)))))). % insertE
thf(fact_91_insertE, axiom,
    ((![A : ty, B : ty, A2 : set_ty]: ((member_ty @ A @ (insert_ty @ B @ A2)) => ((~ ((A = B))) => (member_ty @ A @ A2)))))). % insertE
thf(fact_92_insertE, axiom,
    ((![A : val, B : val, A2 : set_val]: ((member_val @ A @ (insert_val @ B @ A2)) => ((~ ((A = B))) => (member_val @ A @ A2)))))). % insertE
thf(fact_93_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_94_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_95_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_96_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_97_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_98_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_99_Un__left__commute, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, C : set_list_char]: ((sup_su1099679555t_char @ A2 @ (sup_su1099679555t_char @ B2 @ C)) = (sup_su1099679555t_char @ B2 @ (sup_su1099679555t_char @ A2 @ C)))))). % Un_left_commute
thf(fact_100_Un__left__absorb, axiom,
    ((![A2 : set_list_char, B2 : set_list_char]: ((sup_su1099679555t_char @ A2 @ (sup_su1099679555t_char @ A2 @ B2)) = (sup_su1099679555t_char @ A2 @ B2))))). % Un_left_absorb
thf(fact_101_Un__commute, axiom,
    ((sup_su1099679555t_char = (^[A3 : set_list_char]: (^[B4 : set_list_char]: (sup_su1099679555t_char @ B4 @ A3)))))). % Un_commute
thf(fact_102_Un__absorb, axiom,
    ((![A2 : set_list_char]: ((sup_su1099679555t_char @ A2 @ A2) = A2)))). % Un_absorb
thf(fact_103_Un__assoc, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, C : set_list_char]: ((sup_su1099679555t_char @ (sup_su1099679555t_char @ A2 @ B2) @ C) = (sup_su1099679555t_char @ A2 @ (sup_su1099679555t_char @ B2 @ C)))))). % Un_assoc
thf(fact_104_ball__Un, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, P : list_char > $o]: ((![X2 : list_char]: (((member_list_char @ X2 @ (sup_su1099679555t_char @ A2 @ B2))) => ((P @ X2)))) = (((![X2 : list_char]: (((member_list_char @ X2 @ A2)) => ((P @ X2))))) & ((![X2 : list_char]: (((member_list_char @ X2 @ B2)) => ((P @ X2)))))))))). % ball_Un
thf(fact_105_bex__Un, axiom,
    ((![A2 : set_list_char, B2 : set_list_char, P : list_char > $o]: ((?[X2 : list_char]: (((member_list_char @ X2 @ (sup_su1099679555t_char @ A2 @ B2))) & ((P @ X2)))) = (((?[X2 : list_char]: (((member_list_char @ X2 @ A2)) & ((P @ X2))))) | ((?[X2 : list_char]: (((member_list_char @ X2 @ B2)) & ((P @ X2)))))))))). % bex_Un
thf(fact_106_UnI2, axiom,
    ((![C2 : ty, B2 : set_ty, A2 : set_ty]: ((member_ty @ C2 @ B2) => (member_ty @ C2 @ (sup_sup_set_ty @ A2 @ B2)))))). % UnI2
thf(fact_107_UnI2, axiom,
    ((![C2 : val, B2 : set_val, A2 : set_val]: ((member_val @ C2 @ B2) => (member_val @ C2 @ (sup_sup_set_val @ A2 @ B2)))))). % UnI2
thf(fact_108_UnI2, axiom,
    ((![C2 : list_char, B2 : set_list_char, A2 : set_list_char]: ((member_list_char @ C2 @ B2) => (member_list_char @ C2 @ (sup_su1099679555t_char @ A2 @ B2)))))). % UnI2
thf(fact_109_UnI1, axiom,
    ((![C2 : ty, A2 : set_ty, B2 : set_ty]: ((member_ty @ C2 @ A2) => (member_ty @ C2 @ (sup_sup_set_ty @ A2 @ B2)))))). % UnI1
thf(fact_110_UnI1, axiom,
    ((![C2 : val, A2 : set_val, B2 : set_val]: ((member_val @ C2 @ A2) => (member_val @ C2 @ (sup_sup_set_val @ A2 @ B2)))))). % UnI1
thf(fact_111_UnI1, axiom,
    ((![C2 : list_char, A2 : set_list_char, B2 : set_list_char]: ((member_list_char @ C2 @ A2) => (member_list_char @ C2 @ (sup_su1099679555t_char @ A2 @ B2)))))). % UnI1
thf(fact_112_UnE, axiom,
    ((![C2 : ty, A2 : set_ty, B2 : set_ty]: ((member_ty @ C2 @ (sup_sup_set_ty @ A2 @ B2)) => ((~ ((member_ty @ C2 @ A2))) => (member_ty @ C2 @ B2)))))). % UnE
thf(fact_113_UnE, axiom,
    ((![C2 : val, A2 : set_val, B2 : set_val]: ((member_val @ C2 @ (sup_sup_set_val @ A2 @ B2)) => ((~ ((member_val @ C2 @ A2))) => (member_val @ C2 @ B2)))))). % UnE
thf(fact_114_UnE, axiom,
    ((![C2 : list_char, A2 : set_list_char, B2 : set_list_char]: ((member_list_char @ C2 @ (sup_su1099679555t_char @ A2 @ B2)) => ((~ ((member_list_char @ C2 @ A2))) => (member_list_char @ C2 @ B2)))))). % UnE
thf(fact_115_insert__Collect, axiom,
    ((![A : list_char, P : list_char > $o]: ((insert_list_char @ A @ (collect_list_char @ P)) = (collect_list_char @ (^[U : list_char]: (((~ ((U = A)))) => ((P @ U))))))))). % insert_Collect
