% 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_483__5339606_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:11.884

% Could-be-implicit typings (28)
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Type__Oty, type,
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thf(ty_n_t__Nat__Onat, type,
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% Explicit typings (78)
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thf(sy_c_Conform_Olconf_001t__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, type,
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thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OFAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OLAss_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_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, type,
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thf(sy_c_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, type,
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thf(sy_c_If_001t__Option__Ooption_It__Type__Oty_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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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_E____, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T_092_060_094sub_0621____, type,
    t_1 : ty).
thf(sy_v_T_H____, type,
    t : ty).
thf(sy_v_T____, type,
    t2 : ty).
thf(sy_v_V____, type,
    v : list_char).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    ea : exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).
thf(sy_v_v_H____, type,
    v2 : val).
thf(sy_v_v____, type,
    v3 : val).

% Relevant facts (247)
thf(fact_0_T1subT, axiom,
    ((widen_917054840t_char @ p @ t_1 @ t2))). % T1subT
thf(fact_1_wt_092_060_094sub_0621, axiom,
    (((typeof_h @ ha @ v3) = (some_ty @ t_1)))). % wt\<^sub>1
thf(fact_2_v_H, axiom,
    (((l_a @ v) = (some_val @ v2)))). % v'
thf(fact_3_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_4_wt_092_060_094sub_0622, axiom,
    ((wTrt2 @ p @ ha @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2)) @ ea @ t))). % wt\<^sub>2
thf(fact_5_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X @ Y) @ X @ Z) = (fun_up1252458416on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_6_fun__upd__upd, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty, Z : option_ty]: ((fun_up9191ion_ty @ (fun_up9191ion_ty @ F @ X @ Y) @ X @ Z) = (fun_up9191ion_ty @ F @ X @ Z))))). % fun_upd_upd
thf(fact_7_fun__upd__upd, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, Z : option2118145160on_val]: ((fun_up262443479on_val @ (fun_up262443479on_val @ F @ X @ Y) @ X @ Z) = (fun_up262443479on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_8_fun__upd__upd, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val, Z : option_val]: ((fun_up356838326on_val @ (fun_up356838326on_val @ F @ X @ Y) @ X @ Z) = (fun_up356838326on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_9_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X : list_char]: ((fun_up1252458416on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_10_fun__upd__triv, axiom,
    ((![F : list_char > option_ty, X : list_char]: ((fun_up9191ion_ty @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_11_fun__upd__triv, axiom,
    ((![F : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_12_fun__upd__triv, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char]: ((fun_up356838326on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_13_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_14_fun__upd__apply, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[X2 : list_char]: (^[Y2 : option_ty]: (^[Z2 : list_char]: (if_option_ty @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_15_fun__upd__apply, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[X2 : nat]: (^[Y2 : option2118145160on_val]: (^[Z2 : nat]: (if_opt451925058on_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_16_fun__upd__apply, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[X2 : produc1257910179t_char]: (^[Y2 : option_val]: (^[Z2 : produc1257910179t_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_17_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_18_option_Oinject, axiom,
    ((![X22 : ty, Y22 : ty]: (((some_ty @ X22) = (some_ty @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_19_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_20_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A : list_char, X : val, N : list_char > option_val, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ X)) = (fun_up1252458416on_val @ N @ A @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_21_map__upd__eqD1, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, X : val, N : produc1257910179t_char > option_val, Y : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ X)) = (fun_up356838326on_val @ N @ A @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_22_map__upd__eqD1, axiom,
    ((![M : list_char > option_ty, A : list_char, X : ty, N : list_char > option_ty, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ X)) = (fun_up9191ion_ty @ N @ A @ (some_ty @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_23_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_24_map__upd__triv, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (((T @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = T))))). % map_upd_triv
thf(fact_25_map__upd__triv, axiom,
    ((![T : produc1257910179t_char > option_val, K : produc1257910179t_char, X : val]: (((T @ K) = (some_val @ X)) => ((fun_up356838326on_val @ T @ K @ (some_val @ X)) = T))))). % map_upd_triv
thf(fact_26_map__upd__triv, axiom,
    ((![T : list_char > option_ty, K : list_char, X : ty]: (((T @ K) = (some_ty @ X)) => ((fun_up9191ion_ty @ T @ K @ (some_ty @ X)) = T))))). % map_upd_triv
thf(fact_27_map__upd__triv, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = T))))). % map_upd_triv
thf(fact_28_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A : list_char, B : val, X : list_char, Y : val]: (((fun_up1252458416on_val @ M @ A @ (some_val @ B) @ X) = (some_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_29_map__upd__Some__unfold, axiom,
