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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:20.450

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thf(sy_c_Product__Type_Oprod_Ocase__prod_001_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_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc1919805778on_val : ((nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val) > produc515445032on_val > set_Pr1189492743on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_062_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_M_Eo_J, type,
    produc1468025474_val_o : (exp_list_char > produc515445032on_val > produc1097884484on_val > $o) > produc1097884484on_val > produc1097884484on_val > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_Eo, type,
    produc199145871_val_o : (exp_list_char > produc515445032on_val > $o) > produc1097884484on_val > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc848217214on_val : (exp_list_char > produc515445032on_val > set_Pr1189492743on_val) > produc1097884484on_val > set_Pr1189492743on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__String__Ochar_J_001_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_001_Eo, type,
    produc1336856385_val_o : (list_char > (produc1257910179t_char > option_val) > $o) > produc266837688on_val > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__String__Ochar_J_001_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_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc535686448on_val : (list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val) > produc266837688on_val > set_Pr1189492743on_val).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__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_001t__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_001_Eo, type,
    produc50362220_val_o : (produc1097884484on_val > produc1097884484on_val > $o) > produc1172664615on_val > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__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_001t__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_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    produc493625819on_val : (produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val) > produc1172664615on_val > set_Pr1189492743on_val).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oassigned, type,
    assigned : list_char > exp_list_char > $o).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oredp, type,
    redp : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__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, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_TypeRel_Owiden_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,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_WellForm_Owf__prog_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,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__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, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__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,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_Te_H____, type,
    te : ty).
thf(sy_v_Te____, type,
    te2 : 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____, type,
    v2 : val).

% Relevant facts (247)
thf(fact_0_BlockRedSome_Ohyps_I4_J, axiom,
    ((~ ((assigned @ v @ ea))))). % BlockRedSome.hyps(4)
thf(fact_1_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_2_wt, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t @ ea) @ te2))). % wt
thf(fact_3_Some, axiom,
    (((l_a @ v) = (some_val @ v2)))). % Some
thf(fact_4_IH_H, axiom,
    (((wTrt @ p @ h_a @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t)) @ e_a @ te) & (widen_917054840t_char @ p @ te @ te2)))). % IH'
thf(fact_5_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_6_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_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__triv, axiom,
    ((![F : list_char > option_ty, X : list_char]: ((fun_up9191ion_ty @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
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_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_12_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_13_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_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Te_H_O_AP_ME_IV_A_092_060mapsto_062_AT_J_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ATe_H_A_092_060and_062_AP_A_092_060turnstile_062_ATe_H_A_092_060le_062_ATe_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Te : ty]: (~ (((wTrt @ p @ h_a @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t)) @ e_a @ Te) & (widen_917054840t_char @ p @ Te @ te2))))))))). % \<open>\<And>thesis. (\<And>Te'. P,E(V \<mapsto> T),h' \<turnstile> e' : Te' \<and> P \<turnstile> Te' \<le> Te \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_15_option_Oinject, axiom,
    ((![X22 : ty, Y22 : ty]: (((some_ty @ X22) = (some_ty @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_16_option_Oinject, axiom,
    ((![X22 : val, Y22 : val]: (((some_val @ X22) = (some_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_17_option_Oinject, axiom,
