% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_42__5332224_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:18:55.726

% Could-be-implicit typings (27)
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% Explicit typings (71)
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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_C____, type,
    c : list_char).
thf(sy_v_D____, type,
    d : list_char).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_F____, type,
    f : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_TF____, type,
    tf : ty).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_Tv____, type,
    tv : ty).
thf(sy_v_a____, type,
    a : nat).
thf(sy_v_fs____, type,
    fs : produc1257910179t_char > option_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_v____, type,
    v : val).

% Relevant facts (234)
thf(fact_0_sub, axiom,
    ((widen_917054840t_char @ p @ tv @ tf))). % sub
thf(fact_1_typeofv, axiom,
    (((typeof_h @ ha @ v) = (some_ty @ tv)))). % typeofv
thf(fact_2_hconf, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % hconf
thf(fact_3_has, axiom,
    ((has_fi599584195t_char @ p @ c @ f @ tf @ d))). % has
thf(fact_4_RedFAss_Oprems_I2_J, axiom,
    ((hconf_1244167010t_char @ p @ ha))). % RedFAss.prems(2)
thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062TF_ATv_O_A_092_060lbrakk_062typeof_092_060_094bsub_062h_092_060_094esub_062_Av_A_061_A_092_060lfloor_062Tv_092_060rfloor_062_059_AP_A_092_060turnstile_062_AC_Ahas_AF_058TF_Ain_AD_059_AP_A_092_060turnstile_062_ATv_A_092_060le_062_ATF_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![TF : ty, Tv : ty]: (((typeof_h @ ha @ v) = (some_ty @ Tv)) => ((has_fi599584195t_char @ p @ c @ f @ TF @ d) => (~ ((widen_917054840t_char @ p @ Tv @ TF)))))))))). % \<open>\<And>thesis. (\<And>TF Tv. \<lbrakk>typeof\<^bsub>h\<^esub> v = \<lfloor>Tv\<rfloor>; P \<turnstile> C has F:TF in D; P \<turnstile> Tv \<le> TF\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T2 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T2) => (conf_P93989998t_char @ P @ H @ V @ T2)))))). % conf_widen
thf(fact_7__092_060open_062P_Mh_A_092_060turnstile_062_A_IC_M_Afs_J_A_092_060surd_062_092_060close_062, axiom,
    ((oconf_454120169t_char @ p @ ha @ (produc904988266on_val @ c @ fs)))). % \<open>P,h \<turnstile> (C, fs) \<surd>\<close>
thf(fact_8_typeof__conf, axiom,
    ((![H : nat > option2118145160on_val, V : val, T : ty, P : list_P1234162913t_char]: (((typeof_h @ H @ V) = (some_ty @ T)) => (conf_P93989998t_char @ P @ H @ V @ T))))). % typeof_conf
thf(fact_9_defval__conf, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, T : ty]: (conf_P93989998t_char @ P @ H @ (default_val @ T) @ T)))). % defval_conf
thf(fact_10_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[V2 : val]: (^[T3 : ty]: (?[T4 : ty]: ((((typeof_h @ H2 @ V2) = (some_ty @ T4))) & ((widen_917054840t_char @ P2 @ T4 @ T3))))))))))). % conf_def
thf(fact_11_wt, axiom,
    ((wTrt @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % wt
thf(fact_12_conf__hext, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, P : list_P1234162913t_char, V : val, T : ty]: ((hext @ H @ H3) => ((conf_P93989998t_char @ P @ H @ V @ T) => (conf_P93989998t_char @ P @ H3 @ V @ T)))))). % conf_hext
thf(fact_13_ha, axiom,
    (((ha @ a) = (some_P1299442195on_val @ (produc904988266on_val @ c @ fs))))). % ha
thf(fact_14_RedFAss_Oprems_I1_J, axiom,
    ((wTrt @ p @ ha @ e @ (fAss_list_char @ (val_list_char @ (addr @ a)) @ f @ d @ (val_list_char @ v)) @ t))). % RedFAss.prems(1)
thf(fact_15_hconfD, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ Obj)) => (oconf_454120169t_char @ P @ H @ Obj)))))). % hconfD
thf(fact_16_oconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Obj : produc266837688on_val, H3 : nat > option2118145160on_val]: ((oconf_454120169t_char @ P @ H @ Obj) => ((hext @ H @ H3) => (oconf_454120169t_char @ P @ H3 @ Obj)))))). % oconf_hext
thf(fact_17_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V : val, T : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T)) => (wTrt @ P @ H @ E @ (val_list_char @ V) @ T))))). % WTrtVal
thf(fact_18_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, V : val, T : ty]: ((hext @ H @ H3) => (((typeof_h @ H @ V) = (some_ty @ T)) => ((typeof_h @ H3 @ V) = (some_ty @ T))))))). % hext_typeof_mono
thf(fact_19_hextI, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((![A2 : nat, C : list_char, Fs : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H3 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C @ Fs2)))))) => (hext @ H @ H3))))). % hextI
thf(fact_20_hext__def, axiom,
    ((hext = (^[H2 : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A3 : nat]: (![C2 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H2 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H4 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs4)))))))))))))). % hext_def
thf(fact_21_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val]: ((hext @ H @ H3) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs6))))))))). % hext_objD
thf(fact_22_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_23_exp_Oinject_I8_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((X84 = Y84))))))))))). % exp.inject(8)
thf(fact_24_val_Oinject_I3_J, axiom,
    ((![X5 : nat, Y5 : nat]: (((addr @ X5) = (addr @ Y5)) = (X5 = Y5))))). % val.inject(3)
thf(fact_25_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_26_option_Oinject, axiom,
    ((![X2 : ty, Y2 : ty]: (((some_ty @ X2) = (some_ty @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_27_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_28_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_29_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H3) => ((hext @ H3 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_30_exp_Odistinct_I63_J, axiom,
    ((![X3 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X3) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_31_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H3 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H3) => (wTrt @ P @ H3 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_32_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A4 @ B2)) = (((A = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_33_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A4 @ B2)) = (((A = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_34_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A4 @ B2)) = (((A = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_35_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A4 @ B2)) = (((A = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_36_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A4 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A4 @ B2)) = (((A = A4)) & ((B = B2))))))). % old.prod.inject