    ((![M : produc1257910179t_char > option_val, A : produc1257910179t_char, B : val, X : produc1257910179t_char, Y : val]: (((fun_up356838326on_val @ M @ A @ (some_val @ B) @ X) = (some_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_30_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_ty, A : list_char, B : ty, X : list_char, Y : ty]: (((fun_up9191ion_ty @ M @ A @ (some_ty @ B) @ X) = (some_ty @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_ty @ Y)))))))))). % map_upd_Some_unfold
thf(fact_31_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A : nat, B : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A)) & ((B = Y)))) | ((((~ ((X = A)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_32_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_33__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062T_092_060_094sub_0621_O_A_092_060lbrakk_062typeof_092_060_094bsub_062h_092_060_094esub_062_Av_A_061_A_092_060lfloor_062T_092_060_094sub_0621_092_060rfloor_062_059_AP_A_092_060turnstile_062_AT_092_060_094sub_0621_A_092_060le_062_AT_059_AP_ME_IV_A_092_060mapsto_062_AT_J_Mh_A_092_060turnstile_062_Ae_A_058_AT_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![T_1 : ty]: (((typeof_h @ ha @ v3) = (some_ty @ T_1)) => ((widen_917054840t_char @ p @ T_1 @ t2) => (~ ((wTrt2 @ p @ ha @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2)) @ ea @ t)))))))))). % \<open>\<And>thesis. (\<And>T\<^sub>1. \<lbrakk>typeof\<^bsub>h\<^esub> v = \<lfloor>T\<^sub>1\<rfloor>; P \<turnstile> T\<^sub>1 \<le> T; P,E(V \<mapsto> T),h \<turnstile> e : T'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_34_InitBlockRed_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % InitBlockRed.prems(1)
thf(fact_35_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V : val, T2 : ty, V2 : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V @ T2) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)) @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)))))))). % lconf_upd2
thf(fact_36_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T2 : ty, T3 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T2) => ((widen_917054840t_char @ P @ T2 @ T3) => (conf_P93989998t_char @ P @ H @ V @ T3)))))). % conf_widen
thf(fact_37_conf__def, axiom,
    ((conf_P93989998t_char = (^[P2 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[V3 : val]: (^[T4 : ty]: (?[T5 : ty]: ((((typeof_h @ H2 @ V3) = (some_ty @ T5))) & ((widen_917054840t_char @ P2 @ T5 @ T4))))))))))). % conf_def
thf(fact_38_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P2 : list_P1234162913t_char]: (^[H2 : nat > option2118145160on_val]: (^[L2 : list_char > option_val]: (^[E2 : list_char > option_ty]: (![V4 : list_char]: (![V3 : val]: ((((L2 @ V4) = (some_val @ V3))) => ((?[T4 : ty]: ((((E2 @ V4) = (some_ty @ T4))) & ((conf_P93989998t_char @ P2 @ H2 @ V3 @ T4))))))))))))))). % lconf_def
thf(fact_39_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_40_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty]: (((fun_up9191ion_ty @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_41_fun__upd__idem__iff, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_42_fun__upd__idem__iff, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: (((fun_up356838326on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_43_fun__upd__twist, axiom,
    ((![A : list_char, C : list_char, M : list_char > option_val, B : option_val, D : option_val]: ((~ ((A = C))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A @ B) @ C @ D) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_44_fun__upd__twist, axiom,
    ((![A : list_char, C : list_char, M : list_char > option_ty, B : option_ty, D : option_ty]: ((~ ((A = C))) => ((fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ A @ B) @ C @ D) = (fun_up9191ion_ty @ (fun_up9191ion_ty @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_45_fun__upd__twist, axiom,
    ((![A : nat, C : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D : option2118145160on_val]: ((~ ((A = C))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A @ B) @ C @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_46_fun__upd__twist, axiom,
    ((![A : produc1257910179t_char, C : produc1257910179t_char, M : produc1257910179t_char > option_val, B : option_val, D : option_val]: ((~ ((A = C))) => ((fun_up356838326on_val @ (fun_up356838326on_val @ M @ A @ B) @ C @ D) = (fun_up356838326on_val @ (fun_up356838326on_val @ M @ C @ D) @ A @ B)))))). % fun_upd_twist
thf(fact_47_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up1252458416on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_48_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_ty, Y : option_ty]: ((~ ((Z = X))) => ((fun_up9191ion_ty @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_49_fun__upd__other, axiom,
    ((![Z : nat, X : nat, F : nat > option2118145160on_val, Y : option2118145160on_val]: ((~ ((Z = X))) => ((fun_up262443479on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_50_fun__upd__other, axiom,
    ((![Z : produc1257910179t_char, X : produc1257910179t_char, F : produc1257910179t_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up356838326on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_51_fun__upd__same, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: ((fun_up1252458416on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_52_fun__upd__same, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty]: ((fun_up9191ion_ty @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_53_fun__upd__same, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: ((fun_up262443479on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_54_fun__upd__same, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: ((fun_up356838326on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_55_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((F @ X) = Y) => ((fun_up1252458416on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_56_fun__upd__idem, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty]: (((F @ X) = Y) => ((fun_up9191ion_ty @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_57_fun__upd__idem, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val]: (((F @ X) = Y) => ((fun_up262443479on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_58_fun__upd__idem, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val]: (((F @ X) = Y) => ((fun_up356838326on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_59_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = (fun_up1252458416on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_60_fun__upd__eqD, axiom,
