% 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_147__5335360_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:40.178

% Could-be-implicit typings (23)
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thf(ty_n_t__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, type,
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thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_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 (63)
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_DefAss_O_092_060D_062_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_DefAss_OhyperDiff1_001t__List__Olist_It__String__Ochar_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_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,
    seq_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
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__Value__Oval_J, type,
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thf(sy_c_JWellForm_Owf__J__mdecl, type,
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thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, 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_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T______, type,
    t : 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 (234)
thf(fact_0_InitBlockRed_Ohyps_I3_J, axiom,
    (((l_a @ v) = (some_val @ v2)))). % InitBlockRed.hyps(3)
thf(fact_1_InitBlockRed_Oprems, axiom,
    ((d_list_char @ (block_list_char @ v @ t @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v3)) @ ea)) @ (some_set_list_char @ (dom_list_char_val @ la))))). % InitBlockRed.prems
thf(fact_2_InitBlockRed_Ohyps_I2_J, axiom,
    (((d_list_char @ ea @ (some_set_list_char @ (dom_list_char_val @ (fun_up1252458416on_val @ la @ v @ (some_val @ v3))))) => (d_list_char @ e_a @ (some_set_list_char @ (dom_list_char_val @ l_a)))))). % InitBlockRed.hyps(2)
thf(fact_3_InitBlockRed_Ohyps_I1_J, 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)))). % InitBlockRed.hyps(1)
thf(fact_4_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_5_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_6_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_7_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_8_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_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 : nat > option2118145160on_val, X : nat]: ((fun_up262443479on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_11_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_12_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_13_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_14_option_Oinject, axiom,
    ((![X22 : set_list_char, Y22 : set_list_char]: (((some_set_list_char @ X22) = (some_set_list_char @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_15_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_16_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_17__092_060D_062_Osimps_I6_J, axiom,
    ((![V : list_char, E : exp_list_char, A : option_set_list_char]: ((d_list_char @ (lAss_list_char @ V @ E) @ A) = (d_list_char @ E @ A))))). % \<D>.simps(6)
thf(fact_18_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_19_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_20_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_21_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_22_fun__upd__twist, axiom,
    ((![A2 : list_char, C : list_char, M : list_char > option_val, B : option_val, D : option_val]: ((~ ((A2 = C))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A2 @ B) @ C @ D) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C @ D) @ A2 @ B)))))). % fun_upd_twist
thf(fact_23_fun__upd__twist, axiom,
    ((![A2 : nat, C : nat, M : nat > option2118145160on_val, B : option2118145160on_val, D : option2118145160on_val]: ((~ ((A2 = C))) => ((fun_up262443479on_val @ (fun_up262443479on_val @ M @ A2 @ B) @ C @ D) = (fun_up262443479on_val @ (fun_up262443479on_val @ M @ C @ D) @ A2 @ B)))))). % fun_upd_twist
thf(fact_24_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_25_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_26_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_27_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_28_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_29_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_30_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_31_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_32_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A3 : list_char]: (^[B2 : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A3) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_33_fun__upd__def, axiom,
    ((fun_up262443479on_val = (^[F2 : nat > option2118145160on_val]: (^[A3 : nat]: (^[B2 : option2118145160on_val]: (^[X2 : nat]: (if_opt451925058on_val @ (X2 = A3) @ B2 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_34_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_35_exp_Odistinct_I69_J, axiom,
    ((![X3 : val, X111 : exp_list_char, X112 : exp_list_char]: (~ (((val_list_char @ X3) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(69)
thf(fact_36_exp_Odistinct_I67_J, axiom,
    ((![X3 : val, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((val_list_char @ X3) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(67)
thf(fact_37_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_38__092_060D_062_Osimps_I3_J, axiom,