    ((![X22 : produc266837688on_val, Y22 : produc266837688on_val]: (((some_P1299442195on_val @ X22) = (some_P1299442195on_val @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_18_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_19_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_20_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_21_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_22_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_23_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_24_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_25_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_26_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_27_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_28_BlockRedSome_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t @ ea) @ te2))). % BlockRedSome.prems(2)
thf(fact_29_BlockRedSome_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % BlockRedSome.prems(1)
thf(fact_30_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_31_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_32_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_33_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_34_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_35_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_36_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_37_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_38_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_39_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_40_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_41_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_42_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_43_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_44_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_45_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_46_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_47_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_48_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_49_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_50_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_51_BlockRedSome_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) => ((wTrt @ p @ ha @ E @ ea @ T2) => (?[T3 : ty]: ((wTrt @ p @ h_a @ E @ e_a @ T3) & (widen_917054840t_char @ p @ T3 @ T2)))))))). % BlockRedSome.hyps(2)
thf(fact_52_IH, axiom,
    ((![E : list_char > option_ty, T2 : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) => ((wTrt @ p @ ha @ E @ ea @ T2) => (?[T3 : ty]: ((wTrt @ p @ h_a @ E @ e_a @ T3) & (widen_917054840t_char @ p @ T3 @ T2)))))))). % IH
thf(fact_53_WTrtBlock, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, V : list_char, T2 : ty, E2 : exp_list_char, T4 : ty]: ((wTrt @ P @ H @ (fun_up9191ion_ty @ E @ V @ (some_ty @ T2)) @ E2 @ T4) => (wTrt @ P @ H @ E @ (block_list_char @ V @ T2 @ E2) @ T4))))). % WTrtBlock
thf(fact_54_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_55_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_56_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_57_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_58_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_59_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_60_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_61_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_62_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_63_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_64_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_65_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_66_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_67_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_68_lconf__upd2, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T2 : ty, V : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V2 @ T2) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)) @ (fun_up9191ion_ty @ E @ V @ (some_ty @ T2)))))))). % lconf_upd2
thf(fact_69_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T2 : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T2) => (widen_917054840t_char @ P @ S @ T2)))))). % widen_trans
thf(fact_70_not__None__eq, axiom,
    ((![X : option_ty]: ((~ ((X = none_ty))) = (?[Y2 : ty]: (X = (some_ty @ Y2))))))). % not_None_eq
thf(fact_71_not__None__eq, axiom,
    ((![X : option_val]: ((~ ((X = none_val))) = (?[Y2 : val]: (X = (some_val @ Y2))))))). % not_None_eq
thf(fact_72_not__None__eq, axiom,
    ((![X : option2118145160on_val]: ((~ ((X = none_P1535574167on_val))) = (?[Y2 : produc266837688on_val]: (X = (some_P1299442195on_val @ Y2))))))). % not_None_eq
thf(fact_73_not__Some__eq, axiom,
    ((![X : option_ty]: ((![Y2 : ty]: (~ ((X = (some_ty @ Y2))))) = (X = none_ty))))). % not_Some_eq
thf(fact_74_not__Some__eq, axiom,
    ((![X : option_val]: ((![Y2 : val]: (~ ((X = (some_val @ Y2))))) = (X = none_val))))). % not_Some_eq
thf(fact_75_not__Some__eq, axiom,
    ((![X : option2118145160on_val]: ((![Y2 : produc266837688on_val]: (~ ((X = (some_P1299442195on_val @ Y2))))) = (X = none_P1535574167on_val))))). % not_Some_eq
thf(fact_76_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_77_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_78_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_79_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_80_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V2 : val, T2 : ty, T4 : ty]: ((conf_P93989998t_char @ P @ H @ V2 @ T2) => ((widen_917054840t_char @ P @ T2 @ T4) => (conf_P93989998t_char @ P @ H @ V2 @ T4)))))). % conf_widen
thf(fact_81_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T2) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_82_option_Odistinct_I1_J, axiom,