    ((![F : list_char > option_ty, X : list_char, Y : option_ty, G : list_char > option_ty, Z : option_ty]: (((fun_up9191ion_ty @ F @ X @ Y) = (fun_up9191ion_ty @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_61_fun__upd__eqD, axiom,
    ((![F : nat > option2118145160on_val, X : nat, Y : option2118145160on_val, G : nat > option2118145160on_val, Z : option2118145160on_val]: (((fun_up262443479on_val @ F @ X @ Y) = (fun_up262443479on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_62_fun__upd__eqD, axiom,
    ((![F : produc1257910179t_char > option_val, X : produc1257910179t_char, Y : option_val, G : produc1257910179t_char > option_val, Z : option_val]: (((fun_up356838326on_val @ F @ X @ Y) = (fun_up356838326on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_63_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A2 : list_char]: (^[B2 : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A2) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_64_fun__upd__def, axiom,
    ((fun_up9191ion_ty = (^[F2 : list_char > option_ty]: (^[A2 : list_char]: (^[B2 : option_ty]: (^[X2 : list_char]: (if_option_ty @ (X2 = A2) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_65_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A2 : nat]: (^[B2 : option2118145160on_val]: (^[X2 : nat]: (if_opt451925058on_val @ (X2 = A2) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_66_fun__upd__def, axiom,
    ((fun_up356838326on_val = (^[F2 : produc1257910179t_char > option_val]: (^[A2 : produc1257910179t_char]: (^[B2 : option_val]: (^[X2 : produc1257910179t_char]: (if_option_val @ (X2 = A2) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_67_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V : val, T2 : ty, V2 : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V @ T2) => (((E @ V2) = (some_ty @ T2)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)) @ E))))))). % lconf_upd
thf(fact_68_InitBlockRed_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[T6 : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ T6) & (widen_917054840t_char @ p @ T6 @ T2)))))))). % InitBlockRed.hyps(2)
thf(fact_69_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) => ((wTrt2 @ p @ ha @ E @ ea @ T2) => (?[U : ty]: ((wTrt2 @ p @ h_a @ E @ e_a @ U) & (widen_917054840t_char @ p @ U @ T2)))))))). % IH
thf(fact_70_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X22 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X22) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_71_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X22) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_72_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X22 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X22) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_73_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : produc1257910179t_char > option_val, Y1 : list_char, Y22 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X22) = (produc904988266on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_74_prod_Oinject, axiom,
    ((![X1 : list_char, X22 : list_char, Y1 : list_char, Y22 : list_char]: (((produc1304532571t_char @ X1 @ X22) = (produc1304532571t_char @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_75_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_76_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_77_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_78_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_79_old_Oprod_Oinject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B3 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_80_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_81_InitBlockRed_Oprems_I2_J, axiom,
    ((wTrt2 @ p @ ha @ e @ (block_list_char @ v @ t2 @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ t))). % InitBlockRed.prems(2)
thf(fact_82_wt, axiom,
    ((wTrt2 @ p @ ha @ e @ (block_list_char @ v @ t2 @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ t))). % wt
thf(fact_83_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_84_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_85_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_86_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_87_pred__equals__eq2, axiom,
    ((![R : set_Pr164112643t_char, S : set_Pr164112643t_char]: (((^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ R))) = (^[X2 : list_char]: (^[Y2 : list_char]: (member89690956t_char @ (produc1304532571t_char @ X2 @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_88_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_89_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y2 : ty]: (X = (some_ty @ Y2))))))). % not_None_eq
thf(fact_90_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_91_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_92_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y2 : ty]: (~ ((X = (some_ty @ Y2))))) = (X = none_ty))))). % not_Some_eq
thf(fact_93_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_94_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up9191ion_ty @ (^[X2 : list_char]: none_ty) @ X @ none_ty) = (^[X2 : list_char]: none_ty))))). % empty_upd_none
thf(fact_95_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1252458416on_val @ (^[X2 : list_char]: none_val) @ X @ none_val) = (^[X2 : list_char]: none_val))))). % empty_upd_none
thf(fact_96_empty__upd__none, axiom,
    ((![X : produc1257910179t_char]: ((fun_up356838326on_val @ (^[X2 : produc1257910179t_char]: none_val) @ X @ none_val) = (^[X2 : produc1257910179t_char]: none_val))))). % empty_upd_none
