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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_Objects_Ohext, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__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_001t__Set__Oset_It__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_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__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_001_062_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_M_Eo_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__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_001_Eo, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_001t__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_001t__Set__Oset_It__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_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001_Eo, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Set__Oset_It__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_J, type,
    produc1123062041on_val : (list_list_char > exp_list_char > set_Pr1189492743on_val) > produc1294284815t_char > set_Pr1189492743on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Set__Oset_It__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_J, type,
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thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J_J, type,
    member1392938152t_char : produc1689611007t_char > set_Pr1060756575t_char > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__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_Mt__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_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_E, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_a______, type,
    a : exp_list_char).
thf(sy_v_aa______, type,
    aa : exp_list_char).
thf(sy_v_b______, type,
    b : produc515445032on_val).
thf(sy_v_ba______, type,
    ba : produc515445032on_val).
thf(sy_v_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (249)
thf(fact_0_step_Ohyps_I1_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ a @ b) @ (produc2023458740on_val @ aa @ ba)) @ (red @ p)))). % step.hyps(1)
thf(fact_1_step_Oprems, axiom,
    ((typeSa1969945757config @ p @ e @ b @ a @ t))). % step.prems
thf(fact_2_step_Ohyps_I3_J, axiom,
    ((![T : ty]: ((typeSa1969945757config @ p @ e @ ba @ aa @ T) => (?[T2 : ty]: ((typeSa1969945757config @ p @ e @ s2 @ e3 @ T2) & (widen_917054840t_char @ p @ T2 @ T))))))). % step.hyps(3)
thf(fact_3_step_Ohyps_I2_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ aa @ ba) @ (produc2023458740on_val @ e3 @ s2)) @ (transi111096263on_val @ (red @ p))))). % step.hyps(2)
thf(fact_4_reds, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ s) @ (produc2023458740on_val @ e3 @ s2)) @ (transi111096263on_val @ (red @ p))))). % reds
thf(fact_5_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_6_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_7_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_8_Subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((typeSa1969945757config @ P @ E3 @ S2 @ E @ T) => (?[T2 : ty]: ((typeSa1969945757config @ P @ E3 @ S3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T))))))))). % Subject_reduction
thf(fact_9_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_10_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_11_widen__i__i__i__def, axiom,
    ((widen_1673563217t_char = (^[X : list_P1234162913t_char]: (^[Xa : ty]: (^[Xb : ty]: (pred_Product_unit2 @ (^[Y : product_unit]: (widen_917054840t_char @ X @ Xa @ Xb))))))))). % widen_i_i_i_def
thf(fact_12_widen_Oequation_I2_J, axiom,
    ((widen_917054840t_char = (^[X1 : list_P1234162913t_char]: (^[X2 : ty]: (^[X3 : ty]: (holds @ (widen_1673563217t_char @ X1 @ X2 @ X3)))))))). % widen.equation(2)
thf(fact_13_Class__widen, axiom,
    ((![P : list_P1234162913t_char, C : list_char, T : ty]: ((widen_917054840t_char @ P @ (class @ C) @ T) => (?[D : list_char]: (T = (class @ D))))))). % Class_widen
thf(fact_14_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_15_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Ax @ Ay) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_16_rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Ax @ Ay) => ((![A : list_list_char, B : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ A @ B)) @ (transi1892282060t_char @ R)) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_17_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_18_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_19_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Ax @ Ay) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A @ B)) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_20_converse__rtranclE2, axiom,
    ((![Xa2 : produc1097884484on_val, Xb2 : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa2 @ Xb2) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R)) => ((~ (((produc1069526295on_val @ Xa2 @ Xb2) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa2 @ Xb2) @ (produc1069526295on_val @ A @ B)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_21_converse__rtranclE2, axiom,
    ((![Xa2 : list_list_char, Xb2 : exp_list_char, Za : list_list_char, Zb : exp_list_char, R : set_Pr1060756575t_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa2 @ Xb2) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R)) => ((~ (((produc713467969t_char @ Xa2 @ Xb2) = (produc713467969t_char @ Za @ Zb)))) => (~ ((![A : list_list_char, B : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Xa2 @ Xb2) @ (produc713467969t_char @ A @ B)) @ R) => (~ ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ Za @ Zb)) @ (transi1892282060t_char @ R))))))))))))). % converse_rtranclE2
thf(fact_22_converse__rtranclE2, axiom,
    ((![Xa2 : nat > option2118145160on_val, Xb2 : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa2 @ Xb2) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((produc52622304on_val @ Xa2 @ Xb2) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa2 @ Xb2) @ (produc52622304on_val @ A @ B)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_23_converse__rtranclE2, axiom,
    ((![Xa2 : exp_list_char, Xb2 : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa2 @ Xb2) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((produc2023458740on_val @ Xa2 @ Xb2) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa2 @ Xb2) @ (produc2023458740on_val @ A @ B)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_24_converse__rtranclE2, axiom,