    ((![V2 : val, A : option_set_list_char]: (d_list_char @ (val_list_char @ V2) @ A)))). % \<D>.simps(3)
thf(fact_39_red__reds_OInitBlockRed, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, V2 : val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V3 : val, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V) = (some_val @ V3)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V3)) @ E2)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (red @ P))))))). % red_reds.InitBlockRed
thf(fact_40_red__reds_ORedInitBlock, axiom,
    ((![V : list_char, T : ty, V2 : val, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (val_list_char @ U))) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_41_red__reds_ORedBlock, axiom,
    ((![V : list_char, T : ty, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (val_list_char @ U)) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_42_red__reds_ORedSeq, axiom,
    ((![V2 : val, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S) @ (produc2023458740on_val @ E_2 @ S)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_43_red__reds_OLAssRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ E) @ S) @ (produc2023458740on_val @ (lAss_list_char @ V @ E2) @ S2)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_44_red__reds_OSeqRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_45_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_46_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C2 @ D2)))))))))))). % prod_cases4
thf(fact_47_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B) = (produc1069526295on_val @ A5 @ B4)) = (((A2 = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_48_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B) = (produc2023458740on_val @ A5 @ B4)) = (((A2 = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_49_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A2 @ B) = (produc52622304on_val @ A5 @ B4)) = (((A2 = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_50_old_Oprod_Oinject, axiom,
    ((![A2 : list_char, B : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A2 @ B) = (produc904988266on_val @ A5 @ B4)) = (((A2 = A5)) & ((B = B4))))))). % old.prod.inject
thf(fact_51_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_52_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_53_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_54_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_55_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_56_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_57_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_58_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_59_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_60_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_61_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_62_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A4 @ B3)))))))))). % old.prod.exhaust
thf(fact_63_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B) = (produc1069526295on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_64_Pair__inject, axiom,
    ((![A2 : exp_list_char, B : produc515445032on_val, A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B) = (produc2023458740on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_65_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B : list_char > option_val, A5 : nat > option2118145160on_val, B4 : list_char > option_val]: (((produc52622304on_val @ A2 @ B) = (produc52622304on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_66_Pair__inject, axiom,
    ((![A2 : list_char, B : produc1257910179t_char > option_val, A5 : list_char, B4 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A2 @ B) = (produc904988266on_val @ A5 @ B4)) => (~ (((A2 = A5) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_67_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_68_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_69_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_70_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_71_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_72_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_73_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y4 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_74_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X4 : list_char, Y4 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X4 @ Y4)))))). % surj_pair
thf(fact_75_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_76_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C2 : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C2)))) => (P @ X))))). % prod_induct3
thf(fact_77_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_78_Collect__mem__eq, axiom,
    ((![A : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_79_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ C2))))))))))). % prod_cases3
thf(fact_80_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B3 : nat > option2118145160on_val, C2 : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B3 @ C2))))))))))). % prod_cases3
thf(fact_81_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B3 : exp_list_char, C2 : nat > option2118145160on_val, D2 : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B3 @ (produc52622304on_val @ C2 @ D2))))) => (P @ X))))). % prod_induct4
thf(fact_82_red__reds_ORedLAss, axiom,
