% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_528__5340820_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:34.983

% Could-be-implicit typings (24)
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% Explicit typings (71)
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    produc463114774_val_o : (produc335961278on_val > produc335961278on_val > $o) > produc655058983on_val > $o).
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thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_val > $o).
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_a______, type,
    a : nat > option2118145160on_val).
thf(sy_v_aa______, type,
    aa : nat > option2118145160on_val).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_ba______, type,
    ba : list_char > option_val).
thf(sy_v_es_Ha______, type,
    es_a : list_exp_list_char).
thf(sy_v_esa______, type,
    esa : list_exp_list_char).
thf(sy_v_v______, type,
    v : val).

% Relevant facts (249)
thf(fact_0_ListRed2_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ a @ b)))). % ListRed2.prems(1)
thf(fact_1_ListRed2_Oprems_I2_J, axiom,
    ((wTrts @ p @ a @ e @ (cons_exp_list_char @ (val_list_char @ v) @ esa) @ ts))). % ListRed2.prems(2)
thf(fact_2_ListRed2_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, Ts : list_ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ a @ b)) => ((wTrts @ p @ a @ E @ esa @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ p @ aa @ E @ es_a @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts2 @ Ts)))))))). % ListRed2.hyps(2)
thf(fact_3_ListRed2_Ohyps_I1_J, axiom,
    ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ esa @ (produc52622304on_val @ a @ b)) @ (produc1725134254on_val @ es_a @ (produc52622304on_val @ aa @ ba))) @ (reds @ p)))). % ListRed2.hyps(1)
thf(fact_4_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_5_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_6_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_7_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_8_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_9_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_10_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1702871623t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_11_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_12_list_Orel__inject_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, X22 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a212154379t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_13_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_14_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_15_list_Orel__intros_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X22 : list_ty, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a212154379t_char @ R @ X22 @ Y22) => (list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_16_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_17_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, Y21 : exp_list_char, X22 : list_exp_list_char, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a1702871623t_char @ R @ X22 @ Y22) => (list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_18_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_19_list__all2__Cons, axiom,
    ((![P : ty > exp_list_char > $o, X : ty, Xs : list_ty, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a212154379t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_20_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_21_list__all2__Cons, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X : exp_list_char, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X @ Xs) @ (cons_exp_list_char @ Y @ Ys)) = (((P @ X @ Y)) & ((list_a1702871623t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_22_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) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_23_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_24_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) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_25_list__all2__Cons1, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X @ Xs) @ Ys) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z @ Zs))) & ((((P @ X @ Z)) & ((list_a1702871623t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_26_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)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_27_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)) = (?[Z : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_28_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_29_list__all2__Cons2, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Y : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ Xs @ (cons_exp_list_char @ Y @ Ys)) = (?[Z : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z @ Zs))) & ((((P @ Z @ Y)) & ((list_a1702871623t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_30_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_31_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_32_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) = (?[Z : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z @ Zs))) & ((((widen_917054840t_char @ P @ X @ Z)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_33_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_34_not__Cons__self2, axiom,
    ((![X : ty, Xs : list_ty]: (~ (((cons_ty @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_35_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X : list_ty]: ((![X2 : ty]: (Ra @ X2 @ X2)) => (list_all2_ty_ty @ Ra @ X @ X))))). % list.rel_refl
thf(fact_36_list_Orel__refl, axiom,
    ((![Ra : exp_list_char > exp_list_char > $o, X : list_exp_list_char]: ((![X2 : exp_list_char]: (Ra @ X2 @ X2)) => (list_a1702871623t_char @ Ra @ X @ X))))). % list.rel_refl
thf(fact_37_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X2 : ty, Y2 : ty]: ((P @ X2 @ Y2) => ((Q @ Y2 @ X2) => (X2 = Y2)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_38_list__all2__antisym, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Q : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((![X2 : exp_list_char, Y2 : exp_list_char]: ((P @ X2 @ Y2) => ((Q @ Y2 @ X2) => (X2 = Y2)))) => ((list_a1702871623t_char @ P @ Xs @ Ys) => ((list_a1702871623t_char @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_39_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y4 : ty]: (^[Z2 : ty]: (Y4 = Z2)))) = (^[Y4 : list_ty]: (^[Z2 : list_ty]: (Y4 = Z2)))))). % list.rel_eq