    ((![Xa2 : list_exp_list_char, Xb2 : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa2 @ Xb2) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R)) => ((~ (((produc1725134254on_val @ Xa2 @ Xb2) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A : list_exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa2 @ Xb2) @ (produc1725134254on_val @ A @ B)) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_25_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Bx @ By) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_26_converse__rtrancl__induct2, axiom,
    ((![Ax : list_list_char, Ay : exp_list_char, Bx : list_list_char, By : exp_list_char, R : set_Pr1060756575t_char, P : list_list_char > exp_list_char > $o]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Ax @ Ay) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Bx @ By) => ((![A : list_list_char, B : exp_list_char, Aa : list_list_char, Ba : exp_list_char]: ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ A @ B) @ (produc713467969t_char @ Aa @ Ba)) @ R) => ((member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ Aa @ Ba) @ (produc713467969t_char @ Bx @ By)) @ (transi1892282060t_char @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_27_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : set_Pr148564103on_val, P : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Bx @ By) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_28_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Bx @ By) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_29_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Bx @ By) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa @ Ba)) @ R) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_30_prod__cases4, axiom,
    ((![Y2 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y2 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_31_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C2 @ D2))))) => (P @ X4))))). % prod_induct4
thf(fact_32_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_33_old_Oprod_Oinject, axiom,
    ((![A2 : list_list_char, B2 : exp_list_char, A3 : list_list_char, B3 : exp_list_char]: (((produc713467969t_char @ A2 @ B2) = (produc713467969t_char @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_34_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_35_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_36_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_37_prod_Oinject, axiom,
    ((![X12 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X12 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X12 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_38_prod_Oinject, axiom,
    ((![X12 : list_list_char, X22 : exp_list_char, Y1 : list_list_char, Y22 : exp_list_char]: (((produc713467969t_char @ X12 @ X22) = (produc713467969t_char @ Y1 @ Y22)) = (((X12 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_39_prod_Oinject, axiom,
    ((![X12 : list_exp_list_char, X22 : produc515445032on_val, Y1 : list_exp_list_char, Y22 : produc515445032on_val]: (((produc1725134254on_val @ X12 @ X22) = (produc1725134254on_val @ Y1 @ Y22)) = (((X12 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_40_prod_Oinject, axiom,
    ((![X12 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X12 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X12 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_41_prod_Oinject, axiom,
    ((![X12 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X12 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X12 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_42_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R) => (member354538064on_val @ P2 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_43_r__into__rtrancl, axiom,
    ((![P2 : produc655058983on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ P2 @ R) => (member1689761872on_val @ P2 @ (transi325225921on_val @ R)))))). % r_into_rtrancl
thf(fact_44_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_45_rtrancl__idemp, axiom,
    ((![R : set_Pr208351751on_val]: ((transi325225921on_val @ (transi325225921on_val @ R)) = (transi325225921on_val @ R))))). % rtrancl_idemp
thf(fact_46_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_47_old_Oprod_Oinducts, axiom,
    ((![P : produc1294284815t_char > $o, Prod : produc1294284815t_char]: ((![A : list_list_char, B : exp_list_char]: (P @ (produc713467969t_char @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_48_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_49_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_50_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_51_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y2 = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_52_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc1294284815t_char]: (~ ((![A : list_list_char, B : exp_list_char]: (~ ((Y2 = (produc713467969t_char @ A @ B)))))))))). % old.prod.exhaust
thf(fact_53_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : produc515445032on_val]: (~ ((Y2 = (produc1725134254on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_54_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y2 = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_55_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y2 = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_56_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_57_Pair__inject, axiom,
    ((![A2 : list_list_char, B2 : exp_list_char, A3 : list_list_char, B3 : exp_list_char]: (((produc713467969t_char @ A2 @ B2) = (produc713467969t_char @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_58_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_59_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_60_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_61_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_62_prod__cases, axiom,
    ((![P : produc1294284815t_char > $o, P2 : produc1294284815t_char]: ((![A : list_list_char, B : exp_list_char]: (P @ (produc713467969t_char @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_63_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_64_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_65_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_66_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X5 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X5 @ Y3)))))). % surj_pair
thf(fact_67_surj__pair, axiom,
    ((![P2 : produc1294284815t_char]: (?[X5 : list_list_char, Y3 : exp_list_char]: (P2 = (produc713467969t_char @ X5 @ Y3)))))). % surj_pair
thf(fact_68_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X5 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X5 @ Y3)))))). % surj_pair