    ((![V : list_char, V2 : val, H : nat > option2118145160on_val, L : list_char > option_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2))))) @ (red @ P))))). % red_reds.RedLAss
thf(fact_83_assigned__def, axiom,
    ((assigned = (^[V4 : list_char]: (^[E3 : exp_list_char]: (?[V5 : val]: (?[E4 : exp_list_char]: (E3 = (seq_list_char @ (lAss_list_char @ V4 @ (val_list_char @ V5)) @ E4))))))))). % assigned_def
thf(fact_84_red__reds_OBlockRedSome, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V2 : val, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V) = (some_val @ V2)) => ((~ ((assigned @ V @ E))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E2)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedSome
thf(fact_85_domD, axiom,
    ((![A2 : produc1172664615on_val, M : produc1172664615on_val > option_set_list_char]: ((member354538064on_val @ A2 @ (dom_Pr1335625324t_char @ M)) => (?[B3 : set_list_char]: ((M @ A2) = (some_set_list_char @ B3))))))). % domD
thf(fact_86_domD, axiom,
    ((![A2 : list_char, M : list_char > option_val]: ((member_list_char @ A2 @ (dom_list_char_val @ M)) => (?[B3 : val]: ((M @ A2) = (some_val @ B3))))))). % domD
thf(fact_87_domD, axiom,
    ((![A2 : produc1172664615on_val, M : produc1172664615on_val > option_val]: ((member354538064on_val @ A2 @ (dom_Pr162898261al_val @ M)) => (?[B3 : val]: ((M @ A2) = (some_val @ B3))))))). % domD
thf(fact_88_domD, axiom,
    ((![A2 : produc1172664615on_val, M : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A2 @ (dom_Pr269338893on_val @ M)) => (?[B3 : produc266837688on_val]: ((M @ A2) = (some_P1299442195on_val @ B3))))))). % domD
thf(fact_89_domI, axiom,
    ((![M : produc1172664615on_val > option_set_list_char, A2 : produc1172664615on_val, B : set_list_char]: (((M @ A2) = (some_set_list_char @ B)) => (member354538064on_val @ A2 @ (dom_Pr1335625324t_char @ M)))))). % domI
thf(fact_90_domI, axiom,
    ((![M : list_char > option_val, A2 : list_char, B : val]: (((M @ A2) = (some_val @ B)) => (member_list_char @ A2 @ (dom_list_char_val @ M)))))). % domI
thf(fact_91_domI, axiom,
    ((![M : produc1172664615on_val > option_val, A2 : produc1172664615on_val, B : val]: (((M @ A2) = (some_val @ B)) => (member354538064on_val @ A2 @ (dom_Pr162898261al_val @ M)))))). % domI
thf(fact_92_domI, axiom,
    ((![M : produc1172664615on_val > option2118145160on_val, A2 : produc1172664615on_val, B : produc266837688on_val]: (((M @ A2) = (some_P1299442195on_val @ B)) => (member354538064on_val @ A2 @ (dom_Pr269338893on_val @ M)))))). % domI
thf(fact_93_redp__redsp_OInitBlockRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, V2 : val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, V3 : val, T : ty]: ((redp @ P @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2))) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V) = (some_val @ V3)) => (redp @ P @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E)) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V3)) @ E2)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))))))). % redp_redsp.InitBlockRed
thf(fact_94_not__Some__eq, axiom,
    ((![X : option_set_list_char]: ((![Y2 : set_list_char]: (~ ((X = (some_set_list_char @ Y2))))) = (X = none_set_list_char))))). % not_Some_eq
thf(fact_95_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_96_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_97_not__None__eq, axiom,
    ((![X : option_set_list_char]: ((~ ((X = none_set_list_char))) = (?[Y2 : set_list_char]: (X = (some_set_list_char @ Y2))))))). % not_None_eq
thf(fact_98_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_99_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_100_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_101_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_102_domIff, axiom,
    ((![A2 : list_char, M : list_char > option_val]: ((member_list_char @ A2 @ (dom_list_char_val @ M)) = (~ (((M @ A2) = none_val))))))). % domIff
thf(fact_103_domIff, axiom,
    ((![A2 : produc1172664615on_val, M : produc1172664615on_val > option_val]: ((member354538064on_val @ A2 @ (dom_Pr162898261al_val @ M)) = (~ (((M @ A2) = none_val))))))). % domIff
thf(fact_104_domIff, axiom,
    ((![A2 : produc1172664615on_val, M : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A2 @ (dom_Pr269338893on_val @ M)) = (~ (((M @ A2) = none_P1535574167on_val))))))). % domIff
thf(fact_105_dom__def, axiom,
    ((dom_list_char_val = (^[M2 : list_char > option_val]: (collect_list_char @ (^[A3 : list_char]: (~ (((M2 @ A3) = none_val))))))))). % dom_def
thf(fact_106_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A4 : set_list_char, B3 : set_list_char]: ((X = (some_set_list_char @ A4)) => ((Y = (some_set_list_char @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_107_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option_val > $o, Y : option_val]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_val) => (P @ X @ Y)) => ((![A4 : set_list_char, B3 : val]: ((X = (some_set_list_char @ A4)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_108_combine__options__cases, axiom,
    ((![X : option_set_list_char, P : option_set_list_char > option2118145160on_val > $o, Y : option2118145160on_val]: (((X = none_set_list_char) => (P @ X @ Y)) => (((Y = none_P1535574167on_val) => (P @ X @ Y)) => ((![A4 : set_list_char, B3 : produc266837688on_val]: ((X = (some_set_list_char @ A4)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_109_combine__options__cases, axiom,
