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thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__List__Olist_It__List__Olist_It__Type__Oty_J_J, type,
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thf(ty_n_t__Set__Oset_It__List__Olist_It__Type__Oty_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__List__Olist_It__Value__Oval_J, type,
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thf(ty_n_t__Set__Oset_It__Value__Oval_J, type,
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thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
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thf(ty_n_t__Set__Oset_It__Type__Oty_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (191)
thf(sy_c_BigStep_Oeval, type,
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thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_DefAss_O_092_060D_062_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_DefAss_OhyperUn_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ocomp_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Fun_Ocomp_001t__List__Olist_It__Option__Ooption_It__Value__Oval_J_J_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    comp_l1935944006t_char : (list_option_val > list_val) > (list_list_char > list_option_val) > list_list_char > list_val).
thf(sy_c_Fun_Ocomp_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J_001t__List__Olist_It__String__Ochar_J, type,
    comp_l563574263t_char : (list_char > option_val) > (list_char > list_char) > list_char > option_val).
thf(sy_c_Fun_Ocomp_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ocomp_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Value__Oval_J_001t__Option__Ooption_It__Value__Oval_J_001t__List__Olist_It__String__Ochar_J, type,
    comp_o662633318t_char : (option_val > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Value__Oval_J_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ocomp_001t__Value__Oval_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ocomp_001t__Value__Oval_001t__Value__Oval_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_Fun_Ooverride__on_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_List_Ocan__select_001t__List__Olist_It__String__Ochar_J, type,
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    can_se187446692on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val > $o).
thf(sy_c_List_Odistinct_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
    distin433022392t_char : list_list_list_char > $o).
thf(sy_c_List_Odistinct_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Odistinct_001t__String__Ochar, type,
    distinct_char : list_char > $o).
thf(sy_c_List_Oinsert_001t__List__Olist_It__String__Ochar_J, type,
    insert_list_char : list_char > list_list_char > list_list_char).
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    insert285252163on_val : produc1172664615on_val > list_P942933805on_val > list_P942933805on_val).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
    map_li1166989960t_char : (list_char > list_char) > list_list_char > list_list_char).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
    map_li2103738999on_val : (list_char > option_val) > list_list_char > list_option_val).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
    map_list_char_ty : (list_char > ty) > list_list_char > list_ty).
thf(sy_c_List_Olist_Omap_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_list_char_val : (list_char > val) > list_list_char > list_val).
thf(sy_c_List_Olist_Omap_001t__Option__Ooption_It__Value__Oval_J_001t__Value__Oval, type,
    map_option_val_val : (option_val > val) > list_option_val > list_val).
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Omap_001t__Type__Oty_001t__Value__Oval, type,
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thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Type__Oty, type,
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thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Value__Oval, type,
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thf(sy_c_List_Olist_Oset_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    set_li296875899on_val : list_l566969696on_val > set_li1111183366on_val).
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thf(sy_c_List_Olist_Oset_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    set_exp_list_char2 : list_exp_list_char > set_exp_list_char).
thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_Oset_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Type__Oty_J, type,
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thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Value__Oval_J, type,
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thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
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thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Value__Oval_J, type,
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thf(sy_c_Objects_Ohext, type,
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    member_ty : ty > set_ty > $o).
thf(sy_c_member_001t__Value__Oval, type,
    member_val : val > set_val > $o).
thf(sy_v_A, type,
    a : option_set_list_char).
thf(sy_v_Ts, type,
    ts : list_ty).
thf(sy_v_Vs, type,
    vs : list_list_char).
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    e : exp_list_char).
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    vs2 : list_val).

% Relevant facts (249)
thf(fact_0_prod__cases4, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (~ ((Y = (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D)))))))))))). % prod_cases4
thf(fact_1_prod__induct4, axiom,
    ((![P : produc81045532t_char > $o, X : produc81045532t_char]: ((![A : list_list_char, B : list_ty, C : list_val, D : exp_list_char]: (P @ (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ (produc823987298t_char @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_2_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_3_prod_Oinject, axiom,
    ((![X1 : list_val, X2 : exp_list_char, Y1 : list_val, Y2 : exp_list_char]: (((produc823987298t_char @ X1 @ X2) = (produc823987298t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_4_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : produc111478616t_char, Y1 : list_list_char, Y2 : produc111478616t_char]: (((produc1808722894t_char @ X1 @ X2) = (produc1808722894t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_5_prod_Oinject, axiom,
    ((![X1 : list_ty, X2 : produc1109669680t_char, Y1 : list_ty, Y2 : produc1109669680t_char]: (((produc1806338192t_char @ X1 @ X2) = (produc1806338192t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_6_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_7_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_8_old_Oprod_Oinject, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char]: (((produc823987298t_char @ A2 @ B2) = (produc823987298t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_9_old_Oprod_Oinject, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A2 @ B2) = (produc1808722894t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_10_old_Oprod_Oinject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_11_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_12_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_13_prod__cases3, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : list_ty, C : produc1109669680t_char]: (~ ((Y = (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ C))))))))))). % prod_cases3
thf(fact_14_prod__cases3, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : list_val, C : exp_list_char]: (~ ((Y = (produc1806338192t_char @ A @ (produc823987298t_char @ B @ C))))))))))). % prod_cases3
thf(fact_15_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_16_old_Oprod_Oinducts, axiom,
    ((![P : produc1109669680t_char > $o, Prod : produc1109669680t_char]: ((![A : list_val, B : exp_list_char]: (P @ (produc823987298t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_17_old_Oprod_Oinducts, axiom,
    ((![P : produc81045532t_char > $o, Prod : produc81045532t_char]: ((![A : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_18_old_Oprod_Oinducts, axiom,