thf(fact_69_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X5 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X5 @ Y3)))))). % surj_pair
thf(fact_70_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X5 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X5 @ Y3)))))). % surj_pair
thf(fact_71_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C2)))) => (P @ X4))))). % prod_induct3
thf(fact_72_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X4 : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C2)))) => (P @ X4))))). % prod_induct3
thf(fact_73_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C2)))) => (P @ X4))))). % prod_induct3
thf(fact_74_prod__cases3, axiom,
    ((![Y2 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C2 : produc515445032on_val]: (~ ((Y2 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_75_prod__cases3, axiom,
    ((![Y2 : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y2 = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_76_prod__cases3, axiom,
    ((![Y2 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y2 = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C2))))))))))). % prod_cases3
thf(fact_77_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_78_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, C3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C3) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C3) @ (transi325225921on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_79_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ R) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_80_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, C3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C3) @ R) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C3) @ (transi325225921on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_81_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B2) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_82_converse__rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((P @ B2) => ((![Y3 : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ R) => ((member1689761872on_val @ (produc245869591on_val @ Z @ B2) @ (transi325225921on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_83_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_84_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc335961278on_val, R : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A2 @ A2) @ (transi325225921on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_85_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_86_converse__rtranclE, axiom,
    ((![X4 : produc335961278on_val, Z2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Z2) @ (transi325225921on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Y3) @ R) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z2) @ (transi325225921on_val @ R))))))))))))). % converse_rtranclE
thf(fact_87_rtrancl_Oinducts, axiom,
    ((![X12 : produc1097884484on_val, X22 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X12 @ X22) @ (transi111096263on_val @ R)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C2) @ R) => (P @ A @ C2))))) => (P @ X12 @ X22))))))). % rtrancl.inducts
thf(fact_88_rtrancl_Oinducts, axiom,
    ((![X12 : produc335961278on_val, X22 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X12 @ X22) @ (transi325225921on_val @ R)) => ((![A : produc335961278on_val]: (P @ A @ A)) => ((![A : produc335961278on_val, B : produc335961278on_val, C2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R)) => ((P @ A @ B) => ((member1689761872on_val @ (produc245869591on_val @ B @ C2) @ R) => (P @ A @ C2))))) => (P @ X12 @ X22))))))). % rtrancl.inducts
thf(fact_89_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_90_rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((P @ A2) => ((![Y3 : produc335961278on_val, Z : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_91_rtrancl__trans, axiom,
    ((![X4 : produc1097884484on_val, Y2 : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y2 @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_92_rtrancl__trans, axiom,
    ((![X4 : produc335961278on_val, Y2 : produc335961278on_val, R : set_Pr208351751on_val, Z2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X4 @ Y2) @ (transi325225921on_val @ R)) => ((member1689761872on_val @ (produc245869591on_val @ Y2 @ Z2) @ (transi325225921on_val @ R)) => (member1689761872on_val @ (produc245869591on_val @ X4 @ Z2) @ (transi325225921on_val @ R))))))). % rtrancl_trans
thf(fact_93_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_94_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_95_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_96_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X : produc655058983on_val]: (member1689761872on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_97_Collect__cong, axiom,
    ((![P : produc655058983on_val > $o, Q : produc655058983on_val > $o]: ((![X5 : produc655058983on_val]: ((P @ X5) = (Q @ X5))) => ((collec105960082on_val @ P) = (collec105960082on_val @ Q)))))). % Collect_cong
thf(fact_98_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C4 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C4)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C4) @ R)))))))))))))))). % rtrancl.simps
thf(fact_99_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R)) = (((?[A5 : produc335961278on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C4 : produc335961278on_val]: (((A1 = A5)) & ((((A22 = C4)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C4) @ R)))))))))))))))). % rtrancl.simps
thf(fact_100_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_101_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_102_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_103_rtranclE, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y3) @ (transi325225921on_val @ R)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_104_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E4 @ H3 @ L3 @ E4 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_1 @ H_1 @ L_1 @ E5 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E5 @ H4 @ L4)))) => (R2 @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_105_ty_Oinject, axiom,
    ((![X52 : list_char, Y5 : list_char]: (((class @ X52) = (class @ Y5)) = (X52 = Y5))))). % ty.inject
thf(fact_106_pred__equals__eq2, axiom,
    ((![R2 : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X @ Y) @ R2))) = (^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X @ Y) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_107_pred__equals__eq2, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R2))) = (^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_108_pred__equals__eq2, axiom,