thf(fact_40_list_Orel__eq, axiom,
    (((list_a1702871623t_char @ (^[Y4 : exp_list_char]: (^[Z2 : exp_list_char]: (Y4 = Z2)))) = (^[Y4 : list_exp_list_char]: (^[Z2 : list_exp_list_char]: (Y4 = Z2)))))). % list.rel_eq
thf(fact_41_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P2 : 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) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P2 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_42_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P2 : ty > exp_list_char > $o, P3 : ty > exp_list_char > $o, As : list_ty, Bs : list_ty, Cs : list_exp_list_char]: ((![A : ty, B : ty, C : exp_list_char]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_a212154379t_char @ P2 @ Bs @ Cs) => (list_a212154379t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_43_list__all2__trans, axiom,
    ((![P1 : ty > exp_list_char > $o, P2 : exp_list_char > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_exp_list_char, Cs : list_ty]: ((![A : ty, B : exp_list_char, C : ty]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_a212154379t_char @ P1 @ As @ Bs) => ((list_a295513531har_ty @ P2 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_44_list__all2__trans, axiom,
    ((![P1 : ty > exp_list_char > $o, P2 : exp_list_char > exp_list_char > $o, P3 : ty > exp_list_char > $o, As : list_ty, Bs : list_exp_list_char, Cs : list_exp_list_char]: ((![A : ty, B : exp_list_char, C : exp_list_char]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_a212154379t_char @ P1 @ As @ Bs) => ((list_a1702871623t_char @ P2 @ Bs @ Cs) => (list_a212154379t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_45_list__all2__trans, axiom,
    ((![P1 : exp_list_char > ty > $o, P2 : ty > ty > $o, P3 : exp_list_char > ty > $o, As : list_exp_list_char, Bs : list_ty, Cs : list_ty]: ((![A : exp_list_char, B : ty, C : ty]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_a295513531har_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P2 @ Bs @ Cs) => (list_a295513531har_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_46_list__all2__trans, axiom,
    ((![P1 : exp_list_char > ty > $o, P2 : ty > exp_list_char > $o, P3 : exp_list_char > exp_list_char > $o, As : list_exp_list_char, Bs : list_ty, Cs : list_exp_list_char]: ((![A : exp_list_char, B : ty, C : exp_list_char]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_a295513531har_ty @ P1 @ As @ Bs) => ((list_a212154379t_char @ P2 @ Bs @ Cs) => (list_a1702871623t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_47_list__all2__trans, axiom,
    ((![P1 : exp_list_char > exp_list_char > $o, P2 : exp_list_char > ty > $o, P3 : exp_list_char > ty > $o, As : list_exp_list_char, Bs : list_exp_list_char, Cs : list_ty]: ((![A : exp_list_char, B : exp_list_char, C : ty]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_a1702871623t_char @ P1 @ As @ Bs) => ((list_a295513531har_ty @ P2 @ Bs @ Cs) => (list_a295513531har_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_48_list__all2__trans, axiom,
    ((![P1 : exp_list_char > exp_list_char > $o, P2 : exp_list_char > exp_list_char > $o, P3 : exp_list_char > exp_list_char > $o, As : list_exp_list_char, Bs : list_exp_list_char, Cs : list_exp_list_char]: ((![A : exp_list_char, B : exp_list_char, C : exp_list_char]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_a1702871623t_char @ P1 @ As @ Bs) => ((list_a1702871623t_char @ P2 @ Bs @ Cs) => (list_a1702871623t_char @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_49_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X2 : ty]: (P @ X2 @ X2)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_50_list__all2__refl, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char]: ((![X2 : exp_list_char]: (P @ X2 @ X2)) => (list_a1702871623t_char @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_51_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_52_list__all2__mono, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Ys : list_exp_list_char, Q : ty > exp_list_char > $o]: ((list_a212154379t_char @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : exp_list_char]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a212154379t_char @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_53_list__all2__mono, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Ys : list_ty, Q : exp_list_char > ty > $o]: ((list_a295513531har_ty @ P @ Xs @ Ys) => ((![Xs2 : exp_list_char, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a295513531har_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_54_list__all2__mono, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Ys : list_exp_list_char, Q : exp_list_char > exp_list_char > $o]: ((list_a1702871623t_char @ P @ Xs @ Ys) => ((![Xs2 : exp_list_char, Ys2 : exp_list_char]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_a1702871623t_char @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_55_list__all2__eq, axiom,
    (((^[Y4 : list_ty]: (^[Z2 : list_ty]: (Y4 = Z2))) = (list_all2_ty_ty @ (^[Y4 : ty]: (^[Z2 : ty]: (Y4 = Z2))))))). % list_all2_eq
thf(fact_56_list__all2__eq, axiom,
    (((^[Y4 : list_exp_list_char]: (^[Z2 : list_exp_list_char]: (Y4 = Z2))) = (list_a1702871623t_char @ (^[Y4 : exp_list_char]: (^[Z2 : exp_list_char]: (Y4 = Z2))))))). % list_all2_eq
thf(fact_57_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_58_prod__cases4, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_59_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_60_prod__induct4, axiom,
    ((![P : produc655058983on_val > $o, X : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_61_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X))))). % prod_induct4
thf(fact_62_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_63_old_Oprod_Oinject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_64_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_65_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_66_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_67_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X23 : list_char > option_val, Y1 : nat > option2118145160on_val, Y23 : list_char > option_val]: (((produc52622304on_val @ X1 @ X23) = (produc52622304on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_68_prod_Oinject, axiom,