thf(fact_97_empty__upd__none, axiom,
    ((![X : nat]: ((fun_up262443479on_val @ (^[X2 : nat]: none_P1535574167on_val) @ X @ none_P1535574167on_val) = (^[X2 : nat]: none_P1535574167on_val))))). % empty_upd_none
thf(fact_98_red__preserves__lconf, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E3 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H3 @ L3 @ E))))))). % red_preserves_lconf
thf(fact_99_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_100_option_Odistinct_I1_J, axiom,
    ((![X22 : ty]: (~ ((none_ty = (some_ty @ X22))))))). % option.distinct(1)
thf(fact_101_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_102_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_103_option_OdiscI, axiom,
    ((![Option : option_ty, X22 : ty]: ((Option = (some_ty @ X22)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_104_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_105_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_106_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X23 : ty]: (~ ((Y = (some_ty @ X23))))))))))). % option.exhaust
thf(fact_107_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_108_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_109_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_110_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X3 : val]: (P @ (some_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_111_option_Oinducts, axiom,
    ((![P : option_ty > $o, Option : option_ty]: ((P @ none_ty) => ((![X3 : ty]: (P @ (some_ty @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_112_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X3 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_113_split__option__ex, axiom,
    (((^[P3 : option_val > $o]: (?[X4 : option_val]: (P3 @ X4))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) | ((?[X2 : val]: (P2 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_114_split__option__ex, axiom,
    (((^[P3 : option_ty > $o]: (?[X4 : option_ty]: (P3 @ X4))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) | ((?[X2 : ty]: (P2 @ (some_ty @ X2))))))))). % split_option_ex
thf(fact_115_split__option__ex, axiom,
    (((^[P3 : option2118145160on_val > $o]: (?[X4 : option2118145160on_val]: (P3 @ X4))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_116_split__option__all, axiom,
    (((^[P3 : option_val > $o]: (![X4 : option_val]: (P3 @ X4))) = (^[P2 : option_val > $o]: (((P2 @ none_val)) & ((![X2 : val]: (P2 @ (some_val @ X2))))))))). % split_option_all
thf(fact_117_split__option__all, axiom,
    (((^[P3 : option_ty > $o]: (![X4 : option_ty]: (P3 @ X4))) = (^[P2 : option_ty > $o]: (((P2 @ none_ty)) & ((![X2 : ty]: (P2 @ (some_ty @ X2))))))))). % split_option_all
thf(fact_118_split__option__all, axiom,
    (((^[P3 : option2118145160on_val > $o]: (![X4 : option2118145160on_val]: (P3 @ X4))) = (^[P2 : option2118145160on_val > $o]: (((P2 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P2 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_119_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_val > $o, Y : option_val]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A5 : val, B4 : val]: ((X = (some_val @ A5)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_120_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_ty > $o, Y : option_ty]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A5 : val, B4 : ty]: ((X = (some_val @ A5)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_121_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A5 : val, B4 : produc266837688on_val]: ((X = (some_val @ A5)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_122_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_val > $o, Y : option_val]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A5 : ty, B4 : val]: ((X = (some_ty @ A5)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_123_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option_ty > $o, Y : option_ty]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A5 : ty, B4 : ty]: ((X = (some_ty @ A5)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_124_combine__options__cases, axiom,
    ((![X : option_ty, P : option_ty > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_ty) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A5 : ty, B4 : produc266837688on_val]: ((X = (some_ty @ A5)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_125_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_val > $o, Y : option_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A5 : produc266837688on_val, B4 : val]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_126_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_ty > $o, Y : option_ty]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_ty) => (P @ X @ Y)) => ((![A5 : produc266837688on_val, B4 : ty]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_ty @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_127_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A5 : produc266837688on_val, B4 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A5)) => ((Y = (some_P1299442195on_val @ B4)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_128_map__upd__nonempty, axiom,
    ((![T : list_char > option_val, K : list_char, X : val]: (~ (((fun_up1252458416on_val @ T @ K @ (some_val @ X)) = (^[X2 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_129_map__upd__nonempty, axiom,
    ((![T : produc1257910179t_char > option_val, K : produc1257910179t_char, X : val]: (~ (((fun_up356838326on_val @ T @ K @ (some_val @ X)) = (^[X2 : produc1257910179t_char]: none_val))))))). % map_upd_nonempty
thf(fact_130_map__upd__nonempty, axiom,
    ((![T : list_char > option_ty, K : list_char, X : ty]: (~ (((fun_up9191ion_ty @ T @ K @ (some_ty @ X)) = (^[X2 : list_char]: none_ty))))))). % map_upd_nonempty
thf(fact_131_map__upd__nonempty, axiom,
    ((![T : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T @ K @ (some_P1299442195on_val @ X)) = (^[X2 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_132_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_133_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_134_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_135_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_136_old_Oprod_Oinducts, axiom,
