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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:20:26.313

% Could-be-implicit typings (21)
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thf(ty_n_t__Type__Oty, type,
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% Explicit typings (45)
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thf(sy_c_Expr_Oexp_OTryCatch_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OWhile_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_Orel__exp_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Product__Type_OPair_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, type,
    produc1069526295on_val : produc1097884484on_val > produc1097884484on_val > produc1172664615on_val).
thf(sy_c_Product__Type_OPair_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_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,
    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_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_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_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,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_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_Transitive__Closure_Ortrancl_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,
    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_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__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_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,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_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_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member208988944on_val : produc1161703655on_val > set_Pr1368603847on_val > $o).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_bop____, type,
    bop2 : bop).
thf(sy_v_e_092_060_094sub_0622_H____, type,
    e_2 : exp_list_char).
thf(sy_v_e_092_060_094sub_0622____, type,
    e_22 : 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_092_060_094sub_0621____, type,
    v_1 : val).

% Relevant facts (164)
thf(fact_0_wt, axiom,
    ((wTrt @ p @ ha @ e @ (binOp_list_char @ (val_list_char @ v_1) @ bop2 @ e_22) @ t))). % wt
thf(fact_1_exp_Oinject_I4_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (((binOp_list_char @ X41 @ X42 @ X43) = (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((X41 = Y41)) & ((((X42 = Y42)) & ((X43 = Y43))))))))). % exp.inject(4)
thf(fact_2_exp_Oinject_I3_J, axiom,
    ((![X3 : val, Y3 : val]: (((val_list_char @ X3) = (val_list_char @ Y3)) = (X3 = Y3))))). % exp.inject(3)
thf(fact_3_exp_Odistinct_I55_J, axiom,
    ((![X3 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X3) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_4_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_5_BinOpRed2_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (binOp_list_char @ (val_list_char @ v_1) @ bop2 @ e_22) @ t))). % BinOpRed2.prems(2)
thf(fact_6_IH, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ e_22 @ T) => (?[U : ty]: ((wTrt @ p @ h_a @ E @ e_2 @ U) & (widen_917054840t_char @ p @ U @ T)))))))). % IH
thf(fact_7_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_8_redp__redsp_OBinOpRed2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, V_1 : val, Bop : bop]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E3) @ S2))))). % redp_redsp.BinOpRed2
thf(fact_9_exp_Orel__distinct_I56_J, axiom,
    ((![R : list_char > list_char > $o, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char, X3 : val]: (~ ((rel_ex1899005716t_char @ R @ (binOp_list_char @ Y41 @ Y42 @ Y43) @ (val_list_char @ X3))))))). % exp.rel_distinct(56)
thf(fact_10_exp_Orel__distinct_I55_J, axiom,
    ((![R : list_char > list_char > $o, X3 : val, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (val_list_char @ X3) @ (binOp_list_char @ Y41 @ Y42 @ Y43))))))). % exp.rel_distinct(55)
thf(fact_11_red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e_22 @ (produc52622304on_val @ ha @ la)) @ (produc2023458740on_val @ e_2 @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % red
thf(fact_12_BinOpRed2_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % BinOpRed2.prems(1)
thf(fact_13_BinOpRed2_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrt @ p @ ha @ E @ e_22 @ T) => (?[T2 : ty]: ((wTrt @ p @ h_a @ E @ e_2 @ T2) & (widen_917054840t_char @ p @ T2 @ T)))))))). % BinOpRed2.hyps(2)
thf(fact_14_exp_Orel__eq, axiom,
    (((rel_ex1899005716t_char @ (^[Y : list_char]: (^[Z : list_char]: (Y = Z)))) = (^[Y : exp_list_char]: (^[Z : exp_list_char]: (Y = Z)))))). % exp.rel_eq
thf(fact_15_redp__red__eq, axiom,
    ((redp = (^[P2 : list_P1234162913t_char]: (^[X : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P2)))))))))). % redp_red_eq
thf(fact_16_exp_Orel__refl, axiom,
    ((![Ra : list_char > list_char > $o, X2 : exp_list_char]: ((![X4 : list_char]: (Ra @ X4 @ X4)) => (rel_ex1899005716t_char @ Ra @ X2 @ X2))))). % exp.rel_refl
thf(fact_17_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_18_red__reds_OBinOpRed2, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V_1 : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ E3) @ S2)) @ (red @ P)))))). % red_reds.BinOpRed2
thf(fact_19_exp_Orel__intros_I3_J, axiom,
    ((![X3 : val, Y3 : val, R : list_char > list_char > $o]: ((X3 = Y3) => (rel_ex1899005716t_char @ R @ (val_list_char @ X3) @ (val_list_char @ Y3)))))). % exp.rel_intros(3)