    ((![X22 : ty]: (~ ((none_ty = (some_ty @ X22))))))). % option.distinct(1)
thf(fact_83_option_Odistinct_I1_J, axiom,
    ((![X22 : val]: (~ ((none_val = (some_val @ X22))))))). % option.distinct(1)
thf(fact_84_option_Odistinct_I1_J, axiom,
    ((![X22 : produc266837688on_val]: (~ ((none_P1535574167on_val = (some_P1299442195on_val @ X22))))))). % option.distinct(1)
thf(fact_85_option_OdiscI, axiom,
    ((![Option : option_ty, X22 : ty]: ((Option = (some_ty @ X22)) => (~ ((Option = none_ty))))))). % option.discI
thf(fact_86_option_OdiscI, axiom,
    ((![Option : option_val, X22 : val]: ((Option = (some_val @ X22)) => (~ ((Option = none_val))))))). % option.discI
thf(fact_87_option_OdiscI, axiom,
    ((![Option : option2118145160on_val, X22 : produc266837688on_val]: ((Option = (some_P1299442195on_val @ X22)) => (~ ((Option = none_P1535574167on_val))))))). % option.discI
thf(fact_88_option_Oexhaust, axiom,
    ((![Y : option_ty]: ((~ ((Y = none_ty))) => (~ ((![X23 : ty]: (~ ((Y = (some_ty @ X23))))))))))). % option.exhaust
thf(fact_89_option_Oexhaust, axiom,
    ((![Y : option_val]: ((~ ((Y = none_val))) => (~ ((![X23 : val]: (~ ((Y = (some_val @ X23))))))))))). % option.exhaust
thf(fact_90_option_Oexhaust, axiom,
    ((![Y : option2118145160on_val]: ((~ ((Y = none_P1535574167on_val))) => (~ ((![X23 : produc266837688on_val]: (~ ((Y = (some_P1299442195on_val @ X23))))))))))). % option.exhaust
thf(fact_91_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_92_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_93_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_94_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_95_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_96_Collect__cong, axiom,
    ((![P : produc1172664615on_val > $o, Q : produc1172664615on_val > $o]: ((![X3 : produc1172664615on_val]: ((P @ X3) = (Q @ X3))) => ((collec2055896722on_val @ P) = (collec2055896722on_val @ Q)))))). % Collect_cong
thf(fact_97_split__option__ex, axiom,
    (((^[P2 : option_ty > $o]: (?[X4 : option_ty]: (P2 @ X4))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) | ((?[X2 : ty]: (P3 @ (some_ty @ X2))))))))). % split_option_ex
thf(fact_98_split__option__ex, axiom,
    (((^[P2 : option_val > $o]: (?[X4 : option_val]: (P2 @ X4))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) | ((?[X2 : val]: (P3 @ (some_val @ X2))))))))). % split_option_ex
thf(fact_99_split__option__ex, axiom,
    (((^[P2 : option2118145160on_val > $o]: (?[X4 : option2118145160on_val]: (P2 @ X4))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) | ((?[X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_ex
thf(fact_100_split__option__all, axiom,
    (((^[P2 : option_ty > $o]: (![X4 : option_ty]: (P2 @ X4))) = (^[P3 : option_ty > $o]: (((P3 @ none_ty)) & ((![X2 : ty]: (P3 @ (some_ty @ X2))))))))). % split_option_all
thf(fact_101_split__option__all, axiom,
    (((^[P2 : option_val > $o]: (![X4 : option_val]: (P2 @ X4))) = (^[P3 : option_val > $o]: (((P3 @ none_val)) & ((![X2 : val]: (P3 @ (some_val @ X2))))))))). % split_option_all
thf(fact_102_split__option__all, axiom,
    (((^[P2 : option2118145160on_val > $o]: (![X4 : option2118145160on_val]: (P2 @ X4))) = (^[P3 : option2118145160on_val > $o]: (((P3 @ none_P1535574167on_val)) & ((![X2 : produc266837688on_val]: (P3 @ (some_P1299442195on_val @ X2))))))))). % split_option_all
thf(fact_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_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_112_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_113_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_114_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_115_lconf__def, axiom,
    ((lconf_485928294t_char = (^[P3 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (^[E4 : list_char > option_ty]: (![V3 : list_char]: (![V4 : val]: ((((L3 @ V3) = (some_val @ V4))) => ((?[T5 : ty]: ((((E4 @ V3) = (some_ty @ T5))) & ((conf_P93989998t_char @ P3 @ H3 @ V4 @ T5))))))))))))))). % lconf_def
thf(fact_116_lconf__upd, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, V2 : val, T2 : ty, V : list_char]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((conf_P93989998t_char @ P @ H @ V2 @ T2) => (((E @ V) = (some_ty @ T2)) => (lconf_485928294t_char @ P @ H @ (fun_up1252458416on_val @ L @ V @ (some_val @ V2)) @ E))))))). % lconf_upd
thf(fact_117_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_118_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_119_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_120_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_121_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_122_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_123_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A5 : exp_list_char, B4 : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A5 @ B4)))))))))). % old.prod.exhaust