thf(fact_37_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_38_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_39_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_40_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_41_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : list_char, Y1 : list_char, Y2 : list_char]: (((produc1304532571t_char @ X1 @ X2) = (produc1304532571t_char @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_42_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P2 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (((![A3 : nat]: (![Obj2 : produc266837688on_val]: ((((H2 @ A3) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P2 @ H2 @ Obj2)))))) & ((preallocated @ H2)))))))). % hconf_def
thf(fact_43_the__Addr_Osimps, axiom,
    ((![A : nat]: ((the_Addr @ (addr @ A)) = A)))). % the_Addr.simps
thf(fact_44_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[L : list_char > option_val]: (^[E3 : list_char > option_ty]: (![V3 : list_char]: (![V2 : val]: ((((L @ V3) = (some_val @ V2))) => ((?[T3 : ty]: ((((E3 @ V3) = (some_ty @ T3))) & ((conf_P93989998t_char @ P2 @ H2 @ V2 @ T3))))))))))))))). % lconf_def
thf(fact_45_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X : list_char]: (^[Y : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y) @ R))) = (^[X : list_char]: (^[Y : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_46_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ R))) = (^[X : produc1097884484on_val]: (^[Y : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_47_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ R))) = (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_48_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ R))) = (^[X : nat > option2118145160on_val]: (^[Y : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_49_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X : list_char]: (^[Y : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y) @ R))) = (^[X : list_char]: (^[Y : list_char]: (member89690956t_char @ (produc1304532571t_char @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_50_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => ((oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C3 @ Fs7)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))))))))). % hconf_upd_obj
thf(fact_51_typeof__lit__conf, axiom,
    ((![V : val, T : ty, P : list_P1234162913t_char, H : nat > option2118145160on_val]: (((typeof_h @ (^[X : nat]: none_P1535574167on_val) @ V) = (some_ty @ T)) => (conf_P93989998t_char @ P @ H @ V @ T))))). % typeof_lit_conf
thf(fact_52_not__None__eq, axiom,
    ((![X4 : option_ty]: ((~ ((X4 = none_ty))) = (?[Y : ty]: (X4 = (some_ty @ Y))))))). % not_None_eq
thf(fact_53_not__None__eq, axiom,
    ((![X4 : option2118145160on_val]: ((~ ((X4 = none_P1535574167on_val))) = (?[Y : produc266837688on_val]: (X4 = (some_P1299442195on_val @ Y))))))). % not_None_eq
thf(fact_54_not__None__eq, axiom,
    ((![X4 : option_val]: ((~ ((X4 = none_val))) = (?[Y : val]: (X4 = (some_val @ Y))))))). % not_None_eq
thf(fact_55_not__Some__eq, axiom,
    ((![X4 : option_ty]: ((![Y : ty]: (~ ((X4 = (some_ty @ Y))))) = (X4 = none_ty))))). % not_Some_eq
thf(fact_56_not__Some__eq, axiom,
    ((![X4 : option2118145160on_val]: ((![Y : produc266837688on_val]: (~ ((X4 = (some_P1299442195on_val @ Y))))) = (X4 = none_P1535574167on_val))))). % not_Some_eq
thf(fact_57_not__Some__eq, axiom,
    ((![X4 : option_val]: ((![Y : val]: (~ ((X4 = (some_val @ Y))))) = (X4 = none_val))))). % not_Some_eq
thf(fact_58_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X4 : produc266837688on_val]: (((H @ A) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X4))))))). % hext_new
thf(fact_59_oconf__new, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Obj : produc266837688on_val, A : nat, X4 : produc266837688on_val]: ((oconf_454120169t_char @ P @ H @ Obj) => (((H @ A) = none_P1535574167on_val) => (oconf_454120169t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X4)) @ Obj)))))). % oconf_new
thf(fact_60_option_Odistinct_I1_J, axiom,
    ((![X2 : ty]: (~ ((none_ty = (some_ty @ X2))))))). % option.distinct(1)
thf(fact_61_option_Odistinct_I1_J, axiom,
    ((![X2 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X2))))))). % option.distinct(1)
thf(fact_62_option_Odistinct_I1_J, axiom,
    ((![X2 : val]: (~ ((none_val = (some_val @ X2))))))). % option.distinct(1)
thf(fact_63_option_OdiscI, axiom,
    ((![Option : option_ty, X2 : ty]: ((Option = (some_ty @ X2)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_64_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X2 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X2)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_65_option_OdiscI, axiom,
    ((![Option : option_val, X2 : val]: ((Option = (some_val @ X2)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_66_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_67_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_68_option_Oexhaust, axiom,
    ((![Y4 : option_ty]: ((~ ((Y4 = none_ty))) => (~ ((![X22 : ty]: (~ ((Y4 = (some_ty @ X22))))))))))). % option.exhaust
thf(fact_69_option_Oexhaust, axiom,
    ((![Y4 : option2118145160on_val]: ((~ ((Y4 = none_P1535574167on_val))) => (~ ((![X22 : produc266837688on_val]: (~ ((Y4 = (some_P1299442195on_val @ X22))))))))))). % option.exhaust
thf(fact_70_option_Oexhaust, axiom,
    ((![Y4 : option_val]: ((~ ((Y4 = none_val))) => (~ ((![X22 : val]: (~ ((Y4 = (some_val @ X22))))))))))). % option.exhaust
thf(fact_71_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X6 : ty]: (P @ (some_ty @ X6))) => (P @ Option)))))). % option.inducts
thf(fact_72_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X6 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X6))) => (P @ Option)))))). % option.inducts
thf(fact_73_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X6 : val]: (P @ (some_val @ X6))) => (P @ Option)))))). % option.inducts
thf(fact_74_split__option__ex, axiom,
    (((^[P3 : option_ty > $o]: (?[X7 : option_ty]: (P3 @ X7))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) | ((?[X : ty]: (P2 @ (some_ty @ X))))))))). % split_option_ex
thf(fact_75_split__option__ex, axiom,
    (((^[P3 : option2118145160on_val > $o]: (?[X7 : option2118145160on_val]: (P3 @ X7))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) | ((?[X : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X))))))))). % split_option_ex
