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% Explicit typings (201)
thf(sy_c_Auxiliary_Ofun__of_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Value__Oval, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J, type,
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    fun_of1003211849t_char : set_Pr685054290t_char > list_list_char > produc111478616t_char > $o).
thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__String__Ochar_J_001t__Type__Oty, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Type__Oty_J_001t__List__Olist_It__Type__Oty_J, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Value__Oval_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__List__Olist_It__Value__Oval_J_001t__List__Olist_It__Value__Oval_J, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__Type__Oty, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Type__Oty_001t__Value__Oval, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__Type__Oty, type,
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thf(sy_c_Auxiliary_Ofun__of_001t__Value__Oval_001t__Value__Oval, type,
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thf(sy_c_Expr_Oexp_OCall_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olexord_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olexord_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_List_Olist_OCons_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_Ts, type,
    ts : list_ty).
thf(sy_v_es, type,
    es : list_exp_list_char).
thf(sy_v_es_H, type,
    es2 : list_exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (248)
thf(fact_0_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S2))))))). % reds_preserves_sconf
thf(fact_1_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_2_subjects__reduction2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, Ts : list_ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((typeSa1777264139_sconf @ P @ E @ (produc52622304on_val @ H @ L)) => ((wTrts @ P @ H @ E @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ P @ H2 @ E @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction2
thf(fact_3_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_4_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_5_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_6_prod_Oinject, axiom,
    ((![X1 : list_list_char, X2 : produc111478616t_char, Y1 : list_list_char, Y2 : produc111478616t_char]: (((produc1808722894t_char @ X1 @ X2) = (produc1808722894t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_7_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_8_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_9_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_10_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_11_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_12_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_13_old_Oprod_Oinject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_14_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_15_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_16_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_17_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_18_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_19_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_20_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_21_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_22_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_23_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_24_old_Oprod_Oexhaust, axiom,
    ((![Y : produc81045532t_char]: (~ ((![A : list_list_char, B : produc111478616t_char]: (~ ((Y = (produc1808722894t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_25_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_26_old_Oprod_Oexhaust, axiom,
    ((![Y : produc111478616t_char]: (~ ((![A : list_ty, B : produc1109669680t_char]: (~ ((Y = (produc1806338192t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_27_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_28_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_29_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1109669680t_char]: (~ ((![A : list_val, B : exp_list_char]: (~ ((Y = (produc823987298t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_30_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_31_Pair__inject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_32_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_33_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_34_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_35_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_36_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_37_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_38_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_39_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_40_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_41_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_42_surj__pair, axiom,
    ((![P2 : produc81045532t_char]: (?[X3 : list_list_char, Y3 : produc111478616t_char]: (P2 = (produc1808722894t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_43_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X3 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_44_surj__pair, axiom,
    ((![P2 : produc111478616t_char]: (?[X3 : list_ty, Y3 : produc1109669680t_char]: (P2 = (produc1806338192t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_45_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_46_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_47_surj__pair, axiom,
    ((![P2 : produc1109669680t_char]: (?[X3 : list_val, Y3 : exp_list_char]: (P2 = (produc823987298t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_48_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_49_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S3 : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S3 @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S3 @ T)))))). % widen_trans
thf(fact_50_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_51_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_52_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_53_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_54_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_55_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_56_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_57_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_58_reds__preserves__hconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_59_reds__preserves__lconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % reds_preserves_lconf
thf(fact_60_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_61_same__fstI, axiom,
    ((![P : list_list_char > $o, X : list_list_char, Y4 : produc111478616t_char, Y : produc111478616t_char, R : list_list_char > set_Pr1314019591t_char]: ((P @ X) => ((member219943760t_char @ (produc1108858903t_char @ Y4 @ Y) @ (R @ X)) => (member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ X @ Y4) @ (produc1808722894t_char @ X @ Y)) @ (same_f650641465t_char @ P @ R))))))). % same_fstI
thf(fact_62_same__fstI, axiom,
    ((![P : list_exp_list_char > $o, X : list_exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R : list_exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R @ X)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X @ Y4) @ (produc1725134254on_val @ X @ Y)) @ (same_f1555812995on_val @ P @ R))))))). % same_fstI
thf(fact_63_same__fstI, axiom,
    ((![P : list_ty > $o, X : list_ty, Y4 : produc1109669680t_char, Y : produc1109669680t_char, R : list_ty > set_Pr290014113t_char]: ((P @ X) => ((member89029866t_char @ (produc183121785t_char @ Y4 @ Y) @ (R @ X)) => (member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ X @ Y4) @ (produc1806338192t_char @ X @ Y)) @ (same_f1878009829t_char @ P @ R))))))). % same_fstI