thf(fact_124_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_125_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_126_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_127_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_128_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_129_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_130_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_131_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_132_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_133_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_134_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_135_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_136_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_137_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_138_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_139_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P4 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_140_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_141_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_142_surj__pair, axiom,
    ((![P4 : produc266837688on_val]: (?[X3 : list_char, Y3 : produc1257910179t_char > option_val]: (P4 = (produc904988266on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_143_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T2 : ty]: (widen_917054840t_char @ P @ T2 @ T2)))). % widen_refl
thf(fact_144_red__reds_OBlockRedNone, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T2 @ E2) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T2 @ E3) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_145_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((wTrt @ P @ H @ E @ E2 @ T2) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_146_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E3 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T2 : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E3 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T2) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_147_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_148_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_149_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, T2 : ty]: ((redp @ P @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val)) @ E3 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E2))) => (redp @ P @ (block_list_char @ V @ T2 @ E2) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T2 @ E3) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V)))))))))). % redp_redsp.BlockRedNone
thf(fact_150_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_151_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T2 : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T2) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T2)))))). % WTrt_hext_mono
thf(fact_152_lconf__hext, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, L : list_char > option_val, E : list_char > option_ty, H2 : nat > option2118145160on_val]: ((lconf_485928294t_char @ P @ H @ L @ E) => ((hext @ H @ H2) => (lconf_485928294t_char @ P @ H2 @ L @ E)))))). % lconf_hext
thf(fact_153_redp__red__eq, axiom,
    ((redp = (^[P3 : 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 @ P3)))))))))). % redp_red_eq
thf(fact_154_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_155_hext__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: (((H @ A) = none_P1535574167on_val) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X))))))). % hext_new
thf(fact_156_hext__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (hext @ H @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2)))))))). % hext_upd_obj
thf(fact_157_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (?[Fs3 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs3))))))))). % hext_objD
thf(fact_158_hext__def, axiom,
    ((hext = (^[H3 : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A2 : nat]: (![C4 : list_char]: (![Fs4 : produc1257910179t_char > option_val]: ((((H3 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs4)))) => ((?[Fs5 : produc1257910179t_char > option_val]: ((H4 @ A2) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5)))))))))))))). % hext_def
thf(fact_159_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_160_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_161_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A5 : nat, C5 : list_char, Fs6 : produc1257910179t_char > option_val]: (((H @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs6))) => (?[Fs7 : produc1257910179t_char > option_val]: ((H2 @ A5) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs7)))))) => (hext @ H @ H2))))). % hextI
thf(fact_162_hconf__def, axiom,
    ((hconf_1244167010t_char = (^[P3 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (((![A2 : nat]: (![Obj2 : produc266837688on_val]: ((((H3 @ A2) = (some_P1299442195on_val @ Obj2))) => ((oconf_454120169t_char @ P3 @ H3 @ Obj2)))))) & ((preallocated @ H3)))))))). % hconf_def
thf(fact_163_hext__typeof__mono, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, V2 : val, T2 : ty]: ((hext @ H @ H2) => (((typeof_h @ H @ V2) = (some_ty @ T2)) => ((typeof_h @ H2 @ V2) = (some_ty @ T2))))))). % hext_typeof_mono
thf(fact_164_typeof__lit__typeof, axiom,
    ((![V2 : val, T2 : ty, H : nat > option2118145160on_val]: (((typeof_h @ (^[X2 : nat]: none_P1535574167on_val) @ V2) = (some_ty @ T2)) => ((typeof_h @ H @ V2) = (some_ty @ T2)))))). % typeof_lit_typeof
thf(fact_165_conf__def, axiom,
    ((conf_P93989998t_char = (^[P3 : list_P1234162913t_char]: (^[H3 : nat > option2118145160on_val]: (^[V4 : val]: (^[T5 : ty]: (?[T6 : ty]: ((((typeof_h @ H3 @ V4) = (some_ty @ T6))) & ((widen_917054840t_char @ P3 @ T6 @ T5))))))))))). % conf_def
thf(fact_166_preallocated__new, axiom,
    ((![H : nat > option2118145160on_val, A : nat, X : produc266837688on_val]: ((preallocated @ H) => (((H @ A) = none_P1535574167on_val) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ X)))))))). % preallocated_new