thf(fact_76_split__option__ex, axiom,
    (((^[P3 : option_val > $o]: (?[X7 : option_val]: (P3 @ X7))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) | ((?[X : val]: (P2 @ (some_val @ X))))))))). % split_option_ex
thf(fact_77_split__option__all, axiom,
    (((^[P3 : option_ty > $o]: (![X7 : option_ty]: (P3 @ X7))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) & ((![X : ty]: (P2 @ (some_ty @ X))))))))). % split_option_all
thf(fact_78_split__option__all, axiom,
    (((^[P3 : option2118145160on_val > $o]: (![X7 : option2118145160on_val]: (P3 @ X7))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) & ((![X : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X))))))))). % split_option_all
thf(fact_79_split__option__all, axiom,
    (((^[P3 : option_val > $o]: (![X7 : option_val]: (P3 @ X7))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) & ((![X : val]: (P2 @ (some_val @ X))))))))). % split_option_all
thf(fact_80_combine__options__cases, axiom,
    ((![X4 : option_ty, P : option_ty > option_ty > $o, Y4 : option_ty]: (((X4 = none_ty) => (P @ X4 @ Y4)) => (((Y4 = none_ty) => (P @ X4 @ Y4)) => ((![A2 : ty, B3 : ty]: ((X4 = (some_ty @ A2)) => ((Y4 = (some_ty @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_81_combine__options__cases, axiom,
    ((![X4 : option_ty, P : option_ty > option2118145160on_val > $o, Y4 : option2118145160on_val]: (((X4 = none_ty) => (P @ X4 @ Y4)) => (((Y4 = none_P1535574167on_val) => (P @ X4 @ Y4)) => ((![A2 : ty, B3 : produc266837688on_val]: ((X4 = (some_ty @ A2)) => ((Y4 = (some_P1299442195on_val @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_82_combine__options__cases, axiom,
    ((![X4 : option_ty, P : option_ty > option_val > $o, Y4 : option_val]: (((X4 = none_ty) => (P @ X4 @ Y4)) => (((Y4 = none_val) => (P @ X4 @ Y4)) => ((![A2 : ty, B3 : val]: ((X4 = (some_ty @ A2)) => ((Y4 = (some_val @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_83_combine__options__cases, axiom,
    ((![X4 : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y4 : option_ty]: (((X4 = none_P1535574167on_val) => (P @ X4 @ Y4)) => (((Y4 = none_ty) => (P @ X4 @ Y4)) => ((![A2 : produc266837688on_val, B3 : ty]: ((X4 = (some_P1299442195on_val @ A2)) => ((Y4 = (some_ty @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_84_combine__options__cases, axiom,
    ((![X4 : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y4 : option2118145160on_val]: (((X4 = none_P1535574167on_val) => (P @ X4 @ Y4)) => (((Y4 = none_P1535574167on_val) => (P @ X4 @ Y4)) => ((![A2 : produc266837688on_val, B3 : produc266837688on_val]: ((X4 = (some_P1299442195on_val @ A2)) => ((Y4 = (some_P1299442195on_val @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_85_combine__options__cases, axiom,
    ((![X4 : option2118145160on_val, P : option2118145160on_val > option_val > $o, Y4 : option_val]: (((X4 = none_P1535574167on_val) => (P @ X4 @ Y4)) => (((Y4 = none_val) => (P @ X4 @ Y4)) => ((![A2 : produc266837688on_val, B3 : val]: ((X4 = (some_P1299442195on_val @ A2)) => ((Y4 = (some_val @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_86_combine__options__cases, axiom,
    ((![X4 : option_val, P : option_val > option_ty > $o, Y4 : option_ty]: (((X4 = none_val) => (P @ X4 @ Y4)) => (((Y4 = none_ty) => (P @ X4 @ Y4)) => ((![A2 : val, B3 : ty]: ((X4 = (some_val @ A2)) => ((Y4 = (some_ty @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_87_combine__options__cases, axiom,
    ((![X4 : option_val, P : option_val > option2118145160on_val > $o, Y4 : option2118145160on_val]: (((X4 = none_val) => (P @ X4 @ Y4)) => (((Y4 = none_P1535574167on_val) => (P @ X4 @ Y4)) => ((![A2 : val, B3 : produc266837688on_val]: ((X4 = (some_val @ A2)) => ((Y4 = (some_P1299442195on_val @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_88_combine__options__cases, axiom,
    ((![X4 : option_val, P : option_val > option_val > $o, Y4 : option_val]: (((X4 = none_val) => (P @ X4 @ Y4)) => (((Y4 = none_val) => (P @ X4 @ Y4)) => ((![A2 : val, B3 : val]: ((X4 = (some_val @ A2)) => ((Y4 = (some_val @ B3)) => (P @ X4 @ Y4)))) => (P @ X4 @ Y4))))))). % combine_options_cases
thf(fact_89_hconf__new, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, Obj : produc266837688on_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = none_P1535574167on_val) => ((oconf_454120169t_char @ P @ H @ Obj) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ Obj))))))))). % hconf_new
thf(fact_90_typeof__lit__typeof, axiom,
    ((![V : val, T : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X : nat]: none_P1535574167on_val) @ V) = (some_ty @ T)) => ((typeof_h @ H @ V) = (some_ty @ T)))))). % typeof_lit_typeof
thf(fact_91_conf__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, P : list_P1234162913t_char, Fs7 : produc1257910179t_char > option_val, X4 : val, T : ty]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => ((conf_P93989998t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7))) @ X4 @ T) = (conf_P93989998t_char @ P @ H @ X4 @ T)))))). % conf_upd_obj
thf(fact_92_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))))))). % hext_upd_obj
thf(fact_93_surj__pair, axiom,
    ((![P4 : produc266837688on_val]: (?[X6 : list_char, Y6 : produc1257910179t_char > option_val]: (P4 = (produc904988266on_val @ X6 @ Y6)))))). % surj_pair
thf(fact_94_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X6 : produc1097884484on_val, Y6 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X6 @ Y6)))))). % surj_pair
thf(fact_95_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X6 : exp_list_char, Y6 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X6 @ Y6)))))). % surj_pair
thf(fact_96_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X6 : nat > option2118145160on_val, Y6 : list_char > option_val]: (P4 = (produc52622304on_val @ X6 @ Y6)))))). % surj_pair
thf(fact_97_surj__pair, axiom,
    ((![P4 : produc1257910179t_char]: (?[X6 : list_char, Y6 : list_char]: (P4 = (produc1304532571t_char @ X6 @ Y6)))))). % surj_pair
thf(fact_98_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P4 : produc266837688on_val]: ((![A2 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_99_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P4 : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_100_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A2 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_101_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_102_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P4 : produc1257910179t_char]: ((![A2 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A2 @ B3))) => (P @ P4))))). % prod_cases