    ((![R2 : set_Pr2063914181t_char, S : set_Pr2063914181t_char]: (((^[X : list_list_char]: (^[Y : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X @ Y) @ R2))) = (^[X : list_list_char]: (^[Y : exp_list_char]: (member605104934t_char @ (produc713467969t_char @ X @ Y) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_109_pred__equals__eq2, axiom,
    ((![R2 : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X @ Y) @ R2))) = (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X @ Y) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_110_pred__equals__eq2, axiom,
    ((![R2 : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R2))) = (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_111_pred__equals__eq2, axiom,
    ((![R2 : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ R2))) = (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_112_same__fstI, axiom,
    ((![P : list_list_char > $o, X4 : list_list_char, Y4 : exp_list_char, Y2 : exp_list_char, R2 : list_list_char > set_Pr224372167t_char]: ((P @ X4) => ((member1699993616t_char @ (produc240508503t_char @ Y4 @ Y2) @ (R2 @ X4)) => (member1392938152t_char @ (produc618657463t_char @ (produc713467969t_char @ X4 @ Y4) @ (produc713467969t_char @ X4 @ Y2)) @ (same_f605082028t_char @ P @ R2))))))). % same_fstI
thf(fact_113_same__fstI, axiom,
    ((![P : list_exp_list_char > $o, X4 : list_exp_list_char, Y4 : produc515445032on_val, Y2 : produc515445032on_val, R2 : list_exp_list_char > set_Pr148564103on_val]: ((P @ X4) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y2) @ (R2 @ X4)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X4 @ Y4) @ (produc1725134254on_val @ X4 @ Y2)) @ (same_f1555812995on_val @ P @ R2))))))). % same_fstI
thf(fact_114_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X4 : nat > option2118145160on_val, Y4 : list_char > option_val, Y2 : list_char > option_val, R2 : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X4) => ((member1177709994on_val @ (produc746553401on_val @ Y4 @ Y2) @ (R2 @ X4)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X4 @ Y4) @ (produc52622304on_val @ X4 @ Y2)) @ (same_f1752972725on_val @ P @ R2))))))). % same_fstI
thf(fact_115_same__fstI, axiom,
    ((![P : exp_list_char > $o, X4 : exp_list_char, Y4 : produc515445032on_val, Y2 : produc515445032on_val, R2 : exp_list_char > set_Pr148564103on_val]: ((P @ X4) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y2) @ (R2 @ X4)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X4 @ Y4) @ (produc2023458740on_val @ X4 @ Y2)) @ (same_f366220041on_val @ P @ R2))))))). % same_fstI
thf(fact_116_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val, Y4 : produc1097884484on_val, Y2 : produc1097884484on_val, R2 : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X4) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Y2) @ (R2 @ X4)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X4 @ Y4) @ (produc1069526295on_val @ X4 @ Y2)) @ (same_f962657004on_val @ P @ R2))))))). % same_fstI
thf(fact_117_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_118_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_119_red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_120_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt @ P @ H2 @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction2
thf(fact_121_conf__hext, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, P : list_P1234162913t_char, V : val, T : ty]: ((hext @ H @ H2) => ((conf_P93989998t_char @ P @ H @ V @ T) => (conf_P93989998t_char @ P @ H2 @ V @ T)))))). % conf_hext
thf(fact_122_Red__preserves__type, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => (?[T2 : ty]: ((widen_917054840t_char @ P @ T2 @ T) & (wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2)))))))))). % Red_preserves_type
thf(fact_123_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_124_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => (?[T2 : ty]: ((wTrt @ P @ (hp @ S3) @ E3 @ E2 @ T2) & (widen_917054840t_char @ P @ T2 @ T)))))))))). % subject_reduction
thf(fact_125_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3)))))))). % Red_preserves_sconf
thf(fact_126_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_127_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_128_wf__config__def, axiom,
    ((typeSa1969945757config = (^[P3 : list_P1234162913t_char]: (^[E6 : list_char > option_ty]: (^[S4 : produc515445032on_val]: (^[E7 : exp_list_char]: (^[T4 : ty]: (((typeSa1777264139_sconf @ P3 @ E6 @ S4)) & ((wTrt @ P3 @ (hp @ S4) @ E6 @ E7 @ T4))))))))))). % wf_config_def
thf(fact_129_red__preserves__sconf, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E3 @ E @ T) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3))))))). % red_preserves_sconf
thf(fact_130_red__preserves__hconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_131_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E3 @ E @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E3 @ E @ T)))))). % WTrt_hext_mono
thf(fact_132_red__preserves__lconf, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E3 : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E3 @ E @ T) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % red_preserves_lconf
thf(fact_133_subjects__reduction, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, E3 : list_char > option_ty, Ts : list_ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => ((wTrts @ P @ (hp @ S2) @ E3 @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ P @ (hp @ S3) @ E3 @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction
thf(fact_134_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, E3 : 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 @ E3 @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_135_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, E3 : 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 @ E3 @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E3) => (lconf_485928294t_char @ P @ H2 @ L2 @ E3))))))). % reds_preserves_lconf
thf(fact_136_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts @ P @ H @ E3 @ Es @ Ts) => ((hext @ H @ H2) => (wTrts @ P @ H2 @ E3 @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_137_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E3 : 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) @ E3 @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E3 @ S2) => (typeSa1777264139_sconf @ P @ E3 @ S3))))))). % reds_preserves_sconf