thf(fact_20_exp_Orel__inject_I3_J, axiom,
    ((![R : list_char > list_char > $o, X3 : val, Y3 : val]: ((rel_ex1899005716t_char @ R @ (val_list_char @ X3) @ (val_list_char @ Y3)) = (X3 = Y3))))). % exp.rel_inject(3)
thf(fact_21_exp_Orel__intros_I4_J, axiom,
    ((![R : list_char > list_char > $o, X41 : exp_list_char, Y41 : exp_list_char, X42 : bop, Y42 : bop, X43 : exp_list_char, Y43 : exp_list_char]: ((rel_ex1899005716t_char @ R @ X41 @ Y41) => ((X42 = Y42) => ((rel_ex1899005716t_char @ R @ X43 @ Y43) => (rel_ex1899005716t_char @ R @ (binOp_list_char @ X41 @ X42 @ X43) @ (binOp_list_char @ Y41 @ Y42 @ Y43)))))))). % exp.rel_intros(4)
thf(fact_22_exp_Orel__inject_I4_J, axiom,
    ((![R : list_char > list_char > $o, X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y41 : exp_list_char, Y42 : bop, Y43 : exp_list_char]: ((rel_ex1899005716t_char @ R @ (binOp_list_char @ X41 @ X42 @ X43) @ (binOp_list_char @ Y41 @ Y42 @ Y43)) = (((rel_ex1899005716t_char @ R @ X41 @ Y41)) & ((((X42 = Y42)) & ((rel_ex1899005716t_char @ R @ X43 @ Y43))))))))). % exp.rel_inject(4)
thf(fact_23_redp__redsp_OBinOpRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, Bop : bop, E_2 : exp_list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (binOp_list_char @ E2 @ Bop @ E_2) @ S @ (binOp_list_char @ E3 @ Bop @ E_2) @ S2))))). % redp_redsp.BinOpRed1
thf(fact_24_prod__cases4, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y4 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_25_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X2))))). % prod_induct4
thf(fact_26_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, T : 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 @ T) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % red_preserves_hconf
thf(fact_27_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_28_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_29_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_30_old_Oprod_Oinject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_31_old_Oprod_Oinject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_32_old_Oprod_Oinject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_33_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_34_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_35_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_36_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y4 = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y4 = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_38_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y4 = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_39_Pair__inject, axiom,
    ((![A2 : nat > option2118145160on_val, B2 : list_char > option_val, A3 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A2 @ B2) = (produc52622304on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_40_Pair__inject, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, A3 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A2 @ B2) = (produc1069526295on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_41_Pair__inject, axiom,
    ((![A2 : exp_list_char, B2 : produc515445032on_val, A3 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A2 @ B2) = (produc2023458740on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_42_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P3 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_43_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P3 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_44_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P3 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P3))))). % prod_cases
thf(fact_45_surj__pair, axiom,
    ((![P3 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y5 : list_char > option_val]: (P3 = (produc52622304on_val @ X4 @ Y5)))))). % surj_pair
thf(fact_46_surj__pair, axiom,
    ((![P3 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y5 : produc1097884484on_val]: (P3 = (produc1069526295on_val @ X4 @ Y5)))))). % surj_pair
thf(fact_47_surj__pair, axiom,
    ((![P3 : produc1097884484on_val]: (?[X4 : exp_list_char, Y5 : produc515445032on_val]: (P3 = (produc2023458740on_val @ X4 @ Y5)))))). % surj_pair
thf(fact_48_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X2))))). % prod_induct3
thf(fact_49_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X2 : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X2))))). % prod_induct3
thf(fact_50_prod__cases3, axiom,
    ((![Y4 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y4 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_51_prod__cases3, axiom,
    ((![Y4 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y4 = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_52_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, T : 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 @ T) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % red_preserves_lconf
thf(fact_53_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => ((wTrt @ P @ (hp @ S) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S) => (typeSa1777264139_sconf @ P @ E @ S2))))))). % red_preserves_sconf
thf(fact_54_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_55_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_56_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_57_red__reds_OBinOpThrow2, axiom,
    ((![V_1 : val, Bop : bop, E2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.BinOpThrow2