thf(fact_64_same__fstI, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R @ X)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y4) @ (produc2023458740on_val @ X @ Y)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_65_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X : nat > option2118145160on_val, Y4 : list_char > option_val, Y : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X) => ((member1177709994on_val @ (produc746553401on_val @ Y4 @ Y) @ (R @ X)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X @ Y4) @ (produc52622304on_val @ X @ Y)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_66_same__fstI, axiom,
    ((![P : list_val > $o, X : list_val, Y4 : exp_list_char, Y : exp_list_char, R : list_val > set_Pr224372167t_char]: ((P @ X) => ((member1699993616t_char @ (produc240508503t_char @ Y4 @ Y) @ (R @ X)) => (member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ X @ Y4) @ (produc823987298t_char @ X @ Y)) @ (same_f1478405325t_char @ P @ R))))))). % same_fstI
thf(fact_67_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X : list_ty]: ((![X3 : ty]: (Ra @ X3 @ X3)) => (list_all2_ty_ty @ Ra @ X @ X))))). % list.rel_refl
thf(fact_68_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X3 : ty, Y3 : ty]: ((P @ X3 @ Y3) => ((Q @ Y3 @ X3) => (X3 = Y3)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_69_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y5 : ty]: (^[Z : ty]: (Y5 = Z)))) = (^[Y5 : list_ty]: (^[Z : list_ty]: (Y5 = Z)))))). % list.rel_eq
thf(fact_70_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P22 : ty > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A : ty, B : ty, C : ty]: ((P1 @ A @ B) => ((P22 @ B @ C) => (P3 @ A @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P22 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_71_list__all2__eq, axiom,
    (((^[Y5 : list_ty]: (^[Z : list_ty]: (Y5 = Z))) = (list_all2_ty_ty @ (^[Y5 : ty]: (^[Z : ty]: (Y5 = Z))))))). % list_all2_eq
thf(fact_72_list__all2__mono, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty, Q : ty > ty > $o]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_73_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X3 : ty]: (P @ X3 @ X3)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_74_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_75_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E)))))). % lconf_hext
thf(fact_76_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts @ P @ H @ E @ Es @ Ts) => ((hext @ H @ H2) => (wTrts @ P @ H2 @ E @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_77_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_78_ssubst__Pair__rhs, axiom,
    ((![R2 : produc335961278on_val, S : produc335961278on_val, R : set_Pr208351751on_val, S2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ R2 @ S) @ R) => ((S2 = S) => (member1689761872on_val @ (produc245869591on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_79_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S : produc1097884484on_val, R : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S) @ R) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_80_ssubst__Pair__rhs, axiom,
    ((![R2 : list_list_char, S : produc111478616t_char, R : set_Pr685054290t_char, S2 : produc111478616t_char]: ((member772747827t_char @ (produc1808722894t_char @ R2 @ S) @ R) => ((S2 = S) => (member772747827t_char @ (produc1808722894t_char @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_81_ssubst__Pair__rhs, axiom,
    ((![R2 : list_exp_list_char, S : produc515445032on_val, R : set_Pr1511552798on_val, S2 : produc515445032on_val]: ((member184158439on_val @ (produc1725134254on_val @ R2 @ S) @ R) => ((S2 = S) => (member184158439on_val @ (produc1725134254on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_82_ssubst__Pair__rhs, axiom,
    ((![R2 : list_ty, S : produc1109669680t_char, R : set_Pr925902648t_char, S2 : produc1109669680t_char]: ((member1031340033t_char @ (produc1806338192t_char @ R2 @ S) @ R) => ((S2 = S) => (member1031340033t_char @ (produc1806338192t_char @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_83_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S : produc515445032on_val, R : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S) @ R) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_84_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S : list_char > option_val, R : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S) @ R) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_85_ssubst__Pair__rhs, axiom,
    ((![R2 : list_val, S : exp_list_char, R : set_Pr82799206t_char, S2 : exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ R2 @ S) @ R) => ((S2 = S) => (member580484423t_char @ (produc823987298t_char @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_86_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((widen_917054840t_char @ P @ X @ Z2)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_87_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_88_curryI, axiom,
    ((![F : produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((F @ (produc1725134254on_val @ A2 @ B2)) => (produc1199911222_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_89_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_90_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_91_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_92_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_93_list_Oinject, axiom,
    ((![X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X22) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_94_list_Oinject, axiom,
    ((![X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X22) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_95_list_Oinject, axiom,
    ((![X21 : list_char, X22 : list_list_char, Y21 : list_char, Y22 : list_list_char]: (((cons_list_char @ X21 @ X22) = (cons_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_96_list_Oinject, axiom,
    ((![X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: (((cons_val @ X21 @ X22) = (cons_val @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_97_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_98_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_99_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_100_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_101_not__Cons__self2, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_102_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_103_not__Cons__self2, axiom,
    ((![X : list_char, Xs : list_list_char]: (~ (((cons_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_104_not__Cons__self2, axiom,
    ((![X : val, Xs : list_val]: (~ (((cons_val @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_105_list__all2__Cons2, axiom,
    ((![P : val > ty > $o, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z2 : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_all2_val_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_106_list__all2__Cons2, axiom,
    ((![P : ty > val > $o, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_all2_ty_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_107_list__all2__Cons2, axiom,
    ((![P : val > val > $o, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z2 : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_all2_val_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_108_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_109_list__all2__Cons2, axiom,
    ((![P : list_char > ty > $o, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z2 : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_a1770748705har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_110_list__all2__Cons2, axiom,
    ((![P : ty > list_char > $o, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_a1504214817t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_111_list__all2__Cons2, axiom,
    ((![P : val > list_char > $o, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ P @ Xs @ (cons_list_char @ Y @ Ys)) = (?[Z2 : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_a1248766058t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_112_list__all2__Cons2, axiom,