thf(fact_138_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E3) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E3)))))). % lconf_hext
thf(fact_139_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_140_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, E3 : 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 @ E3 @ (produc52622304on_val @ H @ L)) => ((wTrts @ P @ H @ E3 @ Es @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ P @ H2 @ E3 @ Es2 @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts2 @ Ts)))))))))). % subjects_reduction2
thf(fact_141_redsp__reds__eq, axiom,
    ((redsp = (^[P3 : list_P1234162913t_char]: (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (^[Z3 : list_exp_list_char]: (^[Aa2 : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X @ Y) @ (produc1725134254on_val @ Z3 @ Aa2)) @ (reds @ P3)))))))))). % redsp_reds_eq
thf(fact_142_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_143_ListReds1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_144_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P3 : list_P1234162913t_char]: (^[E6 : list_char > option_ty]: (produc99536995_val_o @ (^[H6 : nat > option2118145160on_val]: (^[L5 : list_char > option_val]: (((hconf_1244167010t_char @ P3 @ H6)) & ((lconf_485928294t_char @ P3 @ H6 @ L5 @ E6))))))))))). % sconf_def
thf(fact_145_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_146_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_147_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_148_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_149_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_150_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_151_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_152_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_153_case__prodI, axiom,
    ((![F : list_list_char > exp_list_char > $o, A2 : list_list_char, B2 : exp_list_char]: ((F @ A2 @ B2) => (produc1163547050char_o @ F @ (produc713467969t_char @ A2 @ B2)))))). % case_prodI
thf(fact_154_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_155_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_156_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_157_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_158_case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, C3 : produc1097884484on_val > produc1097884484on_val > $o]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A @ B)) => (C3 @ A @ B))) => (produc50362220_val_o @ C3 @ P2))))). % case_prodI2
thf(fact_159_case__prodI2, axiom,
    ((![P2 : produc1294284815t_char, C3 : list_list_char > exp_list_char > $o]: ((![A : list_list_char, B : exp_list_char]: ((P2 = (produc713467969t_char @ A @ B)) => (C3 @ A @ B))) => (produc1163547050char_o @ C3 @ P2))))). % case_prodI2
thf(fact_160_case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, C3 : exp_list_char > produc515445032on_val > $o]: ((![A : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A @ B)) => (C3 @ A @ B))) => (produc199145871_val_o @ C3 @ P2))))). % case_prodI2
thf(fact_161_case__prodI2, axiom,
    ((![P2 : produc515445032on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A @ B)) => (C3 @ A @ B))) => (produc99536995_val_o @ C3 @ P2))))). % case_prodI2
thf(fact_162_case__prodI2, axiom,
    ((![P2 : produc655058983on_val, C3 : produc335961278on_val > produc335961278on_val > $o]: ((![A : produc335961278on_val, B : produc335961278on_val]: ((P2 = (produc245869591on_val @ A @ B)) => (C3 @ A @ B))) => (produc525028460_val_o @ C3 @ P2))))). % case_prodI2
thf(fact_163_case__prodI2, axiom,
    ((![P2 : produc335961278on_val, C3 : list_exp_list_char > produc515445032on_val > $o]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A @ B)) => (C3 @ A @ B))) => (produc1125182229_val_o @ C3 @ P2))))). % case_prodI2
thf(fact_164_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_165_case__prodD, axiom,
    ((![F : list_list_char > exp_list_char > $o, A2 : list_list_char, B2 : exp_list_char]: ((produc1163547050char_o @ F @ (produc713467969t_char @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_166_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_167_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_168_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_169_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_170_case__prodE, axiom,
    ((![C3 : produc1097884484on_val > produc1097884484on_val > $o, P2 : produc1172664615on_val]: ((produc50362220_val_o @ C3 @ P2) => (~ ((![X5 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3))))))))))). % case_prodE
thf(fact_171_case__prodE, axiom,
    ((![C3 : list_list_char > exp_list_char > $o, P2 : produc1294284815t_char]: ((produc1163547050char_o @ C3 @ P2) => (~ ((![X5 : list_list_char, Y3 : exp_list_char]: ((P2 = (produc713467969t_char @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3))))))))))). % case_prodE
thf(fact_172_case__prodE, axiom,
    ((![C3 : exp_list_char > produc515445032on_val > $o, P2 : produc1097884484on_val]: ((produc199145871_val_o @ C3 @ P2) => (~ ((![X5 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3))))))))))). % case_prodE
thf(fact_173_case__prodE, axiom,
    ((![C3 : (nat > option2118145160on_val) > (list_char > option_val) > $o, P2 : produc515445032on_val]: ((produc99536995_val_o @ C3 @ P2) => (~ ((![X5 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3))))))))))). % case_prodE
thf(fact_174_case__prodE, axiom,
    ((![C3 : produc335961278on_val > produc335961278on_val > $o, P2 : produc655058983on_val]: ((produc525028460_val_o @ C3 @ P2) => (~ ((![X5 : produc335961278on_val, Y3 : produc335961278on_val]: ((P2 = (produc245869591on_val @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3))))))))))). % case_prodE
thf(fact_175_case__prodE, axiom,
    ((![C3 : list_exp_list_char > produc515445032on_val > $o, P2 : produc335961278on_val]: ((produc1125182229_val_o @ C3 @ P2) => (~ ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3))))))))))). % case_prodE
thf(fact_176_old_Oprod_Ocase, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, X12 : nat > option2118145160on_val, X22 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ X12 @ X22)) = (F @ X12 @ X22))))). % old.prod.case
thf(fact_177_old_Oprod_Ocase, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, X12 : produc335961278on_val, X22 : produc335961278on_val]: ((produc525028460_val_o @ F @ (produc245869591on_val @ X12 @ X22)) = (F @ X12 @ X22))))). % old.prod.case