thf(fact_167_preallocated__upd__obj, axiom,
    ((![H : nat > option2118145160on_val, A : nat, C3 : list_char, Fs : produc1257910179t_char > option_val, Fs2 : produc1257910179t_char > option_val]: ((preallocated @ H) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs))) => (preallocated @ (fun_up262443479on_val @ H @ A @ (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs2))))))))). % preallocated_upd_obj
thf(fact_168_preallocated__hext, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((preallocated @ H) => ((hext @ H @ H2) => (preallocated @ H2)))))). % preallocated_hext
thf(fact_169_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : 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 @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_170_sconf__def, axiom,
    ((typeSa1777264139_sconf = (^[P3 : list_P1234162913t_char]: (^[E4 : list_char > option_ty]: (produc99536995_val_o @ (^[H3 : nat > option2118145160on_val]: (^[L3 : list_char > option_val]: (((hconf_1244167010t_char @ P3 @ H3)) & ((lconf_485928294t_char @ P3 @ H3 @ L3 @ E4))))))))))). % sconf_def
thf(fact_171_map__add__assoc, axiom,
    ((![M1 : list_char > option_val, M2 : list_char > option_val, M3 : list_char > option_val]: ((map_ad1615113112ar_val @ M1 @ (map_ad1615113112ar_val @ M2 @ M3)) = (map_ad1615113112ar_val @ (map_ad1615113112ar_val @ M1 @ M2) @ M3))))). % map_add_assoc
thf(fact_172_split__part, axiom,
    ((![P : $o, Q : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((produc99536995_val_o @ (^[A2 : nat > option2118145160on_val]: (^[B2 : list_char > option_val]: ((P) & ((Q @ A2 @ B2)))))) = (^[Ab : produc515445032on_val]: ((P) & ((produc99536995_val_o @ Q @ Ab)))))))). % split_part
thf(fact_173_split__part, axiom,
    ((![P : $o, Q : produc1097884484on_val > produc1097884484on_val > $o]: ((produc50362220_val_o @ (^[A2 : produc1097884484on_val]: (^[B2 : produc1097884484on_val]: ((P) & ((Q @ A2 @ B2)))))) = (^[Ab : produc1172664615on_val]: ((P) & ((produc50362220_val_o @ Q @ Ab)))))))). % split_part
thf(fact_174_split__part, axiom,
    ((![P : $o, Q : exp_list_char > produc515445032on_val > $o]: ((produc199145871_val_o @ (^[A2 : exp_list_char]: (^[B2 : produc515445032on_val]: ((P) & ((Q @ A2 @ B2)))))) = (^[Ab : produc1097884484on_val]: ((P) & ((produc199145871_val_o @ Q @ Ab)))))))). % split_part
thf(fact_175_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
thf(fact_176_map__add__eq__empty__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((map_ad1615113112ar_val @ F @ G) = (^[X2 : list_char]: none_val)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % map_add_eq_empty_iff
thf(fact_177_map__add__None, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char]: (((map_ad1615113112ar_val @ M @ N @ K) = none_val) = ((((N @ K) = none_val)) & (((M @ K) = none_val))))))). % map_add_None
thf(fact_178_case__prod__conv, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_179_case__prod__conv, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_180_case__prod__conv, axiom,
    ((![F : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc1468025474_val_o @ F @ (produc2023458740on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_181_case__prod__conv, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)) = (F @ A @ B))))). % case_prod_conv
thf(fact_182_case__prodI, axiom,
    ((![F : list_char > (produc1257910179t_char > option_val) > $o, A : list_char, B : produc1257910179t_char > option_val]: ((F @ A @ B) => (produc1336856385_val_o @ F @ (produc904988266on_val @ A @ B)))))). % case_prodI
thf(fact_183_case__prodI, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((F @ A @ B) => (produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)))))). % case_prodI
thf(fact_184_case__prodI, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((F @ A @ B) => (produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)))))). % case_prodI
thf(fact_185_case__prodI, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((F @ A @ B) => (produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)))))). % case_prodI
thf(fact_186_case__prodI2, axiom,
    ((![P4 : produc266837688on_val, C : list_char > (produc1257910179t_char > option_val) > $o]: ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: ((P4 = (produc904988266on_val @ A5 @ B4)) => (C @ A5 @ B4))) => (produc1336856385_val_o @ C @ P4))))). % case_prodI2
thf(fact_187_case__prodI2, axiom,
    ((![P4 : produc515445032on_val, C : (nat > option2118145160on_val) > (list_char > option_val) > $o]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: ((P4 = (produc52622304on_val @ A5 @ B4)) => (C @ A5 @ B4))) => (produc99536995_val_o @ C @ P4))))). % case_prodI2
thf(fact_188_case__prodI2, axiom,
    ((![P4 : produc1172664615on_val, C : produc1097884484on_val > produc1097884484on_val > $o]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ A5 @ B4)) => (C @ A5 @ B4))) => (produc50362220_val_o @ C @ P4))))). % case_prodI2
thf(fact_189_case__prodI2, axiom,
    ((![P4 : produc1097884484on_val, C : exp_list_char > produc515445032on_val > $o]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: ((P4 = (produc2023458740on_val @ A5 @ B4)) => (C @ A5 @ B4))) => (produc199145871_val_o @ C @ P4))))). % case_prodI2