    ((![P : list_char > val > $o, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ P @ Xs @ (cons_val @ Y @ Ys)) = (?[Z2 : list_char]: (?[Zs : list_list_char]: (((Xs = (cons_list_char @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_a280217834ar_val @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_113_list__all2__Cons2, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_114_list__all2__Cons2, axiom,
    ((![P : val > exp_list_char > $o, Xs : list_val, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1553663234t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z2 : val]: (?[Zs : list_val]: (((Xs = (cons_val @ Z2 @ Zs))) & ((((P @ Z2 @ Y)) & ((list_a1553663234t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_115_list__all2__Cons1, axiom,
    ((![P : ty > val > $o, X : ty, Xs : list_ty, Ys : list_val]: ((list_all2_ty_val @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z2 : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_all2_ty_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_116_list__all2__Cons1, axiom,
    ((![P : val > ty > $o, X : val, Xs : list_val, Ys : list_ty]: ((list_all2_val_ty @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_all2_val_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_117_list__all2__Cons1, axiom,
    ((![P : val > val > $o, X : val, Xs : list_val, Ys : list_val]: ((list_all2_val_val @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z2 : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_all2_val_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_118_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_119_list__all2__Cons1, axiom,
    ((![P : ty > list_char > $o, X : ty, Xs : list_ty, Ys : list_list_char]: ((list_a1504214817t_char @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z2 : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_a1504214817t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_120_list__all2__Cons1, axiom,
    ((![P : list_char > ty > $o, X : list_char, Xs : list_list_char, Ys : list_ty]: ((list_a1770748705har_ty @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_a1770748705har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_121_list__all2__Cons1, axiom,
    ((![P : list_char > val > $o, X : list_char, Xs : list_list_char, Ys : list_val]: ((list_a280217834ar_val @ P @ (cons_list_char @ X @ Xs) @ Ys) = (?[Z2 : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_a280217834ar_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_122_list__all2__Cons1, axiom,
    ((![P : val > list_char > $o, X : val, Xs : list_val, Ys : list_list_char]: ((list_a1248766058t_char @ P @ (cons_val @ X @ Xs) @ Ys) = (?[Z2 : list_char]: (?[Zs : list_list_char]: (((Ys = (cons_list_char @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_a1248766058t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_123_list__all2__Cons1, axiom,
    ((![P : exp_list_char > ty > $o, X : exp_list_char, Xs : list_exp_list_char, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_124_list__all2__Cons1, axiom,
    ((![P : exp_list_char > val > $o, X : exp_list_char, Xs : list_exp_list_char, Ys : list_val]: ((list_a853659268ar_val @ P @ (cons_exp_list_char @ X @ Xs) @ Ys) = (?[Z2 : val]: (?[Zs : list_val]: (((Ys = (cons_val @ Z2 @ Zs))) & ((((P @ X @ Z2)) & ((list_a853659268ar_val @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_125_list__all2__Cons, axiom,
    ((![P : ty > val > $o, X : ty, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ P @ (cons_ty @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_126_list__all2__Cons, axiom,
    ((![P : val > ty > $o, X : val, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ P @ (cons_val @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_val_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_127_list__all2__Cons, axiom,
    ((![P : val > val > $o, X : val, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ P @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_val_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_128_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_129_list__all2__Cons, axiom,
    ((![P : ty > list_char > $o, X : ty, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ P @ (cons_ty @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1504214817t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_130_list__all2__Cons, axiom,
    ((![P : list_char > ty > $o, X : list_char, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ P @ (cons_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1770748705har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_131_list__all2__Cons, axiom,
    ((![P : list_char > val > $o, X : list_char, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ P @ (cons_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a280217834ar_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_132_list__all2__Cons, axiom,
    ((![P : val > list_char > $o, X : val, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ P @ (cons_val @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1248766058t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_133_list__all2__Cons, axiom,
    ((![P : exp_list_char > ty > $o, X : exp_list_char, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a295513531har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_134_list__all2__Cons, axiom,
    ((![P : exp_list_char > val > $o, X : exp_list_char, Xs : list_exp_list_char, Y : val, Ys : list_val]: ((list_a853659268ar_val @ P @ (cons_exp_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a853659268ar_val @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_135_list_Orel__intros_I2_J, axiom,
    ((![R : ty > val > $o, X21 : ty, Y21 : val, X22 : list_ty, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_all2_ty_val @ R @ X22 @ Y22) => (list_all2_ty_val @ R @ (cons_ty @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_136_list_Orel__intros_I2_J, axiom,
    ((![R : val > ty > $o, X21 : val, Y21 : ty, X22 : list_val, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_val_ty @ R @ X22 @ Y22) => (list_all2_val_ty @ R @ (cons_val @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_137_list_Orel__intros_I2_J, axiom,
    ((![R : val > val > $o, X21 : val, Y21 : val, X22 : list_val, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_all2_val_val @ R @ X22 @ Y22) => (list_all2_val_val @ R @ (cons_val @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_138_list_Orel__intros_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_ty_ty @ R @ X22 @ Y22) => (list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_139_list_Orel__intros_I2_J, axiom,
    ((![R : ty > list_char > $o, X21 : ty, Y21 : list_char, X22 : list_ty, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a1504214817t_char @ R @ X22 @ Y22) => (list_a1504214817t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_140_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > ty > $o, X21 : list_char, Y21 : ty, X22 : list_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a1770748705har_ty @ R @ X22 @ Y22) => (list_a1770748705har_ty @ R @ (cons_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_141_list_Orel__intros_I2_J, axiom,
    ((![R : list_char > val > $o, X21 : list_char, Y21 : val, X22 : list_list_char, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_a280217834ar_val @ R @ X22 @ Y22) => (list_a280217834ar_val @ R @ (cons_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_142_list_Orel__intros_I2_J, axiom,
    ((![R : val > list_char > $o, X21 : val, Y21 : list_char, X22 : list_val, Y22 : list_list_char]: ((R @ X21 @ Y21) => ((list_a1248766058t_char @ R @ X22 @ Y22) => (list_a1248766058t_char @ R @ (cons_val @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_143_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, Y21 : ty, X22 : list_exp_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a295513531har_ty @ R @ X22 @ Y22) => (list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_144_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > val > $o, X21 : exp_list_char, Y21 : val, X22 : list_exp_list_char, Y22 : list_val]: ((R @ X21 @ Y21) => ((list_a853659268ar_val @ R @ X22 @ Y22) => (list_a853659268ar_val @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_145_list_Orel__inject_I2_J, axiom,