thf(fact_116_insert__compr, axiom,
    ((insert_list_char = (^[A4 : list_char]: (^[B4 : set_list_char]: (collect_list_char @ (^[X2 : list_char]: (((X2 = A4)) | ((member_list_char @ X2 @ B4)))))))))). % insert_compr
thf(fact_117_insert__compr, axiom,
    ((insert_ty = (^[A4 : ty]: (^[B4 : set_ty]: (collect_ty @ (^[X2 : ty]: (((X2 = A4)) | ((member_ty @ X2 @ B4)))))))))). % insert_compr
thf(fact_118_insert__compr, axiom,
    ((insert_val = (^[A4 : val]: (^[B4 : set_val]: (collect_val @ (^[X2 : val]: (((X2 = A4)) | ((member_val @ X2 @ B4)))))))))). % insert_compr
thf(fact_119_mem__Collect__eq, axiom,
    ((![A : list_char, P : list_char > $o]: ((member_list_char @ A @ (collect_list_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_120_mem__Collect__eq, axiom,
    ((![A : ty, P : ty > $o]: ((member_ty @ A @ (collect_ty @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_121_mem__Collect__eq, axiom,
    ((![A : val, P : val > $o]: ((member_val @ A @ (collect_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_122_Collect__mem__eq, axiom,
    ((![A2 : set_list_char]: ((collect_list_char @ (^[X2 : list_char]: (member_list_char @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_123_Collect__mem__eq, axiom,
    ((![A2 : set_ty]: ((collect_ty @ (^[X2 : ty]: (member_ty @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_124_Collect__mem__eq, axiom,
    ((![A2 : set_val]: ((collect_val @ (^[X2 : val]: (member_val @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_125_Collect__disj__eq, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((collect_list_char @ (^[X2 : list_char]: (((P @ X2)) | ((Q @ X2))))) = (sup_su1099679555t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)))))). % Collect_disj_eq
thf(fact_126_Un__def, axiom,
    ((sup_sup_set_ty = (^[A3 : set_ty]: (^[B4 : set_ty]: (collect_ty @ (^[X2 : ty]: (((member_ty @ X2 @ A3)) | ((member_ty @ X2 @ B4)))))))))). % Un_def
thf(fact_127_Un__def, axiom,
    ((sup_sup_set_val = (^[A3 : set_val]: (^[B4 : set_val]: (collect_val @ (^[X2 : val]: (((member_val @ X2 @ A3)) | ((member_val @ X2 @ B4)))))))))). % Un_def
thf(fact_128_Un__def, axiom,
    ((sup_su1099679555t_char = (^[A3 : set_list_char]: (^[B4 : set_list_char]: (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ A3)) | ((member_list_char @ X2 @ B4)))))))))). % Un_def
thf(fact_129_list_Oinj__map__strong, axiom,
    ((![X : list_list_char, Xa : list_list_char, F : list_char > option_ty, Fa : list_char > option_ty]: ((![Z : list_char, Za : list_char]: ((member_list_char @ Z @ (set_list_char2 @ X)) => ((member_list_char @ Za @ (set_list_char2 @ Xa)) => (((F @ Z) = (Fa @ Za)) => (Z = Za))))) => (((map_li427973166ion_ty @ F @ X) = (map_li427973166ion_ty @ Fa @ Xa)) => (X = Xa)))))). % list.inj_map_strong
thf(fact_130_list_Oinj__map__strong, axiom,
    ((![X : list_val, Xa : list_val, F : val > exp_list_char, Fa : val > exp_list_char]: ((![Z : val, Za : val]: ((member_val @ Z @ (set_val2 @ X)) => ((member_val @ Za @ (set_val2 @ Xa)) => (((F @ Z) = (Fa @ Za)) => (Z = Za))))) => (((map_va1515327237t_char @ F @ X) = (map_va1515327237t_char @ Fa @ Xa)) => (X = Xa)))))). % list.inj_map_strong
thf(fact_131_list_Omap__cong0, axiom,
    ((![X : list_list_char, F : list_char > option_ty, G : list_char > option_ty]: ((![Z : list_char]: ((member_list_char @ Z @ (set_list_char2 @ X)) => ((F @ Z) = (G @ Z)))) => ((map_li427973166ion_ty @ F @ X) = (map_li427973166ion_ty @ G @ X)))))). % list.map_cong0
thf(fact_132_list_Omap__cong0, axiom,
    ((![X : list_val, F : val > exp_list_char, G : val > exp_list_char]: ((![Z : val]: ((member_val @ Z @ (set_val2 @ X)) => ((F @ Z) = (G @ Z)))) => ((map_va1515327237t_char @ F @ X) = (map_va1515327237t_char @ G @ X)))))). % list.map_cong0
thf(fact_133_list_Omap__cong, axiom,
    ((![X : list_list_char, Ya : list_list_char, F : list_char > option_ty, G : list_char > option_ty]: ((X = Ya) => ((![Z : list_char]: ((member_list_char @ Z @ (set_list_char2 @ Ya)) => ((F @ Z) = (G @ Z)))) => ((map_li427973166ion_ty @ F @ X) = (map_li427973166ion_ty @ G @ Ya))))))). % list.map_cong
thf(fact_134_list_Omap__cong, axiom,