thf(fact_58_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S3 : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y2) @ R))) = (^[X : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y2) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_59_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y2) @ R))) = (^[X : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y2) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_60_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S3 : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y2) @ R))) = (^[X : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y2) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_61_exp_Oinject_I14_J, axiom,
    ((![X14 : exp_list_char, Y14 : exp_list_char]: (((throw_list_char @ X14) = (throw_list_char @ Y14)) = (X14 = Y14))))). % exp.inject(14)
thf(fact_62_exp_Odistinct_I75_J, axiom,
    ((![X3 : val, X14 : exp_list_char]: (~ (((val_list_char @ X3) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_63_exp_Orel__inject_I14_J, axiom,
    ((![R : list_char > list_char > $o, X14 : exp_list_char, Y14 : exp_list_char]: ((rel_ex1899005716t_char @ R @ (throw_list_char @ X14) @ (throw_list_char @ Y14)) = (rel_ex1899005716t_char @ R @ X14 @ Y14))))). % exp.rel_inject(14)
thf(fact_64_exp_Orel__intros_I14_J, axiom,
    ((![R : list_char > list_char > $o, X14 : exp_list_char, Y14 : exp_list_char]: ((rel_ex1899005716t_char @ R @ X14 @ Y14) => (rel_ex1899005716t_char @ R @ (throw_list_char @ X14) @ (throw_list_char @ Y14)))))). % exp.rel_intros(14)
thf(fact_65_redp__redsp_OThrowRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (throw_list_char @ E2) @ S @ (throw_list_char @ E3) @ S2))))). % redp_redsp.ThrowRed
thf(fact_66_redp__redsp_OThrowThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (throw_list_char @ (throw_list_char @ E2)) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.ThrowThrow
thf(fact_67_exp_Odistinct_I97_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X14 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (throw_list_char @ X14))))))). % exp.distinct(97)
thf(fact_68_exp_Orel__distinct_I76_J, axiom,
    ((![R : list_char > list_char > $o, Y14 : exp_list_char, X3 : val]: (~ ((rel_ex1899005716t_char @ R @ (throw_list_char @ Y14) @ (val_list_char @ X3))))))). % exp.rel_distinct(76)
thf(fact_69_exp_Orel__distinct_I75_J, axiom,
    ((![R : list_char > list_char > $o, X3 : val, Y14 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (val_list_char @ X3) @ (throw_list_char @ Y14))))))). % exp.rel_distinct(75)
thf(fact_70_exp_Orel__distinct_I98_J, axiom,
    ((![R : list_char > list_char > $o, Y14 : exp_list_char, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (throw_list_char @ Y14) @ (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.rel_distinct(98)
thf(fact_71_exp_Orel__distinct_I97_J, axiom,
    ((![R : list_char > list_char > $o, X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y14 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (binOp_list_char @ X41 @ X42 @ X43) @ (throw_list_char @ Y14))))))). % exp.rel_distinct(97)
thf(fact_72_redp__redsp_OBinOpThrow1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.BinOpThrow1
thf(fact_73_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_74_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_75_redp__redsp_OBinOpThrow2, axiom,
    ((![P : list_P1234162913t_char, V_1 : val, Bop : bop, E2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (binOp_list_char @ (val_list_char @ V_1) @ Bop @ (throw_list_char @ E2)) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.BinOpThrow2
thf(fact_76_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_77_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_78_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_79_WTrt__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, H2 : nat > option2118145160on_val]: ((wTrt @ P @ H @ E @ E2 @ T) => ((hext @ H @ H2) => (wTrt @ P @ H2 @ E @ E2 @ T)))))). % WTrt_hext_mono
thf(fact_80_red__reds_OFAssThrow2, axiom,
    ((![V : val, F : list_char, D2 : list_char, E2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ (throw_list_char @ E2)) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.FAssThrow2
thf(fact_81_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_82_BinOpRedsThrow2, 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, E2 : exp_list_char, S_2 : produc515445032on_val, Bop : bop]: ((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 @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E_1 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_83_exp_Oinject_I8_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((X84 = Y84))))))))))). % exp.inject(8)
thf(fact_84_FAssReds1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F @ D2 @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds1
thf(fact_85_redp__redsp_OFAssRed1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, F : list_char, D2 : list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (fAss_list_char @ E2 @ F @ D2 @ E_2) @ S @ (fAss_list_char @ E3 @ F @ D2 @ E_2) @ S2))))). % redp_redsp.FAssRed1
thf(fact_86_exp_Odistinct_I63_J, axiom,
    ((![X3 : val, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((val_list_char @ X3) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(63)
thf(fact_87_exp_Orel__intros_I8_J, axiom,