    ((![R : ty > val > $o, X21 : ty, X22 : list_ty, Y21 : val, Y22 : list_val]: ((list_all2_ty_val @ R @ (cons_ty @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_146_list_Orel__inject_I2_J, axiom,
    ((![R : val > ty > $o, X21 : val, X22 : list_val, Y21 : ty, Y22 : list_ty]: ((list_all2_val_ty @ R @ (cons_val @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_val_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_147_list_Orel__inject_I2_J, axiom,
    ((![R : val > val > $o, X21 : val, X22 : list_val, Y21 : val, Y22 : list_val]: ((list_all2_val_val @ R @ (cons_val @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_val_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_148_list_Orel__inject_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_149_list_Orel__inject_I2_J, axiom,
    ((![R : ty > list_char > $o, X21 : ty, X22 : list_ty, Y21 : list_char, Y22 : list_list_char]: ((list_a1504214817t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1504214817t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_150_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > ty > $o, X21 : list_char, X22 : list_list_char, Y21 : ty, Y22 : list_ty]: ((list_a1770748705har_ty @ R @ (cons_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1770748705har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_151_list_Orel__inject_I2_J, axiom,
    ((![R : list_char > val > $o, X21 : list_char, X22 : list_list_char, Y21 : val, Y22 : list_val]: ((list_a280217834ar_val @ R @ (cons_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a280217834ar_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_152_list_Orel__inject_I2_J, axiom,
    ((![R : val > list_char > $o, X21 : val, X22 : list_val, Y21 : list_char, Y22 : list_list_char]: ((list_a1248766058t_char @ R @ (cons_val @ X21 @ X22) @ (cons_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1248766058t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_153_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : ty, Y22 : list_ty]: ((list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a295513531har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_154_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > val > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : val, Y22 : list_val]: ((list_a853659268ar_val @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_val @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a853659268ar_val @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_155_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_156_curryE, axiom,
    ((![F : produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1199911222_val_o @ F @ A2 @ B2) => (F @ (produc1725134254on_val @ A2 @ B2)))))). % curryE
thf(fact_157_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_158_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_159_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_160_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_161_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_162_curryD, axiom,
    ((![F : produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1199911222_val_o @ F @ A2 @ B2) => (F @ (produc1725134254on_val @ A2 @ B2)))))). % curryD
thf(fact_163_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_164_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_165_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_166_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_167_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr1036794744ty_val, X : ty, Xs : list_ty, Y : val, Ys : list_val]: ((list_all2_ty_val @ (fun_of_ty_val @ S3) @ (cons_ty @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member1776226881ty_val @ (product_Pair_ty_val @ X @ Y) @ S3)) & ((list_all2_ty_val @ (fun_of_ty_val @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_168_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr312206840val_ty, X : val, Xs : list_val, Y : ty, Ys : list_ty]: ((list_all2_val_ty @ (fun_of_val_ty @ S3) @ (cons_val @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member1400634561val_ty @ (product_Pair_val_ty @ X @ Y) @ S3)) & ((list_all2_val_ty @ (fun_of_val_ty @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_169_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr1870322241al_val, X : val, Xs : list_val, Y : val, Ys : list_val]: ((list_all2_val_val @ (fun_of_val_val @ S3) @ (cons_val @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member1494223754al_val @ (product_Pair_val_val @ X @ Y) @ S3)) & ((list_all2_val_val @ (fun_of_val_val @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_170_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr1194734255_ty_ty, X : ty, Xs : list_ty, Y : ty, Ys : list_ty]: ((list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ (cons_ty @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Y) @ S3)) & ((list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_171_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr1320471513t_char, X : ty, Xs : list_ty, Y : list_char, Ys : list_list_char]: ((list_a1504214817t_char @ (fun_of_ty_list_char @ S3) @ (cons_ty @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((member1016971042t_char @ (produc751008561t_char @ X @ Y) @ S3)) & ((list_a1504214817t_char @ (fun_of_ty_list_char @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_172_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr349050585har_ty, X : list_char, Xs : list_list_char, Y : ty, Ys : list_ty]: ((list_a1770748705har_ty @ (fun_of_list_char_ty @ S3) @ (cons_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member325880354har_ty @ (produc1017542449har_ty @ X @ Y) @ S3)) & ((list_a1770748705har_ty @ (fun_of_list_char_ty @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_173_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr174107298ar_val, X : list_char, Xs : list_list_char, Y : val, Ys : list_val]: ((list_a280217834ar_val @ (fun_of_list_char_val @ S3) @ (cons_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member1062074475ar_val @ (produc368164090ar_val @ X @ Y) @ S3)) & ((list_a280217834ar_val @ (fun_of_list_char_val @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_174_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr1557683618t_char, X : val, Xs : list_val, Y : list_char, Ys : list_list_char]: ((list_a1248766058t_char @ (fun_of_val_list_char @ S3) @ (cons_val @ X @ Xs) @ (cons_list_char @ Y @ Ys)) = (((member1429154667t_char @ (produc1336712314t_char @ X @ Y) @ S3)) & ((list_a1248766058t_char @ (fun_of_val_list_char @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_175_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr210248295har_ty, X : exp_list_char, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ (fun_of296872230har_ty @ S3) @ (cons_exp_list_char @ X @ Xs) @ (cons_ty @ Y @ Ys)) = (((member138355144har_ty @ (produc2042197419har_ty @ X @ Y) @ S3)) & ((list_a295513531har_ty @ (fun_of296872230har_ty @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_176_rel__list__all2__Cons, axiom,
    ((![S3 : set_Pr1974587184ar_val, X : exp_list_char, Xs : list_exp_list_char, Y : val, Ys : list_val]: ((list_a853659268ar_val @ (fun_of855213167ar_val @ S3) @ (cons_exp_list_char @ X @ Xs) @ (cons_val @ Y @ Ys)) = (((member402857233ar_val @ (produc964238964ar_val @ X @ Y) @ S3)) & ((list_a853659268ar_val @ (fun_of855213167ar_val @ S3) @ Xs @ Ys))))))). % rel_list_all2_Cons
thf(fact_177_member__rec_I1_J, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char, Y : exp_list_char]: ((member_exp_list_char @ (cons_exp_list_char @ X @ Xs) @ Y) = (((X = Y)) | ((member_exp_list_char @ Xs @ Y))))))). % member_rec(1)