    ((![X : option_val, P : option_val > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_val) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A4 : val, B3 : set_list_char]: ((X = (some_val @ A4)) => ((Y = (some_set_list_char @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_110_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)) => ((![A4 : val, B3 : val]: ((X = (some_val @ A4)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_111_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)) => ((![A4 : val, B3 : produc266837688on_val]: ((X = (some_val @ A4)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_112_combine__options__cases, axiom,
    ((![X : option2118145160on_val, P : option2118145160on_val > option_set_list_char > $o, Y : option_set_list_char]: (((X = none_P1535574167on_val) => (P @ X @ Y)) => (((Y = none_set_list_char) => (P @ X @ Y)) => ((![A4 : produc266837688on_val, B3 : set_list_char]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_set_list_char @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_113_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)) => ((![A4 : produc266837688on_val, B3 : val]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_114_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)) => ((![A4 : produc266837688on_val, B3 : produc266837688on_val]: ((X = (some_P1299442195on_val @ A4)) => ((Y = (some_P1299442195on_val @ B3)) => (P @ X @ Y)))) => (P @ X @ Y))))))). % combine_options_cases
thf(fact_115_split__option__all, axiom,
    (((^[P3 : option_set_list_char > $o]: (![X5 : option_set_list_char]: (P3 @ X5))) = (^[P4 : option_set_list_char > $o]: (((P4 @ none_set_list_char)) & ((![X2 : set_list_char]: (P4 @ (some_set_list_char @ X2))))))))). % split_option_all
thf(fact_116_split__option__all, axiom,
    (((^[P3 : option_val > $o]: (![X5 : option_val]: (P3 @ X5))) = (^[P4 : option_val > $o]: (((P4 @ none_val)) & ((![X2 : val]: (P4 @ (some_val @ X2))))))))). % split_option_all
thf(fact_117_split__option__all, axiom,
    (((^[P3 : option2118145160on_val > $o]: (![X5 : option2118145160on_val]: (P3 @ X5))) = (^[P4 : option2118145160on_val > $o]: (((P4 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P4 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_118_split__option__ex, axiom,
    (((^[P3 : option_set_list_char > $o]: (?[X5 : option_set_list_char]: (P3 @ X5))) = (^[P4 : option_set_list_char > $o]: (((P4 @ none_set_list_char)) | ((?[X2 : set_list_char]: (P4 @ (some_set_list_char @ X2))))))))). % split_option_ex
thf(fact_119_split__option__ex, axiom,
    (((^[P3 : option_val > $o]: (?[X5 : option_val]: (P3 @ X5))) = (^[P4 : option_val > $o]: (((P4 @ none_val)) | ((?[X2 : val]: (P4 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_120_split__option__ex, axiom,
    (((^[P3 : option2118145160on_val > $o]: (?[X5 : option2118145160on_val]: (P3 @ X5))) = (^[P4 : option2118145160on_val > $o]: (((P4 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P4 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_121_option_Oinducts, axiom,
    ((![P : option_set_list_char > $o, Option : option_set_list_char]: ((P @ none_set_list_char) => ((![X4 : set_list_char]: (P @ (some_set_list_char @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_122_option_Oinducts, axiom,
    ((![P : option_val > $o, Option : option_val]: ((P @ none_val) => ((![X4 : val]: (P @ (some_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_123_option_Oinducts, axiom,
    ((![P : option2118145160on_val > $o, Option : option2118145160on_val]: ((P @ none_P1535574167on_val) => ((![X4 : produc266837688on_val]: (P @ (some_P1299442195on_val @ X4))) => (P @ Option)))))). % option.inducts
thf(fact_124_option_Oexhaust, axiom,
    ((![Y : option_set_list_char]: ((~ ((Y = none_set_list_char))) => (~ ((![X23 : set_list_char]: (~ ((Y = (some_set_list_char @ X23))))))))))). % option.exhaust
thf(fact_125_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_126_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_127_option_OdiscI, axiom,
    ((![Option : option_set_list_char, X22 : set_list_char]: ((Option = (some_set_list_char @ X22)) => (~ ((Option = none_set_list_char))))))). % option.discI
thf(fact_128_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_129_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_130_option_Odistinct_I1_J, axiom,
    ((![X22 : set_list_char]: (~ ((none_set_list_char = (some_set_list_char @ X22))))))). % option.distinct(1)
thf(fact_131_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_132_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_133_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, V : list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (lAss_list_char @ V @ E) @ S @ (lAss_list_char @ V @ E2) @ S2))))). % redp_redsp.LAssRed
thf(fact_134_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E @ S @ E2 @ S2) => (redp @ P @ (seq_list_char @ E @ E_2) @ S @ (seq_list_char @ E2 @ E_2) @ S2))))). % redp_redsp.SeqRed
thf(fact_135_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, T : ty]: ((redp @ P @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val)) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E))) => (redp @ P @ (block_list_char @ V @ T @ E) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V)))))))))). % redp_redsp.BlockRedNone
thf(fact_136_map__upd__nonempty, axiom,