    ((![P : produc111478616t_char > $o, Prod : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_19_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_20_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_21_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1109669680t_char]: (~ ((![A : list_val, B : exp_list_char]: (~ ((Y = (produc823987298t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_22_old_Oprod_Oexhaust, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : produc111478616t_char]: (~ ((Y = (produc1808722894t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_23_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_24_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_25_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_26_Pair__inject, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char]: (((produc823987298t_char @ A2 @ B2) = (produc823987298t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_27_Pair__inject, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char]: (((produc1808722894t_char @ A2 @ B2) = (produc1808722894t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_28_Pair__inject, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char]: (((produc1806338192t_char @ A2 @ B2) = (produc1806338192t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_29_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_30_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_31_prod__cases, axiom,
    ((![P : produc1109669680t_char > $o, P2 : produc1109669680t_char]: ((![A : list_val, B : exp_list_char]: (P @ (produc823987298t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_32_prod__cases, axiom,
    ((![P : produc81045532t_char > $o, P2 : produc81045532t_char]: ((![A : list_list_char, B : produc111478616t_char]: (P @ (produc1808722894t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_33_prod__cases, axiom,
    ((![P : produc111478616t_char > $o, P2 : produc111478616t_char]: ((![A : list_ty, B : produc1109669680t_char]: (P @ (produc1806338192t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_34_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_35_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_36_surj__pair, axiom,
    ((![P2 : produc1109669680t_char]: (?[X3 : list_val, Y3 : exp_list_char]: (P2 = (produc823987298t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_37_surj__pair, axiom,
    ((![P2 : produc81045532t_char]: (?[X3 : list_list_char, Y3 : produc111478616t_char]: (P2 = (produc1808722894t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_38_surj__pair, axiom,
    ((![P2 : produc111478616t_char]: (?[X3 : list_ty, Y3 : produc1109669680t_char]: (P2 = (produc1806338192t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_39_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_40_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_41_prod__induct3, axiom,
    ((![P : produc81045532t_char > $o, X : produc81045532t_char]: ((![A : list_list_char, B : list_ty, C : produc1109669680t_char]: (P @ (produc1808722894t_char @ A @ (produc1806338192t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_42_prod__induct3, axiom,
    ((![P : produc111478616t_char > $o, X : produc111478616t_char]: ((![A : list_ty, B : list_val, C : exp_list_char]: (P @ (produc1806338192t_char @ A @ (produc823987298t_char @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_43_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_44_hyperUn__assoc, axiom,
    ((![A4 : option_set_list_char, B4 : option_set_list_char, C2 : option_set_list_char]: ((hyperUn_list_char @ (hyperUn_list_char @ A4 @ B4) @ C2) = (hyperUn_list_char @ A4 @ (hyperUn_list_char @ B4 @ C2)))))). % hyperUn_assoc
thf(fact_45_in__set__product__lists__length, axiom,
    ((![Xs : list_char, Xss : list_list_char]: ((member_list_char2 @ Xs @ (set_list_char2 @ (product_lists_char @ Xss))) => ((size_size_list_char @ Xs) = (size_s2008079621t_char @ Xss)))))). % in_set_product_lists_length
thf(fact_46_in__set__product__lists__length, axiom,
    ((![Xs : list_list_char, Xss : list_list_list_char]: ((member568250120t_char @ Xs @ (set_list_list_char2 @ (produc2062551602t_char @ Xss))) => ((size_s2008079621t_char @ Xs) = (size_s1019276181t_char @ Xss)))))). % in_set_product_lists_length
thf(fact_47_in__set__product__lists__length, axiom,
    ((![Xs : list_ty, Xss : list_list_ty]: ((member_list_ty @ Xs @ (set_list_ty2 @ (product_lists_ty @ Xss))) => ((size_size_list_ty @ Xs) = (size_s1063623787ist_ty @ Xss)))))). % in_set_product_lists_length
thf(fact_48_in__set__product__lists__length, axiom,
    ((![Xs : list_val, Xss : list_list_val]: ((member_list_val @ Xs @ (set_list_val2 @ (product_lists_val @ Xss))) => ((size_size_list_val @ Xs) = (size_s527075124st_val @ Xss)))))). % in_set_product_lists_length
thf(fact_49_blocksEval, axiom,
    ((![Ps : list_list_char, Ts : list_ty, Vs : list_val, P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: (((size_s2008079621t_char @ Ps) = (size_size_list_ty @ Ts)) => (((size_s2008079621t_char @ Ps) = (size_size_list_val @ Vs)) => ((eval @ P @ (blocks @ (produc1808722894t_char @ Ps @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (?[L3 : list_char > option_val]: (eval @ P @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Ps @ Vs)) @ E2 @ (produc52622304on_val @ H2 @ L3))))))))). % blocksEval
thf(fact_50_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_51_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_52_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_53_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_list_char]: ((size_s2008079621t_char @ Xs2) = N))))). % Ex_list_of_length
thf(fact_54_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_ty]: ((size_size_list_ty @ Xs2) = N))))). % Ex_list_of_length
thf(fact_55_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs2 : list_val]: ((size_size_list_val @ Xs2) = N))))). % Ex_list_of_length
thf(fact_56_size__neq__size__imp__neq, axiom,
    ((![X : list_list_char, Y : list_list_char]: ((~ (((size_s2008079621t_char @ X) = (size_s2008079621t_char @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_57_size__neq__size__imp__neq, axiom,
    ((![X : list_ty, Y : list_ty]: ((~ (((size_size_list_ty @ X) = (size_size_list_ty @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_58_size__neq__size__imp__neq, axiom,
    ((![X : list_val, Y : list_val]: ((~ (((size_size_list_val @ X) = (size_size_list_val @ Y)))) => (~ ((X = Y))))))). % size_neq_size_imp_neq
thf(fact_59_ssubst__Pair__rhs, axiom,
    ((![R : produc1097884484on_val, S : produc1097884484on_val, R2 : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R @ S) @ R2) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_60_ssubst__Pair__rhs, axiom,
    ((![R : list_val, S : exp_list_char, R2 : set_Pr82799206t_char, S2 : exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ R @ S) @ R2) => ((S2 = S) => (member580484423t_char @ (produc823987298t_char @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_61_ssubst__Pair__rhs, axiom,
    ((![R : list_list_char, S : produc111478616t_char, R2 : set_Pr685054290t_char, S2 : produc111478616t_char]: ((member772747827t_char @ (produc1808722894t_char @ R @ S) @ R2) => ((S2 = S) => (member772747827t_char @ (produc1808722894t_char @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_62_ssubst__Pair__rhs, axiom,
    ((![R : list_ty, S : produc1109669680t_char, R2 : set_Pr925902648t_char, S2 : produc1109669680t_char]: ((member1031340033t_char @ (produc1806338192t_char @ R @ S) @ R2) => ((S2 = S) => (member1031340033t_char @ (produc1806338192t_char @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_63_ssubst__Pair__rhs, axiom,
    ((![R : exp_list_char, S : produc515445032on_val, R2 : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R @ S) @ R2) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_64_ssubst__Pair__rhs, axiom,
    ((![R : nat > option2118145160on_val, S : list_char > option_val, R2 : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R @ S) @ R2) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_65_curryI, axiom,
    ((![F : produc1109669680t_char > $o, A2 : list_val, B2 : exp_list_char]: ((F @ (produc823987298t_char @ A2 @ B2)) => (produc1660716392char_o @ F @ A2 @ B2))))). % curryI