    ((![X1 : produc335961278on_val, X23 : produc335961278on_val, Y1 : produc335961278on_val, Y23 : produc335961278on_val]: (((produc245869591on_val @ X1 @ X23) = (produc245869591on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_69_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X23 : produc515445032on_val, Y1 : list_exp_list_char, Y23 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X23) = (produc1725134254on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_70_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X23 : produc1097884484on_val, Y1 : produc1097884484on_val, Y23 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X23) = (produc1069526295on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_71_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X23 : produc515445032on_val, Y1 : exp_list_char, Y23 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X23) = (produc2023458740on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_72_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_73_old_Oprod_Oinducts, axiom,
    ((![P : produc655058983on_val > $o, Prod : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_74_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_75_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_76_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_77_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_78_old_Oprod_Oexhaust, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : produc335961278on_val]: (~ ((Y = (produc245869591on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_79_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_80_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_81_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_82_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_83_Pair__inject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_84_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_85_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_86_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_87_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_88_prod__cases, axiom,
    ((![P : produc655058983on_val > $o, P4 : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_89_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P4 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_90_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_91_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_92_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X2 : nat > option2118145160on_val, Y2 : list_char > option_val]: (P4 = (produc52622304on_val @ X2 @ Y2)))))). % surj_pair
thf(fact_93_surj__pair, axiom,
    ((![P4 : produc655058983on_val]: (?[X2 : produc335961278on_val, Y2 : produc335961278on_val]: (P4 = (produc245869591on_val @ X2 @ Y2)))))). % surj_pair
thf(fact_94_surj__pair, axiom,
    ((![P4 : produc335961278on_val]: (?[X2 : list_exp_list_char, Y2 : produc515445032on_val]: (P4 = (produc1725134254on_val @ X2 @ Y2)))))). % surj_pair
thf(fact_95_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X2 : produc1097884484on_val, Y2 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X2 @ Y2)))))). % surj_pair
thf(fact_96_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X2 : exp_list_char, Y2 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X2 @ Y2)))))). % surj_pair
thf(fact_97_prod__induct3, axiom,
    ((![P : produc655058983on_val > $o, X : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_98_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_99_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_100_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_101_prod__cases3, axiom,
    ((![Y : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C))))))))))). % prod_cases3
thf(fact_102_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_103_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_104_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_105_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_106_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_107_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_108_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_109_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_110_Collect__cong, axiom,
    ((![P : produc655058983on_val > $o, Q : produc655058983on_val > $o]: ((![X2 : produc655058983on_val]: ((P @ X2) = (Q @ X2))) => ((collec105960082on_val @ P) = (collec105960082on_val @ Q)))))). % Collect_cong
thf(fact_111_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_112_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S2) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % reds_preserves_sconf
thf(fact_113_redsp__reds__eq, axiom,
    ((redsp = (^[P5 : list_P1234162913t_char]: (^[X4 : list_exp_list_char]: (^[Y5 : produc515445032on_val]: (^[Z : list_exp_list_char]: (^[Aa : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X4 @ Y5) @ (produc1725134254on_val @ Z @ Aa)) @ (reds @ P5)))))))))). % redsp_reds_eq
thf(fact_114_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_115_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)) = (((?[E2 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E3 : exp_list_char]: (?[S5 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E2 @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ E3 @ Es3))) & ((((A42 = S5)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S4) @ (produc2023458740on_val @ E3 @ 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.simps
thf(fact_116_red__hext__incr, axiom,
    ((![E4 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_117_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S2 @ Es2 @ S3) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2 @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3))))). % redp_redsp.ListRed2
thf(fact_118_red__reds_OListRed1, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E4 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E5 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_119_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)) => ((![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.cases
thf(fact_120_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_121_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_122_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_123_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_124_red__preserves__sconf, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E4 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_125_red__preserves__lconf, axiom,