    ((![R : list_char > list_char > $o, X81 : exp_list_char, Y81 : exp_list_char, X82 : list_char, Y82 : list_char, X83 : list_char, Y83 : list_char, X84 : exp_list_char, Y84 : exp_list_char]: ((rel_ex1899005716t_char @ R @ X81 @ Y81) => ((X82 = Y82) => ((X83 = Y83) => ((rel_ex1899005716t_char @ R @ X84 @ Y84) => (rel_ex1899005716t_char @ R @ (fAss_list_char @ X81 @ X82 @ X83 @ X84) @ (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84))))))))). % exp.rel_intros(8)
thf(fact_88_exp_Orel__inject_I8_J, axiom,
    ((![R : list_char > list_char > $o, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: ((rel_ex1899005716t_char @ R @ (fAss_list_char @ X81 @ X82 @ X83 @ X84) @ (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84)) = (((rel_ex1899005716t_char @ R @ X81 @ Y81)) & ((((X82 = Y82)) & ((((X83 = Y83)) & ((rel_ex1899005716t_char @ R @ X84 @ Y84))))))))))). % exp.rel_inject(8)
thf(fact_89_exp_Odistinct_I165_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X14 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (throw_list_char @ X14))))))). % exp.distinct(165)
thf(fact_90_exp_Odistinct_I85_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(85)
thf(fact_91_FAssReds2, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ E2) @ S) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAssReds2
thf(fact_92_FAssRedsThrow1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAssRedsThrow1
thf(fact_93_FAssRedsThrow2, axiom,
    ((![E_1 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E2 : exp_list_char, S_2 : produc515445032on_val, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_1 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E_1 @ F @ D2 @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % FAssRedsThrow2
thf(fact_94_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_95_redp__redsp_OFAssRed2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, V : val, F : list_char, D2 : list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ E2) @ S @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ E3) @ S2))))). % redp_redsp.FAssRed2
thf(fact_96_redp__redsp_OFAssThrow1, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, F : list_char, D2 : list_char, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (fAss_list_char @ (throw_list_char @ E2) @ F @ D2 @ E_2) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.FAssThrow1
thf(fact_97_exp_Orel__distinct_I63_J, axiom,
    ((![R : list_char > list_char > $o, X3 : val, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (val_list_char @ X3) @ (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84))))))). % exp.rel_distinct(63)
thf(fact_98_exp_Orel__distinct_I64_J, axiom,
    ((![R : list_char > list_char > $o, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char, X3 : val]: (~ ((rel_ex1899005716t_char @ R @ (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84) @ (val_list_char @ X3))))))). % exp.rel_distinct(64)
thf(fact_99_exp_Orel__distinct_I166_J, axiom,
    ((![R : list_char > list_char > $o, Y14 : exp_list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (throw_list_char @ Y14) @ (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.rel_distinct(166)
thf(fact_100_exp_Orel__distinct_I165_J, axiom,
    ((![R : list_char > list_char > $o, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, Y14 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (fAss_list_char @ X81 @ X82 @ X83 @ X84) @ (throw_list_char @ Y14))))))). % exp.rel_distinct(165)
thf(fact_101_exp_Orel__distinct_I85_J, axiom,
    ((![R : list_char > list_char > $o, X41 : exp_list_char, X42 : bop, X43 : exp_list_char, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (binOp_list_char @ X41 @ X42 @ X43) @ (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84))))))). % exp.rel_distinct(85)
thf(fact_102_exp_Orel__distinct_I86_J, axiom,
    ((![R : list_char > list_char > $o, Y81 : exp_list_char, Y82 : list_char, Y83 : list_char, Y84 : exp_list_char, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (fAss_list_char @ Y81 @ Y82 @ Y83 @ Y84) @ (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.rel_distinct(86)
thf(fact_103_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_104_ThrowReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_105_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ E3 @ Bop @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds
thf(fact_106_red__reds_OFAssRed1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ E2 @ F @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (fAss_list_char @ E3 @ F @ D2 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.FAssRed1
thf(fact_107_redp__redsp_OFAssThrow2, axiom,
    ((![P : list_P1234162913t_char, V : val, F : list_char, D2 : list_char, E2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ (throw_list_char @ E2)) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.FAssThrow2
thf(fact_108_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, Bop : bop]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V) @ Bop @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_109_BinOpRedsThrow1, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_110_red__reds_OFAssRed2, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : val, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ E3 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ E2) @ S) @ (produc2023458740on_val @ (fAss_list_char @ (val_list_char @ V) @ F @ D2 @ E3) @ S2)) @ (red @ P)))))). % red_reds.FAssRed2
thf(fact_111_red__reds_OFAssThrow1, axiom,