    ((![X : list_val, Ya : list_val, F : val > exp_list_char, G : val > exp_list_char]: ((X = Ya) => ((![Z : val]: ((member_val @ Z @ (set_val2 @ Ya)) => ((F @ Z) = (G @ Z)))) => ((map_va1515327237t_char @ F @ X) = (map_va1515327237t_char @ G @ Ya))))))). % list.map_cong
thf(fact_135_ex__map__conv, axiom,
    ((![Ys : list_exp_list_char, F : val > exp_list_char]: ((?[Xs3 : list_val]: (Ys = (map_va1515327237t_char @ F @ Xs3))) = (![X2 : exp_list_char]: (((member_exp_list_char @ X2 @ (set_exp_list_char2 @ Ys))) => ((?[Y2 : val]: (X2 = (F @ Y2)))))))))). % ex_map_conv
thf(fact_136_ex__map__conv, axiom,
    ((![Ys : list_option_ty, F : list_char > option_ty]: ((?[Xs3 : list_list_char]: (Ys = (map_li427973166ion_ty @ F @ Xs3))) = (![X2 : option_ty]: (((member_option_ty @ X2 @ (set_option_ty2 @ Ys))) => ((?[Y2 : list_char]: (X2 = (F @ Y2)))))))))). % ex_map_conv
thf(fact_137_map__cong, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, F : list_char > option_ty, G : list_char > option_ty]: ((Xs = Ys) => ((![X3 : list_char]: ((member_list_char @ X3 @ (set_list_char2 @ Ys)) => ((F @ X3) = (G @ X3)))) => ((map_li427973166ion_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Ys))))))). % map_cong
thf(fact_138_map__cong, axiom,
    ((![Xs : list_val, Ys : list_val, F : val > exp_list_char, G : val > exp_list_char]: ((Xs = Ys) => ((![X3 : val]: ((member_val @ X3 @ (set_val2 @ Ys)) => ((F @ X3) = (G @ X3)))) => ((map_va1515327237t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys))))))). % map_cong
thf(fact_139_map__idI, axiom,
    ((![Xs : list_ty, F : ty > ty]: ((![X3 : ty]: ((member_ty @ X3 @ (set_ty2 @ Xs)) => ((F @ X3) = X3))) => ((map_ty_ty @ F @ Xs) = Xs))))). % map_idI
thf(fact_140_map__idI, axiom,
    ((![Xs : list_list_char, F : list_char > list_char]: ((![X3 : list_char]: ((member_list_char @ X3 @ (set_list_char2 @ Xs)) => ((F @ X3) = X3))) => ((map_li1166989960t_char @ F @ Xs) = Xs))))). % map_idI
thf(fact_141_map__idI, axiom,
    ((![Xs : list_val, F : val > val]: ((![X3 : val]: ((member_val @ X3 @ (set_val2 @ Xs)) => ((F @ X3) = X3))) => ((map_val_val @ F @ Xs) = Xs))))). % map_idI
thf(fact_142_map__ext, axiom,
    ((![Xs : list_list_char, F : list_char > option_ty, G : list_char > option_ty]: ((![X3 : list_char]: ((member_list_char @ X3 @ (set_list_char2 @ Xs)) => ((F @ X3) = (G @ X3)))) => ((map_li427973166ion_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Xs)))))). % map_ext
thf(fact_143_map__ext, axiom,
    ((![Xs : list_val, F : val > exp_list_char, G : val > exp_list_char]: ((![X3 : val]: ((member_val @ X3 @ (set_val2 @ Xs)) => ((F @ X3) = (G @ X3)))) => ((map_va1515327237t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Xs)))))). % map_ext
thf(fact_144_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : val > exp_list_char, Ys : list_val]: (((map_va1515327237t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_145_map__eq__imp__length__eq, axiom,
    ((![F : val > option_ty, Xs : list_val, G : list_char > option_ty, Ys : list_list_char]: (((map_val_option_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_146_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : list_char > exp_list_char, Ys : list_list_char]: (((map_va1515327237t_char @ F @ Xs) = (map_li1930351204t_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_147_map__eq__imp__length__eq, axiom,
    ((![F : val > exp_list_char, Xs : list_val, G : ty > exp_list_char, Ys : list_ty]: (((map_va1515327237t_char @ F @ Xs) = (map_ty_exp_list_char @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_148_map__eq__imp__length__eq, axiom,
    ((![F : list_char > exp_list_char, Xs : list_list_char, G : val > exp_list_char, Ys : list_val]: (((map_li1930351204t_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_149_map__eq__imp__length__eq, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char, G : val > option_ty, Ys : list_val]: (((map_li427973166ion_ty @ F @ Xs) = (map_val_option_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_150_map__eq__imp__length__eq, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char, G : list_char > option_ty, Ys : list_list_char]: (((map_li427973166ion_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_151_map__eq__imp__length__eq, axiom,