thf(fact_103_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A4 : list_char, B2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A4 @ B2)) => (~ (((A = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_104_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A4 : produc1097884484on_val, B2 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A4 @ B2)) => (~ (((A = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_105_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A4 : exp_list_char, B2 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A4 @ B2)) => (~ (((A = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_106_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A4 : nat > option2118145160on_val, B2 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A4 @ B2)) => (~ (((A = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_107_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A4 : list_char, B2 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A4 @ B2)) => (~ (((A = A4) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_108_prod__cases3, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (~ ((Y4 = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_109_prod__cases3, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (~ ((Y4 = (produc2023458740on_val @ A2 @ (produc52622304on_val @ B3 @ C4))))))))))). % prod_cases3
thf(fact_110_prod__cases4, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y4 = (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D)))))))))))). % prod_cases4
thf(fact_111_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B3 : exp_list_char, C4 : produc515445032on_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B3 @ C4)))) => (P @ X4))))). % prod_induct3
thf(fact_112_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A2 : exp_list_char, B3 : nat > option2118145160on_val, C4 : list_char > option_val]: (P @ (produc2023458740on_val @ A2 @ (produc52622304on_val @ B3 @ C4)))) => (P @ X4))))). % prod_induct3
thf(fact_113_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B3 : exp_list_char, C4 : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A2 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C4 @ D))))) => (P @ X4))))). % prod_induct4
thf(fact_114_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc266837688on_val]: (~ ((![A2 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y4 = (produc904988266on_val @ A2 @ B3)))))))))). % old.prod.exhaust
thf(fact_115_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A2 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y4 = (produc1069526295on_val @ A2 @ B3)))))))))). % old.prod.exhaust
thf(fact_116_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A2 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y4 = (produc2023458740on_val @ A2 @ B3)))))))))). % old.prod.exhaust
thf(fact_117_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc515445032on_val]: (~ ((![A2 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y4 = (produc52622304on_val @ A2 @ B3)))))))))). % old.prod.exhaust
thf(fact_118_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1257910179t_char]: (~ ((![A2 : list_char, B3 : list_char]: (~ ((Y4 = (produc1304532571t_char @ A2 @ B3)))))))))). % old.prod.exhaust
thf(fact_119_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A2 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A2 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_120_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A2 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A2 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_121_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A2 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A2 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_122_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A2 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A2 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_123_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A2 : list_char, B3 : list_char]: (P @ (produc1304532571t_char @ A2 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_124_oconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Obj : produc266837688on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: ((oconf_454120169t_char @ P @ H @ Obj) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (oconf_454120169t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7))) @ Obj)))))). % oconf_upd_obj
thf(fact_125_empty__upd__none, axiom,
    ((![X4 : produc1257910179t_char]: ((fun_up356838326on_val @ (^[X : produc1257910179t_char]: none_val) @ X4 @ none_val) = (^[X : produc1257910179t_char]: none_val))))). % empty_upd_none
thf(fact_126_empty__upd__none, axiom,
    ((![X4 : list_char]: ((fun_up1252458416on_val @ (^[X : list_char]: none_val) @ X4 @ none_val) = (^[X : list_char]: none_val))))). % empty_upd_none
thf(fact_127_empty__upd__none, axiom,
    ((![X4 : nat]: ((fun_up262443479on_val @ (^[X : nat]: none_P1535574167on_val) @ X4 @ none_P1535574167on_val) = (^[X : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_128_preallocated__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X4 : produc266837688on_val]: ((preallocated @ H) => (((H @ A) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X4)))))))). % preallocated_new
thf(fact_129_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7))))))))). % preallocated_upd_obj
thf(fact_130_map__upd__nonempty, axiom,
    ((![T5 : nat > option2118145160on_val, K : nat, X4 : produc266837688on_val]: (~ (((fun_up262443479on_val @ T5 @ K @ (some_P1299442195on_val @ X4)) = (^[X : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_131_map__upd__nonempty, axiom,
    ((![T5 : produc1257910179t_char > option_val, K : produc1257910179t_char, X4 : val]: (~ (((fun_up356838326on_val @ T5 @ K @ (some_val @ X4)) = (^[X : produc1257910179t_char]: none_val))))))). % map_upd_nonempty
thf(fact_132_map__upd__nonempty, axiom,
    ((![T5 : list_char > option_val, K : list_char, X4 : val]: (~ (((fun_up1252458416on_val @ T5 @ K @ (some_val @ X4)) = (^[X : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_133_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X4 : nat, Y4 : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X4 @ Y4) @ X4 @ Z) = (fun_up262443479on_val @ F @ X4 @ Z))))). % fun_upd_upd
thf(fact_134_fun__upd__upd, axiom,
    ((![F : produc1257910179t_char > option_val, X4 : produc1257910179t_char, Y4 : option_val, Z : option_val]: ((fun_up356838326on_val @ (fun_up356838326on_val @ F @ X4 @ Y4) @ X4 @ Z) = (fun_up356838326on_val @ F @ X4 @ Z))))). % fun_upd_upd
thf(fact_135_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X4 : list_char, Y4 : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X4 @ Y4) @ X4 @ Z) = (fun_up1252458416on_val @ F @ X4 @ Z))))). % fun_upd_upd