    ((![T2 : list_char > option_val, K : list_char, X : val]: (~ (((fun_up1252458416on_val @ T2 @ K @ (some_val @ X)) = (^[X2 : list_char]: none_val))))))). % map_upd_nonempty
thf(fact_137_map__upd__nonempty, axiom,
    ((![T2 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (~ (((fun_up262443479on_val @ T2 @ K @ (some_P1299442195on_val @ X)) = (^[X2 : nat]: none_P1535574167on_val))))))). % map_upd_nonempty
thf(fact_138_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V2 : val, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S @ E_2 @ S)))). % redp_redsp.RedSeq
thf(fact_139_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V : list_char, T : ty, U : val, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V @ T @ (val_list_char @ U)) @ S @ (val_list_char @ U) @ S)))). % redp_redsp.RedBlock
thf(fact_140_redp__redsp_ORedLAss, axiom,
    ((![P : list_P1234162913t_char, V : list_char, V2 : val, H : nat > option2118145160on_val, L : list_char > option_val]: (redp @ P @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (produc52622304on_val @ H @ L) @ (val_list_char @ unit) @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2))))))). % redp_redsp.RedLAss
thf(fact_141_redp__redsp_OBlockRedSome, axiom,
    ((![P : list_P1234162913t_char, E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, V2 : val, T : ty]: ((redp @ P @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val)) @ E2 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V) = (some_val @ V2)) => ((~ ((assigned @ V @ E))) => (redp @ P @ (block_list_char @ V @ T @ E) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E2)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V)))))))))). % redp_redsp.BlockRedSome
thf(fact_142_redp__red__eq, axiom,
    ((redp = (^[P4 : 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 @ P4)))))))))). % redp_red_eq
thf(fact_143_redp__redsp_ORedInitBlock, axiom,
    ((![P : list_P1234162913t_char, V : list_char, T : ty, V2 : val, U : val, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (val_list_char @ U))) @ S @ (val_list_char @ U) @ S)))). % redp_redsp.RedInitBlock
thf(fact_144_red__reds_OBlockRedNone, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_145_map__upd__Some__unfold, axiom,
    ((![M : list_char > option_val, A2 : list_char, B : val, X : list_char, Y : val]: (((fun_up1252458416on_val @ M @ A2 @ (some_val @ B) @ X) = (some_val @ Y)) = (((((X = A2)) & ((B = Y)))) | ((((~ ((X = A2)))) & (((M @ X) = (some_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_146_map__upd__Some__unfold, axiom,
    ((![M : nat > option2118145160on_val, A2 : nat, B : produc266837688on_val, X : nat, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A2 @ (some_P1299442195on_val @ B) @ X) = (some_P1299442195on_val @ Y)) = (((((X = A2)) & ((B = Y)))) | ((((~ ((X = A2)))) & (((M @ X) = (some_P1299442195on_val @ Y)))))))))). % map_upd_Some_unfold
thf(fact_147_map__upd__triv, axiom,
    ((![T2 : list_char > option_val, K : list_char, X : val]: (((T2 @ K) = (some_val @ X)) => ((fun_up1252458416on_val @ T2 @ K @ (some_val @ X)) = T2))))). % map_upd_triv
thf(fact_148_map__upd__triv, axiom,
    ((![T2 : nat > option2118145160on_val, K : nat, X : produc266837688on_val]: (((T2 @ K) = (some_P1299442195on_val @ X)) => ((fun_up262443479on_val @ T2 @ K @ (some_P1299442195on_val @ X)) = T2))))). % map_upd_triv
thf(fact_149_map__upd__eqD1, axiom,
    ((![M : list_char > option_val, A2 : list_char, X : val, N : list_char > option_val, Y : val]: (((fun_up1252458416on_val @ M @ A2 @ (some_val @ X)) = (fun_up1252458416on_val @ N @ A2 @ (some_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_150_map__upd__eqD1, axiom,
    ((![M : nat > option2118145160on_val, A2 : nat, X : produc266837688on_val, N : nat > option2118145160on_val, Y : produc266837688on_val]: (((fun_up262443479on_val @ M @ A2 @ (some_P1299442195on_val @ X)) = (fun_up262443479on_val @ N @ A2 @ (some_P1299442195on_val @ Y))) => (X = Y))))). % map_upd_eqD1
thf(fact_151_LAssRedsVal, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, V2 : val, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, V : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ E) @ S) @ (produc2023458740on_val @ (val_list_char @ unit) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (some_val @ V2))))) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsVal
thf(fact_152_red__lcl__incr, axiom,
    ((![E : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E2 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_0) @ (dom_list_char_val @ L_1)))))). % red_lcl_incr
thf(fact_153_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_154__092_060D_062_Osimps_I10_J, axiom,
    ((![V : list_char, T : ty, E : exp_list_char, A : option_set_list_char]: ((d_list_char @ (block_list_char @ V @ T @ E) @ A) = (d_list_char @ E @ (hyperDiff1_list_char @ A @ V)))))). % \<D>.simps(10)
thf(fact_155_InitBlockRedsFinal, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, V2 : val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E2) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (transi111096263on_val @ (red @ P)))))))). % InitBlockRedsFinal
thf(fact_156_LAssReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V @ E) @ S) @ (produc2023458740on_val @ (lAss_list_char @ V @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_157_SeqReds, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_158_BlockRedsFinal, axiom,