thf(fact_178_old_Oprod_Ocase, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X12 : list_exp_list_char, X22 : produc515445032on_val]: ((produc58203522_val_o @ F @ (produc1725134254on_val @ X12 @ X22)) = (F @ X12 @ X22))))). % old.prod.case
thf(fact_179_old_Oprod_Ocase, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, X12 : list_exp_list_char, X22 : produc515445032on_val]: ((produc1125182229_val_o @ F @ (produc1725134254on_val @ X12 @ X22)) = (F @ X12 @ X22))))). % old.prod.case
thf(fact_180_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_181_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_182_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_183_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 @ (^[X1 : nat > option2118145160on_val]: (^[X2 : list_char > option_val]: (H @ (F @ X1 @ X2)))) @ Prod))))). % prod.case_distrib
thf(fact_184_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 @ (^[X1 : produc335961278on_val]: (^[X2 : produc335961278on_val]: (H @ (F @ X1 @ X2)))) @ Prod))))). % prod.case_distrib
thf(fact_185_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 @ (^[X1 : list_exp_list_char]: (^[X2 : produc515445032on_val]: (H @ (F @ X1 @ X2)))) @ Prod))))). % prod.case_distrib
thf(fact_186_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 @ (^[X1 : list_exp_list_char]: (^[X2 : produc515445032on_val]: (H @ (F @ X1 @ X2)))) @ Prod))))). % prod.case_distrib
thf(fact_187_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 @ (^[X1 : list_exp_list_char]: (^[X2 : produc515445032on_val]: (H @ (F @ X1 @ X2)))) @ Prod))))). % prod.case_distrib
thf(fact_188_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 @ (^[X1 : list_exp_list_char]: (^[X2 : produc515445032on_val]: (H @ (F @ X1 @ X2)))) @ Prod))))). % prod.case_distrib
thf(fact_189_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z2 : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z2)) => (~ ((![X5 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((Z2 = (produc52622304on_val @ X5 @ Y3)) => (~ ((Q @ (P @ X5 @ Y3)))))))))))). % case_prodE2
thf(fact_190_case__prodE2, axiom,
    ((![Q : $o > $o, P : produc335961278on_val > produc335961278on_val > $o, Z2 : produc655058983on_val]: ((Q @ (produc525028460_val_o @ P @ Z2)) => (~ ((![X5 : produc335961278on_val, Y3 : produc335961278on_val]: ((Z2 = (produc245869591on_val @ X5 @ Y3)) => (~ ((Q @ (P @ X5 @ Y3)))))))))))). % case_prodE2
thf(fact_191_case__prodE2, axiom,
    ((![Q : (produc335961278on_val > $o) > $o, P : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, Z2 : produc335961278on_val]: ((Q @ (produc58203522_val_o @ P @ Z2)) => (~ ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((Z2 = (produc1725134254on_val @ X5 @ Y3)) => (~ ((Q @ (P @ X5 @ Y3)))))))))))). % case_prodE2
thf(fact_192_case__prodE2, axiom,
    ((![Q : $o > $o, P : list_exp_list_char > produc515445032on_val > $o, Z2 : produc335961278on_val]: ((Q @ (produc1125182229_val_o @ P @ Z2)) => (~ ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((Z2 = (produc1725134254on_val @ X5 @ Y3)) => (~ ((Q @ (P @ X5 @ Y3)))))))))))). % case_prodE2
thf(fact_193_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (F @ (produc52622304on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_194_case__prod__eta, axiom,
    ((![F : produc655058983on_val > $o]: ((produc525028460_val_o @ (^[X : produc335961278on_val]: (^[Y : produc335961278on_val]: (F @ (produc245869591on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_195_case__prod__eta, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o]: ((produc58203522_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (F @ (produc1725134254on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_196_case__prod__eta, axiom,
    ((![F : produc335961278on_val > $o]: ((produc1125182229_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (F @ (produc1725134254on_val @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_197_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X5 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((F @ X5 @ Y3) = (G @ (produc52622304on_val @ X5 @ Y3)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_198_cond__case__prod__eta, axiom,
    ((![F : produc335961278on_val > produc335961278on_val > $o, G : produc655058983on_val > $o]: ((![X5 : produc335961278on_val, Y3 : produc335961278on_val]: ((F @ X5 @ Y3) = (G @ (produc245869591on_val @ X5 @ Y3)))) => ((produc525028460_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_199_cond__case__prod__eta, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, G : produc335961278on_val > produc335961278on_val > $o]: ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((F @ X5 @ Y3) = (G @ (produc1725134254on_val @ X5 @ Y3)))) => ((produc58203522_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_200_cond__case__prod__eta, axiom,
    ((![F : list_exp_list_char > produc515445032on_val > $o, G : produc335961278on_val > $o]: ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((F @ X5 @ Y3) = (G @ (produc1725134254on_val @ X5 @ Y3)))) => ((produc1125182229_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_201_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_202_internal__case__prod__def, axiom,
    ((produc463114774_val_o = produc525028460_val_o))). % internal_case_prod_def
thf(fact_203_internal__case__prod__def, axiom,
    ((produc1326103384_val_o = produc58203522_val_o))). % internal_case_prod_def
thf(fact_204_internal__case__prod__def, axiom,
    ((produc1075415231_val_o = produc1125182229_val_o))). % internal_case_prod_def
thf(fact_205_ListRedsVal, axiom,
    ((![E : 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 @ E @ 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 @ E @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_206_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, S5 : produc515445032on_val, E5 : exp_list_char, S6 : produc515445032on_val, Es3 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E4 @ Es3)) => ((A22 = S5) => ((A32 = (cons_exp_list_char @ E5 @ Es3)) => ((A42 = S6) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E4 @ S5) @ (produc2023458740on_val @ E5 @ S6)) @ (red @ P))))))))) => (~ ((![Es3 : list_exp_list_char, S5 : produc515445032on_val, Es4 : list_exp_list_char, S6 : produc515445032on_val, V2 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3)) => ((A22 = S5) => ((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4)) => ((A42 = S6) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S5) @ (produc1725134254on_val @ Es4 @ S6)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_207_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)) = (((?