thf(fact_136_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X4 : nat]: ((fun_up262443479on_val @ F @ X4 @ (F @ X4)) = F)))). % fun_upd_triv
thf(fact_137_fun__upd__triv, axiom,
    ((![F : produc1257910179t_char > option_val, X4 : produc1257910179t_char]: ((fun_up356838326on_val @ F @ X4 @ (F @ X4)) = F)))). % fun_upd_triv
thf(fact_138_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X4 : list_char]: ((fun_up1252458416on_val @ F @ X4 @ (F @ X4)) = F)))). % fun_upd_triv
thf(fact_139_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X : nat]: (^[Y : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X) @ Y @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_140_fun__upd__apply, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[X : produc1257910179t_char]: (^[Y : option_val]: (^[Z2 : produc1257910179t_char]: (if_option_val @ (Z2 = X) @ Y @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_141_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X : list_char]: (^[Y : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X) @ Y @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_142_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, V : val, T : ty, V4 : list_char]: ((lconf_485928294t_char @ P @ H @ L2 @ E) => ((conf_P93989998t_char @ P @ H @ V @ T) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V)) @ (fun_up9191ion_ty @ E @ V4 @ (some_ty @ T)))))))). % lconf_upd2
thf(fact_143_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X4 : nat, Y4 : option2118145160on_val]: (((fun_up262443479on_val @ F @ X4 @ Y4) = F) = ((F @ X4) = Y4))))). % fun_upd_idem_iff
thf(fact_144_fun__upd__idem__iff, axiom,
    ((![F : produc1257910179t_char > option_val, X4 : produc1257910179t_char, Y4 : option_val]: (((fun_up356838326on_val @ F @ X4 @ Y4) = F) = ((F @ X4) = Y4))))). % fun_upd_idem_iff
thf(fact_145_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X4 : list_char, Y4 : option_val]: (((fun_up1252458416on_val @ F @ X4 @ Y4) = F) = ((F @ X4) = Y4))))). % fun_upd_idem_iff
thf(fact_146_fun__upd__twist, axiom,
    ((![A : nat, C5 : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D2 : option2118145160on_val]: ((~ ((A = C5))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C5 @ D2) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C5 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_147_fun__upd__twist, axiom,
    ((![A : produc1257910179t_char, C5 : produc1257910179t_char, M : produc1257910179t_char > option_val, B : option_val, D2 : option_val]: ((~ ((A = C5))) => ((fun_up356838326on_val @ (fun_up356838326on_val @ M @ A @ B) @ C5 @ D2) = (fun_up356838326on_val @ (fun_up356838326on_val @ M @ C5 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_148_fun__upd__twist, axiom,
    ((![A : list_char, C5 : list_char, M : list_char > option_val, B : option_val, D2 : option_val]: ((~ ((A = C5))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A @ B) @ C5 @ D2) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C5 @ D2) @ A @ B)))))). % fun_upd_twist
thf(fact_149_fun__upd__other, axiom,
    ((![Z : nat, X4 : nat, F : nat > option2118145160on_val, Y4 : option2118145160on_val]: ((~ ((Z = X4))) => ((fun_up262443479on_val @ F @ X4 @ Y4 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_150_fun__upd__other, axiom,
    ((![Z : produc1257910179t_char, X4 : produc1257910179t_char, F : produc1257910179t_char > option_val, Y4 : option_val]: ((~ ((Z = X4))) => ((fun_up356838326on_val @ F @ X4 @ Y4 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_151_fun__upd__other, axiom,
    ((![Z : list_char, X4 : list_char, F : list_char > option_val, Y4 : option_val]: ((~ ((Z = X4))) => ((fun_up1252458416on_val @ F @ X4 @ Y4 @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_152_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X4 : nat, Y4 : option2118145160on_val]: ((fun_up262443479on_val @ F @ X4 @ Y4 @ X4) = Y4)))). % fun_upd_same
thf(fact_153_fun__upd__same, axiom,
    ((![F : produc1257910179t_char > option_val, X4 : produc1257910179t_char, Y4 : option_val]: ((fun_up356838326on_val @ F @ X4 @ Y4 @ X4) = Y4)))). % fun_upd_same
thf(fact_154_fun__upd__same, axiom,
    ((![F : list_char > option_val, X4 : list_char, Y4 : option_val]: ((fun_up1252458416on_val @ F @ X4 @ Y4 @ X4) = Y4)))). % fun_upd_same
thf(fact_155_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X4 : nat, Y4 : option2118145160on_val]: (((F @ X4) = Y4) => ((fun_up262443479on_val @ F @ X4 @ Y4) = F))))). % fun_upd_idem
thf(fact_156_fun__upd__idem, axiom,
    ((![F : produc1257910179t_char > option_val, X4 : produc1257910179t_char, Y4 : option_val]: (((F @ X4) = Y4) => ((fun_up356838326on_val @ F @ X4 @ Y4) = F))))). % fun_upd_idem
thf(fact_157_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X4 : list_char, Y4 : option_val]: (((F @ X4) = Y4) => ((fun_up1252458416on_val @ F @ X4 @ Y4) = F))))). % fun_upd_idem
thf(fact_158_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X4 : nat, Y4 : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X4 @ Y4) = (fun_up262443479on_val @ G @ X4 @ Z)) => (Y4 = Z))))). % fun_upd_eqD
thf(fact_159_fun__upd__eqD, axiom,
    ((![F : produc1257910179t_char > option_val, X4 : produc1257910179t_char, Y4 : option_val, G : produc1257910179t_char > option_val, Z : option_val]: (((fun_up356838326on_val @ F @ X4 @ Y4) = (fun_up356838326on_val @ G @ X4 @ Z)) => (Y4 = Z))))). % fun_upd_eqD
thf(fact_160_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X4 : list_char, Y4 : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X4 @ Y4) = (fun_up1252458416on_val @ G @ X4 @ Z)) => (Y4 = Z))))). % fun_upd_eqD
thf(fact_161_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A3 : nat]: (^[B4 : option2118145160on_val]: (^[X : nat]: (if_opt451925058on_val @ (X = A3) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_162_fun__upd__def, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[A3 : produc1257910179t_char]: (^[B4 : option_val]: (^[X : produc1257910179t_char]: (if_option_val @ (X = A3) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_163_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A3 : list_char]: (^[B4 : option_val]: (^[X : list_char]: (if_option_val @ (X = A3) @ B4 @ (F2 @ X))))))))). % fun_upd_def
thf(fact_164_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, V : val, T : ty, V4 : list_char]: ((lconf_485928294t_char @ P @ H @ L2 @ E) => ((conf_P93989998t_char @ P @ H @ V @ T) => (((E @ V4) = (some_ty @ T)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V)) @ E))))))). % lconf_upd
thf(fact_165_oconf__fupd, axiom,