    ((![F : list_char > option_ty, Xs : list_list_char, G : ty > option_ty, Ys : list_ty]: (((map_li427973166ion_ty @ F @ Xs) = (map_ty_option_ty @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_152_map__eq__imp__length__eq, axiom,
    ((![F : ty > exp_list_char, Xs : list_ty, G : val > exp_list_char, Ys : list_val]: (((map_ty_exp_list_char @ F @ Xs) = (map_va1515327237t_char @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_153_map__eq__imp__length__eq, axiom,
    ((![F : ty > option_ty, Xs : list_ty, G : list_char > option_ty, Ys : list_list_char]: (((map_ty_option_ty @ F @ Xs) = (map_li427973166ion_ty @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_154_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A5 : produc266837688on_val, B5 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_P1299442195on_val @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_155_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A5 : produc266837688on_val, B5 : set_list_char]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_set_list_char @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_156_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y : option_ty]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A5 : produc266837688on_val, B5 : ty]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_ty @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_157_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A5 : set_list_char, B5 : produc266837688on_val]: ((X = (some_set_list_char @ A5)) => ((Y = (some_P1299442195on_val @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_158_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A5 : set_list_char, B5 : set_list_char]: ((X = (some_set_list_char @ A5)) => ((Y = (some_set_list_char @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_159_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_ty > $o, Y : option_ty]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A5 : set_list_char, B5 : ty]: ((X = (some_set_list_char @ A5)) => ((Y = (some_ty @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_160_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A5 : ty, B5 : produc266837688on_val]: ((X = (some_ty @ A5)) => ((Y = (some_P1299442195on_val @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_161_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A5 : ty, B5 : set_list_char]: ((X = (some_ty @ A5)) => ((Y = (some_set_list_char @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_162_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_ty > $o, Y : option_ty]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A5 : ty, B5 : ty]: ((X = (some_ty @ A5)) => ((Y = (some_ty @ B5)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_163_split__option__all, axiom,
    (((^[P2 : option2118145160on_val > $o]: (![X4 : option2118145160on_val]: (P2 @ X4))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_164_split__option__all, axiom,
    (((^[P2 : option_set_list_char > $o]: (![X4 : option_set_list_char]: (P2 @ X4))) = (^[P3 : option_set_list_char > $o]: (((P3 @ none_set_list_char)) & ((![X2 : set_list_char]: (P3 @ (some_set_list_char @ X2))))))))). % split_option_all
thf(fact_165_split__option__all, axiom,
    (((^[P2 : option_ty > $o]: (![X4 : option_ty]: (P2 @ X4))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) & ((![X2 : ty]: (P3 @ (some_ty @ X2))))))))). % split_option_all
thf(fact_166_split__option__ex, axiom,
    (((^[P2 : option2118145160on_val > $o]: (?[X4 : option2118145160on_val]: (P2 @ X4))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_167_split__option__ex, axiom,
    (((^[P2 : option_set_list_char > $o]: (?[X4 : option_set_list_char]: (P2 @ X4))) = (^[P3 : option_set_list_char > $o]: (((P3 @ none_set_list_char)) | ((?[X2 : set_list_char]: (P3 @ (some_set_list_char @ X2))))))))). % split_option_ex
thf(fact_168_split__option__ex, axiom,
    (((^[P2 : option_ty > $o]: (?[X4 : option_ty]: (P2 @ X4))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) | ((?[X2 : ty]: (P3 @ (some_ty @ X2))))))))). % split_option_ex
thf(fact_169_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X3 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_170_option_Oinducts, axiom,