    ((![P : produc1257910179t_char > $o, Prod : produc1257910179t_char]: ((![A5 : list_char, B4 : list_char]: (P @ (produc1304532571t_char @ A5 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_137_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_138_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_139_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_140_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_141_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1257910179t_char]: (~ ((![A5 : list_char, B4 : list_char]: (~ ((Y = (produc1304532571t_char @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_142_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_143_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_144_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A5 @ (produc52622304on_val @ B4 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_145_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_146_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ (produc2023458740on_val @ B4 @ C2))))))))))). % prod_cases3
thf(fact_147_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A5 @ (produc52622304on_val @ B4 @ C2))))))))))). % prod_cases3
thf(fact_148_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B) = (produc52622304on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_149_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_150_Pair__inject, axiom,
    ((![A : exp_list_char, B : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_151_Pair__inject, axiom,
    ((![A : list_char, B : produc1257910179t_char > option_val, A3 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B) = (produc904988266on_val @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_152_Pair__inject, axiom,
    ((![A : list_char, B : list_char, A3 : list_char, B3 : list_char]: (((produc1304532571t_char @ A @ B) = (produc1304532571t_char @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_153_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (P @ (produc52622304on_val @ A5 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_154_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P4 : produc1172664615on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A5 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_155_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (P @ (produc2023458740on_val @ A5 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_156_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P4 : produc266837688on_val]: ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A5 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_157_prod__cases, axiom,
    ((![P : produc1257910179t_char > $o, P4 : produc1257910179t_char]: ((![A5 : list_char, B4 : list_char]: (P @ (produc1304532571t_char @ A5 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_158_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P4 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_159_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_160_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_161_surj__pair, axiom,
    ((![P4 : produc266837688on_val]: (?[X3 : list_char, Y3 : produc1257910179t_char > option_val]: (P4 = (produc904988266on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_162_surj__pair, axiom,
    ((![P4 : produc1257910179t_char]: (?[X3 : list_char, Y3 : list_char]: (P4 = (produc1304532571t_char @ X3 @ Y3)))))). % surj_pair
thf(fact_163_red__reds_OInitBlockRed, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V5 : val, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V2) = (some_val @ V5)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V5)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (red @ P))))))). % red_reds.InitBlockRed
thf(fact_164_red__reds_ORedInitBlock, axiom,
    ((![V2 : list_char, T2 : ty, V : val, U2 : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (val_list_char @ U2))) @ S2) @ (produc2023458740on_val @ (val_list_char @ U2) @ S2)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_165_red__reds_ORedBlock, axiom,
    ((![V2 : list_char, T2 : ty, U2 : val, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (val_list_char @ U2)) @ S2) @ (produc2023458740on_val @ (val_list_char @ U2) @ S2)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_166_red__reds_ORedSeq, axiom,
    ((![V : val, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V) @ E_2) @ S2) @ (produc2023458740on_val @ E_2 @ S2)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_167_WTrtBlock, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, T2 : ty, E3 : exp_list_char, T3 : ty]: ((wTrt2 @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)) @ E3 @ T3) => (wTrt2 @ P @ H @ E @ (block_list_char @ V2 @ T2 @ E3) @ T3))))). % WTrtBlock
thf(fact_168_WTrtVal, axiom,
    ((![H : nat > option2118145160on_val, V : val, T2 : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T2)) => (wTrt2 @ P @ H @ E @ (val_list_char @ V) @ T2))))). % WTrtVal
thf(fact_169_red__reds_OSeqRed, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_170_lconf__empty, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty]: (lconf_485928294t_char @ P @ H @ (^[X2 : list_char]: none_val) @ E)))). % lconf_empty
thf(fact_171_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt2 @ P @ H @ E @ E_1 @ T_12) => ((wTrt2 @ P @ H @ E @ E_2 @ T_2) => (wTrt2 @ P @ H @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_172_red__reds_OLAssRed, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E4) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_173_red__reds_OBlockRedSome, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V : val, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V2) = (some_val @ V)) => ((~ ((assigned @ V2 @ E3))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E3) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (red @ P)))))))). % red_reds.BlockRedSome