    ((![P : list_P1234162913t_char, C3 : list_char, F3 : list_char, T : ty, D3 : list_char, H : nat > option2118145160on_val, V : val, Fs5 : produc1257910179t_char > option_val]: ((has_fi599584195t_char @ P @ C3 @ F3 @ T @ D3) => ((conf_P93989998t_char @ P @ H @ V @ T) => ((oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C3 @ Fs5)) => (oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V)))))))))). % oconf_fupd
thf(fact_166_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X4 : produc266837688on_val, N : nat > option2118145160on_val, Y4 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X4)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y4))) => (X4 = Y4))))). % map_upd_eqD1
thf(fact_167_map__upd__eqD1, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, X4 : val, N : produc1257910179t_char > option_val, Y4 : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ X4)) = (fun_up356838326on_val @ N @ A @ (some_val @ Y4))) => (X4 = Y4))))). % map_upd_eqD1
thf(fact_168_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A : list_char, X4 : val, N : list_char > option_val, Y4 : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ X4)) = (fun_up1252458416on_val @ N @ A @ (some_val @ Y4))) => (X4 = Y4))))). % map_upd_eqD1
thf(fact_169_map__upd__triv, axiom,
    ((![T5 : nat > option2118145160on_val, K : nat, X4 : produc266837688on_val]: (((T5 @ K) = (some_P1299442195on_val @ X4)) => ((fun_up262443479on_val @ T5 @ K @ (some_P1299442195on_val @ X4)) = T5))))). % map_upd_triv
thf(fact_170_map__upd__triv, axiom,
    ((![T5 : produc1257910179t_char > option_val, K : produc1257910179t_char, X4 : val]: (((T5 @ K) = (some_val @ X4)) => ((fun_up356838326on_val @ T5 @ K @ (some_val @ X4)) = T5))))). % map_upd_triv
thf(fact_171_map__upd__triv, axiom,
    ((![T5 : list_char > option_val, K : list_char, X4 : val]: (((T5 @ K) = (some_val @ X4)) => ((fun_up1252458416on_val @ T5 @ K @ (some_val @ X4)) = T5))))). % map_upd_triv
thf(fact_172_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X4 : nat, Y4 : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X4) = (some_P1299442195on_val @ Y4)) = (((((X4 = A)) & ((B = Y4)))) | ((((~ ((X4 = A)))) & (((M @ X4) = (some_P1299442195on_val @ Y4)))))))))). % map_upd_Some_unfold
thf(fact_173_map__upd__Some__unfold, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, B : val, X4 : produc1257910179t_char, Y4 : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ B) @ X4) = (some_val @ Y4)) = (((((X4 = A)) & ((B = Y4)))) | ((((~ ((X4 = A)))) & (((M @ X4) = (some_val @ Y4)))))))))). % map_upd_Some_unfold
thf(fact_174_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A : list_char, B : val, X4 : list_char, Y4 : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ B) @ X4) = (some_val @ Y4)) = (((((X4 = A)) & ((B = Y4)))) | ((((~ ((X4 = A)))) & (((M @ X4) = (some_val @ Y4)))))))))). % map_upd_Some_unfold
thf(fact_175_preallocated__hext, axiom,
    ((![H : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((preallocated @ H) => ((hext @ H @ H3) => (preallocated @ H3)))))). % preallocated_hext
thf(fact_176_red__reds_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, L2 : list_char > option_val, P : list_P1234162913t_char]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L2))) @ (red @ P)))))). % red_reds.RedFAss
thf(fact_177_redp__redsp_ORedFAss, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char, V : val, L2 : list_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (redp @ P @ (fAss_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L2) @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L2)))))). % redp_redsp.RedFAss
thf(fact_178_FAss, axiom,
    ((![P : list_P1234162913t_char, E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, E_2 : exp_list_char, V : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs5 : produc1257910179t_char > option_val, Fs7 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, H_22 : nat > option2118145160on_val]: ((eval @ P @ E_1 @ S_0 @ (val_list_char @ (addr @ A)) @ S_1) => ((eval @ P @ E_2 @ S_1 @ (val_list_char @ V) @ (produc52622304on_val @ H_2 @ L_2)) => (((H_2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => ((Fs7 = (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))) => ((H_22 = (fun_up262443479on_val @ H_2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs7)))) => (eval @ P @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0 @ (val_list_char @ unit) @ (produc52622304on_val @ H_22 @ L_2)))))))))). % FAss
thf(fact_179_red__reds_OFAssRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E4 @ F3 @ D3 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_180_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (hext @ H @ H3))))). % red_hext_incr
thf(fact_181_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X : exp_list_char]: (^[Y : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_182_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H @ L2) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (hext @ H @ H3))))). % eval_hext
thf(fact_183_red__reds_OFAssRed2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E4) @ S3)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_184_val_Odistinct_I7_J, axiom,
    ((![X5 : nat]: (~ ((unit = (addr @ X5))))))). % val.distinct(7)
thf(fact_185_redp__redsp_OFAssRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S2 @ E4 @ S3) => (redp @ P @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2 @ (fAss_list_char @ E4 @ F3 @ D3 @ E_2) @ S3))))). % redp_redsp.FAssRed1
thf(fact_186_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S2 @ (val_list_char @ V) @ S2)))). % Val
thf(fact_187_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E4 @ S3) => (~ (((E4 = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_188_redp__redsp_OFAssRed2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, V : val, F3 : list_char, D3 : list_char]: ((redp @ P @ E2 @ S2 @ E4 @ S3) => (redp @ P @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E2) @ S2 @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E4) @ S3))))). % redp_redsp.FAssRed2
thf(fact_189_FAssRedsVal, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, A : nat, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, V : val, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => (((some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5)) = (H_2 @ A)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_1 @ F3 @ D3 @ E_2) @ S_0) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ (fun_up262443479on_val @ H_2 @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ (fun_up356838326on_val @ Fs5 @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L_2))) @ (transi111096263on_val @ (red @ P))))))))). % FAssRedsVal