thf(fact_178_member__rec_I1_J, axiom,
    ((![X : ty, Xs : list_ty, Y : ty]: ((member_ty @ (cons_ty @ X @ Xs) @ Y) = (((X = Y)) | ((member_ty @ Xs @ Y))))))). % member_rec(1)
thf(fact_179_member__rec_I1_J, axiom,
    ((![X : list_char, Xs : list_list_char, Y : list_char]: ((member_list_char @ (cons_list_char @ X @ Xs) @ Y) = (((X = Y)) | ((member_list_char @ Xs @ Y))))))). % member_rec(1)
thf(fact_180_member__rec_I1_J, axiom,
    ((![X : val, Xs : list_val, Y : val]: ((member_val @ (cons_val @ X @ Xs) @ Y) = (((X = Y)) | ((member_val @ Xs @ Y))))))). % member_rec(1)
thf(fact_181_lexord__cons__cons, axiom,
    ((![A2 : produc335961278on_val, X : list_P682203204on_val, B2 : produc335961278on_val, Y : list_P682203204on_val, R2 : set_Pr208351751on_val]: ((member884479824on_val @ (produc234842647on_val @ (cons_P1492043380on_val @ A2 @ X) @ (cons_P1492043380on_val @ B2 @ Y)) @ (lexord718263729on_val @ R2)) = (((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R2)) | ((((A2 = B2)) & ((member884479824on_val @ (produc234842647on_val @ X @ Y) @ (lexord718263729on_val @ R2)))))))))). % lexord_cons_cons
thf(fact_182_lexord__cons__cons, axiom,
    ((![A2 : produc1097884484on_val, X : list_P1873028426on_val, B2 : produc1097884484on_val, Y : list_P1873028426on_val, R2 : set_Pr1189492743on_val]: ((member321179984on_val @ (produc2055752471on_val @ (cons_P766091258on_val @ A2 @ X) @ (cons_P766091258on_val @ B2 @ Y)) @ (lexord75837879on_val @ R2)) = (((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2)) | ((((A2 = B2)) & ((member321179984on_val @ (produc2055752471on_val @ X @ Y) @ (lexord75837879on_val @ R2)))))))))). % lexord_cons_cons
thf(fact_183_lexord__cons__cons, axiom,
    ((![A2 : exp_list_char, X : list_exp_list_char, B2 : exp_list_char, Y : list_exp_list_char, R2 : set_Pr224372167t_char]: ((member462435472t_char @ (produc1721801175t_char @ (cons_exp_list_char @ A2 @ X) @ (cons_exp_list_char @ B2 @ Y)) @ (lexord_exp_list_char @ R2)) = (((member1699993616t_char @ (produc240508503t_char @ A2 @ B2) @ R2)) | ((((A2 = B2)) & ((member462435472t_char @ (produc1721801175t_char @ X @ Y) @ (lexord_exp_list_char @ R2)))))))))). % lexord_cons_cons
thf(fact_184_lexord__cons__cons, axiom,
    ((![A2 : ty, X : list_ty, B2 : ty, Y : list_ty, R2 : set_Pr1194734255_ty_ty]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ (cons_ty @ A2 @ X) @ (cons_ty @ B2 @ Y)) @ (lexord_ty @ R2)) = (((member2070851320_ty_ty @ (product_Pair_ty_ty @ A2 @ B2) @ R2)) | ((((A2 = B2)) & ((member1942114840ist_ty @ (produc1089615911ist_ty @ X @ Y) @ (lexord_ty @ R2)))))))))). % lexord_cons_cons
thf(fact_185_lexord__cons__cons, axiom,
    ((![A2 : list_char, X : list_list_char, B2 : list_char, Y : list_list_char, R2 : set_Pr164112643t_char]: ((member725442668t_char @ (produc1181934459t_char @ (cons_list_char @ A2 @ X) @ (cons_list_char @ B2 @ Y)) @ (lexord_list_char @ R2)) = (((member89690956t_char @ (produc1304532571t_char @ A2 @ B2) @ R2)) | ((((A2 = B2)) & ((member725442668t_char @ (produc1181934459t_char @ X @ Y) @ (lexord_list_char @ R2)))))))))). % lexord_cons_cons
thf(fact_186_lexord__cons__cons, axiom,
    ((![A2 : val, X : list_val, B2 : val, Y : list_val, R2 : set_Pr1870322241al_val]: ((member1382006826st_val @ (produc180957881st_val @ (cons_val @ A2 @ X) @ (cons_val @ B2 @ Y)) @ (lexord_val @ R2)) = (((member1494223754al_val @ (product_Pair_val_val @ A2 @ B2) @ R2)) | ((((A2 = B2)) & ((member1382006826st_val @ (produc180957881st_val @ X @ Y) @ (lexord_val @ R2)))))))))). % lexord_cons_cons
thf(fact_187_in__lex__prod, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val, R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A2 @ B2) @ (produc245869591on_val @ A3 @ B3)) @ (lex_pr601255983on_val @ R2 @ S)) = (((member1689761872on_val @ (produc245869591on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1689761872on_val @ (produc245869591on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_188_in__lex__prod, axiom,
    ((![A2 : produc335961278on_val, B2 : produc1097884484on_val, A3 : produc335961278on_val, B3 : produc1097884484on_val, R2 : set_Pr208351751on_val, S : set_Pr1189492743on_val]: ((member939451536on_val @ (produc1914110935on_val @ (produc974123805on_val @ A2 @ B2) @ (produc974123805on_val @ A3 @ B3)) @ (lex_pr1117889333on_val @ R2 @ S)) = (((member1689761872on_val @ (produc245869591on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_189_in__lex__prod, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc335961278on_val, A3 : produc1097884484on_val, B3 : produc335961278on_val, R2 : set_Pr1189492743on_val, S : set_Pr208351751on_val]: ((member1284182416on_val @ (produc625175255on_val @ (produc367337745on_val @ A2 @ B2) @ (produc367337745on_val @ A3 @ B3)) @ (lex_pr511103273on_val @ R2 @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1689761872on_val @ (produc245869591on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_190_in__lex__prod, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val, R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B2) @ (produc1069526295on_val @ A3 @ B3)) @ (lex_pr186272047on_val @ R2 @ S)) = (((member354538064on_val @ (produc1069526295on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_191_in__lex__prod, axiom,
    ((![A2 : list_list_char, B2 : produc111478616t_char, A3 : list_list_char, B3 : produc111478616t_char, R2 : set_Pr2117892643t_char, S : set_Pr1314019591t_char]: ((member668803778t_char @ (produc1080972113t_char @ (produc1808722894t_char @ A2 @ B2) @ (produc1808722894t_char @ A3 @ B3)) @ (lex_pr1470672310t_char @ R2 @ S)) = (((member725442668t_char @ (produc1181934459t_char @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member219943760t_char @ (produc1108858903t_char @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_192_in__lex__prod, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val, R2 : set_Pr1932514887t_char, S : set_Pr148564103on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A2 @ B2) @ (produc1725134254on_val @ A3 @ B3)) @ (lex_pr263313862on_val @ R2 @ S)) = (((member462435472t_char @ (produc1721801175t_char @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member2027247312on_val @ (produc2106877847on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_193_in__lex__prod, axiom,
    ((![A2 : list_ty, B2 : produc1109669680t_char, A3 : list_ty, B3 : produc1109669680t_char, R2 : set_Pr1785354703ist_ty, S : set_Pr290014113t_char]: ((member219943760t_char @ (produc1108858903t_char @ (produc1806338192t_char @ A2 @ B2) @ (produc1806338192t_char @ A3 @ B3)) @ (lex_pr579745960t_char @ R2 @ S)) = (((member1942114840ist_ty @ (produc1089615911ist_ty @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member89029866t_char @ (produc183121785t_char @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_194_in__lex__prod, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val, R2 : set_Pr224372167t_char, S : set_Pr148564103on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B2) @ (produc2023458740on_val @ A3 @ B3)) @ (lex_pr1764546508on_val @ R2 @ S)) = (((member1699993616t_char @ (produc240508503t_char @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member2027247312on_val @ (produc2106877847on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_195_in__lex__prod, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val, R2 : set_Pr1465729071on_val, S : set_Pr1104486497on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B2) @ (produc52622304on_val @ A3 @ B3)) @ (lex_pr683585528on_val @ R2 @ S)) = (((member78096504on_val @ (produc1392944775on_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1177709994on_val @ (produc746553401on_val @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_196_in__lex__prod, axiom,