thf(fact_190_empty__eq__map__add__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((^[X2 : list_char]: none_val) = (map_ad1615113112ar_val @ F @ G)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % empty_eq_map_add_iff
thf(fact_191_map__add__empty, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ M @ (^[X2 : list_char]: none_val)) = M)))). % map_add_empty
thf(fact_192_empty__map__add, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ (^[X2 : list_char]: none_val) @ M) = M)))). % empty_map_add
thf(fact_193_map__add__upd, axiom,
    ((![F : list_char > option_ty, G : list_char > option_ty, X : list_char, Y : ty]: ((map_add_list_char_ty @ F @ (fun_up9191ion_ty @ G @ X @ (some_ty @ Y))) = (fun_up9191ion_ty @ (map_add_list_char_ty @ F @ G) @ X @ (some_ty @ Y)))))). % map_add_upd
thf(fact_194_map__add__upd, axiom,
    ((![F : list_char > option_val, G : list_char > option_val, X : list_char, Y : val]: ((map_ad1615113112ar_val @ F @ (fun_up1252458416on_val @ G @ X @ (some_val @ Y))) = (fun_up1252458416on_val @ (map_ad1615113112ar_val @ F @ G) @ X @ (some_val @ Y)))))). % map_add_upd
thf(fact_195_map__add__upd, axiom,
    ((![F : nat > option2118145160on_val, G : nat > option2118145160on_val, X : nat, Y : produc266837688on_val]: ((map_ad109059391on_val @ F @ (fun_up262443479on_val @ G @ X @ (some_P1299442195on_val @ Y))) = (fun_up262443479on_val @ (map_ad109059391on_val @ F @ G) @ X @ (some_P1299442195on_val @ Y)))))). % map_add_upd
thf(fact_196_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, Prod : produc515445032on_val]: ((H @ (produc99536995_val_o @ F @ Prod)) = (produc99536995_val_o @ (^[X12 : nat > option2118145160on_val]: (^[X24 : list_char > option_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_197_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : produc1097884484on_val > produc1097884484on_val > $o, Prod : produc1172664615on_val]: ((H @ (produc50362220_val_o @ F @ Prod)) = (produc50362220_val_o @ (^[X12 : produc1097884484on_val]: (^[X24 : produc1097884484on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_198_prod_Ocase__distrib, axiom,
    ((![H : (produc1097884484on_val > $o) > produc1097884484on_val > $o, F : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((H @ (produc1468025474_val_o @ F @ Prod)) = (produc1468025474_val_o @ (^[X12 : exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_199_prod_Ocase__distrib, axiom,
    ((![H : (produc1097884484on_val > $o) > $o, F : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((H @ (produc1468025474_val_o @ F @ Prod)) = (produc199145871_val_o @ (^[X12 : exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_200_prod_Ocase__distrib, axiom,
    ((![H : $o > produc1097884484on_val > $o, F : exp_list_char > produc515445032on_val > $o, Prod : produc1097884484on_val]: ((H @ (produc199145871_val_o @ F @ Prod)) = (produc1468025474_val_o @ (^[X12 : exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_201_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : exp_list_char > produc515445032on_val > $o, Prod : produc1097884484on_val]: ((H @ (produc199145871_val_o @ F @ Prod)) = (produc199145871_val_o @ (^[X12 : exp_list_char]: (^[X24 : produc515445032on_val]: (H @ (F @ X12 @ X24)))) @ Prod))))). % prod.case_distrib
thf(fact_202_prod_Odisc__eq__case, axiom,
    ((![Prod : produc515445032on_val]: (produc99536995_val_o @ (^[Uu : nat > option2118145160on_val]: (^[Uv : list_char > option_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_203_prod_Odisc__eq__case, axiom,
    ((![Prod : produc1172664615on_val]: (produc50362220_val_o @ (^[Uu : produc1097884484on_val]: (^[Uv : produc1097884484on_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_204_prod_Odisc__eq__case, axiom,
    ((![Prod : produc1097884484on_val]: (produc199145871_val_o @ (^[Uu : exp_list_char]: (^[Uv : produc515445032on_val]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_205_old_Oprod_Ocase, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, X1 : nat > option2118145160on_val, X22 : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ X1 @ X22)) = (F @ X1 @ X22))))). % old.prod.case
thf(fact_206_old_Oprod_Ocase, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, X1 : produc1097884484on_val, X22 : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ X1 @ X22)) = (F @ X1 @ X22))))). % old.prod.case
thf(fact_207_old_Oprod_Ocase, axiom,
    ((![F : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, X1 : exp_list_char, X22 : produc515445032on_val]: ((produc1468025474_val_o @ F @ (produc2023458740on_val @ X1 @ X22)) = (F @ X1 @ X22))))). % old.prod.case
thf(fact_208_old_Oprod_Ocase, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, X1 : exp_list_char, X22 : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ X1 @ X22)) = (F @ X1 @ X22))))). % old.prod.case
thf(fact_209_case__prodD, axiom,
    ((![F : list_char > (produc1257910179t_char > option_val) > $o, A : list_char, B : produc1257910179t_char > option_val]: ((produc1336856385_val_o @ F @ (produc904988266on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_210_case__prodD, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, A : nat > option2118145160on_val, B : list_char > option_val]: ((produc99536995_val_o @ F @ (produc52622304on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_211_case__prodD, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, A : produc1097884484on_val, B : produc1097884484on_val]: ((produc50362220_val_o @ F @ (produc1069526295on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_212_case__prodD, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, A : exp_list_char, B : produc515445032on_val]: ((produc199145871_val_o @ F @ (produc2023458740on_val @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_213_case__prodE, axiom,