thf(fact_174_red__reds_OBlockRedNone, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => (((L3 @ V2) = none_val) => ((~ ((assigned @ V2 @ E3))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E3) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_175_typeof__lit__typeof, axiom,
    ((![V : val, T2 : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X2 : nat]: none_P1535574167on_val) @ V) = (some_ty @ T2)) => ((typeof_h @ H @ V) = (some_ty @ T2)))))). % typeof_lit_typeof
thf(fact_176_assigned__def, axiom,
    ((assigned = (^[V4 : list_char]: (^[E5 : exp_list_char]: (?[V3 : val]: (?[E6 : exp_list_char]: (E5 = (seq_list_char @ (lAss_list_char @ V4 @ (val_list_char @ V3)) @ E6))))))))). % assigned_def
thf(fact_177_red__reds_ORedLAss, axiom,
    ((![V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_178_redp__redsp_OBlockRedSome, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, V : val, T2 : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V2) = (some_val @ V)) => ((~ ((assigned @ V2 @ E3))) => (redp @ P @ (block_list_char @ V2 @ T2 @ E3) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2)))))))))). % redp_redsp.BlockRedSome
thf(fact_179_exp_Oinject_I10_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, Y101 : list_char, Y102 : ty, Y103 : exp_list_char]: (((block_list_char @ X101 @ X102 @ X103) = (block_list_char @ Y101 @ Y102 @ Y103)) = (((X101 = Y101)) & ((((X102 = Y102)) & ((X103 = Y103))))))))). % exp.inject(10)
thf(fact_180_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_181_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_182_exp_Oinject_I11_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, Y111 : exp_list_char, Y112 : exp_list_char]: (((seq_list_char @ X111 @ X112) = (seq_list_char @ Y111 @ Y112)) = (((X111 = Y111)) & ((X112 = Y112))))))). % exp.inject(11)
thf(fact_183_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E3 @ S2 @ E4 @ S3) => (redp @ P @ (seq_list_char @ E3 @ E_2) @ S2 @ (seq_list_char @ E4 @ E_2) @ S3))))). % redp_redsp.SeqRed
thf(fact_184_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, V2 : list_char]: ((redp @ P @ E3 @ S2 @ E4 @ S3) => (redp @ P @ (lAss_list_char @ V2 @ E3) @ S2 @ (lAss_list_char @ V2 @ E4) @ S3))))). % redp_redsp.LAssRed
thf(fact_185_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V : val, E_2 : exp_list_char, S2 : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V) @ E_2) @ S2 @ E_2 @ S2)))). % redp_redsp.RedSeq
thf(fact_186_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T2 : ty, U2 : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T2 @ (val_list_char @ U2)) @ S2 @ (val_list_char @ U2) @ S2)))). % redp_redsp.RedBlock
thf(fact_187_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, V : val, H : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))))))). % redp_redsp.RedLAss
thf(fact_188_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_189_redp__redsp_ORedInitBlock, axiom,
    ((![P : list_P1234162913t_char, V2 : list_char, T2 : ty, V : val, U2 : val, S2 : produc515445032on_val]: (redp @ P @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ (val_list_char @ U2))) @ S2 @ (val_list_char @ U2) @ S2)))). % redp_redsp.RedInitBlock
thf(fact_190_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, T2 : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ none_val)) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V2) = none_val) => ((~ ((assigned @ V2 @ E3))) => (redp @ P @ (block_list_char @ V2 @ T2 @ E3) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T2 @ E4) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2)))))))))). % redp_redsp.BlockRedNone
thf(fact_191_redp__redsp_OInitBlockRed, axiom,
    ((![P : list_P1234162913t_char, E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, V5 : val, T2 : ty]: ((redp @ P @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V))) @ E4 @ (produc52622304on_val @ H3 @ L3)) => (((L3 @ V2) = (some_val @ V5)) => (redp @ P @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V5)) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))))))). % redp_redsp.InitBlockRed
thf(fact_192_exp_Odistinct_I69_J, axiom,
    ((![X32 : val, X111 : exp_list_char, X112 : exp_list_char]: (~ (((val_list_char @ X32) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(69)
thf(fact_193_exp_Odistinct_I59_J, axiom,
    ((![X32 : val, X61 : list_char, X62 : exp_list_char]: (~ (((val_list_char @ X32) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(59)
thf(fact_194_exp_Odistinct_I67_J, axiom,
    ((![X32 : val, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((val_list_char @ X32) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(67)
thf(fact_195_exp_Odistinct_I129_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(129)
thf(fact_196_exp_Odistinct_I181_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((block_list_char @ X101 @ X102 @ X103) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(181)
thf(fact_197_exp_Odistinct_I127_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(127)
thf(fact_198_red__preserves__hconf, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (red @ P)) => ((wTrt2 @ P @ H @ E @ E3 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H3))))))). % red_preserves_hconf
thf(fact_199_red__preserves__sconf, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((wTrt2 @ P @ (hp @ S2) @ E @ E3 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_200_WTrt_H__WTrts_H_Ointros_I16_J, axiom,
    ((![H : nat > option2118145160on_val, V : val, T_12 : ty, P : list_P1234162913t_char, T2 : ty, E : list_char > option_ty, V2 : list_char, E_2 : exp_list_char, T_2 : ty]: (((typeof_h @ H @ V) = (some_ty @ T_12)) => ((widen_917054840t_char @ P @ T_12 @ T2) => ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)) @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E_2)) @ T_2))))))). % WTrt'_WTrts'.intros(16)
thf(fact_201_wt_H__wt, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E3 : exp_list_char, T2 : ty]: ((wTrt @ P @ H @ E @ E3 @ T2) => (wTrt2 @ P @ H @ E @ E3 @ T2))))). % wt'_wt
thf(fact_202_wt__wt_H, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E3 : exp_list_char, T2 : ty]: ((wTrt2 @ P @ H @ E @ E3 @ T2) => (wTrt @ P @ H @ E @ E3 @ T2))))). % wt_wt'
thf(fact_203_wt_H__iff__wt, axiom,