    ((![E4 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E4 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E4 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_126_exp_Oinject_I9_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, Y91 : exp_list_char, Y92 : list_char, Y93 : list_exp_list_char]: (((call_list_char @ X91 @ X92 @ X93) = (call_list_char @ Y91 @ Y92 @ Y93)) = (((X91 = Y91)) & ((((X92 = Y92)) & ((X93 = Y93))))))))). % exp.inject(9)
thf(fact_127_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E4 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E4 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E4 @ T)))))). % WTrt_hext_mono
thf(fact_128_exp_Odistinct_I65_J, axiom,
    ((![X3 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X3) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_129_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E4 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E @ E4 @ T) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E4 @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_130_red__reds_OCallObj, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E4 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E5 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_131_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_132_red__preserves__hconf, axiom,
    ((![E4 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E4 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E4 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_133_WTrtCallNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E4 : exp_list_char, Es : list_exp_list_char, Ts : list_ty, M : list_char, T : ty]: ((wTrt @ P @ H @ E @ E4 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E4 @ M @ Es) @ T)))))). % WTrtCallNT
thf(fact_134_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X4 : nat > option2118145160on_val]: (^[Y5 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y5) @ R))) = (^[X4 : nat > option2118145160on_val]: (^[Y5 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_135_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X4 : produc335961278on_val]: (^[Y5 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X4 @ Y5) @ R))) = (^[X4 : produc335961278on_val]: (^[Y5 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_136_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X4 : list_exp_list_char]: (^[Y5 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X4 @ Y5) @ R))) = (^[X4 : list_exp_list_char]: (^[Y5 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_137_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X4 : produc1097884484on_val]: (^[Y5 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y5) @ R))) = (^[X4 : produc1097884484on_val]: (^[Y5 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_138_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X4 : exp_list_char]: (^[Y5 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y5) @ R))) = (^[X4 : exp_list_char]: (^[Y5 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y5) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_139_red__lcl__add, axiom,
    ((![E4 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E4 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_140_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P5 : list_P1234162913t_char]: (^[E8 : list_char > option_ty]: (produc99536995_val_o @ (^[H4 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (((hconf_1244167010t_char @ P5 @ H4)) & ((lconf_485928294t_char @ P5 @ H4 @ L3 @ E8))))))))))). % sconf_def
thf(fact_141_split__part, axiom,
    ((![P : $o, Q : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((produc99536995_val_o @ (^[A5 : nat > option2118145160on_val]: (^[B4 : list_char > option_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc515445032on_val]: ((P) & ((produc99536995_val_o @ Q @ Ab)))))))). % split_part
thf(fact_142_split__part, axiom,
    ((![P : $o, Q : produc335961278on_val > produc335961278on_val > $o]: ((produc525028460_val_o @ (^[A5 : produc335961278on_val]: (^[B4 : produc335961278on_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc655058983on_val]: ((P) & ((produc525028460_val_o @ Q @ Ab)))))))). % split_part
thf(fact_143_split__part, axiom,
    ((![P : $o, Q : list_exp_list_char > produc515445032on_val > $o]: ((produc1125182229_val_o @ (^[A5 : list_exp_list_char]: (^[B4 : produc515445032on_val]: ((P) & ((Q @ A5 @ B4)))))) = (^[Ab : produc335961278on_val]: ((P) & ((produc1125182229_val_o @ Q @ Ab)))))))). % split_part
thf(fact_144_case__prod__conv, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A2 @ B2)) = (F @ A2 @ B2))))). % case_prod_conv
thf(fact_145_case__prod__conv, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ A2 @ B2)) = (F @ A2 @ B2))))). % case_prod_conv
thf(fact_146_case__prod__conv, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc58203522_val_o @ F @ (produc1725134254on_val @ A2 @ B2)) = (F @ A2 @ B2))))). % case_prod_conv
thf(fact_147_case__prod__conv, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ A2 @ B2)) = (F @ A2 @ B2))))). % case_prod_conv
thf(fact_148_case__prodI, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((F @ A2 @ B2) => (produc50362220_val_o @ F @ (produc1069526295on_val @ A2 @ B2)))))). % case_prodI
thf(fact_149_case__prodI, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((F @ A2 @ B2) => (produc199145871_val_o @ F @ (produc2023458740on_val @ A2 @ B2)))))). % case_prodI
thf(fact_150_case__prodI, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((F @ A2 @ B2) => (produc99536995_val_o @ F @ (produc52622304on_val @ A2 @ B2)))))). % case_prodI
thf(fact_151_case__prodI, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((F @ A2 @ B2) => (produc525028460_val_o @ F @ (produc245869591on_val @ A2 @ B2)))))). % case_prodI
thf(fact_152_case__prodI, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((F @ A2 @ B2) => (produc1125182229_val_o @ F @ (produc1725134254on_val @ A2 @ B2)))))). % case_prodI
thf(fact_153_case__prodI2, axiom,
    ((![P4 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ A @ B)) => (C2 @ A @ B))) => (produc50362220_val_o @ C2 @ P4))))). % case_prodI2
thf(fact_154_case__prodI2, axiom,