    ((![P : option_set_list_char > $o, Option : option_set_list_char]: ((P @ none_set_list_char) => ((![X3 : set_list_char]: (P @ (some_set_list_char @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_171_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X3 : ty]: (P @ (some_ty @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_172_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_173_option_Oexhaust, axiom,
    ((![Y : option_set_list_char]: ((~ ((Y = none_set_list_char))) => (~ ((![X23 : set_list_char]: (~ ((Y = (some_set_list_char @ X23))))))))))). % option.exhaust
thf(fact_174_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X23 : ty]: (~ ((Y = (some_ty @ X23))))))))))). % option.exhaust
thf(fact_175_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_176_option_OdiscI, axiom,
    ((![Option : option_set_list_char, X22 : set_list_char]: ((Option = (some_set_list_char @ X22)) => (~ ((Option = none_set_list_char))))))). % option.discI
thf(fact_177_option_OdiscI, axiom,
    ((![Option : option_ty, X22 : ty]: ((Option = (some_ty @ X22)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_178_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_179_option_Odistinct_I1_J, axiom,
    ((![X22 : set_list_char]: (~ ((none_set_list_char = (some_set_list_char @ X22))))))). % option.distinct(1)
thf(fact_180_option_Odistinct_I1_J, axiom,
    ((![X22 : ty]: (~ ((none_ty = (some_ty @ X22))))))). % option.distinct(1)
thf(fact_181_map__upd__Some__unfold, axiom,
    ((![M : list_char > option2118145160on_val, A : list_char, B : produc266837688on_val, X : list_char, Y : produc266837688on_val]: (((fun_up1219402600on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_182_map__upd__Some__unfold, axiom,
    ((![M : ty > option2118145160on_val, A : ty, B : produc266837688on_val, X : ty, Y : produc266837688on_val]: (((fun_up1126010942on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_183_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_set_list_char, A : list_char, B : set_list_char, X : list_char, Y : set_list_char]: (((fun_up357931335t_char @ M @ A @ (some_set_list_char @ B) @ X) = (some_set_list_char @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_set_list_char @ Y)))))))))). % map_upd_Some_unfold
thf(fact_184_map__upd__Some__unfold, axiom,
    ((![M : ty > option_set_list_char, A : ty, B : set_list_char, X : ty, Y : set_list_char]: (((fun_up1035206173t_char @ M @ A @ (some_set_list_char @ B) @ X) = (some_set_list_char @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_set_list_char @ Y)))))))))). % map_upd_Some_unfold
thf(fact_185_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_ty, A : list_char, B : ty, X : list_char, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ B) @ X) = (some_ty @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_ty @ Y)))))))))). % map_upd_Some_unfold
thf(fact_186_map__upd__Some__unfold, axiom,
    ((![M : ty > option_ty, A : ty, B : ty, X : ty, Y : ty]: (((fun_upd_ty_option_ty @ M @ A @ (some_ty @ B) @ X) = (some_ty @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_ty @ Y)))))))))). % map_upd_Some_unfold
thf(fact_187_map__upd__triv, axiom,
    ((![T : list_char > option2118145160on_val, K : list_char, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up1219402600on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_188_map__upd__triv, axiom,
    ((![T : ty > option2118145160on_val, K : ty, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up1126010942on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_189_map__upd__triv, axiom,
    ((![T : list_char > option_set_list_char, K : list_char, X : set_list_char]: (((T @ K) = (some_set_list_char @ X)) => ((fun_up357931335t_char @ T @ K @ (some_set_list_char @ X)) = T))))). % map_upd_triv
thf(fact_190_map__upd__triv, axiom,
    ((![T : ty > option_set_list_char, K : ty, X : set_list_char]: (((T @ K) = (some_set_list_char @ X)) => ((fun_up1035206173t_char @ T @ K @ (some_set_list_char @ X)) = T))))). % map_upd_triv
thf(fact_191_map__upd__triv, axiom,
    ((![T : list_char > option_ty, K : list_char, X : ty]: (((T @ K) = (some_ty @ X)) => ((fun_up9191ion_ty @ T @ K @ (some_ty @ X)) = T))))). % map_upd_triv
thf(fact_192_map__upd__triv, axiom,