thf(fact_66_curryI, axiom,
    ((![F : produc81045532t_char > $o, A2 : list_list_char, B2 : produc111478616t_char]: ((F @ (produc1808722894t_char @ A2 @ B2)) => (produc309442300char_o @ F @ A2 @ B2))))). % curryI
thf(fact_67_curryI, axiom,
    ((![F : produc111478616t_char > $o, A2 : list_ty, B2 : produc1109669680t_char]: ((F @ (produc1806338192t_char @ A2 @ B2)) => (produc1133082708char_o @ F @ A2 @ B2))))). % curryI
thf(fact_68_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((F @ (produc2023458740on_val @ A2 @ B2)) => (produc699483184_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_69_curryI, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((F @ (produc52622304on_val @ A2 @ B2)) => (produc761261956_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_70_curryD, axiom,
    ((![F : produc1109669680t_char > $o, A2 : list_val, B2 : exp_list_char]: ((produc1660716392char_o @ F @ A2 @ B2) => (F @ (produc823987298t_char @ A2 @ B2)))))). % curryD
thf(fact_71_curryD, axiom,
    ((![F : produc81045532t_char > $o, A2 : list_list_char, B2 : produc111478616t_char]: ((produc309442300char_o @ F @ A2 @ B2) => (F @ (produc1808722894t_char @ A2 @ B2)))))). % curryD
thf(fact_72_curryD, axiom,
    ((![F : produc111478616t_char > $o, A2 : list_ty, B2 : produc1109669680t_char]: ((produc1133082708char_o @ F @ A2 @ B2) => (F @ (produc1806338192t_char @ A2 @ B2)))))). % curryD
thf(fact_73_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryD
thf(fact_74_curryD, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryD
thf(fact_75_curryE, axiom,
    ((![F : produc1109669680t_char > $o, A2 : list_val, B2 : exp_list_char]: ((produc1660716392char_o @ F @ A2 @ B2) => (F @ (produc823987298t_char @ A2 @ B2)))))). % curryE
thf(fact_76_curryE, axiom,
    ((![F : produc81045532t_char > $o, A2 : list_list_char, B2 : produc111478616t_char]: ((produc309442300char_o @ F @ A2 @ B2) => (F @ (produc1808722894t_char @ A2 @ B2)))))). % curryE
thf(fact_77_curryE, axiom,
    ((![F : produc111478616t_char > $o, A2 : list_ty, B2 : produc1109669680t_char]: ((produc1133082708char_o @ F @ A2 @ B2) => (F @ (produc1806338192t_char @ A2 @ B2)))))). % curryE
thf(fact_78_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryE
thf(fact_79_curryE, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryE
thf(fact_80_map__upds__apply__nontin, axiom,
    ((![X : list_char, Xs : list_list_char, F : list_char > option_val, Ys : list_val]: ((~ ((member_list_char2 @ X @ (set_list_char2 @ Xs)))) => ((map_up576607321ar_val @ F @ Xs @ Ys @ X) = (F @ X)))))). % map_upds_apply_nontin
thf(fact_81_length__n__lists__elem, axiom,
    ((![Ys : list_char, N : nat, Xs : list_char]: ((member_list_char2 @ Ys @ (set_list_char2 @ (n_lists_char @ N @ Xs))) => ((size_size_list_char @ Ys) = N))))). % length_n_lists_elem
thf(fact_82_length__n__lists__elem, axiom,
    ((![Ys : list_list_char, N : nat, Xs : list_list_char]: ((member568250120t_char @ Ys @ (set_list_list_char2 @ (n_lists_list_char @ N @ Xs))) => ((size_s2008079621t_char @ Ys) = N))))). % length_n_lists_elem
thf(fact_83_length__n__lists__elem, axiom,
    ((![Ys : list_ty, N : nat, Xs : list_ty]: ((member_list_ty @ Ys @ (set_list_ty2 @ (n_lists_ty @ N @ Xs))) => ((size_size_list_ty @ Ys) = N))))). % length_n_lists_elem
thf(fact_84_length__n__lists__elem, axiom,
    ((![Ys : list_val, N : nat, Xs : list_val]: ((member_list_val @ Ys @ (set_list_val2 @ (n_lists_val @ N @ Xs))) => ((size_size_list_val @ Ys) = N))))). % length_n_lists_elem
thf(fact_85_blocksFinal, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((final_list_char @ E) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L))) @ (transi111096263on_val @ (red @ P))))))))). % blocksFinal
thf(fact_86_in__set__member, axiom,
    ((![X : produc1172664615on_val, Xs : list_P942933805on_val]: ((member354538064on_val @ X @ (set_Pr348738748on_val @ Xs)) = (member1610570434on_val @ Xs @ X))))). % in_set_member
thf(fact_87_in__set__member, axiom,
    ((![X : list_char, Xs : list_list_char]: ((member_list_char2 @ X @ (set_list_char2 @ Xs)) = (member_list_char @ Xs @ X))))). % in_set_member
thf(fact_88_in__set__insert, axiom,
    ((![X : produc1172664615on_val, Xs : list_P942933805on_val]: ((member354538064on_val @ X @ (set_Pr348738748on_val @ Xs)) => ((insert285252163on_val @ X @ Xs) = Xs))))). % in_set_insert
thf(fact_89_in__set__insert, axiom,
    ((![X : list_char, Xs : list_list_char]: ((member_list_char2 @ X @ (set_list_char2 @ Xs)) => ((insert_list_char @ X @ Xs) = Xs))))). % in_set_insert
thf(fact_90_list__ex1__iff, axiom,
    ((list_e1221120112on_val = (^[P3 : produc1172664615on_val > $o]: (^[Xs3 : list_P942933805on_val]: (?[X4 : produc1172664615on_val]: (((((member354538064on_val @ X4 @ (set_Pr348738748on_val @ Xs3))) & ((P3 @ X4)))) & ((![Y4 : produc1172664615on_val]: (((((member354538064on_val @ Y4 @ (set_Pr348738748on_val @ Xs3))) & ((P3 @ Y4)))) => ((Y4 = X4)))))))))))). % list_ex1_iff
thf(fact_91_list__ex1__iff, axiom,
    ((list_ex1_list_char = (^[P3 : list_char > $o]: (^[Xs3 : list_list_char]: (?[X4 : list_char]: (((((member_list_char2 @ X4 @ (set_list_char2 @ Xs3))) & ((P3 @ X4)))) & ((![Y4 : list_char]: (((((member_list_char2 @ Y4 @ (set_list_char2 @ Xs3))) & ((P3 @ Y4)))) => ((Y4 = X4)))))))))))). % list_ex1_iff
thf(fact_92_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_ty, Ys : list_ty, X : ty]: (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)) => ((member_ty @ X @ (set_ty2 @ Xs)) => (~ ((![Y3 : ty]: (~ ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y3) @ (set_Pr1353626468_ty_ty @ (zip_ty_ty @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_93_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_ty, Ys : list_val, X : ty]: (((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)) => ((member_ty @ X @ (set_ty2 @ Xs)) => (~ ((![Y3 : val]: (~ ((member1776226881ty_val @ (product_Pair_ty_val @ X @ Y3) @ (set_Pr1284219053ty_val @ (zip_ty_val @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_94_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_val, Ys : list_ty, X : val]: (((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) => (~ ((![Y3 : ty]: (~ ((member1400634561val_ty @ (product_Pair_val_ty @ X @ Y3) @ (set_Pr908626733val_ty @ (zip_val_ty @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_95_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_val, Ys : list_val, X : val]: (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) => (~ ((![Y3 : val]: (~ ((member1494223754al_val @ (product_Pair_val_val @ X @ Y3) @ (set_Pr1199842294al_val @ (zip_val_val @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_96_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_list_char, Ys : list_ty, X : list_char]: (((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)) => ((member_list_char2 @ X @ (set_list_char2 @ Xs)) => (~ ((![Y3 : ty]: (~ ((member325880354har_ty @ (produc1017542449har_ty @ X @ Y3) @ (set_Pr1046707342har_ty @ (zip_list_char_ty @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_97_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_list_char, Ys : list_val, X : list_char]: (((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)) => ((member_list_char2 @ X @ (set_list_char2 @ Xs)) => (~ ((![Y3 : val]: (~ ((member1062074475ar_val @ (produc368164090ar_val @ X @ Y3) @ (set_Pr790262999ar_val @ (zip_list_char_val @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_98_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_ty, Ys : list_list_char, X : ty]: (((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_ty @ X @ (set_ty2 @ Xs)) => (~ ((![Y3 : list_char]: (~ ((member1016971042t_char @ (produc751008561t_char @ X @ Y3) @ (set_Pr1737798030t_char @ (zip_ty_list_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_99_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_val, Ys : list_list_char, X : val]: (((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) => (~ ((![Y3 : list_char]: (~ ((member1429154667t_char @ (produc1336712314t_char @ X @ Y3) @ (set_Pr1157343191t_char @ (zip_val_list_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_100_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, X : list_char]: (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_list_char2 @ X @ (set_list_char2 @ Xs)) => (~ ((![Y3 : list_char]: (~ ((member89690956t_char @ (produc1304532571t_char @ X @ Y3) @ (set_Pr1342796728t_char @ (zip_li503151995t_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_101_in__set__impl__in__set__zip1, axiom,