    ((wTrt = wTrt2))). % wt'_iff_wt
thf(fact_204_WTrt_H__WTrts_H_Ointros_I18_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (seq_list_char @ E_1 @ E_2) @ T_2)))))). % WTrt'_WTrts'.intros(18)
thf(fact_205_WTrt_H__WTrts_H_Ointros_I3_J, axiom,
    ((![H : nat > option2118145160on_val, V : val, T2 : ty, P : list_P1234162913t_char, E : list_char > option_ty]: (((typeof_h @ H @ V) = (some_ty @ T2)) => (wTrt @ P @ H @ E @ (val_list_char @ V) @ T2))))). % WTrt'_WTrts'.intros(3)
thf(fact_206_WTrt_H__WTrts_H_Ointros_I17_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V2 : list_char, T2 : ty, E3 : exp_list_char, T3 : ty]: ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V2 @ (some_ty @ T2)) @ E3 @ T3) => ((~ ((assigned @ V2 @ E3))) => (wTrt @ P @ H @ E @ (block_list_char @ V2 @ T2 @ E3) @ T3)))))). % WTrt'_WTrts'.intros(17)
thf(fact_207_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_208_hconf__upd__obj, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((hconf_1244167010t_char @ P @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => ((oconf_454120169t_char @ P @ H @ (produc904988266on_val @ C3 @ Fs2)) => (hconf_1244167010t_char @ P @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))))). % hconf_upd_obj
thf(fact_209_LAssRedsVal, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, V : val, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ (val_list_char @ V) @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S2) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (some_val @ V))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_210_LAssReds, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E3) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_211_SeqReds, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_212_SeqReds2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E_22 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E_1 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % SeqReds2
thf(fact_213_converse__rtrancl__induct__red, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : 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 @ E3 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((![E7 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E7 @ H4 @ L4 @ E7 @ H4 @ 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, E8 : exp_list_char, H5 : 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 @ E8 @ H5 @ L5) => (R @ E_0 @ H_0 @ L_0 @ E8 @ H5 @ L5)))) => (R @ E3 @ H @ L @ E4 @ H3 @ L3))))))). % converse_rtrancl_induct_red
thf(fact_214_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_215_InitBlockRedsFinal, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E4) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (transi111096263on_val @ (red @ P)))))))). % InitBlockRedsFinal
thf(fact_216_InitBlockReds__aux, axiom,
    ((![E3 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (![H6 : nat > option2118145160on_val, L6 : list_char > option_val, H7 : nat > option2118145160on_val, L7 : list_char > option_val, V6 : val]: ((S2 = (produc52622304on_val @ H6 @ (fun_up1252458416on_val @ L6 @ V2 @ (some_val @ V6)))) => ((S3 = (produc52622304on_val @ H7 @ L7)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V6)) @ E3)) @ (produc52622304on_val @ H6 @ L6)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ (the_val @ (L7 @ V2)))) @ E4)) @ (produc52622304on_val @ H7 @ (fun_up1252458416on_val @ L7 @ V2 @ (L6 @ V2))))) @ (transi111096263on_val @ (red @ P)))))))))). % InitBlockReds_aux
thf(fact_217_option_Ocollapse, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => ((some_val @ (the_val @ Option)) = Option))))). % option.collapse
thf(fact_218_option_Ocollapse, axiom,
    ((![Option : option_ty]: ((~ ((Option = none_ty))) => ((some_ty @ (the_ty @ Option)) = Option))))). % option.collapse
thf(fact_219_option_Ocollapse, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => ((some_P1299442195on_val @ (the_Pr901949220on_val @ Option)) = Option))))). % option.collapse
thf(fact_220_option_Osel, axiom,
    ((![X22 : val]: ((the_val @ (some_val @ X22)) = X22)))). % option.sel
thf(fact_221_option_Osel, axiom,
    ((![X22 : ty]: ((the_ty @ (some_ty @ X22)) = X22)))). % option.sel
thf(fact_222_option_Osel, axiom,
    ((![X22 : produc266837688on_val]: ((the_Pr901949220on_val @ (some_P1299442195on_val @ X22)) = X22)))). % option.sel
thf(fact_223_option_Oexpand, axiom,
    ((![Option : option_val, Option2 : option_val]: (((Option = none_val) = (Option2 = none_val)) => (((~ ((Option = none_val))) => ((~ ((Option2 = none_val))) => ((the_val @ Option) = (the_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_224_option_Oexpand, axiom,
    ((![Option : option2118145160on_val, Option2 : option2118145160on_val]: (((Option = none_P1535574167on_val) = (Option2 = none_P1535574167on_val)) => (((~ ((Option = none_P1535574167on_val))) => ((~ ((Option2 = none_P1535574167on_val))) => ((the_Pr901949220on_val @ Option) = (the_Pr901949220on_val @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_225_option_Oexhaust__sel, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => (Option = (some_val @ (the_val @ Option))))))). % option.exhaust_sel
thf(fact_226_option_Oexhaust__sel, axiom,
    ((![Option : option_ty]: ((~ ((Option = none_ty))) => (Option = (some_ty @ (the_ty @ Option))))))). % option.exhaust_sel
thf(fact_227_option_Oexhaust__sel, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => (Option = (some_P1299442195on_val @ (the_Pr901949220on_val @ Option))))))). % option.exhaust_sel
thf(fact_228_BlockRedsFinal, axiom,
    ((![E_02 : exp_list_char, S_0 : produc515445032on_val, E_2 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, P : list_P1234162913t_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, V2 : list_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_02 @ S_0) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E_2) => ((S_0 = (produc52622304on_val @ H_02 @ (fun_up1252458416on_val @ L_02 @ V2 @ none_val))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ E_02) @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V2 @ (L_02 @ V2))))) @ (transi111096263on_val @ (red @ P))))))))). % BlockRedsFinal