thf(fact_190_FAcc, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, A : nat, H : nat > option2118145160on_val, L2 : list_char > option_val, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ (addr @ A)) @ (produc52622304on_val @ H @ L2)) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (eval @ P @ (fAcc_list_char @ E2 @ F3 @ D3) @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L2)))))))). % FAcc
thf(fact_191_red__reds_ORedLAss, axiom,
    ((![V4 : list_char, V : val, H : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V4 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_192_exp_Oinject_I6_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, Y61 : list_char, Y62 : exp_list_char]: (((lAss_list_char @ X61 @ X62) = (lAss_list_char @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % exp.inject(6)
thf(fact_193_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_194_LAssReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V4 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V4 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_195_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F3 @ D3) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_196_exp_Odistinct_I59_J, axiom,
    ((![X3 : val, X61 : list_char, X62 : exp_list_char]: (~ (((val_list_char @ X3) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(59)
thf(fact_197_exp_Odistinct_I61_J, axiom,
    ((![X3 : val, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((val_list_char @ X3) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(61)
thf(fact_198_exp_Odistinct_I123_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(123)
thf(fact_199_exp_Odistinct_I139_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(139)
thf(fact_200_exp_Odistinct_I121_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(121)
thf(fact_201_FAssReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F3 @ D3 @ E_2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ E4 @ F3 @ D3 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_202_red__reds_OLAssRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V4 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V4 @ E4) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_203_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F3 @ D3) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_204_LAssRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, V : val, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V4 @ E2) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V4 @ (some_val @ V))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_205_FAssReds2, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, F3 : list_char, D3 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E2) @ S2) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F3 @ D3 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_206_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L2 : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, R : exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > exp_list_char > (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L2)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H6 @ L4 @ E5 @ H6 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E6 : exp_list_char, H7 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E6 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E6 @ H7 @ L5)))) => (R @ E2 @ H @ L2 @ E4 @ H3 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_207_LAss, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, V : val, H : nat > option2118145160on_val, L2 : list_char > option_val, L3 : list_char > option_val, V4 : list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ V) @ (produc52622304on_val @ H @ L2)) => ((L3 = (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V))) => (eval @ P @ (lAss_list_char @ V4 @ E2) @ S_0 @ (val_list_char @ unit) @ (produc52622304on_val @ H @ L3))))))). % LAss
thf(fact_208_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V4 : list_char, V : val, H : nat > option2118145160on_val, L2 : list_char > option_val]: (redp @ P @ (lAss_list_char @ V4 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L2) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L2 @ V4 @ (some_val @ V))))))). % redp_redsp.RedLAss
thf(fact_209_FAccRedsVal, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A : nat, S3 : produc515445032on_val, P : list_P1234162913t_char, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ (addr @ A)) @ S3)) @ (transi111096263on_val @ (red @ P))) => (((hp @ S3 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S3)) @ (transi111096263on_val @ (red @ P))))))))). % FAccRedsVal
thf(fact_210_red__reds_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3) @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (red @ P))))))). % red_reds.RedFAcc
thf(fact_211_redp__redsp_ORedFAcc, axiom,
    ((![S2 : produc515445032on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val, F3 : list_char, D3 : list_char, V : val, P : list_P1234162913t_char]: (((hp @ S2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (((Fs5 @ (produc1304532571t_char @ F3 @ D3)) = (some_val @ V)) => (redp @ P @ (fAcc_list_char @ (val_list_char @ (addr @ A)) @ F3 @ D3) @ S2 @ (val_list_char @ V) @ S2)))))). % redp_redsp.RedFAcc
thf(fact_212_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : produc1257910179t_char > option_val, Bx : list_char, By : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val, P : list_char > (produc1257910179t_char > option_val) > $o]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Ax @ Ay) @ (produc904988266on_val @ A2 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_213_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R2 : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A2 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_214_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R2 : 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 @ R2)) => ((P @ Ax @ Ay) => ((![A2 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A2 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_215_rtrancl__induct2, axiom,