    ((![C : list_char > (produc1257910179t_char > option_val) > $o, P4 : produc266837688on_val]: ((produc1336856385_val_o @ C @ P4) => (~ ((![X3 : list_char, Y3 : produc1257910179t_char > option_val]: ((P4 = (produc904988266on_val @ X3 @ Y3)) => (~ ((C @ X3 @ Y3))))))))))). % case_prodE
thf(fact_214_case__prodE, axiom,
    ((![C : (nat > option2118145160on_val) > (list_char > option_val) > $o, P4 : produc515445032on_val]: ((produc99536995_val_o @ C @ P4) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((P4 = (produc52622304on_val @ X3 @ Y3)) => (~ ((C @ X3 @ Y3))))))))))). % case_prodE
thf(fact_215_case__prodE, axiom,
    ((![C : produc1097884484on_val > produc1097884484on_val > $o, P4 : produc1172664615on_val]: ((produc50362220_val_o @ C @ P4) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ X3 @ Y3)) => (~ ((C @ X3 @ Y3))))))))))). % case_prodE
thf(fact_216_case__prodE, axiom,
    ((![C : exp_list_char > produc515445032on_val > $o, P4 : produc1097884484on_val]: ((produc199145871_val_o @ C @ P4) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((P4 = (produc2023458740on_val @ X3 @ Y3)) => (~ ((C @ X3 @ Y3))))))))))). % case_prodE
thf(fact_217_case__prodE2, axiom,
    ((![Q : $o > $o, P : (nat > option2118145160on_val) > (list_char > option_val) > $o, Z : produc515445032on_val]: ((Q @ (produc99536995_val_o @ P @ Z)) => (~ ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((Z = (produc52622304on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_218_case__prodE2, axiom,
    ((![Q : $o > $o, P : produc1097884484on_val > produc1097884484on_val > $o, Z : produc1172664615on_val]: ((Q @ (produc50362220_val_o @ P @ Z)) => (~ ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((Z = (produc1069526295on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_219_case__prodE2, axiom,
    ((![Q : (produc1097884484on_val > $o) > $o, P : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, Z : produc1097884484on_val]: ((Q @ (produc1468025474_val_o @ P @ Z)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((Z = (produc2023458740on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_220_case__prodE2, axiom,
    ((![Q : $o > $o, P : exp_list_char > produc515445032on_val > $o, Z : produc1097884484on_val]: ((Q @ (produc199145871_val_o @ P @ Z)) => (~ ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((Z = (produc2023458740on_val @ X3 @ Y3)) => (~ ((Q @ (P @ X3 @ Y3)))))))))))). % case_prodE2
thf(fact_221_case__prod__eta, axiom,
    ((![F : produc515445032on_val > $o]: ((produc99536995_val_o @ (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (F @ (produc52622304on_val @ X2 @ Y2))))) = F)))). % case_prod_eta
thf(fact_222_case__prod__eta, axiom,
    ((![F : produc1172664615on_val > $o]: ((produc50362220_val_o @ (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (F @ (produc1069526295on_val @ X2 @ Y2))))) = F)))). % case_prod_eta
thf(fact_223_case__prod__eta, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o]: ((produc1468025474_val_o @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (F @ (produc2023458740on_val @ X2 @ Y2))))) = F)))). % case_prod_eta
thf(fact_224_case__prod__eta, axiom,
    ((![F : produc1097884484on_val > $o]: ((produc199145871_val_o @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (F @ (produc2023458740on_val @ X2 @ Y2))))) = F)))). % case_prod_eta
thf(fact_225_cond__case__prod__eta, axiom,
    ((![F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : produc515445032on_val > $o]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((F @ X3 @ Y3) = (G @ (produc52622304on_val @ X3 @ Y3)))) => ((produc99536995_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_226_cond__case__prod__eta, axiom,
    ((![F : produc1097884484on_val > produc1097884484on_val > $o, G : produc1172664615on_val > $o]: ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((F @ X3 @ Y3) = (G @ (produc1069526295on_val @ X3 @ Y3)))) => ((produc50362220_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_227_cond__case__prod__eta, axiom,
    ((![F : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, G : produc1097884484on_val > produc1097884484on_val > $o]: ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((F @ X3 @ Y3) = (G @ (produc2023458740on_val @ X3 @ Y3)))) => ((produc1468025474_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_228_cond__case__prod__eta, axiom,
    ((![F : exp_list_char > produc515445032on_val > $o, G : produc1097884484on_val > $o]: ((![X3 : exp_list_char, Y3 : produc515445032on_val]: ((F @ X3 @ Y3) = (G @ (produc2023458740on_val @ X3 @ Y3)))) => ((produc199145871_val_o @ F) = G))))). % cond_case_prod_eta
thf(fact_229_internal__case__prod__def, axiom,
    ((produc563955725_val_o = produc99536995_val_o))). % internal_case_prod_def
thf(fact_230_internal__case__prod__def, axiom,
    ((produc1351546646_val_o = produc50362220_val_o))). % internal_case_prod_def
thf(fact_231_internal__case__prod__def, axiom,
    ((produc914566744_val_o = produc1468025474_val_o))). % internal_case_prod_def
thf(fact_232_internal__case__prod__def, axiom,
    ((produc1875489849_val_o = produc199145871_val_o))). % internal_case_prod_def