thf(fact_229_InitBlockReds, axiom,
    ((![E3 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V2 : list_char, V : val, E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V2 @ (some_val @ V)))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H3 @ L3))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ V)) @ E3)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V2 @ T2 @ (seq_list_char @ (lAss_list_char @ V2 @ (val_list_char @ (the_val @ (L3 @ V2)))) @ E4)) @ (produc52622304on_val @ H3 @ (fun_up1252458416on_val @ L3 @ V2 @ (L @ V2))))) @ (transi111096263on_val @ (red @ P))))))). % InitBlockReds
thf(fact_230_converse__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 @ Bx @ By) => ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B4) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A5 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_231_converse__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 @ Bx @ By) => ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B4) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A5 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_232_converse__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 @ Bx @ By) => ((![A5 : list_char, B4 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A5 @ B4) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A5 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_233_converse__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 @ Bx @ By) => ((![A5 : list_char, B4 : list_char, Aa2 : list_char, Ba : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B4) @ (produc1304532571t_char @ Aa2 @ Ba)) @ R2) => ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Aa2 @ Ba) @ (produc1304532571t_char @ Bx @ By)) @ (transi858104614t_char @ R2)) => ((P @ Aa2 @ Ba) => (P @ A5 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_234_converse__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 @ Bx @ By) => ((![A5 : exp_list_char, B4 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B4) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A5 @ B4))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_235_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)))) => (~ ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A5 @ B4)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A5 @ B4) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_236_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)))) => (~ ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A5 @ B4)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A5 @ B4) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_237_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)))) => (~ ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A5 @ B4)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A5 @ B4) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_238_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)))) => (~ ((![A5 : list_char, B4 : list_char]: ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ Xa @ Xb) @ (produc1304532571t_char @ A5 @ B4)) @ R2) => (~ ((member803902992t_char @ (produc395356247t_char @ (produc1304532571t_char @ A5 @ B4) @ (produc1304532571t_char @ Za @ Zb)) @ (transi858104614t_char @ R2))))))))))))). % converse_rtranclE2
thf(fact_239_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)))) => (~ ((![A5 : exp_list_char, B4 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A5 @ B4)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A5 @ B4) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_240_converse__rtrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ B @ C) @ (transi1879726366t_char @ R2)) => (member89690956t_char @ (produc1304532571t_char @ A @ C) @ (transi1879726366t_char @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_241_converse__rtrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A @ C) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_242_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : list_char, B : list_char, R2 : set_Pr164112643t_char, C : list_char]: ((member89690956t_char @ (produc1304532571t_char @ A @ B) @ (transi1879726366t_char @ R2)) => ((member89690956t_char @ (produc1304532571t_char @ B @ C) @ R2) => (member89690956t_char @ (produc1304532571t_char @ A @ C) @ (transi1879726366t_char @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_243_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A @ C) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_244_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) => ((![Y3 : list_char, Z3 : list_char]: ((member89690956t_char @ (produc1304532571t_char @ Y3 @ Z3) @ R2) => ((member89690956t_char @ (produc1304532571t_char @ Z3 @ B) @ (transi1879726366t_char @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_245_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) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A))))))). % converse_rtrancl_induct
thf(fact_246_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, Fs : 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 @ Fs)) = (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 @ Fs @ (produc1304532571t_char @ F3 @ D3) @ (some_val @ V))))) @ L_2))) @ (transi111096263on_val @ (red @ P))))))))). % FAssRedsVal

% Helper facts (7)
thf(help_If_2_1_If_001t__Option__Ooption_It__Type__Oty_J_T, axiom,
    ((![X : option_ty, Y : option_ty]: ((if_option_ty @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Type__Oty_J_T, axiom,
    ((![X : option_ty, Y : option_ty]: ((if_option_ty @ $true @ X @ Y) = X)))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $true @ X @ Y) = X)))).
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,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $false @ X @ Y) = Y)))).
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,
    ((![X : option2118145160on_val, Y : option2118145160on_val]: ((if_opt451925058on_val @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((lconf_485928294t_char @ p @ ha @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3)) @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t2))))).