    ((![E2 : exp_list_char, F : list_char, D2 : list_char, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAss_list_char @ (throw_list_char @ E2) @ F @ D2 @ E_2) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S)) @ (red @ P))))). % red_reds.FAssThrow1
thf(fact_112_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))) => ((![E4 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H3 @ L3 @ E4 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_02)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_12 @ H_1 @ L_1 @ E5 @ H4 @ L4) => (R @ E_0 @ H_0 @ L_02 @ E5 @ H4 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_113_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_114_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa2 @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_115_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa2 @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_116_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa2 @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_117_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)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa @ Xb) @ (produc52622304on_val @ A @ B)) @ R2) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_118_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)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa @ Xb) @ (produc1069526295on_val @ A @ B)) @ R2) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_119_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)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa @ Xb) @ (produc2023458740on_val @ A @ B)) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_120_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) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa2 : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R2)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_121_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) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa2 : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R2)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_122_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) => ((![A : exp_list_char, B : produc515445032on_val, Aa2 : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_123_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_124_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_125_r__into__rtrancl, axiom,
    ((![P3 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P3 @ R2) => (member354538064on_val @ P3 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_126_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y5) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y5 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_127_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_128_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C2 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C2)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C2) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_129_rtrancl__trans, axiom,
    ((![X2 : produc1097884484on_val, Y4 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X2 @ Y4) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Z3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X2 @ Z3) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_130_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ A2) => ((![Y5 : produc1097884484on_val, Z4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y5) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y5 @ Z4) @ R2) => ((P @ Y5) => (P @ Z4))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_131_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)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R2)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X22))))))). % rtrancl.inducts
thf(fact_132_converse__rtranclE, axiom,
    ((![X2 : produc1097884484on_val, Z3 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X2 @ Z3) @ (transi111096263on_val @ R2)) => ((~ ((X2 = Z3))) => (~ ((![Y5 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X2 @ Y5) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y5 @ Z3) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_133_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_134_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((P @ B2) => ((![Y5 : produc1097884484on_val, Z4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y5 @ Z4) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z4 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z4) => (P @ Y5))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_135_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_136_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C3) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_137_WhileRedsThrow, axiom,
    ((![B2 : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C3 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C3) @ S) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_138_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_139_TryRedsVal, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, V : val, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V2 : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C4 @ V2 @ E_2) @ S) @ (produc2023458740on_val @ (val_list_char @ V) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_140_exp_Oinject_I7_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, Y71 : exp_list_char, Y72 : list_char, Y73 : list_char]: (((fAcc_list_char @ X71 @ X72 @ X73) = (fAcc_list_char @ Y71 @ Y72 @ Y73)) = (((X71 = Y71)) & ((((X72 = Y72)) & ((X73 = Y73))))))))). % exp.inject(7)