    ((![P4 : produc1097884484on_val, C2 : exp_list_char > produc515445032on_val > $o]: ((![A : exp_list_char, B : produc515445032on_val]: ((P4 = (produc2023458740on_val @ A @ B)) => (C2 @ A @ B))) => (produc199145871_val_o @ C2 @ P4))))). % case_prodI2
thf(fact_155_case__prodI2, axiom,
    ((![P4 : produc515445032on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P4 = (produc52622304on_val @ A @ B)) => (C2 @ A @ B))) => (produc99536995_val_o @ C2 @ P4))))). % case_prodI2
thf(fact_156_case__prodI2, axiom,
    ((![P4 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > $o]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P4 = (produc245869591on_val @ A @ B)) => (C2 @ A @ B))) => (produc525028460_val_o @ C2 @ P4))))). % case_prodI2
thf(fact_157_case__prodI2, axiom,
    ((![P4 : produc335961278on_val, C2 : list_exp_list_char > produc515445032on_val > $o]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P4 = (produc1725134254on_val @ A @ B)) => (C2 @ A @ B))) => (produc1125182229_val_o @ C2 @ P4))))). % case_prodI2
thf(fact_158_old_Oprod_Ocase, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, X1 : nat > option2118145160on_val, X23 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ X1 @ X23)) = (F @ X1 @ X23))))). % old.prod.case
thf(fact_159_old_Oprod_Ocase, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, X1 : produc335961278on_val, X23 : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ X1 @ X23)) = (F @ X1 @ X23))))). % old.prod.case
thf(fact_160_old_Oprod_Ocase, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X1 : list_exp_list_char, X23 : produc515445032on_val]: ((produc58203522_val_o @ F @ (produc1725134254on_val @ X1 @ X23)) = (F @ X1 @ X23))))). % old.prod.case
thf(fact_161_old_Oprod_Ocase, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, X1 : list_exp_list_char, X23 : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ X1 @ X23)) = (F @ X1 @ X23))))). % old.prod.case
thf(fact_162_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_163_internal__case__prod__def, axiom,
    ((produc463114774_val_o = produc525028460_val_o))). % internal_case_prod_def
thf(fact_164_internal__case__prod__def, axiom,
    ((produc1326103384_val_o = produc58203522_val_o))). % internal_case_prod_def
thf(fact_165_internal__case__prod__def, axiom,
    ((produc1075415231_val_o = produc1125182229_val_o))). % internal_case_prod_def
thf(fact_166_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, Prod : produc515445032on_val]: ((H @ (produc99536995_val_o @ F @ Prod)) = (produc99536995_val_o @ (^[X12 : nat > option2118145160on_val]: (^[X24 : list_char > option_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_167_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : produc335961278on_val > produc335961278on_val > $o, Prod : produc655058983on_val]: ((H @ (produc525028460_val_o @ F @ Prod)) = (produc525028460_val_o @ (^[X12 : produc335961278on_val]: (^[X24 : produc335961278on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_168_prod_Ocase__distrib, axiom,
    ((![H : (produc335961278on_val > $o) > produc335961278on_val > $o, F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Prod : produc335961278on_val]: ((H @ (produc58203522_val_o @ F @ Prod)) = (produc58203522_val_o @ (^[X12 : list_exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_169_prod_Ocase__distrib, axiom,
    ((![H : (produc335961278on_val > $o) > $o, F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Prod : produc335961278on_val]: ((H @ (produc58203522_val_o @ F @ Prod)) = (produc1125182229_val_o @ (^[X12 : list_exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_170_prod_Ocase__distrib, axiom,
    ((![H : $o > produc335961278on_val > $o, F : list_exp_list_char > produc515445032on_val > $o, Prod : produc335961278on_val]: ((H @ (produc1125182229_val_o @ F @ Prod)) = (produc58203522_val_o @ (^[X12 : list_exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_171_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : list_exp_list_char > produc515445032on_val > $o, Prod : produc335961278on_val]: ((H @ (produc1125182229_val_o @ F @ Prod)) = (produc1125182229_val_o @ (^[X12 : list_exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_172_prod_Odisc__eq__case, axiom,
    ((![Prod : produc515445032on_val]: (produc99536995_val_o @ (^[Uu : nat > option2118145160on_val]: (^[Uv : list_char > option_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_173_prod_Odisc__eq__case, axiom,
    ((![Prod : produc655058983on_val]: (produc525028460_val_o @ (^[Uu : produc335961278on_val]: (^[Uv : produc335961278on_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_174_prod_Odisc__eq__case, axiom,
    ((![Prod : produc335961278on_val]: (produc1125182229_val_o @ (^[Uu : list_exp_list_char]: (^[Uv : produc515445032on_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_175_case__prodD, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_176_case__prodD, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_177_case__prodD, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_178_case__prodD, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_179_case__prodD, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_180_case__prodE, axiom,
    ((![C2 : produc1097884484on_val > produc1097884484on_val > $o, P4 : produc1172664615on_val]: ((produc50362220_val_o @ C2 @ P4) => (~ ((![X2 : produc1097884484on_val, Y2 : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ X2 @ Y2)) => (~ ((C2 @ X2 @ Y2))))))))))). % case_prodE
thf(fact_181_case__prodE, axiom,
    ((![C2 : exp_list_char > produc515445032on_val > $o, P4 : produc1097884484on_val]: ((produc199145871_val_o @ C2 @ P4) => (~ ((![X2 : exp_list_char, Y2 : produc515445032on_val]: ((P4 = (produc2023458740on_val @ X2 @ Y2)) => (~ ((C2 @ X2 @ Y2))))))))))). % case_prodE
thf(fact_182_case__prodE, axiom,
    ((![C2 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P4 : produc515445032on_val]: ((produc99536995_val_o @ C2 @ P4) => (~ ((![X2 : nat > option2118145160on_val, Y2 : list_char > option_val]: ((P4 = (produc52622304on_val @ X2 @ Y2)) => (~ ((C2 @ X2 @ Y2))))))))))). % case_prodE
thf(fact_183_case__prodE, axiom,
    ((![C2 : produc335961278on_val > produc335961278on_val > $o, P4 : produc655058983on_val]: ((produc525028460_val_o @ C2 @ P4) => (~ ((![X2 : produc335961278on_val, Y2 : produc335961278on_val]: ((P4 = (produc245869591on_val @ X2 @ Y2)) => (~ ((C2 @ X2 @ Y2))))))))))). % case_prodE