    ((![E_0 : 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_0 : nat > option2118145160on_val, L_0 : list_char > option_val, V : list_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ 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_0 @ (fun_up1252458416on_val @ L_0 @ V @ none_val))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E_0) @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V @ (L_0 @ V))))) @ (transi111096263on_val @ (red @ P))))))))). % BlockRedsFinal
thf(fact_159_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_160_converse__rtrancl__induct__red, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, 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 @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E5 @ H3 @ L3 @ E5 @ H3 @ L3)) => ((![E_02 : exp_list_char, H_02 : nat > option2118145160on_val, L_02 : list_char > option_val, E_12 : exp_list_char, H_12 : nat > option2118145160on_val, L_12 : list_char > option_val, E6 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_02 @ (produc52622304on_val @ H_02 @ L_02)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_12 @ L_12))) @ (red @ P)) => ((R @ E_12 @ H_12 @ L_12 @ E6 @ H4 @ L4) => (R @ E_02 @ H_02 @ L_02 @ E6 @ H4 @ L4)))) => (R @ E @ H @ L @ E2 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_161_InitBlockReds, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, V2 : val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ E)) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ (the_val @ (L2 @ V)))) @ E2)) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (transi111096263on_val @ (red @ P))))))). % InitBlockReds
thf(fact_162_InitBlockReds__aux, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : list_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (transi111096263on_val @ (red @ P))) => (![H5 : nat > option2118145160on_val, L5 : list_char > option_val, H6 : nat > option2118145160on_val, L6 : list_char > option_val, V6 : val]: ((S = (produc52622304on_val @ H5 @ (fun_up1252458416on_val @ L5 @ V @ (some_val @ V6)))) => ((S2 = (produc52622304on_val @ H6 @ L6)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V6)) @ E)) @ (produc52622304on_val @ H5 @ L5)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ (the_val @ (L6 @ V)))) @ E2)) @ (produc52622304on_val @ H6 @ (fun_up1252458416on_val @ L6 @ V @ (L5 @ V))))) @ (transi111096263on_val @ (red @ P)))))))))). % InitBlockReds_aux
thf(fact_163_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_164_option_Ocollapse, axiom,
    ((![Option : option_set_list_char]: ((~ ((Option = none_set_list_char))) => ((some_set_list_char @ (the_set_list_char @ Option)) = Option))))). % option.collapse
thf(fact_165_option_Ocollapse, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => ((some_val @ (the_val @ Option)) = Option))))). % option.collapse
thf(fact_166_option_Ocollapse, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => ((some_P1299442195on_val @ (the_Pr901949220on_val @ Option)) = Option))))). % option.collapse
thf(fact_167_option_Osel, axiom,
    ((![X22 : set_list_char]: ((the_set_list_char @ (some_set_list_char @ X22)) = X22)))). % option.sel
thf(fact_168_option_Osel, axiom,
    ((![X22 : val]: ((the_val @ (some_val @ X22)) = X22)))). % option.sel
thf(fact_169_option_Osel, axiom,
    ((![X22 : produc266837688on_val]: ((the_Pr901949220on_val @ (some_P1299442195on_val @ X22)) = X22)))). % option.sel
thf(fact_170_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_171_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_172_option_Oexhaust__sel, axiom,
    ((![Option : option_set_list_char]: ((~ ((Option = none_set_list_char))) => (Option = (some_set_list_char @ (the_set_list_char @ Option))))))). % option.exhaust_sel
thf(fact_173_option_Oexhaust__sel, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) => (Option = (some_val @ (the_val @ Option))))))). % option.exhaust_sel
thf(fact_174_option_Oexhaust__sel, axiom,
    ((![Option : option2118145160on_val]: ((~ ((Option = none_P1535574167on_val))) => (Option = (some_P1299442195on_val @ (the_Pr901949220on_val @ Option))))))). % option.exhaust_sel
thf(fact_175_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H7 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H7) => (hext @ H @ H7)))))). % hext_trans
thf(fact_176_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, X : produc266837688on_val]: (((H @ A2) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_177_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A2 @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))). % hext_upd_obj
thf(fact_178_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A2 : nat, C3 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H2 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3))))))))). % hext_objD
thf(fact_179_hext__def, axiom,
    ((hext = (^[H8 : nat > option2118145160on_val]: (^[H9 : nat > option2118145160on_val]: (![A3 : nat]: (![C4 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H8 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H9 @ A3) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5)))))))))))))). % hext_def
thf(fact_180_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A4 : nat, C5 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H2 @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs7)))))) => (hext @ H @ H2))))). % hextI