[E7 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E8 : exp_list_char]: (?[S7 : produc515445032on_val]: (?[Es5 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E7 @ Es5))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ E8 @ Es5))) & ((((A42 = S7)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E7 @ S4) @ (produc2023458740on_val @ E8 @ S7)) @ (red @ P)))))))))))))))) | ((?[Es5 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es6 : list_exp_list_char]: (?[S7 : produc515445032on_val]: (?[V3 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6))) & ((((A42 = S7)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S4) @ (produc1725134254on_val @ Es6 @ S7)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_208_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z2 : produc1172664615on_val, C3 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A @ B)) => (member354538064on_val @ Z2 @ (C3 @ A @ B)))) => (member354538064on_val @ Z2 @ (produc493625819on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_209_mem__case__prodI2, axiom,
    ((![P2 : produc1172664615on_val, Z2 : produc655058983on_val, C3 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ A @ B)) => (member1689761872on_val @ Z2 @ (C3 @ A @ B)))) => (member1689761872on_val @ Z2 @ (produc1067722715on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_210_mem__case__prodI2, axiom,
    ((![P2 : produc1294284815t_char, Z2 : produc1172664615on_val, C3 : list_list_char > exp_list_char > set_Pr1189492743on_val]: ((![A : list_list_char, B : exp_list_char]: ((P2 = (produc713467969t_char @ A @ B)) => (member354538064on_val @ Z2 @ (C3 @ A @ B)))) => (member354538064on_val @ Z2 @ (produc1123062041on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_211_mem__case__prodI2, axiom,
    ((![P2 : produc1294284815t_char, Z2 : produc655058983on_val, C3 : list_list_char > exp_list_char > set_Pr208351751on_val]: ((![A : list_list_char, B : exp_list_char]: ((P2 = (produc713467969t_char @ A @ B)) => (member1689761872on_val @ Z2 @ (C3 @ A @ B)))) => (member1689761872on_val @ Z2 @ (produc399550745on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_212_mem__case__prodI2, axiom,
    ((![P2 : produc335961278on_val, Z2 : produc1172664615on_val, C3 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A @ B)) => (member354538064on_val @ Z2 @ (C3 @ A @ B)))) => (member354538064on_val @ Z2 @ (produc379229956on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_213_mem__case__prodI2, axiom,
    ((![P2 : produc335961278on_val, Z2 : produc655058983on_val, C3 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: ((P2 = (produc1725134254on_val @ A @ B)) => (member1689761872on_val @ Z2 @ (C3 @ A @ B)))) => (member1689761872on_val @ Z2 @ (produc1745783812on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_214_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z2 : produc1172664615on_val, C3 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A @ B)) => (member354538064on_val @ Z2 @ (C3 @ A @ B)))) => (member354538064on_val @ Z2 @ (produc848217214on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_215_mem__case__prodI2, axiom,
    ((![P2 : produc1097884484on_val, Z2 : produc655058983on_val, C3 : exp_list_char > produc515445032on_val > set_Pr208351751on_val]: ((![A : exp_list_char, B : produc515445032on_val]: ((P2 = (produc2023458740on_val @ A @ B)) => (member1689761872on_val @ Z2 @ (C3 @ A @ B)))) => (member1689761872on_val @ Z2 @ (produc356855678on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_216_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z2 : produc1172664615on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A @ B)) => (member354538064on_val @ Z2 @ (C3 @ A @ B)))) => (member354538064on_val @ Z2 @ (produc1919805778on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_217_mem__case__prodI2, axiom,
    ((![P2 : produc515445032on_val, Z2 : produc655058983on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((P2 = (produc52622304on_val @ A @ B)) => (member1689761872on_val @ Z2 @ (C3 @ A @ B)))) => (member1689761872on_val @ Z2 @ (produc98852946on_val @ C3 @ P2)))))). % mem_case_prodI2
thf(fact_218_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C3 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((member354538064on_val @ Z2 @ (C3 @ A2 @ B2)) => (member354538064on_val @ Z2 @ (produc493625819on_val @ C3 @ (produc1069526295on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_219_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C3 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((member1689761872on_val @ Z2 @ (C3 @ A2 @ B2)) => (member1689761872on_val @ Z2 @ (produc1067722715on_val @ C3 @ (produc1069526295on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_220_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C3 : list_list_char > exp_list_char > set_Pr1189492743on_val, A2 : list_list_char, B2 : exp_list_char]: ((member354538064on_val @ Z2 @ (C3 @ A2 @ B2)) => (member354538064on_val @ Z2 @ (produc1123062041on_val @ C3 @ (produc713467969t_char @ A2 @ B2))))))). % mem_case_prodI
thf(fact_221_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C3 : list_list_char > exp_list_char > set_Pr208351751on_val, A2 : list_list_char, B2 : exp_list_char]: ((member1689761872on_val @ Z2 @ (C3 @ A2 @ B2)) => (member1689761872on_val @ Z2 @ (produc399550745on_val @ C3 @ (produc713467969t_char @ A2 @ B2))))))). % mem_case_prodI
thf(fact_222_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C3 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z2 @ (C3 @ A2 @ B2)) => (member354538064on_val @ Z2 @ (produc379229956on_val @ C3 @ (produc1725134254on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_223_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C3 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, A2 : list_exp_list_char, B2 : produc515445032on_val]: ((member1689761872on_val @ Z2 @ (C3 @ A2 @ B2)) => (member1689761872on_val @ Z2 @ (produc1745783812on_val @ C3 @ (produc1725134254on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_224_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C3 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, A2 : exp_list_char, B2 : produc515445032on_val]: ((member354538064on_val @ Z2 @ (C3 @ A2 @ B2)) => (member354538064on_val @ Z2 @ (produc848217214on_val @ C3 @ (produc2023458740on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_225_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C3 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, A2 : exp_list_char, B2 : produc515445032on_val]: ((member1689761872on_val @ Z2 @ (C3 @ A2 @ B2)) => (member1689761872on_val @ Z2 @ (produc356855678on_val @ C3 @ (produc2023458740on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_226_mem__case__prodI, axiom,