    ((![Xs : list_list_val, Ys : list_exp_list_char, X : list_val]: (((size_s527075124st_val @ Xs) = (size_s329991613t_char @ Ys)) => ((member_list_val @ X @ (set_list_val2 @ Xs)) => (~ ((![Y3 : exp_list_char]: (~ ((member580484423t_char @ (produc823987298t_char @ X @ Y3) @ (set_Pr311521755t_char @ (zip_li656530754t_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip1
thf(fact_102_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_ty, Ys : list_ty, Y : ty]: (((size_size_list_ty @ Xs) = (size_size_list_ty @ Ys)) => ((member_ty @ Y @ (set_ty2 @ Ys)) => (~ ((![X3 : ty]: (~ ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ Y) @ (set_Pr1353626468_ty_ty @ (zip_ty_ty @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_103_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_ty, Ys : list_val, Y : val]: (((size_size_list_ty @ Xs) = (size_size_list_val @ Ys)) => ((member_val @ Y @ (set_val2 @ Ys)) => (~ ((![X3 : ty]: (~ ((member1776226881ty_val @ (product_Pair_ty_val @ X3 @ Y) @ (set_Pr1284219053ty_val @ (zip_ty_val @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_104_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_val, Ys : list_ty, Y : ty]: (((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)) => ((member_ty @ Y @ (set_ty2 @ Ys)) => (~ ((![X3 : val]: (~ ((member1400634561val_ty @ (product_Pair_val_ty @ X3 @ Y) @ (set_Pr908626733val_ty @ (zip_val_ty @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_105_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_val, Ys : list_val, Y : val]: (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) => ((member_val @ Y @ (set_val2 @ Ys)) => (~ ((![X3 : val]: (~ ((member1494223754al_val @ (product_Pair_val_val @ X3 @ Y) @ (set_Pr1199842294al_val @ (zip_val_val @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_106_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_list_char, Ys : list_ty, Y : ty]: (((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)) => ((member_ty @ Y @ (set_ty2 @ Ys)) => (~ ((![X3 : list_char]: (~ ((member325880354har_ty @ (produc1017542449har_ty @ X3 @ Y) @ (set_Pr1046707342har_ty @ (zip_list_char_ty @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_107_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_list_char, Ys : list_val, Y : val]: (((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)) => ((member_val @ Y @ (set_val2 @ Ys)) => (~ ((![X3 : list_char]: (~ ((member1062074475ar_val @ (produc368164090ar_val @ X3 @ Y) @ (set_Pr790262999ar_val @ (zip_list_char_val @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_108_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_ty, Ys : list_list_char, Y : list_char]: (((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_list_char2 @ Y @ (set_list_char2 @ Ys)) => (~ ((![X3 : ty]: (~ ((member1016971042t_char @ (produc751008561t_char @ X3 @ Y) @ (set_Pr1737798030t_char @ (zip_ty_list_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_109_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_val, Ys : list_list_char, Y : list_char]: (((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_list_char2 @ Y @ (set_list_char2 @ Ys)) => (~ ((![X3 : val]: (~ ((member1429154667t_char @ (produc1336712314t_char @ X3 @ Y) @ (set_Pr1157343191t_char @ (zip_val_list_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_110_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, Y : list_char]: (((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_list_char2 @ Y @ (set_list_char2 @ Ys)) => (~ ((![X3 : list_char]: (~ ((member89690956t_char @ (produc1304532571t_char @ X3 @ Y) @ (set_Pr1342796728t_char @ (zip_li503151995t_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_111_in__set__impl__in__set__zip2, axiom,
    ((![Xs : list_list_val, Ys : list_exp_list_char, Y : exp_list_char]: (((size_s527075124st_val @ Xs) = (size_s329991613t_char @ Ys)) => ((member_exp_list_char @ Y @ (set_exp_list_char2 @ Ys)) => (~ ((![X3 : list_val]: (~ ((member580484423t_char @ (produc823987298t_char @ X3 @ Y) @ (set_Pr311521755t_char @ (zip_li656530754t_char @ Xs @ Ys))))))))))))). % in_set_impl_in_set_zip2
thf(fact_112_set__zip__rightD, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, Xs : list_P1873028426on_val, Ys : list_P1873028426on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (set_Pr348738748on_val @ (zip_Pr1944470583on_val @ Xs @ Ys))) => (member1888679917on_val @ Y @ (set_Pr871277657on_val @ Ys)))))). % set_zip_rightD
thf(fact_113_set__zip__rightD, axiom,
    ((![X : list_val, Y : exp_list_char, Xs : list_list_val, Ys : list_exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ X @ Y) @ (set_Pr311521755t_char @ (zip_li656530754t_char @ Xs @ Ys))) => (member_exp_list_char @ Y @ (set_exp_list_char2 @ Ys)))))). % set_zip_rightD
thf(fact_114_set__zip__rightD, axiom,
    ((![X : list_list_char, Y : produc111478616t_char, Xs : list_list_list_char, Ys : list_P364227422t_char]: ((member772747827t_char @ (produc1808722894t_char @ X @ Y) @ (set_Pr258496199t_char @ (zip_li1501838510t_char @ Xs @ Ys))) => (member1031340033t_char @ Y @ (set_Pr1196907629t_char @ Ys)))))). % set_zip_rightD
thf(fact_115_set__zip__rightD, axiom,
    ((![X : list_ty, Y : produc1109669680t_char, Xs : list_list_ty, Ys : list_P1602847424t_char]: ((member1031340033t_char @ (produc1806338192t_char @ X @ Y) @ (set_Pr1196907629t_char @ (zip_li2137198512t_char @ Xs @ Ys))) => (member580484423t_char @ Y @ (set_Pr311521755t_char @ Ys)))))). % set_zip_rightD
thf(fact_116_set__zip__rightD, axiom,
    ((![X : exp_list_char, Y : produc515445032on_val, Xs : list_exp_list_char, Ys : list_P1914305198on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ (set_Pr871277657on_val @ (zip_ex2061471444on_val @ Xs @ Ys))) => (member652041809on_val @ Y @ (set_Pr567931069on_val @ Ys)))))). % set_zip_rightD
thf(fact_117_set__zip__rightD, axiom,
    ((![X : nat > option2118145160on_val, Y : list_char > option_val, Xs : list_n1514066695on_val, Ys : list_l566969696on_val]: ((member652041809on_val @ (produc52622304on_val @ X @ Y) @ (set_Pr567931069on_val @ (zip_na94309120on_val @ Xs @ Ys))) => (member301160679on_val @ Y @ (set_li296875899on_val @ Ys)))))). % set_zip_rightD
thf(fact_118_set__zip__leftD, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, Xs : list_P1873028426on_val, Ys : list_P1873028426on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (set_Pr348738748on_val @ (zip_Pr1944470583on_val @ Xs @ Ys))) => (member1888679917on_val @ X @ (set_Pr871277657on_val @ Xs)))))). % set_zip_leftD
thf(fact_119_set__zip__leftD, axiom,
    ((![X : list_val, Y : exp_list_char, Xs : list_list_val, Ys : list_exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ X @ Y) @ (set_Pr311521755t_char @ (zip_li656530754t_char @ Xs @ Ys))) => (member_list_val @ X @ (set_list_val2 @ Xs)))))). % set_zip_leftD
thf(fact_120_set__zip__leftD, axiom,
    ((![X : list_list_char, Y : produc111478616t_char, Xs : list_list_list_char, Ys : list_P364227422t_char]: ((member772747827t_char @ (produc1808722894t_char @ X @ Y) @ (set_Pr258496199t_char @ (zip_li1501838510t_char @ Xs @ Ys))) => (member568250120t_char @ X @ (set_list_list_char2 @ Xs)))))). % set_zip_leftD
thf(fact_121_set__zip__leftD, axiom,
    ((![X : list_ty, Y : produc1109669680t_char, Xs : list_list_ty, Ys : list_P1602847424t_char]: ((member1031340033t_char @ (produc1806338192t_char @ X @ Y) @ (set_Pr1196907629t_char @ (zip_li2137198512t_char @ Xs @ Ys))) => (member_list_ty @ X @ (set_list_ty2 @ Xs)))))). % set_zip_leftD
thf(fact_122_set__zip__leftD, axiom,
    ((![X : exp_list_char, Y : produc515445032on_val, Xs : list_exp_list_char, Ys : list_P1914305198on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ (set_Pr871277657on_val @ (zip_ex2061471444on_val @ Xs @ Ys))) => (member_exp_list_char @ X @ (set_exp_list_char2 @ Xs)))))). % set_zip_leftD
thf(fact_123_set__zip__leftD, axiom,