thf(fact_184_case__prodE, axiom,
    ((![C2 : list_exp_list_char > produc515445032on_val > $o, P4 : produc335961278on_val]: ((produc1125182229_val_o @ C2 @ P4) => (~ ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((P4 = (produc1725134254on_val @ X2 @ Y2)) => (~ ((C2 @ X2 @ Y2))))))))))). % case_prodE
thf(fact_185_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z3 : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z3)) => (~ ((![X2 : nat > option2118145160on_val, Y2 : list_char > option_val]: ((Z3 = (produc52622304on_val @ X2 @ Y2)) => (~ ((Q @ (P @ X2 @ Y2)))))))))))). % case_prodE2
thf(fact_186_case__prodE2, axiom,
    ((![Q : $o > $o, P : produc335961278on_val > produc335961278on_val > $o, Z3 : produc655058983on_val]: ((Q @ (produc525028460_val_o @ P @ Z3)) => (~ ((![X2 : produc335961278on_val, Y2 : produc335961278on_val]: ((Z3 = (produc245869591on_val @ X2 @ Y2)) => (~ ((Q @ (P @ X2 @ Y2)))))))))))). % case_prodE2
thf(fact_187_case__prodE2, axiom,
    ((![Q : (produc335961278on_val > $o) > $o, P : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Z3 : produc335961278on_val]: ((Q @ (produc58203522_val_o @ P @ Z3)) => (~ ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((Z3 = (produc1725134254on_val @ X2 @ Y2)) => (~ ((Q @ (P @ X2 @ Y2)))))))))))). % case_prodE2
thf(fact_188_case__prodE2, axiom,
    ((![Q : $o > $o, P : list_exp_list_char > produc515445032on_val > $o, Z3 : produc335961278on_val]: ((Q @ (produc1125182229_val_o @ P @ Z3)) => (~ ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((Z3 = (produc1725134254on_val @ X2 @ Y2)) => (~ ((Q @ (P @ X2 @ Y2)))))))))))). % case_prodE2
thf(fact_189_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X4 : nat > option2118145160on_val]: (^[Y5 : list_char > option_val]: (F @ (produc52622304on_val @ X4 @ Y5))))) = F)))). % case_prod_eta
thf(fact_190_case__prod__eta, axiom,
    ((![F : produc655058983on_val > $o]: ((produc525028460_val_o @ (^[X4 : produc335961278on_val]: (^[Y5 : produc335961278on_val]: (F @ (produc245869591on_val @ X4 @ Y5))))) = F)))). % case_prod_eta
thf(fact_191_case__prod__eta, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o]: ((produc58203522_val_o @ (^[X4 : list_exp_list_char]: (^[Y5 : produc515445032on_val]: (F @ (produc1725134254on_val @ X4 @ Y5))))) = F)))). % case_prod_eta
thf(fact_192_case__prod__eta, axiom,
    ((![F : produc335961278on_val > $o]: ((produc1125182229_val_o @ (^[X4 : list_exp_list_char]: (^[Y5 : produc515445032on_val]: (F @ (produc1725134254on_val @ X4 @ Y5))))) = F)))). % case_prod_eta
thf(fact_193_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X2 : nat > option2118145160on_val, Y2 : list_char > option_val]: ((F @ X2 @ Y2) = (G @ (produc52622304on_val @ X2 @ Y2)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_194_cond__case__prod__eta, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, G : produc655058983on_val > $o]: ((![X2 : produc335961278on_val, Y2 : produc335961278on_val]: ((F @ X2 @ Y2) = (G @ (produc245869591on_val @ X2 @ Y2)))) => ((produc525028460_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_195_cond__case__prod__eta, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, G : produc335961278on_val > produc335961278on_val > $o]: ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((F @ X2 @ Y2) = (G @ (produc1725134254on_val @ X2 @ Y2)))) => ((produc58203522_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_196_cond__case__prod__eta, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, G : produc335961278on_val > $o]: ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((F @ X2 @ Y2) = (G @ (produc1725134254on_val @ X2 @ Y2)))) => ((produc1125182229_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_197_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_198_split__cong, axiom,
    ((![Q2 : produc515445032on_val, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : (nat > option2118145160on_val) > (list_char > option_val) > $o, P4 : produc515445032on_val]: ((![X2 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X2 @ Y2) = Q2) => ((F @ X2 @ Y2) = (G @ X2 @ Y2)))) => ((P4 = Q2) => ((produc99536995_val_o @ F @ P4) = (produc99536995_val_o @ G @ Q2))))))). % split_cong
thf(fact_199_split__cong, axiom,
    ((![Q2 : produc655058983on_val, F : produc335961278on_val > produc335961278on_val > $o, G : produc335961278on_val > produc335961278on_val > $o, P4 : produc655058983on_val]: ((![X2 : produc335961278on_val, Y2 : produc335961278on_val]: (((produc245869591on_val @ X2 @ Y2) = Q2) => ((F @ X2 @ Y2) = (G @ X2 @ Y2)))) => ((P4 = Q2) => ((produc525028460_val_o @ F @ P4) = (produc525028460_val_o @ G @ Q2))))))). % split_cong
thf(fact_200_split__cong, axiom,
    ((![Q2 : produc335961278on_val, F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, G : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, P4 : produc335961278on_val]: ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X2 @ Y2) = Q2) => ((F @ X2 @ Y2) = (G @ X2 @ Y2)))) => ((P4 = Q2) => ((produc58203522_val_o @ F @ P4) = (produc58203522_val_o @ G @ Q2))))))). % split_cong
thf(fact_201_split__cong, axiom,
    ((![Q2 : produc335961278on_val, F : list_exp_list_char > produc515445032on_val > $o, G : list_exp_list_char > produc515445032on_val > $o, P4 : produc335961278on_val]: ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X2 @ Y2) = Q2) => ((F @ X2 @ Y2) = (G @ X2 @ Y2)))) => ((P4 = Q2) => ((produc1125182229_val_o @ F @ P4) = (produc1125182229_val_o @ G @ Q2))))))). % split_cong
thf(fact_202_Red__lcl__add, axiom,
    ((![E4 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E4 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_203_case__prod__app, axiom,
    ((produc58203522_val_o = (^[F2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o]: (^[X4 : produc335961278on_val]: (^[Y5 : produc335961278on_val]: (produc1125182229_val_o @ (^[L3 : list_exp_list_char]: (^[R2 : produc515445032on_val]: (F2 @ L3 @ R2 @ Y5))) @ X4))))))). % case_prod_app
thf(fact_204_mem__case__prodI2, axiom,
    ((![P4 : produc515445032on_val, Z3 : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P4 = (produc52622304on_val @ A @ B)) => (member1689761872on_val @ Z3 @ (C2 @ A @ B)))) => (member1689761872on_val @ Z3 @ (produc98852946on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_205_mem__case__prodI2, axiom,