    ((![T : ty > option_ty, K : ty, X : ty]: (((T @ K) = (some_ty @ X)) => ((fun_upd_ty_option_ty @ T @ K @ (some_ty @ X)) = T))))). % map_upd_triv
thf(fact_193_map__upd__eqD1, axiom,
    ((![M : list_char > option2118145160on_val, A : list_char, X : produc266837688on_val, N : list_char > option2118145160on_val, Y : produc266837688on_val]: (((fun_up1219402600on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up1219402600on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_194_map__upd__eqD1, axiom,
    ((![M : ty > option2118145160on_val, A : ty, X : produc266837688on_val, N : ty > option2118145160on_val, Y : produc266837688on_val]: (((fun_up1126010942on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up1126010942on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_195_map__upd__eqD1, axiom,
    ((![M : list_char > option_set_list_char, A : list_char, X : set_list_char, N : list_char > option_set_list_char, Y : set_list_char]: (((fun_up357931335t_char @ M @ A @ (some_set_list_char @ X)) = (fun_up357931335t_char @ N @ A @ (some_set_list_char @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_196_map__upd__eqD1, axiom,
    ((![M : ty > option_set_list_char, A : ty, X : set_list_char, N : ty > option_set_list_char, Y : set_list_char]: (((fun_up1035206173t_char @ M @ A @ (some_set_list_char @ X)) = (fun_up1035206173t_char @ N @ A @ (some_set_list_char @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_197_map__upd__eqD1, axiom,
    ((![M : list_char > option_ty, A : list_char, X : ty, N : list_char > option_ty, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ X)) = (fun_up9191ion_ty @ N @ A @ (some_ty @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_198_map__upd__eqD1, axiom,
    ((![M : ty > option_ty, A : ty, X : ty, N : ty > option_ty, Y : ty]: (((fun_upd_ty_option_ty @ M @ A @ (some_ty @ X)) = (fun_upd_ty_option_ty @ N @ A @ (some_ty @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_199_domI, axiom,
    ((![M : list_char > option_val, A : list_char, B : val]: (((M @ A) = (some_val @ B)) => (member_list_char @ A @ (dom_list_char_val @ M)))))). % domI
thf(fact_200_domI, axiom,
    ((![M : list_char > option2118145160on_val, A : list_char, B : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B)) => (member_list_char @ A @ (dom_li1284435309on_val @ M)))))). % domI
thf(fact_201_domI, axiom,
    ((![M : ty > option2118145160on_val, A : ty, B : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B)) => (member_ty @ A @ (dom_ty5603011on_val @ M)))))). % domI
thf(fact_202_domI, axiom,
    ((![M : val > option2118145160on_val, A : val, B : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B)) => (member_val @ A @ (dom_va253830796on_val @ M)))))). % domI
thf(fact_203_domI, axiom,
    ((![M : list_char > option_set_list_char, A : list_char, B : set_list_char]: (((M @ A) = (some_set_list_char @ B)) => (member_list_char @ A @ (dom_li665594572t_char @ M)))))). % domI
thf(fact_204_domI, axiom,
    ((![M : ty > option_set_list_char, A : ty, B : set_list_char]: (((M @ A) = (some_set_list_char @ B)) => (member_ty @ A @ (dom_ty_set_list_char @ M)))))). % domI
thf(fact_205_domI, axiom,
    ((![M : val > option_set_list_char, A : val, B : set_list_char]: (((M @ A) = (some_set_list_char @ B)) => (member_val @ A @ (dom_va1099316203t_char @ M)))))). % domI
thf(fact_206_domI, axiom,
    ((![M : list_char > option_ty, A : list_char, B : ty]: (((M @ A) = (some_ty @ B)) => (member_list_char @ A @ (dom_list_char_ty @ M)))))). % domI
thf(fact_207_domI, axiom,
    ((![M : ty > option_ty, A : ty, B : ty]: (((M @ A) = (some_ty @ B)) => (member_ty @ A @ (dom_ty_ty @ M)))))). % domI
thf(fact_208_domI, axiom,
    ((![M : val > option_ty, A : val, B : ty]: (((M @ A) = (some_ty @ B)) => (member_val @ A @ (dom_val_ty @ M)))))). % domI
thf(fact_209_domD, axiom,
    ((![A : list_char, M : list_char > option_val]: ((member_list_char @ A @ (dom_list_char_val @ M)) => (?[B5 : val]: ((M @ A) = (some_val @ B5))))))). % domD
thf(fact_210_domD, axiom,
    ((![A : list_char, M : list_char > option2118145160on_val]: ((member_list_char @ A @ (dom_li1284435309on_val @ M)) => (?[B5 : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B5))))))). % domD
thf(fact_211_domD, axiom,