thf(fact_141_exp_Oinject_I15_J, axiom,
    ((![X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (((tryCatch_list_char @ X151 @ X152 @ X153 @ X154) = (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154)) = (((X151 = Y151)) & ((((X152 = Y152)) & ((((X153 = Y153)) & ((X154 = Y154))))))))))). % exp.inject(15)
thf(fact_142_exp_Oinject_I13_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, Y131 : exp_list_char, Y132 : exp_list_char]: (((while_list_char @ X131 @ X132) = (while_list_char @ Y131 @ Y132)) = (((X131 = Y131)) & ((X132 = Y132))))))). % exp.inject(13)
thf(fact_143_exp_Odistinct_I167_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(167)
thf(fact_144_exp_Odistinct_I163_J, axiom,
    ((![X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((fAss_list_char @ X81 @ X82 @ X83 @ X84) = (while_list_char @ X131 @ X132))))))). % exp.distinct(163)
thf(fact_145_exp_Odistinct_I139_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X81 : exp_list_char, X82 : list_char, X83 : list_char, X84 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (fAss_list_char @ X81 @ X82 @ X83 @ X84))))))). % exp.distinct(139)
thf(fact_146_redp__redsp_ORedTry, axiom,
    ((![P : list_P1234162913t_char, V : val, C4 : list_char, V2 : list_char, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (tryCatch_list_char @ (val_list_char @ V) @ C4 @ V2 @ E_2) @ S @ (val_list_char @ V) @ S)))). % redp_redsp.RedTry
thf(fact_147_redp__redsp_OFAccThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, F : list_char, D2 : list_char, S : produc515445032on_val]: (redp @ P @ (fAcc_list_char @ (throw_list_char @ E2) @ F @ D2) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.FAccThrow
thf(fact_148_exp_Orel__distinct_I78_J, axiom,
    ((![R : list_char > list_char > $o, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char, X3 : val]: (~ ((rel_ex1899005716t_char @ R @ (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154) @ (val_list_char @ X3))))))). % exp.rel_distinct(78)
thf(fact_149_exp_Orel__distinct_I77_J, axiom,
    ((![R : list_char > list_char > $o, X3 : val, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (val_list_char @ X3) @ (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154))))))). % exp.rel_distinct(77)
thf(fact_150_exp_Odistinct_I207_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(207)
thf(fact_151_exp_Odistinct_I153_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(153)
thf(fact_152_exp_Odistinct_I149_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (while_list_char @ X131 @ X132))))))). % exp.distinct(149)
thf(fact_153_exp_Orel__distinct_I150_J, axiom,
    ((![R : list_char > list_char > $o, Y131 : exp_list_char, Y132 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ ((rel_ex1899005716t_char @ R @ (while_list_char @ Y131 @ Y132) @ (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.rel_distinct(150)
thf(fact_154_exp_Orel__distinct_I149_J, axiom,
    ((![R : list_char > list_char > $o, X71 : exp_list_char, X72 : list_char, X73 : list_char, Y131 : exp_list_char, Y132 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (fAcc_list_char @ X71 @ X72 @ X73) @ (while_list_char @ Y131 @ Y132))))))). % exp.rel_distinct(149)
thf(fact_155_exp_Orel__distinct_I154_J, axiom,
    ((![R : list_char > list_char > $o, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ ((rel_ex1899005716t_char @ R @ (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154) @ (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.rel_distinct(154)
thf(fact_156_exp_Orel__distinct_I153_J, axiom,
    ((![R : list_char > list_char > $o, X71 : exp_list_char, X72 : list_char, X73 : list_char, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (fAcc_list_char @ X71 @ X72 @ X73) @ (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154))))))). % exp.rel_distinct(153)
thf(fact_157_exp_Orel__distinct_I208_J, axiom,
    ((![R : list_char > list_char > $o, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154) @ (while_list_char @ X131 @ X132))))))). % exp.rel_distinct(208)
thf(fact_158_exp_Orel__distinct_I207_J, axiom,
    ((![R : list_char > list_char > $o, X131 : exp_list_char, X132 : exp_list_char, Y151 : exp_list_char, Y152 : list_char, Y153 : list_char, Y154 : exp_list_char]: (~ ((rel_ex1899005716t_char @ R @ (while_list_char @ X131 @ X132) @ (tryCatch_list_char @ Y151 @ Y152 @ Y153 @ Y154))))))). % exp.rel_distinct(207)
thf(fact_159_exp_Odistinct_I83_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(83)
thf(fact_160_exp_Odistinct_I95_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (while_list_char @ X131 @ X132))))))). % exp.distinct(95)
thf(fact_161_exp_Odistinct_I99_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(99)
thf(fact_162_exp_Odistinct_I151_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X14 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (throw_list_char @ X14))))))). % exp.distinct(151)
thf(fact_163_exp_Odistinct_I205_J, axiom,
    ((![X131 : exp_list_char, X132 : exp_list_char, X14 : exp_list_char]: (~ (((while_list_char @ X131 @ X132) = (throw_list_char @ X14))))))). % exp.distinct(205)

% Conjectures (1)
thf(conj_0, conjecture,
    ((wTrt @ p @ h_a @ e @ (binOp_list_char @ (val_list_char @ v_1) @ bop2 @ e_2) @ t))).