    ((![P4 : produc515445032on_val, Z3 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P4 = (produc52622304on_val @ A @ B)) => (member354538064on_val @ Z3 @ (C2 @ A @ B)))) => (member354538064on_val @ Z3 @ (produc1919805778on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_206_mem__case__prodI2, axiom,
    ((![P4 : produc655058983on_val, Z3 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P4 = (produc245869591on_val @ A @ B)) => (member1689761872on_val @ Z3 @ (C2 @ A @ B)))) => (member1689761872on_val @ Z3 @ (produc1707441371on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_207_mem__case__prodI2, axiom,
    ((![P4 : produc655058983on_val, Z3 : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P4 = (produc245869591on_val @ A @ B)) => (member354538064on_val @ Z3 @ (C2 @ A @ B)))) => (member354538064on_val @ Z3 @ (produc1705670363on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_208_mem__case__prodI2, axiom,
    ((![P4 : produc335961278on_val, Z3 : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P4 = (produc1725134254on_val @ A @ B)) => (member1689761872on_val @ Z3 @ (C2 @ A @ B)))) => (member1689761872on_val @ Z3 @ (produc1745783812on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_209_mem__case__prodI2, axiom,
    ((![P4 : produc335961278on_val, Z3 : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P4 = (produc1725134254on_val @ A @ B)) => (member354538064on_val @ Z3 @ (C2 @ A @ B)))) => (member354538064on_val @ Z3 @ (produc379229956on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_210_mem__case__prodI2, axiom,
    ((![P4 : produc1172664615on_val, Z3 : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ A @ B)) => (member1689761872on_val @ Z3 @ (C2 @ A @ B)))) => (member1689761872on_val @ Z3 @ (produc1067722715on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_211_mem__case__prodI2, axiom,
    ((![P4 : produc1172664615on_val, Z3 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ A @ B)) => (member354538064on_val @ Z3 @ (C2 @ A @ B)))) => (member354538064on_val @ Z3 @ (produc493625819on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_212_mem__case__prodI2, axiom,
    ((![P4 : produc1097884484on_val, Z3 : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A : exp_list_char, B : produc515445032on_val]: ((P4 = (produc2023458740on_val @ A @ B)) => (member1689761872on_val @ Z3 @ (C2 @ A @ B)))) => (member1689761872on_val @ Z3 @ (produc356855678on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_213_mem__case__prodI2, axiom,
    ((![P4 : produc1097884484on_val, Z3 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A : exp_list_char, B : produc515445032on_val]: ((P4 = (produc2023458740on_val @ A @ B)) => (member354538064on_val @ Z3 @ (C2 @ A @ B)))) => (member354538064on_val @ Z3 @ (produc848217214on_val @ C2 @ P4)))))). % mem_case_prodI2
thf(fact_214_mem__case__prodI, axiom,
    ((![Z3 : produc655058983on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((member1689761872on_val @ Z3 @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z3 @ (produc98852946on_val @ C2 @ (produc52622304on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_215_mem__case__prodI, axiom,
    ((![Z3 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((member354538064on_val @ Z3 @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z3 @ (produc1919805778on_val @ C2 @ (produc52622304on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_216_mem__case__prodI, axiom,
    ((![Z3 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((member1689761872on_val @ Z3 @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z3 @ (produc1707441371on_val @ C2 @ (produc245869591on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_217_mem__case__prodI, axiom,
    ((![Z3 : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val, A2 : produc335961278on_val, B2 : produc335961278on_val]: ((member354538064on_val @ Z3 @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z3 @ (produc1705670363on_val @ C2 @ (produc245869591on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_218_mem__case__prodI, axiom,
    ((![Z3 : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((member1689761872on_val @ Z3 @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z3 @ (produc1745783812on_val @ C2 @ (produc1725134254on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_219_mem__case__prodI, axiom,
    ((![Z3 : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z3 @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z3 @ (produc379229956on_val @ C2 @ (produc1725134254on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_220_mem__case__prodI, axiom,
    ((![Z3 : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((member1689761872on_val @ Z3 @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z3 @ (produc1067722715on_val @ C2 @ (produc1069526295on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_221_mem__case__prodI, axiom,
    ((![Z3 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((member354538064on_val @ Z3 @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z3 @ (produc493625819on_val @ C2 @ (produc1069526295on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_222_mem__case__prodI, axiom,
    ((![Z3 : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, A2 : exp_list_char, B2 : produc515445032on_val]: ((member1689761872on_val @ Z3 @ (C2 @ A2 @ B2)) => (member1689761872on_val @ Z3 @ (produc356855678on_val @ C2 @ (produc2023458740on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_223_mem__case__prodI, axiom,
    ((![Z3 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A2 : exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z3 @ (C2 @ A2 @ B2)) => (member354538064on_val @ Z3 @ (produc848217214on_val @ C2 @ (produc2023458740on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_224_case__prodI2_H, axiom,
    ((![P4 : produc335961278on_val, C2 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = P4) => (C2 @ A @ B @ X))) => (produc58203522_val_o @ C2 @ P4 @ X))))). % case_prodI2'
thf(fact_225_mem__case__prodE, axiom,
    ((![Z3 : produc1172664615on_val, C2 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P4 : produc515445032on_val]: ((member354538064on_val @ Z3 @ (produc1919805778on_val @ C2 @ P4)) => (~ ((![X2 : nat > option2118145160on_val, Y2 : list_char > option_val]: ((P4 = (produc52622304on_val @ X2 @ Y2)) => (~ ((member354538064on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_226_mem__case__prodE, axiom,