    ((![X : nat > option2118145160on_val, Y : list_char > option_val, Xs : list_n1514066695on_val, Ys : list_l566969696on_val]: ((member652041809on_val @ (produc52622304on_val @ X @ Y) @ (set_Pr567931069on_val @ (zip_na94309120on_val @ Xs @ Ys))) => (member1749232398on_val @ X @ (set_na2049794978on_val @ Xs)))))). % set_zip_leftD
thf(fact_124_in__set__zipE, axiom,
    ((![X : produc1172664615on_val, Y : produc1172664615on_val, Xs : list_P942933805on_val, Ys : list_P942933805on_val]: ((member208988944on_val @ (produc564964183on_val @ X @ Y) @ (set_Pr1298471292on_val @ (zip_Pr1475371639on_val @ Xs @ Ys))) => (~ (((member354538064on_val @ X @ (set_Pr348738748on_val @ Xs)) => (~ ((member354538064on_val @ Y @ (set_Pr348738748on_val @ Ys))))))))))). % in_set_zipE
thf(fact_125_in__set__zipE, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, Xs : list_P1873028426on_val, Ys : list_P1873028426on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (set_Pr348738748on_val @ (zip_Pr1944470583on_val @ Xs @ Ys))) => (~ (((member1888679917on_val @ X @ (set_Pr871277657on_val @ Xs)) => (~ ((member1888679917on_val @ Y @ (set_Pr871277657on_val @ Ys))))))))))). % in_set_zipE
thf(fact_126_in__set__zipE, axiom,
    ((![X : produc1172664615on_val, Y : list_char, Xs : list_P942933805on_val, Ys : list_list_char]: ((member203697230t_char @ (produc873303857t_char @ X @ Y) @ (set_Pr1058538722t_char @ (zip_Pr1675542545t_char @ Xs @ Ys))) => (~ (((member354538064on_val @ X @ (set_Pr348738748on_val @ Xs)) => (~ ((member_list_char2 @ Y @ (set_list_char2 @ Ys))))))))))). % in_set_zipE
thf(fact_127_in__set__zipE, axiom,
    ((![X : list_char, Y : produc1172664615on_val, Xs : list_list_char, Ys : list_P942933805on_val]: ((member956950162on_val @ (produc1413156781on_val @ X @ Y) @ (set_Pr1811791654on_val @ (zip_li67911821on_val @ Xs @ Ys))) => (~ (((member_list_char2 @ X @ (set_list_char2 @ Xs)) => (~ ((member354538064on_val @ Y @ (set_Pr348738748on_val @ Ys))))))))))). % in_set_zipE
thf(fact_128_in__set__zipE, axiom,
    ((![X : list_char, Y : list_char, Xs : list_list_char, Ys : list_list_char]: ((member89690956t_char @ (produc1304532571t_char @ X @ Y) @ (set_Pr1342796728t_char @ (zip_li503151995t_char @ Xs @ Ys))) => (~ (((member_list_char2 @ X @ (set_list_char2 @ Xs)) => (~ ((member_list_char2 @ Y @ (set_list_char2 @ Ys))))))))))). % in_set_zipE
thf(fact_129_in__set__zipE, axiom,
    ((![X : list_val, Y : exp_list_char, Xs : list_list_val, Ys : list_exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ X @ Y) @ (set_Pr311521755t_char @ (zip_li656530754t_char @ Xs @ Ys))) => (~ (((member_list_val @ X @ (set_list_val2 @ Xs)) => (~ ((member_exp_list_char @ Y @ (set_exp_list_char2 @ Ys))))))))))). % in_set_zipE
thf(fact_130_in__set__zipE, axiom,
    ((![X : list_list_char, Y : produc111478616t_char, Xs : list_list_list_char, Ys : list_P364227422t_char]: ((member772747827t_char @ (produc1808722894t_char @ X @ Y) @ (set_Pr258496199t_char @ (zip_li1501838510t_char @ Xs @ Ys))) => (~ (((member568250120t_char @ X @ (set_list_list_char2 @ Xs)) => (~ ((member1031340033t_char @ Y @ (set_Pr1196907629t_char @ Ys))))))))))). % in_set_zipE
thf(fact_131_in__set__zipE, axiom,
    ((![X : list_ty, Y : produc1109669680t_char, Xs : list_list_ty, Ys : list_P1602847424t_char]: ((member1031340033t_char @ (produc1806338192t_char @ X @ Y) @ (set_Pr1196907629t_char @ (zip_li2137198512t_char @ Xs @ Ys))) => (~ (((member_list_ty @ X @ (set_list_ty2 @ Xs)) => (~ ((member580484423t_char @ Y @ (set_Pr311521755t_char @ Ys))))))))))). % in_set_zipE
thf(fact_132_in__set__zipE, axiom,
    ((![X : exp_list_char, Y : produc515445032on_val, Xs : list_exp_list_char, Ys : list_P1914305198on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ (set_Pr871277657on_val @ (zip_ex2061471444on_val @ Xs @ Ys))) => (~ (((member_exp_list_char @ X @ (set_exp_list_char2 @ Xs)) => (~ ((member652041809on_val @ Y @ (set_Pr567931069on_val @ Ys))))))))))). % in_set_zipE
thf(fact_133_in__set__zipE, axiom,
    ((![X : nat > option2118145160on_val, Y : list_char > option_val, Xs : list_n1514066695on_val, Ys : list_l566969696on_val]: ((member652041809on_val @ (produc52622304on_val @ X @ Y) @ (set_Pr567931069on_val @ (zip_na94309120on_val @ Xs @ Ys))) => (~ (((member1749232398on_val @ X @ (set_na2049794978on_val @ Xs)) => (~ ((member301160679on_val @ Y @ (set_li296875899on_val @ Ys))))))))))). % in_set_zipE
thf(fact_134_zip__same, axiom,
    ((![A2 : produc1172664615on_val, B2 : produc1172664615on_val, Xs : list_P942933805on_val]: ((member208988944on_val @ (produc564964183on_val @ A2 @ B2) @ (set_Pr1298471292on_val @ (zip_Pr1475371639on_val @ Xs @ Xs))) = (((member354538064on_val @ A2 @ (set_Pr348738748on_val @ Xs))) & ((A2 = B2))))))). % zip_same
thf(fact_135_zip__same, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, Xs : list_P1873028426on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (set_Pr348738748on_val @ (zip_Pr1944470583on_val @ Xs @ Xs))) = (((member1888679917on_val @ A2 @ (set_Pr871277657on_val @ Xs))) & ((A2 = B2))))))). % zip_same
thf(fact_136_zip__same, axiom,
    ((![A2 : list_char, B2 : list_char, Xs : list_list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ (set_Pr1342796728t_char @ (zip_li503151995t_char @ Xs @ Xs))) = (((member_list_char2 @ A2 @ (set_list_char2 @ Xs))) & ((A2 = B2))))))). % zip_same
thf(fact_137_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E3 : exp_list_char, H3 : nat > option2118145160on_val, L4 : list_char > option_val]: (R2 @ E3 @ H3 @ L4 @ E3 @ H3 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E4 : exp_list_char, H4 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_1 @ H_1 @ L_1 @ E4 @ H4 @ L5) => (R2 @ E_0 @ H_0 @ L_0 @ E4 @ H4 @ L5)))) => (R2 @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_138_converse__rtrancl__induct2, axiom,
    ((![Ax : list_val, Ay : exp_list_char, Bx : list_val, By : exp_list_char, R : set_Pr290014113t_char, P : list_val > exp_list_char > $o]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ Ax @ Ay) @ (produc823987298t_char @ Bx @ By)) @ (transi643776237t_char @ R)) => ((P @ Bx @ By) => ((![A : list_val, B : exp_list_char, Aa : list_val, Ba : exp_list_char]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ A @ B) @ (produc823987298t_char @ Aa @ Ba)) @ R) => ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ Aa @ Ba) @ (produc823987298t_char @ Bx @ By)) @ (transi643776237t_char @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_139_converse__rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : produc111478616t_char, Bx : list_list_char, By : produc111478616t_char, R : set_Pr1872960889t_char, P : list_list_char > produc111478616t_char > $o]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ Ax @ Ay) @ (produc1808722894t_char @ Bx @ By)) @ (transi1501469657t_char @ R)) => ((P @ Bx @ By) => ((![A : list_list_char, B : produc111478616t_char, Aa : list_list_char, Ba : produc111478616t_char]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ A @ B) @ (produc1808722894t_char @ Aa @ Ba)) @ R) => ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ Aa @ Ba) @ (produc1808722894t_char @ Bx @ By)) @ (transi1501469657t_char @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_140_converse__rtrancl__induct2, axiom,
    ((![Ax : list_ty, Ay : produc1109669680t_char, Bx : list_ty, By : produc1109669680t_char, R : set_Pr1314019591t_char, P : list_ty > produc1109669680t_char > $o]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Ax @ Ay) @ (produc1806338192t_char @ Bx @ By)) @ (transi311435739t_char @ R)) => ((P @ Bx @ By) => ((![A : list_ty, B : produc1109669680t_char, Aa : list_ty, Ba : produc1109669680t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A @ B) @ (produc1806338192t_char @ Aa @ Ba)) @ R) => ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Aa @ Ba) @ (produc1806338192t_char @ Bx @ By)) @ (transi311435739t_char @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_141_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Bx @ By) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_142_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Bx @ By) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_143_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_144_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_145_converse__rtranclE2, axiom,