    ((![A2 : list_val, B2 : exp_list_char, A3 : list_val, B3 : exp_list_char, R2 : set_Pr723931873st_val, S : set_Pr224372167t_char]: ((member89029866t_char @ (produc183121785t_char @ (produc823987298t_char @ A2 @ B2) @ (produc823987298t_char @ A3 @ B3)) @ (lex_pr143617610t_char @ R2 @ S)) = (((member1382006826st_val @ (produc180957881st_val @ A2 @ A3) @ R2)) | ((((A2 = A3)) & ((member1699993616t_char @ (produc240508503t_char @ B2 @ B3) @ S))))))))). % in_lex_prod
thf(fact_197_confs__widens, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts : list_ty, Ts3 : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) => (list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts3)))))). % confs_widens
thf(fact_198_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ S) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => (?[T2 : ty]: ((wTrt @ P @ (hp @ S2) @ E @ E3 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_199_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_200_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_201_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_202_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S2))))))). % red_preserves_sconf
thf(fact_203_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_204_lexord__linear, axiom,
    ((![R2 : set_Pr208351751on_val, X : list_P682203204on_val, Y : list_P682203204on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ R2) | ((A = B) | (member1689761872on_val @ (produc245869591on_val @ B @ A) @ R2)))) => ((member884479824on_val @ (produc234842647on_val @ X @ Y) @ (lexord718263729on_val @ R2)) | ((X = Y) | (member884479824on_val @ (produc234842647on_val @ Y @ X) @ (lexord718263729on_val @ R2)))))))). % lexord_linear
thf(fact_205_lexord__linear, axiom,
    ((![R2 : set_Pr1189492743on_val, X : list_P1873028426on_val, Y : list_P1873028426on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) | ((A = B) | (member354538064on_val @ (produc1069526295on_val @ B @ A) @ R2)))) => ((member321179984on_val @ (produc2055752471on_val @ X @ Y) @ (lexord75837879on_val @ R2)) | ((X = Y) | (member321179984on_val @ (produc2055752471on_val @ Y @ X) @ (lexord75837879on_val @ R2)))))))). % lexord_linear
thf(fact_206_lexord__irreflexive, axiom,
    ((![R2 : set_Pr208351751on_val, Xs : list_P682203204on_val]: ((![X3 : produc335961278on_val]: (~ ((member1689761872on_val @ (produc245869591on_val @ X3 @ X3) @ R2)))) => (~ ((member884479824on_val @ (produc234842647on_val @ Xs @ Xs) @ (lexord718263729on_val @ R2)))))))). % lexord_irreflexive
thf(fact_207_lexord__irreflexive, axiom,
    ((![R2 : set_Pr1189492743on_val, Xs : list_P1873028426on_val]: ((![X3 : produc1097884484on_val]: (~ ((member354538064on_val @ (produc1069526295on_val @ X3 @ X3) @ R2)))) => (~ ((member321179984on_val @ (produc2055752471on_val @ Xs @ Xs) @ (lexord75837879on_val @ R2)))))))). % lexord_irreflexive
thf(fact_208_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T3 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T3) => (conf_P93989998t_char @ P @ H @ V @ T3)))))). % conf_widen
thf(fact_209_red__reds_OListRed1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ E3 @ Es) @ S2)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_210_rel__list__all2__refl, axiom,
    ((![S3 : set_Pr208351751on_val, Xs : list_P682203204on_val]: ((![X3 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ X3) @ S3)) => (list_a1113096199on_val @ (fun_of1372490972on_val @ S3) @ Xs @ Xs))))). % rel_list_all2_refl
thf(fact_211_rel__list__all2__refl, axiom,
    ((![S3 : set_Pr1189492743on_val, Xs : list_P1873028426on_val]: ((![X3 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ X3) @ S3)) => (list_a1904865543on_val @ (fun_of1872337628on_val @ S3) @ Xs @ Xs))))). % rel_list_all2_refl
thf(fact_212_rel__list__all2__refl, axiom,
    ((![S3 : set_Pr1194734255_ty_ty, Xs : list_ty]: ((![X3 : ty]: (member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ X3) @ S3)) => (list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ Xs @ Xs))))). % rel_list_all2_refl
thf(fact_213_rel__list__all2__trans, axiom,
    ((![R : set_Pr1194734255_ty_ty, S3 : set_Pr1194734255_ty_ty, T : set_Pr1194734255_ty_ty, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A : ty, B : ty, C : ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ A @ B) @ R) => ((member2070851320_ty_ty @ (product_Pair_ty_ty @ B @ C) @ S3) => (member2070851320_ty_ty @ (product_Pair_ty_ty @ A @ C) @ T)))) => ((list_all2_ty_ty @ (fun_of_ty_ty @ R) @ As @ Bs) => ((list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ Bs @ Cs) => (list_all2_ty_ty @ (fun_of_ty_ty @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_214_rel__list__all2__trans, axiom,
    ((![R : set_Pr723931873st_val, S3 : set_Pr82799206t_char, T : set_Pr82799206t_char, As : list_list_val, Bs : list_list_val, Cs : list_exp_list_char]: ((![A : list_val, B : list_val, C : exp_list_char]: ((member1382006826st_val @ (produc180957881st_val @ A @ B) @ R) => ((member580484423t_char @ (produc823987298t_char @ B @ C) @ S3) => (member580484423t_char @ (produc823987298t_char @ A @ C) @ T)))) => ((list_a602111657st_val @ (fun_of1684577790st_val @ R) @ As @ Bs) => ((list_a1105622130t_char @ (fun_of161265885t_char @ S3) @ Bs @ Cs) => (list_a1105622130t_char @ (fun_of161265885t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_215_rel__list__all2__trans, axiom,
    ((![R : set_Pr82799206t_char, S3 : set_Pr224372167t_char, T : set_Pr82799206t_char, As : list_list_val, Bs : list_exp_list_char, Cs : list_exp_list_char]: ((![A : list_val, B : exp_list_char, C : exp_list_char]: ((member580484423t_char @ (produc823987298t_char @ A @ B) @ R) => ((member1699993616t_char @ (produc240508503t_char @ B @ C) @ S3) => (member580484423t_char @ (produc823987298t_char @ A @ C) @ T)))) => ((list_a1105622130t_char @ (fun_of161265885t_char @ R) @ As @ Bs) => ((list_a1702871623t_char @ (fun_of64219676t_char @ S3) @ Bs @ Cs) => (list_a1105622130t_char @ (fun_of161265885t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_216_rel__list__all2__trans, axiom,
    ((![R : set_Pr1785354703ist_ty, S3 : set_Pr925902648t_char, T : set_Pr925902648t_char, As : list_list_ty, Bs : list_list_ty, Cs : list_P1602847424t_char]: ((![A : list_ty, B : list_ty, C : produc1109669680t_char]: ((member1942114840ist_ty @ (produc1089615911ist_ty @ A @ B) @ R) => ((member1031340033t_char @ (produc1806338192t_char @ B @ C) @ S3) => (member1031340033t_char @ (produc1806338192t_char @ A @ C) @ T)))) => ((list_a1317958679ist_ty @ (fun_of397150316ist_ty @ R) @ As @ Bs) => ((list_a226366592t_char @ (fun_of1649676245t_char @ S3) @ Bs @ Cs) => (list_a226366592t_char @ (fun_of1649676245t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_217_rel__list__all2__trans, axiom,
    ((![R : set_Pr925902648t_char, S3 : set_Pr290014113t_char, T : set_Pr925902648t_char, As : list_list_ty, Bs : list_P1602847424t_char, Cs : list_P1602847424t_char]: ((![A : list_ty, B : produc1109669680t_char, C : produc1109669680t_char]: ((member1031340033t_char @ (produc1806338192t_char @ A @ B) @ R) => ((member89029866t_char @ (produc183121785t_char @ B @ C) @ S3) => (member1031340033t_char @ (produc1806338192t_char @ A @ C) @ T)))) => ((list_a226366592t_char @ (fun_of1649676245t_char @ R) @ As @ Bs) => ((list_a761598825t_char @ (fun_of446723518t_char @ S3) @ Bs @ Cs) => (list_a226366592t_char @ (fun_of1649676245t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_218_rel__list__all2__trans, axiom,
    ((![R : set_Pr2117892643t_char, S3 : set_Pr685054290t_char, T : set_Pr685054290t_char, As : list_list_list_char, Bs : list_list_list_char, Cs : list_P364227422t_char]: ((![A : list_list_char, B : list_list_char, C : produc111478616t_char]: ((member725442668t_char @ (produc1181934459t_char @ A @ B) @ R) => ((member772747827t_char @ (produc1808722894t_char @ B @ C) @ S3) => (member772747827t_char @ (produc1808722894t_char @ A @ C) @ T)))) => ((list_a1460260715t_char @ (fun_of681401536t_char @ R) @ As @ Bs) => ((list_a1227756510t_char @ (fun_of1003211849t_char @ S3) @ Bs @ Cs) => (list_a1227756510t_char @ (fun_of1003211849t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_219_rel__list__all2__trans, axiom,