    ((![A : ty, M : ty > option2118145160on_val]: ((member_ty @ A @ (dom_ty5603011on_val @ M)) => (?[B5 : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B5))))))). % domD
thf(fact_212_domD, axiom,
    ((![A : val, M : val > option2118145160on_val]: ((member_val @ A @ (dom_va253830796on_val @ M)) => (?[B5 : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B5))))))). % domD
thf(fact_213_domD, axiom,
    ((![A : list_char, M : list_char > option_set_list_char]: ((member_list_char @ A @ (dom_li665594572t_char @ M)) => (?[B5 : set_list_char]: ((M @ A) = (some_set_list_char @ B5))))))). % domD
thf(fact_214_domD, axiom,
    ((![A : ty, M : ty > option_set_list_char]: ((member_ty @ A @ (dom_ty_set_list_char @ M)) => (?[B5 : set_list_char]: ((M @ A) = (some_set_list_char @ B5))))))). % domD
thf(fact_215_domD, axiom,
    ((![A : val, M : val > option_set_list_char]: ((member_val @ A @ (dom_va1099316203t_char @ M)) => (?[B5 : set_list_char]: ((M @ A) = (some_set_list_char @ B5))))))). % domD
thf(fact_216_domD, axiom,
    ((![A : list_char, M : list_char > option_ty]: ((member_list_char @ A @ (dom_list_char_ty @ M)) => (?[B5 : ty]: ((M @ A) = (some_ty @ B5))))))). % domD
thf(fact_217_domD, axiom,
    ((![A : ty, M : ty > option_ty]: ((member_ty @ A @ (dom_ty_ty @ M)) => (?[B5 : ty]: ((M @ A) = (some_ty @ B5))))))). % domD
thf(fact_218_domD, axiom,
    ((![A : val, M : val > option_ty]: ((member_val @ A @ (dom_val_ty @ M)) => (?[B5 : ty]: ((M @ A) = (some_ty @ B5))))))). % domD
thf(fact_219_domIff, axiom,
    ((![A : list_char, M : list_char > option_val]: ((member_list_char @ A @ (dom_list_char_val @ M)) = (~ (((M @ A) = none_val))))))). % domIff
thf(fact_220_domIff, axiom,
    ((![A : list_char, M : list_char > option_ty]: ((member_list_char @ A @ (dom_list_char_ty @ M)) = (~ (((M @ A) = none_ty))))))). % domIff
thf(fact_221_domIff, axiom,
    ((![A : ty, M : ty > option_ty]: ((member_ty @ A @ (dom_ty_ty @ M)) = (~ (((M @ A) = none_ty))))))). % domIff
thf(fact_222_domIff, axiom,
    ((![A : val, M : val > option_ty]: ((member_val @ A @ (dom_val_ty @ M)) = (~ (((M @ A) = none_ty))))))). % domIff
thf(fact_223_domIff, axiom,
    ((![A : list_char, M : list_char > option_set_list_char]: ((member_list_char @ A @ (dom_li665594572t_char @ M)) = (~ (((M @ A) = none_set_list_char))))))). % domIff
thf(fact_224_domIff, axiom,
    ((![A : ty, M : ty > option_set_list_char]: ((member_ty @ A @ (dom_ty_set_list_char @ M)) = (~ (((M @ A) = none_set_list_char))))))). % domIff
thf(fact_225_domIff, axiom,
    ((![A : val, M : val > option_set_list_char]: ((member_val @ A @ (dom_va1099316203t_char @ M)) = (~ (((M @ A) = none_set_list_char))))))). % domIff
thf(fact_226_domIff, axiom,
    ((![A : list_char, M : list_char > option2118145160on_val]: ((member_list_char @ A @ (dom_li1284435309on_val @ M)) = (~ (((M @ A) = none_P1535574167on_val))))))). % domIff
thf(fact_227_domIff, axiom,
    ((![A : ty, M : ty > option2118145160on_val]: ((member_ty @ A @ (dom_ty5603011on_val @ M)) = (~ (((M @ A) = none_P1535574167on_val))))))). % domIff
thf(fact_228_domIff, axiom,
    ((![A : val, M : val > option2118145160on_val]: ((member_val @ A @ (dom_va253830796on_val @ M)) = (~ (((M @ A) = none_P1535574167on_val))))))). % domIff
thf(fact_229_insert__def, axiom,
    ((insert_list_char = (^[A4 : list_char]: (sup_su1099679555t_char @ (collect_list_char @ (^[X2 : list_char]: (X2 = A4)))))))). % insert_def
thf(fact_230_dom__def, axiom,
    ((dom_list_char_val = (^[M2 : list_char > option_val]: (collect_list_char @ (^[A4 : list_char]: (~ (((M2 @ A4) = none_val))))))))). % dom_def
thf(fact_231_insert__dom, axiom,
    ((![F : list_char > option_val, X : list_char, Y : val]: (((F @ X) = (some_val @ Y)) => ((insert_list_char @ X @ (dom_list_char_val @ F)) = (dom_list_char_val @ F)))))). % insert_dom
thf(fact_232_insert__dom, axiom,
    ((![F : list_char > option2118145160on_val, X : list_char, Y : produc266837688on_val]: (((F @ X) = (some_P1299442195on_val @ Y)) => ((insert_list_char @ X @ (dom_li1284435309on_val @ F)) = (dom_li1284435309on_val @ F)))))). % insert_dom
thf(fact_233_insert__dom, axiom,