thf(fact_233_map__add__SomeD, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) => (((N @ K) = (some_val @ X)) | (((N @ K) = none_val) & ((M @ K) = (some_val @ X)))))))). % map_add_SomeD
thf(fact_234_map__add__Some__iff, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char, X : val]: (((map_ad1615113112ar_val @ M @ N @ K) = (some_val @ X)) = ((((N @ K) = (some_val @ X))) | (((((N @ K) = none_val)) & (((M @ K) = (some_val @ X)))))))))). % map_add_Some_iff
thf(fact_235_split__cong, axiom,
    ((![Q2 : produc515445032on_val, F : (nat > option2118145160on_val) > (list_char > option_val) > $o, G : (nat > option2118145160on_val) > (list_char > option_val) > $o, P4 : produc515445032on_val]: ((![X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (((produc52622304on_val @ X3 @ Y3) = Q2) => ((F @ X3 @ Y3) = (G @ X3 @ Y3)))) => ((P4 = Q2) => ((produc99536995_val_o @ F @ P4) = (produc99536995_val_o @ G @ Q2))))))). % split_cong
thf(fact_236_split__cong, axiom,
    ((![Q2 : produc1172664615on_val, F : produc1097884484on_val > produc1097884484on_val > $o, G : produc1097884484on_val > produc1097884484on_val > $o, P4 : produc1172664615on_val]: ((![X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (((produc1069526295on_val @ X3 @ Y3) = Q2) => ((F @ X3 @ Y3) = (G @ X3 @ Y3)))) => ((P4 = Q2) => ((produc50362220_val_o @ F @ P4) = (produc50362220_val_o @ G @ Q2))))))). % split_cong
thf(fact_237_split__cong, axiom,
    ((![Q2 : produc1097884484on_val, F : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, G : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![X3 : exp_list_char, Y3 : produc515445032on_val]: (((produc2023458740on_val @ X3 @ Y3) = Q2) => ((F @ X3 @ Y3) = (G @ X3 @ Y3)))) => ((P4 = Q2) => ((produc1468025474_val_o @ F @ P4) = (produc1468025474_val_o @ G @ Q2))))))). % split_cong
thf(fact_238_split__cong, axiom,
    ((![Q2 : produc1097884484on_val, F : exp_list_char > produc515445032on_val > $o, G : exp_list_char > produc515445032on_val > $o, P4 : produc1097884484on_val]: ((![X3 : exp_list_char, Y3 : produc515445032on_val]: (((produc2023458740on_val @ X3 @ Y3) = Q2) => ((F @ X3 @ Y3) = (G @ X3 @ Y3)))) => ((P4 = Q2) => ((produc199145871_val_o @ F @ P4) = (produc199145871_val_o @ G @ Q2))))))). % split_cong
thf(fact_239_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : 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 @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_0 @ L))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_0 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_240_case__prodI2_H, axiom,
    ((![P4 : produc1097884484on_val, C : exp_list_char > produc515445032on_val > produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: (((produc2023458740on_val @ A5 @ B4) = P4) => (C @ A5 @ B4 @ X))) => (produc1468025474_val_o @ C @ P4 @ X))))). % case_prodI2'
thf(fact_241_mem__case__prodI2, axiom,
    ((![P4 : produc515445032on_val, Z : produc1172664615on_val, C : (nat > option2118145160on_val) > (list_char > option_val) > set_Pr1189492743on_val]: ((![A5 : nat > option2118145160on_val, B4 : list_char > option_val]: ((P4 = (produc52622304on_val @ A5 @ B4)) => (member354538064on_val @ Z @ (C @ A5 @ B4)))) => (member354538064on_val @ Z @ (produc1919805778on_val @ C @ P4)))))). % mem_case_prodI2
thf(fact_242_mem__case__prodI2, axiom,
    ((![P4 : produc1172664615on_val, Z : produc1172664615on_val, C : produc1097884484on_val > produc1097884484on_val > set_Pr1189492743on_val]: ((![A5 : produc1097884484on_val, B4 : produc1097884484on_val]: ((P4 = (produc1069526295on_val @ A5 @ B4)) => (member354538064on_val @ Z @ (C @ A5 @ B4)))) => (member354538064on_val @ Z @ (produc493625819on_val @ C @ P4)))))). % mem_case_prodI2
thf(fact_243_mem__case__prodI2, axiom,
    ((![P4 : produc1097884484on_val, Z : produc1172664615on_val, C : exp_list_char > produc515445032on_val > set_Pr1189492743on_val]: ((![A5 : exp_list_char, B4 : produc515445032on_val]: ((P4 = (produc2023458740on_val @ A5 @ B4)) => (member354538064on_val @ Z @ (C @ A5 @ B4)))) => (member354538064on_val @ Z @ (produc848217214on_val @ C @ P4)))))). % mem_case_prodI2
thf(fact_244_mem__case__prodI2, axiom,
    ((![P4 : produc266837688on_val, Z : produc1172664615on_val, C : list_char > (produc1257910179t_char > option_val) > set_Pr1189492743on_val]: ((![A5 : list_char, B4 : produc1257910179t_char > option_val]: ((P4 = (produc904988266on_val @ A5 @ B4)) => (member354538064on_val @ Z @ (C @ A5 @ B4)))) => (member354538064on_val @ Z @ (produc535686448on_val @ C @ P4)))))). % mem_case_prodI2
thf(fact_245_red__def, axiom,
    ((red = (^[P3 : list_P1234162913t_char]: (collec2055896722on_val @ (produc50362220_val_o @ (produc1468025474_val_o @ (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (produc199145871_val_o @ (redp @ P3 @ X2 @ Y2))))))))))). % red_def
thf(fact_246_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E3 : 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 @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H6 : nat > option2118145160on_val, L4 : list_char > option_val]: (R @ E5 @ H6 @ L4 @ E5 @ H6 @ L4)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E6 : exp_list_char, H7 : nat > option2118145160on_val, L5 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E6 @ H7 @ L5) => (R @ E_0 @ H_0 @ L_02 @ E6 @ H7 @ L5)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red

% 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 @ h_a @ l_a @ (fun_up9191ion_ty @ e @ v @ (some_ty @ t))))).