    ((![R : set_Pr685054290t_char, S3 : set_Pr1314019591t_char, T : set_Pr685054290t_char, As : list_list_list_char, Bs : list_P364227422t_char, Cs : list_P364227422t_char]: ((![A : list_list_char, B : produc111478616t_char, C : produc111478616t_char]: ((member772747827t_char @ (produc1808722894t_char @ A @ B) @ R) => ((member219943760t_char @ (produc1108858903t_char @ B @ C) @ S3) => (member772747827t_char @ (produc1808722894t_char @ A @ C) @ T)))) => ((list_a1227756510t_char @ (fun_of1003211849t_char @ R) @ As @ Bs) => ((list_a787061767t_char @ (fun_of756510172t_char @ S3) @ Bs @ Cs) => (list_a1227756510t_char @ (fun_of1003211849t_char @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_220_rel__list__all2__trans, axiom,
    ((![R : set_Pr723149704on_val, S3 : set_Pr1104486497on_val, T : set_Pr723149704on_val, As : list_n1514066695on_val, Bs : list_l566969696on_val, Cs : list_l566969696on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val, C : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ A @ B) @ R) => ((member1177709994on_val @ (produc746553401on_val @ B @ C) @ S3) => (member652041809on_val @ (produc52622304on_val @ A @ C) @ T)))) => ((list_a729577424on_val @ (fun_of1502879141on_val @ R) @ As @ Bs) => ((list_a1722502185on_val @ (fun_of461468542on_val @ S3) @ Bs @ Cs) => (list_a729577424on_val @ (fun_of1502879141on_val @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_221_rel__list__all2__trans, axiom,
    ((![R : set_Pr82799206t_char, S3 : set_Pr556513572on_val, T : set_Pr1448963139on_val, As : list_list_val, Bs : list_exp_list_char, Cs : list_P1914305198on_val]: ((![A : list_val, B : exp_list_char, C : produc515445032on_val]: ((member580484423t_char @ (produc823987298t_char @ A @ B) @ R) => ((member1888679917on_val @ (produc2023458740on_val @ B @ C) @ S3) => (member1782804388on_val @ (produc79611455on_val @ A @ C) @ T)))) => ((list_a1105622130t_char @ (fun_of161265885t_char @ R) @ As @ Bs) => ((list_a810242980on_val @ (fun_of1470380793on_val @ S3) @ Bs @ Cs) => (list_a502548047on_val @ (fun_of1367878458on_val @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_222_rel__list__all2__trans, axiom,
    ((![R : set_Pr224372167t_char, S3 : set_Pr556513572on_val, T : set_Pr556513572on_val, As : list_exp_list_char, Bs : list_exp_list_char, Cs : list_P1914305198on_val]: ((![A : exp_list_char, B : exp_list_char, C : produc515445032on_val]: ((member1699993616t_char @ (produc240508503t_char @ A @ B) @ R) => ((member1888679917on_val @ (produc2023458740on_val @ B @ C) @ S3) => (member1888679917on_val @ (produc2023458740on_val @ A @ C) @ T)))) => ((list_a1702871623t_char @ (fun_of64219676t_char @ R) @ As @ Bs) => ((list_a810242980on_val @ (fun_of1470380793on_val @ S3) @ Bs @ Cs) => (list_a810242980on_val @ (fun_of1470380793on_val @ T) @ As @ Cs))))))). % rel_list_all2_trans
thf(fact_223_rel__list__all2__antisym, axiom,
    ((![S3 : set_Pr208351751on_val, T : set_Pr208351751on_val, Xs : list_P682203204on_val, Ys : list_P682203204on_val]: ((![X3 : produc335961278on_val, Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X3 @ Y3) @ S3) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ X3) @ T) => (X3 = Y3)))) => ((list_a1113096199on_val @ (fun_of1372490972on_val @ S3) @ Xs @ Ys) => ((list_a1113096199on_val @ (fun_of1372490972on_val @ T) @ Ys @ Xs) => (Xs = Ys))))))). % rel_list_all2_antisym
thf(fact_224_rel__list__all2__antisym, axiom,
    ((![S3 : set_Pr1189492743on_val, T : set_Pr1189492743on_val, Xs : list_P1873028426on_val, Ys : list_P1873028426on_val]: ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X3 @ Y3) @ S3) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ X3) @ T) => (X3 = Y3)))) => ((list_a1904865543on_val @ (fun_of1872337628on_val @ S3) @ Xs @ Ys) => ((list_a1904865543on_val @ (fun_of1872337628on_val @ T) @ Ys @ Xs) => (Xs = Ys))))))). % rel_list_all2_antisym
thf(fact_225_rel__list__all2__antisym, axiom,
    ((![S3 : set_Pr1194734255_ty_ty, T : set_Pr1194734255_ty_ty, Xs : list_ty, Ys : list_ty]: ((![X3 : ty, Y3 : ty]: ((member2070851320_ty_ty @ (product_Pair_ty_ty @ X3 @ Y3) @ S3) => ((member2070851320_ty_ty @ (product_Pair_ty_ty @ Y3 @ X3) @ T) => (X3 = Y3)))) => ((list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ Xs @ Ys) => ((list_all2_ty_ty @ (fun_of_ty_ty @ T) @ Ys @ Xs) => (Xs = Ys))))))). % rel_list_all2_antisym
thf(fact_226_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_227_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E @ E2 @ T) => (?[T2 : ty]: ((wTrt @ P @ H2 @ E @ E3 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_228_rel__list__all2__Cons1, axiom,
    ((![S3 : set_Pr556513572on_val, X : exp_list_char, Xs : list_exp_list_char, Ys : list_P1914305198on_val]: ((list_a810242980on_val @ (fun_of1470380793on_val @ S3) @ (cons_exp_list_char @ X @ Xs) @ Ys) = (?[Z2 : produc515445032on_val]: (?[Zs : list_P1914305198on_val]: (((Ys = (cons_P636485854on_val @ Z2 @ Zs))) & ((((member1888679917on_val @ (produc2023458740on_val @ X @ Z2) @ S3)) & ((list_a810242980on_val @ (fun_of1470380793on_val @ S3) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_229_rel__list__all2__Cons1, axiom,
    ((![S3 : set_Pr723149704on_val, X : nat > option2118145160on_val, Xs : list_n1514066695on_val, Ys : list_l566969696on_val]: ((list_a729577424on_val @ (fun_of1502879141on_val @ S3) @ (cons_n1930706881on_val @ X @ Xs) @ Ys) = (?[Z2 : list_char > option_val]: (?[Zs : list_l566969696on_val]: (((Ys = (cons_l1212975130on_val @ Z2 @ Zs))) & ((((member652041809on_val @ (produc52622304on_val @ X @ Z2) @ S3)) & ((list_a729577424on_val @ (fun_of1502879141on_val @ S3) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_230_rel__list__all2__Cons1, axiom,
    ((![S3 : set_Pr82799206t_char, X : list_val, Xs : list_list_val, Ys : list_exp_list_char]: ((list_a1105622130t_char @ (fun_of161265885t_char @ S3) @ (cons_list_val @ X @ Xs) @ Ys) = (?[Z2 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z2 @ Zs))) & ((((member580484423t_char @ (produc823987298t_char @ X @ Z2) @ S3)) & ((list_a1105622130t_char @ (fun_of161265885t_char @ S3) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_231_rel__list__all2__Cons1, axiom,
    ((![S3 : set_Pr1194734255_ty_ty, X : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ (cons_ty @ X @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((member2070851320_ty_ty @ (product_Pair_ty_ty @ X @ Z2) @ S3)) & ((list_all2_ty_ty @ (fun_of_ty_ty @ S3) @ Xs @ Zs))))))))))). % rel_list_all2_Cons1
thf(fact_232_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E4 : exp_list_char, S4 : produc515445032on_val, E5 : exp_list_char, S5 : produc515445032on_val, Es3 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E4 @ Es3)) => ((A22 = S4) => ((A32 = (cons_exp_list_char @ E5 @ Es3)) => ((A42 = S5) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S4) @ (produc2023458740on_val @ E5 @ S5)) @ (red @ P))))))))) => (~ ((![Es3 : list_exp_list_char, S4 : produc515445032on_val, Es4 : list_exp_list_char, S5 : produc515445032on_val, V2 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3)) => ((A22 = S4) => ((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4)) => ((A42 = S5) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_233_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E6 : exp_list_char]: (?[S6 : produc515445032on_val]: (?[E7 : exp_list_char]: (?[S7 : produc515445032on_val]: (?[Es5 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E6 @ Es5))) & ((((A22 = S6)) & ((((A32 = (cons_exp_list_char @ E7 @ Es5))) & ((((A42 = S7)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E6 @ S6) @ (produc2023458740on_val @ E7 @ S7)) @ (red @ P)))))))))))))))) | ((?[Es5 : list_exp_list_char]: (?[S6 : produc515445032on_val]: (?[Es6 : list_exp_list_char]: (?[S7 : produc515445032on_val]: (?[V3 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5))) & ((((A22 = S6)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6))) & ((((A42 = S7)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S6) @ (produc1725134254on_val @ Es6 @ S7)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_234_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_235_blocks_Ocases, axiom,