    ((![F : list_char > option_set_list_char, X : list_char, Y : set_list_char]: (((F @ X) = (some_set_list_char @ Y)) => ((insert_list_char @ X @ (dom_li665594572t_char @ F)) = (dom_li665594572t_char @ F)))))). % insert_dom
thf(fact_234_insert__dom, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : ty]: (((F @ X) = (some_ty @ Y)) => ((insert_list_char @ X @ (dom_list_char_ty @ F)) = (dom_list_char_ty @ F)))))). % insert_dom
thf(fact_235_map__upd__nonempty, axiom,
    ((![T : list_char > option2118145160on_val, K : list_char, X : produc266837688on_val]: (~ (((fun_up1219402600on_val @ T @ K @ (some_P1299442195on_val @ X)) = (^[X2 : list_char]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_236_map__upd__nonempty, axiom,
    ((![T : ty > option2118145160on_val, K : ty, X : produc266837688on_val]: (~ (((fun_up1126010942on_val @ T @ K @ (some_P1299442195on_val @ X)) = (^[X2 : ty]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_237_map__upd__nonempty, axiom,
    ((![T : list_char > option_set_list_char, K : list_char, X : set_list_char]: (~ (((fun_up357931335t_char @ T @ K @ (some_set_list_char @ X)) = (^[X2 : list_char]: none_set_list_char))))))). % map_upd_nonempty
thf(fact_238_map__upd__nonempty, axiom,
    ((![T : ty > option_set_list_char, K : ty, X : set_list_char]: (~ (((fun_up1035206173t_char @ T @ K @ (some_set_list_char @ X)) = (^[X2 : ty]: none_set_list_char))))))). % map_upd_nonempty
thf(fact_239_map__upd__nonempty, axiom,
    ((![T : list_char > option_ty, K : list_char, X : ty]: (~ (((fun_up9191ion_ty @ T @ K @ (some_ty @ X)) = (^[X2 : list_char]: none_ty))))))). % map_upd_nonempty
thf(fact_240_map__upd__nonempty, axiom,
    ((![T : ty > option_ty, K : ty, X : ty]: (~ (((fun_upd_ty_option_ty @ T @ K @ (some_ty @ X)) = (^[X2 : ty]: none_ty))))))). % map_upd_nonempty
thf(fact_241_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_242_ty_Oinject, axiom,
    ((![X5 : list_char, Y5 : list_char]: (((class @ X5) = (class @ Y5)) = (X5 = Y5))))). % ty.inject
thf(fact_243_RedCall_Oprems, axiom,
    ((d_list_char @ (call_list_char @ (val_list_char @ (addr @ aa)) @ m @ (map_va1515327237t_char @ val_list_char @ vs)) @ (some_set_list_char @ (dom_list_char_val @ b))))). % RedCall.prems
thf(fact_244_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_245_wf__J__mdecl, axiom,
    ((![P : list_P1234162913t_char, C : list_char, M3 : list_char, Ts : list_ty, T2 : ty, Pns : list_list_char, Body : exp_list_char]: ((wf_J_mdecl @ P @ C @ (produc1238538255t_char @ M3 @ (produc1730359111t_char @ Ts @ (produc248075743t_char @ T2 @ (produc713467969t_char @ Pns @ Body))))) = ((((size_size_list_ty @ Ts) = (size_s2008079621t_char @ Pns))) & ((((distinct_list_char @ Pns)) & ((((~ ((member_list_char @ this @ (set_list_char2 @ Pns))))) & ((((?[T3 : ty]: (((wt @ P @ (map_up703499792har_ty @ (fun_up9191ion_ty @ (^[X2 : list_char]: none_ty) @ this @ (some_ty @ (class @ C))) @ Pns @ Ts) @ Body @ T3)) & ((widen_917054840t_char @ P @ T3 @ T2))))) & ((d_list_char @ Body @ (some_set_list_char @ (sup_su1099679555t_char @ (insert_list_char @ this @ bot_bo1263509675t_char) @ (set_list_char2 @ Pns)))))))))))))))). % wf_J_mdecl

% Conjectures (11)
thf(conj_0, hypothesis,
    (((a @ aa) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))).
thf(conj_1, hypothesis,
    ($true)).
thf(conj_2, hypothesis,
    ($true)).
thf(conj_3, hypothesis,
    ((d_s_list_char @ (map_va1515327237t_char @ val_list_char @ vs) @ (some_set_list_char @ (dom_list_char_val @ b))))).
thf(conj_4, hypothesis,
    ((![X6 : ty]: ((member_ty @ X6 @ (set_ty2 @ ts)) => (is_typ250416522t_char @ p @ X6))))).
thf(conj_5, hypothesis,
    ((is_typ250416522t_char @ p @ t2))).
thf(conj_6, hypothesis,
    ((distinct_list_char @ pns))).
thf(conj_7, hypothesis,
    ((~ ((member_list_char @ this @ (set_list_char2 @ pns)))))).
thf(conj_8, hypothesis,
    ((wt @ p @ (fun_up9191ion_ty @ (map_up703499792har_ty @ (^[X2 : list_char]: none_ty) @ pns @ ts) @ this @ (some_ty @ (class @ d))) @ body @ t))).
thf(conj_9, hypothesis,
    ((widen_917054840t_char @ p @ t @ t2))).
thf(conj_10, conjecture,
    ((hyper_1448788648t_char @ (some_set_list_char @ (insert_list_char @ this @ (set_list_char2 @ pns))) @ (some_set_list_char @ (insert_list_char @ this @ (sup_su1099679555t_char @ (dom_list_char_val @ b) @ (set_list_char2 @ pns))))))).