    ((![Ax : list_char, Ay : list_char, Bx : list_char, By : list_char, R2 : set_Pr729957319t_char, P : list_char > list_char > $o]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Ax @ Ay) => ((![A2 : list_char, B3 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Ax @ Ay) @ (produc1304532571t_char @ A2 @ B3)) @ (transi858104614t_char @ R2)) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A2 @ B3) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_216_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R2 : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Ax @ Ay) => ((![A2 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A2 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A2 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_217_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : produc1257910179t_char > option_val, Za : list_char, Zb : produc1257910179t_char > option_val, R2 : set_Pr2110063281on_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2)) => ((~ (((produc904988266on_val @ Xa @ Xb) = (produc904988266on_val @ Za @ Zb)))) => (~ ((![A2 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A2 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A2 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_218_converse__rtranclE2, axiom,
    ((![Xa : produc1097884484on_val, Xb : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R2 : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2)) => ((~ (((produc1069526295on_val @ Xa @ Xb) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A2 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A2 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A2 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_219_converse__rtranclE2, axiom,
    ((![Xa : nat > option2118145160on_val, Xb : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R2 : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2)) => ((~ (((produc52622304on_val @ Xa @ Xb) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A2 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A2 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A2 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_220_converse__rtranclE2, axiom,
    ((![Xa : list_char, Xb : list_char, Za : list_char, Zb : list_char, R2 : set_Pr729957319t_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2)) => ((~ (((produc1304532571t_char @ Xa @ Xb) = (produc1304532571t_char @ Za @ Zb)))) => (~ ((![A2 : list_char, B3 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A2 @ B3)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A2 @ B3) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_221_converse__rtranclE2, axiom,
    ((![Xa : exp_list_char, Xb : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2)) => ((~ (((produc2023458740on_val @ Xa @ Xb) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A2 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A2 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A2 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_222_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C5) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A @ C5) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_223_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_224_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C5 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C5) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A @ C5) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_225_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C5) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C5) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_226_converse__rtrancl__induct, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, P : list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((P @ B) => ((![Y6 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y6 @ Z3) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z3 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z3) => (P @ Y6))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_227_converse__rtrancl__induct, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y6 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y6 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y6))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_228_rtrancl_Ortrancl__refl, axiom,
    ((![A : list_char, R2 : set_Pr164112643t_char]: (member89690956t_char @ (produc1304532571t_char @ A @ A) @ (transi1879726366t_char @ R2))))). % rtrancl.rtrancl_refl
thf(fact_229_rtrancl_Ortrancl__refl, axiom,
    ((![A : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A @ A) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_230_converse__rtranclE, axiom,
    ((![X4 : list_char, Z : list_char, R2 : set_Pr164112643t_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Z) @ (transi1879726366t_char @ R2)) => ((~ ((X4 = Z))) => (~ ((![Y6 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ X4 @ Y6) @ R2) => (~ ((member89690956t_char @ (produc1304532571t_char @ Y6 @ Z) @ (transi1879726366t_char @ R2))))))))))))). % converse_rtranclE
thf(fact_231_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X4 = Z))) => (~ ((![Y6 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y6) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y6 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_232_rtrancl_Oinducts, axiom,
    ((![X1 : list_char, X2 : list_char, R2 : set_Pr164112643t_char, P : list_char > list_char > $o]: ((member89690956t_char @ (produc1304532571t_char @ X1 @ X2) @ (transi1879726366t_char @ R2)) => ((![A2 : list_char]: (P @ A2 @ A2)) => ((![A2 : list_char, B3 : list_char, C4 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A2 @ B3) @ (transi1879726366t_char @ R2)) => ((P @ A2 @ B3) => ((member89690956t_char @ (produc1304532571t_char @ B3 @ C4) @ R2) => (P @ A2 @ C4))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_233_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R2)) => ((![A2 : produc1097884484on_val]: (P @ A2 @ A2)) => ((![A2 : produc1097884484on_val, B3 : produc1097884484on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A2 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C4) @ R2) => (P @ A2 @ C4))))) => (P @ X1 @ X2))))))). % rtrancl.inducts

% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X4 : option_val, Y4 : option_val]: ((if_option_val @ $false @ X4 @ Y4) = Y4)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X4 : option_val, Y4 : option_val]: ((if_option_val @ $true @ X4 @ Y4) = X4)))).
thf(help_If_3_1_If_001t__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_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__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_T, axiom,
    ((![X4 : option2118145160on_val, Y4 : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X4 @ Y4) = Y4)))).
thf(help_If_1_1_If_001t__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_T, axiom,
    ((![X4 : option2118145160on_val, Y4 : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X4 @ Y4) = X4)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((conf_P93989998t_char @ p @ ha @ v @ tf))).