    ((![X : produc81045532t_char]: ((![V4 : list_char, Vs2 : list_list_char, T4 : ty, Ts4 : list_ty, V2 : val, Vs3 : list_val, E4 : exp_list_char]: (~ ((X = (produc1808722894t_char @ (cons_list_char @ V4 @ Vs2) @ (produc1806338192t_char @ (cons_ty @ T4 @ Ts4) @ (produc823987298t_char @ (cons_val @ V2 @ Vs3) @ E4))))))) => ((![E4 : exp_list_char]: (~ ((X = (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ nil_val @ E4))))))) => ((![Vc : ty, Vd : list_ty, Vb : produc1109669680t_char]: (~ ((X = (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ (cons_ty @ Vc @ Vd) @ Vb)))))) => ((![V2 : list_ty, Ve : val, Vf : list_val, Vd : exp_list_char]: (~ ((X = (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ V2 @ (produc823987298t_char @ (cons_val @ Ve @ Vf) @ Vd))))))) => ((![Va : list_char, Vb : list_list_char, Vc : produc1109669680t_char]: (~ ((X = (produc1808722894t_char @ (cons_list_char @ Va @ Vb) @ (produc1806338192t_char @ nil_ty @ Vc)))))) => ((![V2 : list_list_char, Vd : val, Ve : list_val, Vb : exp_list_char]: (~ ((X = (produc1808722894t_char @ V2 @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ (cons_val @ Vd @ Ve) @ Vb))))))) => ((![Va : list_char, Vc : list_list_char, Vb : list_ty, Ve : exp_list_char]: (~ ((X = (produc1808722894t_char @ (cons_list_char @ Va @ Vc) @ (produc1806338192t_char @ Vb @ (produc823987298t_char @ nil_val @ Ve))))))) => (~ ((![V2 : list_list_char, Va : ty, Vc : list_ty, Ve : exp_list_char]: (~ ((X = (produc1808722894t_char @ V2 @ (produc1806338192t_char @ (cons_ty @ Va @ Vc) @ (produc823987298t_char @ nil_val @ Ve))))))))))))))))))). % blocks.cases
thf(fact_236_blocks_Oinduct, axiom,
    ((![P : produc81045532t_char > $o, A0 : produc81045532t_char]: ((![V4 : list_char, Vs2 : list_list_char, T4 : ty, Ts4 : list_ty, V2 : val, Vs3 : list_val, E4 : exp_list_char]: ((P @ (produc1808722894t_char @ Vs2 @ (produc1806338192t_char @ Ts4 @ (produc823987298t_char @ Vs3 @ E4)))) => (P @ (produc1808722894t_char @ (cons_list_char @ V4 @ Vs2) @ (produc1806338192t_char @ (cons_ty @ T4 @ Ts4) @ (produc823987298t_char @ (cons_val @ V2 @ Vs3) @ E4)))))) => ((![E4 : exp_list_char]: (P @ (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ nil_val @ E4))))) => ((![Vc : ty, Vd : list_ty, Vb : produc1109669680t_char]: (P @ (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ (cons_ty @ Vc @ Vd) @ Vb)))) => ((![V2 : list_ty, Ve : val, Vf : list_val, Vd : exp_list_char]: (P @ (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ V2 @ (produc823987298t_char @ (cons_val @ Ve @ Vf) @ Vd))))) => ((![Va : list_char, Vb : list_list_char, Vc : produc1109669680t_char]: (P @ (produc1808722894t_char @ (cons_list_char @ Va @ Vb) @ (produc1806338192t_char @ nil_ty @ Vc)))) => ((![V2 : list_list_char, Vd : val, Ve : list_val, Vb : exp_list_char]: (P @ (produc1808722894t_char @ V2 @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ (cons_val @ Vd @ Ve) @ Vb))))) => ((![Va : list_char, Vc : list_list_char, Vb : list_ty, Ve : exp_list_char]: (P @ (produc1808722894t_char @ (cons_list_char @ Va @ Vc) @ (produc1806338192t_char @ Vb @ (produc823987298t_char @ nil_val @ Ve))))) => ((![V2 : list_list_char, Va : ty, Vc : list_ty, Ve : exp_list_char]: (P @ (produc1808722894t_char @ V2 @ (produc1806338192t_char @ (cons_ty @ Va @ Vc) @ (produc823987298t_char @ nil_val @ Ve))))) => (P @ A0)))))))))))). % blocks.induct
thf(fact_237_blocks__induct, axiom,
    ((![P : list_list_char > list_ty > list_val > exp_list_char > $o, A0a : list_list_char, A0b : list_ty, A0c : list_val, A0d : exp_list_char]: ((![V4 : list_char, Vs2 : list_list_char, T4 : ty, Ts4 : list_ty, V2 : val, Vs3 : list_val, E4 : exp_list_char]: ((P @ Vs2 @ Ts4 @ Vs3 @ E4) => (P @ (cons_list_char @ V4 @ Vs2) @ (cons_ty @ T4 @ Ts4) @ (cons_val @ V2 @ Vs3) @ E4))) => ((![X_1 : exp_list_char]: (P @ nil_list_char @ nil_ty @ nil_val @ X_1)) => ((![Vc : ty, Vd : list_ty, A : list_val, X_1 : exp_list_char]: (P @ nil_list_char @ (cons_ty @ Vc @ Vd) @ A @ X_1)) => ((![V2 : list_ty, Ve : val, Vf : list_val, X_1 : exp_list_char]: (P @ nil_list_char @ V2 @ (cons_val @ Ve @ Vf) @ X_1)) => ((![Va : list_char, Vb : list_list_char, A : list_val, X_1 : exp_list_char]: (P @ (cons_list_char @ Va @ Vb) @ nil_ty @ A @ X_1)) => ((![V2 : list_list_char, Vd : val, Ve : list_val, X_1 : exp_list_char]: (P @ V2 @ nil_ty @ (cons_val @ Vd @ Ve) @ X_1)) => ((![Va : list_char, Vc : list_list_char, Vb : list_ty, X_1 : exp_list_char]: (P @ (cons_list_char @ Va @ Vc) @ Vb @ nil_val @ X_1)) => ((![V2 : list_list_char, Va : ty, Vc : list_ty, X_1 : exp_list_char]: (P @ V2 @ (cons_ty @ Va @ Vc) @ nil_val @ X_1)) => (P @ A0a @ A0b @ A0c @ A0d)))))))))))). % blocks_induct
thf(fact_238_WTrtNil, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty]: (wTrts @ P @ H @ E @ nil_exp_list_char @ nil_ty)))). % WTrtNil
thf(fact_239_WTrts_Osimps, axiom,
    ((wTrts = (^[P4 : list_P1234162913t_char]: (^[H4 : nat > option2118145160on_val]: (^[A12 : list_char > option_ty]: (^[A23 : list_exp_list_char]: (^[A33 : list_ty]: (((?[E8 : list_char > option_ty]: (((A12 = E8)) & ((((A23 = nil_exp_list_char)) & ((A33 = nil_ty))))))) | ((?[E8 : list_char > option_ty]: (?[E6 : exp_list_char]: (?[T5 : ty]: (?[Es5 : list_exp_list_char]: (?[Ts5 : list_ty]: (((A12 = E8)) & ((((A23 = (cons_exp_list_char @ E6 @ Es5))) & ((((A33 = (cons_ty @ T5 @ Ts5))) & ((((wTrt @ P4 @ H4 @ E8 @ E6 @ T5)) & ((wTrts @ P4 @ H4 @ E8 @ Es5 @ Ts5)))))))))))))))))))))))). % WTrts.simps
thf(fact_240_WTrts_Ocases, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A1 : list_char > option_ty, A22 : list_exp_list_char, A32 : list_ty]: ((wTrts @ P @ H @ A1 @ A22 @ A32) => (((A22 = nil_exp_list_char) => (~ ((A32 = nil_ty)))) => (~ ((![E4 : exp_list_char, T4 : ty, Es3 : list_exp_list_char]: ((A22 = (cons_exp_list_char @ E4 @ Es3)) => (![Ts4 : list_ty]: ((A32 = (cons_ty @ T4 @ Ts4)) => ((wTrt @ P @ H @ A1 @ E4 @ T4) => (~ ((wTrts @ P @ H @ A1 @ Es3 @ Ts4))))))))))))))). % WTrts.cases
thf(fact_241_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S2)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_242_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S : produc515445032on_val, Es2 : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S) @ (produc1725134254on_val @ Es2 @ S2)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S2)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_243_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S2)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_244_blocks_Osimps_I2_J, axiom,
    ((![E2 : exp_list_char]: ((blocks @ (produc1808722894t_char @ nil_list_char @ (produc1806338192t_char @ nil_ty @ (produc823987298t_char @ nil_val @ E2)))) = E2)))). % blocks.simps(2)
thf(fact_245_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_246_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E4 : exp_list_char, H5 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H5 @ L3 @ E4 @ H5 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E5 @ H6 @ L4) => (R @ E_0 @ H_0 @ L_02 @ E5 @ H6 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_247_CallRedsObj, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S) @ (produc2023458740on_val @ (call_list_char @ E3 @ M @ Es) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj

% Conjectures (5)
thf(conj_0, hypothesis,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))).
thf(conj_1, hypothesis,
    ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ es @ s) @ (produc1725134254on_val @ es2 @ s2)) @ (reds @ p)))).
thf(conj_2, hypothesis,
    ((typeSa1777264139_sconf @ p @ e @ s))).
thf(conj_3, hypothesis,
    ((wTrts @ p @ (hp @ s) @ e @ es @ ts))).
thf(conj_4, conjecture,
    ((?[Ts6 : list_ty]: ((wTrts @ p @ (hp @ s2) @ e @ es2 @ Ts6) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts6 @ ts))))).