    ((![Xa : list_val, Xb : exp_list_char, Za : list_val, Zb : exp_list_char, R : set_Pr290014113t_char]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ Xa @ Xb) @ (produc823987298t_char @ Za @ Zb)) @ (transi643776237t_char @ R)) => ((~ (((produc823987298t_char @ Xa @ Xb) = (produc823987298t_char @ Za @ Zb)))) => (~ ((![A : list_val, B : exp_list_char]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ Xa @ Xb) @ (produc823987298t_char @ A @ B)) @ R) => (~ ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ A @ B) @ (produc823987298t_char @ Za @ Zb)) @ (transi643776237t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_146_converse__rtranclE2, axiom,
    ((![Xa : list_list_char, Xb : produc111478616t_char, Za : list_list_char, Zb : produc111478616t_char, R : set_Pr1872960889t_char]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ Xa @ Xb) @ (produc1808722894t_char @ Za @ Zb)) @ (transi1501469657t_char @ R)) => ((~ (((produc1808722894t_char @ Xa @ Xb) = (produc1808722894t_char @ Za @ Zb)))) => (~ ((![A : list_list_char, B : produc111478616t_char]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ Xa @ Xb) @ (produc1808722894t_char @ A @ B)) @ R) => (~ ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ A @ B) @ (produc1808722894t_char @ Za @ Zb)) @ (transi1501469657t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_147_converse__rtranclE2, axiom,
    ((![Xa : list_ty, Xb : produc1109669680t_char, Za : list_ty, Zb : produc1109669680t_char, R : set_Pr1314019591t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Xa @ Xb) @ (produc1806338192t_char @ Za @ Zb)) @ (transi311435739t_char @ R)) => ((~ (((produc1806338192t_char @ Xa @ Xb) = (produc1806338192t_char @ Za @ Zb)))) => (~ ((![A : list_ty, B : produc1109669680t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Xa @ Xb) @ (produc1806338192t_char @ A @ B)) @ R) => (~ ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A @ B) @ (produc1806338192t_char @ Za @ Zb)) @ (transi311435739t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_148_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_149_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_150_rtrancl__induct2, axiom,
    ((![Ax : list_val, Ay : exp_list_char, Bx : list_val, By : exp_list_char, R : set_Pr290014113t_char, P : list_val > exp_list_char > $o]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ Ax @ Ay) @ (produc823987298t_char @ Bx @ By)) @ (transi643776237t_char @ R)) => ((P @ Ax @ Ay) => ((![A : list_val, B : exp_list_char, Aa : list_val, Ba : exp_list_char]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ Ax @ Ay) @ (produc823987298t_char @ A @ B)) @ (transi643776237t_char @ R)) => ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ A @ B) @ (produc823987298t_char @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_151_rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : produc111478616t_char, Bx : list_list_char, By : produc111478616t_char, R : set_Pr1872960889t_char, P : list_list_char > produc111478616t_char > $o]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ Ax @ Ay) @ (produc1808722894t_char @ Bx @ By)) @ (transi1501469657t_char @ R)) => ((P @ Ax @ Ay) => ((![A : list_list_char, B : produc111478616t_char, Aa : list_list_char, Ba : produc111478616t_char]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ Ax @ Ay) @ (produc1808722894t_char @ A @ B)) @ (transi1501469657t_char @ R)) => ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ A @ B) @ (produc1808722894t_char @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_152_rtrancl__induct2, axiom,
    ((![Ax : list_ty, Ay : produc1109669680t_char, Bx : list_ty, By : produc1109669680t_char, R : set_Pr1314019591t_char, P : list_ty > produc1109669680t_char > $o]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Ax @ Ay) @ (produc1806338192t_char @ Bx @ By)) @ (transi311435739t_char @ R)) => ((P @ Ax @ Ay) => ((![A : list_ty, B : produc1109669680t_char, Aa : list_ty, Ba : produc1109669680t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ Ax @ Ay) @ (produc1806338192t_char @ A @ B)) @ (transi311435739t_char @ R)) => ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A @ B) @ (produc1806338192t_char @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_153_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_154_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_155_blocksRedsFinal, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L6 : list_char > option_val]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((distinct_list_char @ Vs2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Vs2 @ Vs))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E2) => ((L6 = (overri1171685873on_val @ L2 @ L @ (set_list_char2 @ Vs2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L6))) @ (transi111096263on_val @ (red @ P)))))))))))). % blocksRedsFinal
thf(fact_156_can__select__set__list__ex1, axiom,
    ((![P : list_char > $o, A4 : list_list_char]: ((can_select_list_char @ P @ (set_list_char2 @ A4)) = (list_ex1_list_char @ P @ A4))))). % can_select_set_list_ex1
thf(fact_157_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_158_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R) => (member354538064on_val @ P2 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_159_distinct__insert, axiom,
    ((![X : list_char, Xs : list_list_char]: ((distinct_list_char @ (insert_list_char @ X @ Xs)) = (distinct_list_char @ Xs))))). % distinct_insert
thf(fact_160_can__select__def, axiom,
    ((can_se187446692on_val = (^[P3 : produc1172664615on_val > $o]: (^[A5 : set_Pr1189492743on_val]: (?[X4 : produc1172664615on_val]: (((((member354538064on_val @ X4 @ A5)) & ((P3 @ X4)))) & ((![Y4 : produc1172664615on_val]: (((((member354538064on_val @ Y4 @ A5)) & ((P3 @ Y4)))) => ((Y4 = X4)))))))))))). % can_select_def
thf(fact_161_distinct__product__lists, axiom,
    ((![Xss : list_list_list_char]: ((![X3 : list_list_char]: ((member568250120t_char @ X3 @ (set_list_list_char2 @ Xss)) => (distinct_list_char @ X3))) => (distin433022392t_char @ (produc2062551602t_char @ Xss)))))). % distinct_product_lists
thf(fact_162_distinct__product__lists, axiom,
    ((![Xss : list_list_char]: ((![X3 : list_char]: ((member_list_char2 @ X3 @ (set_list_char2 @ Xss)) => (distinct_char @ X3))) => (distinct_list_char @ (product_lists_char @ Xss)))))). % distinct_product_lists
thf(fact_163_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_164_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_165_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A6 : produc1097884484on_val]: (((A1 = A6)) & ((A22 = A6))))) | ((?[A6 : produc1097884484on_val]: (?[B5 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A6)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A6 @ B5) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B5 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_166_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_167_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_168_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_169_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_170_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_171_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z2 @ B2) @ (transi111096263on_val @ R)) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_172_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C4) @ R) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C4) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_173_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C4) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C4) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_174_distinct__n__lists, axiom,
    ((![Xs : list_char, N : nat]: ((distinct_char @ Xs) => (distinct_list_char @ (n_lists_char @ N @ Xs)))))). % distinct_n_lists
thf(fact_175_distinct__n__lists, axiom,
    ((![Xs : list_list_char, N : nat]: ((distinct_list_char @ Xs) => (distin433022392t_char @ (n_lists_list_char @ N @ Xs)))))). % distinct_n_lists
thf(fact_176_override__on__apply__notin, axiom,
    ((![A2 : list_char, A4 : set_list_char, F : list_char > option_val, G : list_char > option_val]: ((~ ((member_list_char2 @ A2 @ A4))) => ((overri1171685873on_val @ F @ G @ A4 @ A2) = (F @ A2)))))). % override_on_apply_notin