    ((![Z2 : produc1172664615on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((member354538064on_val @ Z2 @ (C3 @ A2 @ B2)) => (member354538064on_val @ Z2 @ (produc1919805778on_val @ C3 @ (produc52622304on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_227_mem__case__prodI, axiom,
    ((![Z2 : produc655058983on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((member1689761872on_val @ Z2 @ (C3 @ A2 @ B2)) => (member1689761872on_val @ Z2 @ (produc98852946on_val @ C3 @ (produc52622304on_val @ A2 @ B2))))))). % mem_case_prodI
thf(fact_228_case__prodI2_H, axiom,
    ((![P2 : produc335961278on_val, C3 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, X4 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (((produc1725134254on_val @ A @ B) = P2) => (C3 @ A @ B @ X4))) => (produc58203522_val_o @ C3 @ P2 @ X4))))). % case_prodI2'
thf(fact_229_reds__def, axiom,
    ((reds = (^[P3 : list_P1234162913t_char]: (collec105960082on_val @ (produc525028460_val_o @ (produc58203522_val_o @ (^[X : list_exp_list_char]: (^[Y : produc515445032on_val]: (produc1125182229_val_o @ (redsp @ P3 @ X @ Y))))))))))). % reds_def
thf(fact_230_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C3 : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val, P2 : produc1172664615on_val]: ((member354538064on_val @ Z2 @ (produc493625819on_val @ C3 @ P2)) => (~ ((![X5 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X5 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_231_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C3 : produc1097884484on_val > produc1097884484on_val > set_Pr208351751on_val, P2 : produc1172664615on_val]: ((member1689761872on_val @ Z2 @ (produc1067722715on_val @ C3 @ P2)) => (~ ((![X5 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P2 = (produc1069526295on_val @ X5 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_232_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C3 : list_list_char > exp_list_char > set_Pr1189492743on_val, P2 : produc1294284815t_char]: ((member354538064on_val @ Z2 @ (produc1123062041on_val @ C3 @ P2)) => (~ ((![X5 : list_list_char, Y3 : exp_list_char]: ((P2 = (produc713467969t_char @ X5 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_233_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C3 : list_list_char > exp_list_char > set_Pr208351751on_val, P2 : produc1294284815t_char]: ((member1689761872on_val @ Z2 @ (produc399550745on_val @ C3 @ P2)) => (~ ((![X5 : list_list_char, Y3 : exp_list_char]: ((P2 = (produc713467969t_char @ X5 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_234_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C3 : list_exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc335961278on_val]: ((member354538064on_val @ Z2 @ (produc379229956on_val @ C3 @ P2)) => (~ ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X5 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_235_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C3 : list_exp_list_char > produc515445032on_val > set_Pr208351751on_val, P2 : produc335961278on_val]: ((member1689761872on_val @ Z2 @ (produc1745783812on_val @ C3 @ P2)) => (~ ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X5 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_236_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C3 : exp_list_char > produc515445032on_val > set_Pr1189492743on_val, P2 : produc1097884484on_val]: ((member354538064on_val @ Z2 @ (produc848217214on_val @ C3 @ P2)) => (~ ((![X5 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X5 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_237_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C3 : exp_list_char > produc515445032on_val > set_Pr208351751on_val, P2 : produc1097884484on_val]: ((member1689761872on_val @ Z2 @ (produc356855678on_val @ C3 @ P2)) => (~ ((![X5 : exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc2023458740on_val @ X5 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_238_mem__case__prodE, axiom,
    ((![Z2 : produc1172664615on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val, P2 : produc515445032on_val]: ((member354538064on_val @ Z2 @ (produc1919805778on_val @ C3 @ P2)) => (~ ((![X5 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X5 @ Y3)) => (~ ((member354538064on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_239_mem__case__prodE, axiom,
    ((![Z2 : produc655058983on_val, C3 : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr208351751on_val, P2 : produc515445032on_val]: ((member1689761872on_val @ Z2 @ (produc98852946on_val @ C3 @ P2)) => (~ ((![X5 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P2 = (produc52622304on_val @ X5 @ Y3)) => (~ ((member1689761872on_val @ Z2 @ (C3 @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_240_case__prodE_H, axiom,
    ((![C3 : list_exp_list_char > produc515445032on_val > produc335961278on_val > $o, P2 : produc335961278on_val, Z2 : produc335961278on_val]: ((produc58203522_val_o @ C3 @ P2 @ Z2) => (~ ((![X5 : list_exp_list_char, Y3 : produc515445032on_val]: ((P2 = (produc1725134254on_val @ X5 @ Y3)) => (~ ((C3 @ X5 @ Y3 @ Z2))))))))))). % case_prodE'
thf(fact_241_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_242_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_243_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_244_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_245_red__reds_OCallObj, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_246_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E3 @ E @ T) => ((wTrts @ P @ H @ E3 @ Es @ Ts) => (wTrts @ P @ H @ E3 @ (cons_exp_list_char @ E @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_247_CallRedsObj, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_248_WTrtCall, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E3 : list_char > option_ty, E : exp_list_char, C : list_char, M : list_char, Ts : list_ty, T : ty, Pns : list_list_char, Body : exp_list_char, D3 : list_char, Es : list_exp_list_char, Ts3 : list_ty]: ((wTrt @ P @ H @ E3 @ E @ (class @ C)) => ((method297381284t_char @ P @ C @ M @ Ts @ T @ (produc713467969t_char @ Pns @ Body) @ D3) => ((wTrts @ P @ H @ E3 @ Es @ Ts3) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts3 @ Ts) => (wTrt @ P @ H @ E3 @ (call_list_char @ E @ M @ Es) @ T)))))))). % WTrtCall

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T5 : ty]: ((typeSa1969945757config @ p @ e @ s2 @ e3 @ T5) & (widen_917054840t_char @ p @ T5 @ t))))).