thf(fact_181_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) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A4 @ B3)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_182_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) => ((![A4 : 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 @ A4 @ B3)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_183_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) => ((![A4 : 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 @ A4 @ B3)) @ (transi2071064181on_val @ R2)) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A4 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_184_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) => ((![A4 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A4 @ B3)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A4 @ B3) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_185_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)))) => (~ ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A4 @ B3)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_186_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)))) => (~ ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A4 @ B3)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_187_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)))) => (~ ((![A4 : list_char, B3 : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Xa @ Xb) @ (produc904988266on_val @ A4 @ B3)) @ R2) => (~ ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A4 @ B3) @ (produc904988266on_val @ Za @ Zb)) @ (transi2071064181on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_188_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)))) => (~ ((![A4 : exp_list_char, B3 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A4 @ B3)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_189_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) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A4 @ B3) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_190_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) => ((![A4 : nat > option2118145160on_val, B3 : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A4 @ B3) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_191_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) => ((![A4 : list_char, B3 : produc1257910179t_char > option_val, Aa2 : list_char, Ba : produc1257910179t_char > option_val]: ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ A4 @ B3) @ (produc904988266on_val @ Aa2 @ Ba)) @ R2) => ((member197592058on_val @ (produc881885833on_val @ (produc904988266on_val @ Aa2 @ Ba) @ (produc904988266on_val @ Bx @ By)) @ (transi2071064181on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_192_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) => ((![A4 : exp_list_char, B3 : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A4 @ B3) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A4 @ B3))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_193_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_194_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_195_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y4) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ B) @ R2)))))))))))). % rtranclE
thf(fact_196_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B3 @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_197_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A3 : produc1097884484on_val]: (((A1 = A3)) & ((A22 = A3))))) | ((?[A3 : produc1097884484on_val]: (?[B2 : produc1097884484on_val]: (?[C6 : produc1097884484on_val]: (((A1 = A3)) & ((((A22 = C6)) & ((((member354538064on_val @ (produc1069526295on_val @ A3 @ B2) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B2 @ C6) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_198_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_199_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R2)) => ((P @ A2) => ((![Y4 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ R2) => ((P @ Y4) => (P @ Z3))))) => (P @ B))))))). % rtrancl_induct
thf(fact_200_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X22 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X22) @ (transi111096263on_val @ R2)) => ((![A4 : produc1097884484on_val]: (P @ A4 @ A4)) => ((![A4 : produc1097884484on_val, B3 : produc1097884484on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A4 @ B3) @ (transi111096263on_val @ R2)) => ((P @ A4 @ B3) => ((member354538064on_val @ (produc1069526295on_val @ B3 @ C2) @ R2) => (P @ A4 @ C2))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_201_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_202_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_203_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R2)) => ((P @ B) => ((![Y4 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y4))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_204_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_205_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B : produc1097884484on_val, R2 : set_Pr1189492743on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_206_subset__antisym, axiom,
    ((![A : set_list_char, B5 : set_list_char]: ((ord_le1836582007t_char @ A @ B5) => ((ord_le1836582007t_char @ B5 @ A) => (A = B5)))))). % subset_antisym
thf(fact_207_subsetI, axiom,
    ((![A : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: ((member354538064on_val @ X4 @ A) => (member354538064on_val @ X4 @ B5))) => (ord_le837504935on_val @ A @ B5))))). % subsetI