thf(fact_177_override__on__apply__in, axiom,
    ((![A2 : list_char, A4 : set_list_char, F : list_char > option_val, G : list_char > option_val]: ((member_list_char2 @ A2 @ A4) => ((overri1171685873on_val @ F @ G @ A4 @ A2) = (G @ A2)))))). % override_on_apply_in
thf(fact_178_eval__finalId, axiom,
    ((![E : exp_list_char, P : list_P1234162913t_char, S : produc515445032on_val]: ((final_list_char @ E) => (eval @ P @ E @ S @ E @ S))))). % eval_finalId
thf(fact_179_eval__final, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val]: ((eval @ P @ E @ S @ E2 @ S2) => (final_list_char @ E2))))). % eval_final
thf(fact_180_distinct__union, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((distinct_list_char @ (union_list_char @ Xs @ Ys)) = (distinct_list_char @ Ys))))). % distinct_union
thf(fact_181_override__on__def, axiom,
    ((overri1171685873on_val = (^[F2 : list_char > option_val]: (^[G2 : list_char > option_val]: (^[A5 : set_list_char]: (^[A6 : list_char]: (if_option_val @ (member_list_char2 @ A6 @ A5) @ (G2 @ A6) @ (F2 @ A6))))))))). % override_on_def
thf(fact_182_blocksReds, axiom,
    ((![Vs2 : list_list_char, Ts : list_ty, Vs : list_val, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: (((size_s2008079621t_char @ Vs2) = (size_size_list_ty @ Ts)) => (((size_size_list_val @ Vs) = (size_size_list_ty @ Ts)) => ((distinct_list_char @ Vs2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_up576607321ar_val @ L @ Vs2 @ Vs))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ Vs @ E)))) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (blocks @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts @ (produc823987298t_char @ (map_list_char_val @ (comp_o345283222t_char @ the_val @ L2) @ Vs2) @ E2)))) @ (produc52622304on_val @ H2 @ (overri1171685873on_val @ L2 @ L @ (set_list_char2 @ Vs2))))) @ (transi111096263on_val @ (red @ P)))))))))). % blocksReds
thf(fact_183_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_184_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_185_distinct__product, axiom,
    ((![Xs : list_list_char, Ys : list_list_char]: ((distinct_list_char @ Xs) => ((distinct_list_char @ Ys) => (distin1292865692t_char @ (produc1010127113t_char @ Xs @ Ys))))))). % distinct_product
thf(fact_186_comp__apply, axiom,
    ((comp_o345283222t_char = (^[F2 : option_val > val]: (^[G2 : list_char > option_val]: (^[X4 : list_char]: (F2 @ (G2 @ X4)))))))). % comp_apply
thf(fact_187_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_188_map__eq__conv, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : list_char > val]: (((map_list_char_val @ F @ Xs) = (map_list_char_val @ G @ Xs)) = (![X4 : list_char]: (((member_list_char2 @ X4 @ (set_list_char2 @ Xs))) => (((F @ X4) = (G @ X4))))))))). % map_eq_conv
thf(fact_189_map__map, axiom,
    ((![F : option_val > val, G : list_char > option_val, Xs : list_list_char]: ((map_option_val_val @ F @ (map_li2103738999on_val @ G @ Xs)) = (map_list_char_val @ (comp_o345283222t_char @ F @ G) @ Xs))))). % map_map
thf(fact_190_map__map, axiom,
    ((![F : val > val, G : list_char > val, Xs : list_list_char]: ((map_val_val @ F @ (map_list_char_val @ G @ Xs)) = (map_list_char_val @ (comp_v1629299782t_char @ F @ G) @ Xs))))). % map_map
thf(fact_191_map__map, axiom,
    ((![F : list_char > val, G : list_char > list_char, Xs : list_list_char]: ((map_list_char_val @ F @ (map_li1166989960t_char @ G @ Xs)) = (map_list_char_val @ (comp_l167379623t_char @ F @ G) @ Xs))))). % map_map
thf(fact_192_List_Omap_Ocomp, axiom,
    ((![F : option_val > val, G : list_char > option_val]: ((comp_l1935944006t_char @ (map_option_val_val @ F) @ (map_li2103738999on_val @ G)) = (map_list_char_val @ (comp_o345283222t_char @ F @ G)))))). % List.map.comp
thf(fact_193_List_Omap_Ocomp, axiom,
    ((![F : val > val, G : list_char > val]: ((comp_l1842341494t_char @ (map_val_val @ F) @ (map_list_char_val @ G)) = (map_list_char_val @ (comp_v1629299782t_char @ F @ G)))))). % List.map.comp
thf(fact_194_List_Omap_Ocomp, axiom,
    ((![F : list_char > val, G : list_char > list_char]: ((comp_l1763050071t_char @ (map_list_char_val @ F) @ (map_li1166989960t_char @ G)) = (map_list_char_val @ (comp_l167379623t_char @ F @ G)))))). % List.map.comp
thf(fact_195_map__comp__map, axiom,
    ((![F : option_val > val, G : list_char > option_val]: ((comp_l1935944006t_char @ (map_option_val_val @ F) @ (map_li2103738999on_val @ G)) = (map_list_char_val @ (comp_o345283222t_char @ F @ G)))))). % map_comp_map
thf(fact_196_map__comp__map, axiom,
    ((![F : val > val, G : list_char > val]: ((comp_l1842341494t_char @ (map_val_val @ F) @ (map_list_char_val @ G)) = (map_list_char_val @ (comp_v1629299782t_char @ F @ G)))))). % map_comp_map
thf(fact_197_map__comp__map, axiom,
    ((![F : list_char > val, G : list_char > list_char]: ((comp_l1763050071t_char @ (map_list_char_val @ F) @ (map_li1166989960t_char @ G)) = (map_list_char_val @ (comp_l167379623t_char @ F @ G)))))). % map_comp_map
thf(fact_198_list_Omap__comp, axiom,
    ((![G : option_val > val, F : list_char > option_val, V : list_list_char]: ((map_option_val_val @ G @ (map_li2103738999on_val @ F @ V)) = (map_list_char_val @ (comp_o345283222t_char @ G @ F) @ V))))). % list.map_comp
thf(fact_199_list_Omap__comp, axiom,
    ((![G : val > val, F : list_char > val, V : list_list_char]: ((map_val_val @ G @ (map_list_char_val @ F @ V)) = (map_list_char_val @ (comp_v1629299782t_char @ G @ F) @ V))))). % list.map_comp
thf(fact_200_list_Omap__comp, axiom,
    ((![G : list_char > val, F : list_char > list_char, V : list_list_char]: ((map_list_char_val @ G @ (map_li1166989960t_char @ F @ V)) = (map_list_char_val @ (comp_l167379623t_char @ G @ F) @ V))))). % list.map_comp
thf(fact_201_List_Omap_Ocompositionality, axiom,
    ((![F : option_val > val, G : list_char > option_val, List : list_list_char]: ((map_option_val_val @ F @ (map_li2103738999on_val @ G @ List)) = (map_list_char_val @ (comp_o345283222t_char @ F @ G) @ List))))). % List.map.compositionality
thf(fact_202_List_Omap_Ocompositionality, axiom,
    ((![F : val > val, G : list_char > val, List : list_list_char]: ((map_val_val @ F @ (map_list_char_val @ G @ List)) = (map_list_char_val @ (comp_v1629299782t_char @ F @ G) @ List))))). % List.map.compositionality
thf(fact_203_List_Omap_Ocompositionality, axiom,
    ((![F : list_char > val, G : list_char > list_char, List : list_list_char]: ((map_list_char_val @ F @ (map_li1166989960t_char @ G @ List)) = (map_list_char_val @ (comp_l167379623t_char @ F @ G) @ List))))). % List.map.compositionality
thf(fact_204_length__map, axiom,
    ((![F : list_char > list_char, Xs : list_list_char]: ((size_s2008079621t_char @ (map_li1166989960t_char @ F @ Xs)) = (size_s2008079621t_char @ Xs))))). % length_map
thf(fact_205_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_206_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_207_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_208_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_209_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_210_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_211_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_212_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_213_map__add__find__right, axiom,
    ((![N : list_char > option_val, K : list_char, Xx : val, M : list_char > option_val]: (((N @ K) = (some_val @ Xx)) => ((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ Xx)))))). % map_add_find_right
thf(fact_214_map__add__upds, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, Xs : list_list_char, Ys : list_val]: ((map_ad1615113112ar_val @ M1 @ (map_up576607321ar_val @ M2 @ Xs @ Ys)) = (map_up576607321ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ Xs @ Ys))))). % map_add_upds
thf(fact_215_comp__def, axiom,
    ((comp_o345283222t_char = (^[F2 : option_val > val]: (^[G2 : list_char > option_val]: (^[X4 : list_char]: (F2 @ (G2 @ X4)))))))). % comp_def
thf(fact_216_comp__assoc, axiom,
    ((![F : option_val > val, G : list_char > option_val, H : list_char > list_char]: ((comp_l167379623t_char @ (comp_o345283222t_char @ F @ G) @ H) = (comp_o345283222t_char @ F @ (comp_l563574263t_char @ G @ H)))))). % comp_assoc