    ((![Z3 : produc655058983on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr208351751on_val, P4 : produc655058983on_val]: ((member1689761872on_val @ Z3 @ (produc1707441371on_val @ C2 @ P4)) => (~ ((![X2 : produc335961278on_val, Y2 : produc335961278on_val]: ((P4 = (produc245869591on_val @ X2 @ Y2)) => (~ ((member1689761872on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_227_mem__case__prodE, axiom,
    ((![Z3 : produc1172664615on_val, C2 : produc335961278on_val > produc335961278on_val > set_Pr1189492743on_val, P4 : produc655058983on_val]: ((member354538064on_val @ Z3 @ (produc1705670363on_val @ C2 @ P4)) => (~ ((![X2 : produc335961278on_val, Y2 : produc335961278on_val]: ((P4 = (produc245869591on_val @ X2 @ Y2)) => (~ ((member354538064on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_228_mem__case__prodE, axiom,
    ((![Z3 : produc655058983on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, P4 : produc335961278on_val]: ((member1689761872on_val @ Z3 @ (produc1745783812on_val @ C2 @ P4)) => (~ ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((P4 = (produc1725134254on_val @ X2 @ Y2)) => (~ ((member1689761872on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_229_mem__case__prodE, axiom,
    ((![Z3 : produc1172664615on_val, C2 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P4 : produc335961278on_val]: ((member354538064on_val @ Z3 @ (produc379229956on_val @ C2 @ P4)) => (~ ((![X2 : list_exp_list_char, Y2 : produc515445032on_val]: ((P4 = (produc1725134254on_val @ X2 @ Y2)) => (~ ((member354538064on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_230_mem__case__prodE, axiom,
    ((![Z3 : produc655058983on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, P4 : produc1172664615on_val]: ((member1689761872on_val @ Z3 @ (produc1067722715on_val @ C2 @ P4)) => (~ ((![X2 : produc1097884484on_val, Y2 : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ X2 @ Y2)) => (~ ((member1689761872on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_231_mem__case__prodE, axiom,
    ((![Z3 : produc1172664615on_val, C2 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P4 : produc1172664615on_val]: ((member354538064on_val @ Z3 @ (produc493625819on_val @ C2 @ P4)) => (~ ((![X2 : produc1097884484on_val, Y2 : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ X2 @ Y2)) => (~ ((member354538064on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_232_mem__case__prodE, axiom,
    ((![Z3 : produc655058983on_val, C2 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, P4 : produc1097884484on_val]: ((member1689761872on_val @ Z3 @ (produc356855678on_val @ C2 @ P4)) => (~ ((![X2 : exp_list_char, Y2 : produc515445032on_val]: ((P4 = (produc2023458740on_val @ X2 @ Y2)) => (~ ((member1689761872on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_233_mem__case__prodE, axiom,
    ((![Z3 : produc1172664615on_val, C2 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P4 : produc1097884484on_val]: ((member354538064on_val @ Z3 @ (produc848217214on_val @ C2 @ P4)) => (~ ((![X2 : exp_list_char, Y2 : produc515445032on_val]: ((P4 = (produc2023458740on_val @ X2 @ Y2)) => (~ ((member354538064on_val @ Z3 @ (C2 @ X2 @ Y2)))))))))))). % mem_case_prodE
thf(fact_234_reds__def, axiom,
    ((reds = (^[P5 : list_P1234162913t_char]: (collec105960082on_val @ (produc525028460_val_o @ (produc58203522_val_o @ (^[X4 : list_exp_list_char]: (^[Y5 : produc515445032on_val]: (produc1125182229_val_o @ (redsp @ P5 @ X4 @ Y5))))))))))). % reds_def
thf(fact_235_converse__rtrancl__induct__red, axiom,
    ((![E4 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E4 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H5 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E6 @ H5 @ L4 @ E6 @ H5 @ L4)) => ((![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, E7 : exp_list_char, H6 : nat > option2118145160on_val, L5 : 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 @ E7 @ H6 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E7 @ H6 @ L5)))) => (R @ E4 @ H @ L @ E5 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_236_CallRedsObj, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E4 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E5 @ M @ Es) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_237_ListReds2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_238_ListReds1, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E4 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E5 @ Es) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_239_ListRedsVal, axiom,
    ((![E4 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E4 @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_240_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_241_CallRedsThrowObj, axiom,
    ((![E4 : exp_list_char, S0 : produc515445032on_val, A2 : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E4 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_242_red__reds_OThrowThrow, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E4)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_243_red__reds_OThrowRed, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E4) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_244_ThrowReds, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E4) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_245_ThrowRedsThrow, axiom,
    ((![E4 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E4) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_246_red__reds_OCallThrowObj, axiom,
    ((![E4 : exp_list_char, M : list_char, Es : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E4) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S2)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_247_CallRedsThrowParams, axiom,
    ((![E4 : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A2 : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A2) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E4 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_248_BinOpRedsThrow2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E4 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[Ts3 : list_ty]: ((wTrts @ p @ aa @ e @ (cons_exp_list_char @ (val_list_char @ v) @ es_a) @ Ts3) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts3 @ ts))))).