thf(fact_208_subsetI, axiom,
    ((![A : set_list_char, B5 : set_list_char]: ((![X4 : list_char]: ((member_list_char @ X4 @ A) => (member_list_char @ X4 @ B5))) => (ord_le1836582007t_char @ A @ B5))))). % subsetI
thf(fact_209_rtrancl__mono, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R2 @ S) => (ord_le837504935on_val @ (transi111096263on_val @ R2) @ (transi111096263on_val @ S)))))). % rtrancl_mono
thf(fact_210_rtrancl__subset, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R @ S3) => ((ord_le837504935on_val @ S3 @ (transi111096263on_val @ R)) => ((transi111096263on_val @ S3) = (transi111096263on_val @ R))))))). % rtrancl_subset
thf(fact_211_rtrancl__subset__rtrancl, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((ord_le837504935on_val @ R2 @ (transi111096263on_val @ S)) => (ord_le837504935on_val @ (transi111096263on_val @ R2) @ (transi111096263on_val @ S)))))). % rtrancl_subset_rtrancl
thf(fact_212_in__mono, axiom,
    ((![A : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val, X : produc1172664615on_val]: ((ord_le837504935on_val @ A @ B5) => ((member354538064on_val @ X @ A) => (member354538064on_val @ X @ B5)))))). % in_mono
thf(fact_213_in__mono, axiom,
    ((![A : set_list_char, B5 : set_list_char, X : list_char]: ((ord_le1836582007t_char @ A @ B5) => ((member_list_char @ X @ A) => (member_list_char @ X @ B5)))))). % in_mono
thf(fact_214_subsetD, axiom,
    ((![A : set_Pr1189492743on_val, B5 : set_Pr1189492743on_val, C : produc1172664615on_val]: ((ord_le837504935on_val @ A @ B5) => ((member354538064on_val @ C @ A) => (member354538064on_val @ C @ B5)))))). % subsetD
thf(fact_215_subsetD, axiom,
    ((![A : set_list_char, B5 : set_list_char, C : list_char]: ((ord_le1836582007t_char @ A @ B5) => ((member_list_char @ C @ A) => (member_list_char @ C @ B5)))))). % subsetD
thf(fact_216_equalityE, axiom,
    ((![A : set_list_char, B5 : set_list_char]: ((A = B5) => (~ (((ord_le1836582007t_char @ A @ B5) => (~ ((ord_le1836582007t_char @ B5 @ A)))))))))). % equalityE
thf(fact_217_subset__eq, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A6)) => ((member354538064on_val @ X2 @ B6))))))))). % subset_eq
thf(fact_218_subset__eq, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (![X2 : list_char]: (((member_list_char @ X2 @ A6)) => ((member_list_char @ X2 @ B6))))))))). % subset_eq
thf(fact_219_equalityD1, axiom,
    ((![A : set_list_char, B5 : set_list_char]: ((A = B5) => (ord_le1836582007t_char @ A @ B5))))). % equalityD1
thf(fact_220_equalityD2, axiom,
    ((![A : set_list_char, B5 : set_list_char]: ((A = B5) => (ord_le1836582007t_char @ B5 @ A))))). % equalityD2
thf(fact_221_subset__iff, axiom,
    ((ord_le837504935on_val = (^[A6 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![T3 : produc1172664615on_val]: (((member354538064on_val @ T3 @ A6)) => ((member354538064on_val @ T3 @ B6))))))))). % subset_iff
thf(fact_222_subset__iff, axiom,
    ((ord_le1836582007t_char = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (![T3 : list_char]: (((member_list_char @ T3 @ A6)) => ((member_list_char @ T3 @ B6))))))))). % subset_iff
thf(fact_223_subset__refl, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ A)))). % subset_refl
thf(fact_224_Collect__mono, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((![X4 : list_char]: ((P @ X4) => (Q @ X4))) => (ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)))))). % Collect_mono
thf(fact_225_subset__trans, axiom,
    ((![A : set_list_char, B5 : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ B5) => ((ord_le1836582007t_char @ B5 @ C3) => (ord_le1836582007t_char @ A @ C3)))))). % subset_trans
thf(fact_226_set__eq__subset, axiom,
    (((^[Y5 : set_list_char]: (^[Z4 : set_list_char]: (Y5 = Z4))) = (^[A6 : set_list_char]: (^[B6 : set_list_char]: (((ord_le1836582007t_char @ A6 @ B6)) & ((ord_le1836582007t_char @ B6 @ A6)))))))). % set_eq_subset
thf(fact_227_Collect__mono__iff, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)) = (![X2 : list_char]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_228_Collect__subset, axiom,
    ((![A : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (((member354538064on_val @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_229_Collect__subset, axiom,
    ((![A : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X2 : list_char]: (((member_list_char @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_230_order__refl, axiom,
    ((![X : set_list_char]: (ord_le1836582007t_char @ X @ X)))). % order_refl
thf(fact_231_Red__lcl__add, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_0 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_232_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M22 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M22 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M22) @ M3))))). % map_add_assoc
thf(fact_233_map__add__find__right, axiom,
    ((![N : list_char > option_val, K : list_char, Xx : val, M : list_char > option_val]: (((N @ K) = (some_val @ Xx)) => ((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ Xx)))))). % map_add_find_right

% Helper facts (5)
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,
    ((d_list_char @ (block_list_char @ v @ t @ (seq_list_char @ (lAss_list_char @ v @ (val_list_char @ v2)) @ e_a)) @ (some_set_list_char @ (dom_list_char_val @ (fun_up1252458416on_val @ l_a @ v @ (la @ v))))))).