thf(fact_217_comp__assoc, axiom,
    ((![F : val > val, G : option_val > val, H : list_char > option_val]: ((comp_o345283222t_char @ (comp_v32361781on_val @ F @ G) @ H) = (comp_v1629299782t_char @ F @ (comp_o345283222t_char @ G @ H)))))). % comp_assoc
thf(fact_218_comp__assoc, axiom,
    ((![F : option_val > val, G : option_val > option_val, H : list_char > option_val]: ((comp_o345283222t_char @ (comp_o745479045on_val @ F @ G) @ H) = (comp_o345283222t_char @ F @ (comp_o662633318t_char @ G @ H)))))). % comp_assoc
thf(fact_219_comp__eq__dest, axiom,
    ((![A2 : option_val > val, B2 : list_char > option_val, C4 : option_val > val, D2 : list_char > option_val, V : list_char]: (((comp_o345283222t_char @ A2 @ B2) = (comp_o345283222t_char @ C4 @ D2)) => ((A2 @ (B2 @ V)) = (C4 @ (D2 @ V))))))). % comp_eq_dest
thf(fact_220_comp__eq__elim, axiom,
    ((![A2 : option_val > val, B2 : list_char > option_val, C4 : option_val > val, D2 : list_char > option_val]: (((comp_o345283222t_char @ A2 @ B2) = (comp_o345283222t_char @ C4 @ D2)) => (![V2 : list_char]: ((A2 @ (B2 @ V2)) = (C4 @ (D2 @ V2)))))))). % comp_eq_elim
thf(fact_221_comp__eq__dest__lhs, axiom,
    ((![A2 : option_val > val, B2 : list_char > option_val, C4 : list_char > val, V : list_char]: (((comp_o345283222t_char @ A2 @ B2) = C4) => ((A2 @ (B2 @ V)) = (C4 @ V)))))). % comp_eq_dest_lhs
thf(fact_222_list_Oinj__map__strong, axiom,
    ((![X : list_list_char, Xa : list_list_char, F : list_char > val, Fa : list_char > val]: ((![Z2 : list_char, Za2 : list_char]: ((member_list_char2 @ Z2 @ (set_list_char2 @ X)) => ((member_list_char2 @ Za2 @ (set_list_char2 @ Xa)) => (((F @ Z2) = (Fa @ Za2)) => (Z2 = Za2))))) => (((map_list_char_val @ F @ X) = (map_list_char_val @ Fa @ Xa)) => (X = Xa)))))). % list.inj_map_strong
thf(fact_223_list_Omap__cong0, axiom,
    ((![X : list_list_char, F : list_char > val, G : list_char > val]: ((![Z2 : list_char]: ((member_list_char2 @ Z2 @ (set_list_char2 @ X)) => ((F @ Z2) = (G @ Z2)))) => ((map_list_char_val @ F @ X) = (map_list_char_val @ G @ X)))))). % list.map_cong0
thf(fact_224_list_Omap__cong, axiom,
    ((![X : list_list_char, Ya : list_list_char, F : list_char > val, G : list_char > val]: ((X = Ya) => ((![Z2 : list_char]: ((member_list_char2 @ Z2 @ (set_list_char2 @ Ya)) => ((F @ Z2) = (G @ Z2)))) => ((map_list_char_val @ F @ X) = (map_list_char_val @ G @ Ya))))))). % list.map_cong
thf(fact_225_ex__map__conv, axiom,
    ((![Ys : list_val, F : list_char > val]: ((?[Xs3 : list_list_char]: (Ys = (map_list_char_val @ F @ Xs3))) = (![X4 : val]: (((member_val @ X4 @ (set_val2 @ Ys))) => ((?[Y4 : list_char]: (X4 = (F @ Y4)))))))))). % ex_map_conv
thf(fact_226_map__cong, axiom,
    ((![Xs : list_list_char, Ys : list_list_char, F : list_char > val, G : list_char > val]: ((Xs = Ys) => ((![X3 : list_char]: ((member_list_char2 @ X3 @ (set_list_char2 @ Ys)) => ((F @ X3) = (G @ X3)))) => ((map_list_char_val @ F @ Xs) = (map_list_char_val @ G @ Ys))))))). % map_cong
thf(fact_227_map__idI, axiom,
    ((![Xs : list_P942933805on_val, F : produc1172664615on_val > produc1172664615on_val]: ((![X3 : produc1172664615on_val]: ((member354538064on_val @ X3 @ (set_Pr348738748on_val @ Xs)) => ((F @ X3) = X3))) => ((map_Pr1357533188on_val @ F @ Xs) = Xs))))). % map_idI
thf(fact_228_map__idI, axiom,
    ((![Xs : list_list_char, F : list_char > list_char]: ((![X3 : list_char]: ((member_list_char2 @ X3 @ (set_list_char2 @ Xs)) => ((F @ X3) = X3))) => ((map_li1166989960t_char @ F @ Xs) = Xs))))). % map_idI
thf(fact_229_map__ext, axiom,
    ((![Xs : list_list_char, F : list_char > val, G : list_char > val]: ((![X3 : list_char]: ((member_list_char2 @ X3 @ (set_list_char2 @ Xs)) => ((F @ X3) = (G @ X3)))) => ((map_list_char_val @ F @ Xs) = (map_list_char_val @ G @ Xs)))))). % map_ext
thf(fact_230_map__eq__imp__length__eq, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : list_char > val, Ys : list_list_char]: (((map_list_char_val @ F @ Xs) = (map_list_char_val @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_231_map__eq__imp__length__eq, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : ty > val, Ys : list_ty]: (((map_list_char_val @ F @ Xs) = (map_ty_val @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_ty @ Ys)))))). % map_eq_imp_length_eq
thf(fact_232_map__eq__imp__length__eq, axiom,
    ((![F : list_char > val, Xs : list_list_char, G : val > val, Ys : list_val]: (((map_list_char_val @ F @ Xs) = (map_val_val @ G @ Ys)) => ((size_s2008079621t_char @ Xs) = (size_size_list_val @ Ys)))))). % map_eq_imp_length_eq
thf(fact_233_map__eq__imp__length__eq, axiom,
    ((![F : ty > val, Xs : list_ty, G : list_char > val, Ys : list_list_char]: (((map_ty_val @ F @ Xs) = (map_list_char_val @ G @ Ys)) => ((size_size_list_ty @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_234_map__eq__imp__length__eq, axiom,
    ((![F : val > val, Xs : list_val, G : list_char > val, Ys : list_list_char]: (((map_val_val @ F @ Xs) = (map_list_char_val @ G @ Ys)) => ((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)))))). % map_eq_imp_length_eq
thf(fact_235_option_Osel, axiom,
    ((![X2 : val]: ((the_val @ (some_val @ X2)) = X2)))). % option.sel
thf(fact_236_option_Osel, axiom,
    ((![X2 : set_list_char]: ((the_set_list_char @ (some_set_list_char @ X2)) = X2)))). % option.sel
thf(fact_237_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((eval @ P @ E @ (produc52622304on_val @ H @ L) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (hext @ H @ H2))))). % eval_hext
thf(fact_238_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_239_map__eq__map__tailrec, axiom,
    ((map_list_char_val = map_ta1467130225ar_val))). % map_eq_map_tailrec
thf(fact_240_map__of__zip__is__Some, axiom,
    ((![Xs : list_val, Ys : list_set_list_char, X : val]: (((size_size_list_val @ Xs) = (size_s1951532219t_char @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) = (?[Y4 : set_list_char]: ((map_of220264828t_char @ (zip_va1979598416t_char @ Xs @ Ys) @ X) = (some_set_list_char @ Y4)))))))). % map_of_zip_is_Some
thf(fact_241_map__of__zip__is__Some, axiom,
    ((![Xs : list_val, Ys : list_list_char, X : val]: (((size_size_list_val @ Xs) = (size_s2008079621t_char @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) = (?[Y4 : list_char]: ((map_of_val_list_char @ (zip_val_list_char @ Xs @ Ys) @ X) = (some_list_char @ Y4)))))))). % map_of_zip_is_Some
thf(fact_242_map__of__zip__is__Some, axiom,
    ((![Xs : list_val, Ys : list_ty, X : val]: (((size_size_list_val @ Xs) = (size_size_list_ty @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) = (?[Y4 : ty]: ((map_of_val_ty @ (zip_val_ty @ Xs @ Ys) @ X) = (some_ty @ Y4)))))))). % map_of_zip_is_Some
thf(fact_243_map__of__zip__is__Some, axiom,
    ((![Xs : list_val, Ys : list_val, X : val]: (((size_size_list_val @ Xs) = (size_size_list_val @ Ys)) => ((member_val @ X @ (set_val2 @ Xs)) = (?[Y4 : val]: ((map_of_val_val @ (zip_val_val @ Xs @ Ys) @ X) = (some_val @ Y4)))))))). % map_of_zip_is_Some
thf(fact_244_ThrowRedsThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_245_ThrowReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_246_eval__evals_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S_0 : produc515445032on_val, E2 : exp_list_char, S_1 : produc515445032on_val]: ((eval @ P @ E @ S_0 @ (throw_list_char @ E2) @ S_1) => (eval @ P @ (throw_list_char @ E) @ S_0 @ (throw_list_char @ E2) @ S_1))))). % eval_evals.ThrowThrow
thf(fact_247_red__reds_OThrowRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_248_red__reds_OThrowThrow, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E) @ S)) @ (red @ P))))). % red_reds.ThrowThrow

% Helper facts (3)
thf(help_If_3_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $true @ X @ Y) = X)))).

% Conjectures (3)
thf(conj_0, hypothesis,
    (((size_s2008079621t_char @ vs) = (size_size_list_ty @ ts)))).
thf(conj_1, hypothesis,
    (((size_size_list_val @ vs2) = (size_size_list_ty @ ts)))).
thf(conj_2, conjecture,
    (((d_list_char @ (blocks @ (produc1808722894t_char @ vs @ (produc1806338192t_char @ ts @ (produc823987298t_char @ vs2 @ e)))) @ a) = (d_list_char @ e @ (hyperUn_list_char @ a @ (some_set_list_char @ (set_list_char2 @ vs))))))).
