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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:47.661

% Could-be-implicit typings (22)
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% Explicit typings (49)
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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_Product__Type_Oprod_Ofst_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, type,
    produc1246629324on_val : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_Product__Type_Oprod_Ofst_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, type,
    produc1141111712on_val : produc1097884484on_val > exp_list_char).
thf(sy_c_Product__Type_Oprod_Ofst_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,
    produc708556547on_val : produc1172664615on_val > produc1097884484on_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_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_TypeRel_Owiden__i__i__i_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_1673563217t_char : list_P1234162913t_char > ty > ty > pred_Product_unit).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_Type_Oty_OBoolean, type,
    boolean : ty).
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_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_e, type,
    e2 : exp_list_char).
thf(sy_v_e_H, type,
    e3 : exp_list_char).
thf(sy_v_s, type,
    s : produc515445032on_val).
thf(sy_v_s_H, type,
    s2 : produc515445032on_val).

% Relevant facts (173)
thf(fact_0_refl_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ s2))). % refl.prems(1)
thf(fact_1_refl_Oprems_I2_J, axiom,
    ((wTrt @ p @ (hp @ s2) @ e @ e3 @ t))). % refl.prems(2)
thf(fact_2_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_3_widen__trans, axiom,
    ((![P : list_P1234162913t_char, S : ty, U : ty, T : ty]: ((widen_917054840t_char @ P @ S @ U) => ((widen_917054840t_char @ P @ U @ T) => (widen_917054840t_char @ P @ S @ T)))))). % widen_trans
thf(fact_4_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_5_Red, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ e2 @ s) @ (produc2023458740on_val @ e3 @ s2)) @ (transi111096263on_val @ (red @ p))))). % Red
thf(fact_6_WTrt__elim__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, T : ty]: ((wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T) => (~ (((wTrt @ P @ H @ E @ E2 @ boolean) => (![T_1 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_1) => (![T_2 : ty]: ((wTrt @ P @ H @ E @ E_2 @ T_2) => (((widen_917054840t_char @ P @ T_1 @ T_2) | (widen_917054840t_char @ P @ T_2 @ T_1)) => (((widen_917054840t_char @ P @ T_1 @ T_2) => (T = T_2)) => (~ (((widen_917054840t_char @ P @ T_2 @ T_1) => (T = T_1))))))))))))))))). % WTrt_elim_cases(2)
thf(fact_7_WTrtCond, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_22 : ty, T : ty]: ((wTrt @ P @ H @ E @ E2 @ boolean) => ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (((widen_917054840t_char @ P @ T_12 @ T_22) | (widen_917054840t_char @ P @ T_22 @ T_12)) => (((widen_917054840t_char @ P @ T_12 @ T_22) => (T = T_22)) => (((widen_917054840t_char @ P @ T_22 @ T_12) => (T = T_12)) => (wTrt @ P @ H @ E @ (cond_list_char @ E2 @ E_1 @ E_2) @ T)))))))))). % WTrtCond
thf(fact_8_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_9_WTrt__env__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, E3 : list_char > option_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((map_le_list_char_ty @ E @ E3) => (wTrt @ P @ H @ E3 @ E2 @ T)))))). % WTrt_env_mono
thf(fact_10_conf__widen, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, V : val, T : ty, T2 : ty]: ((conf_P93989998t_char @ P @ H @ V @ T) => ((widen_917054840t_char @ P @ T @ T2) => (conf_P93989998t_char @ P @ H @ V @ T2)))))). % conf_widen
thf(fact_11_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_12_widen__i__i__i__def, axiom,
    ((widen_1673563217t_char = (^[X : list_P1234162913t_char]: (^[Xa : ty]: (^[Xb : ty]: (pred_Product_unit2 @ (^[Y : product_unit]: (widen_917054840t_char @ X @ Xa @ Xb))))))))). % widen_i_i_i_def
thf(fact_13_hp__def, axiom,
    ((hp = produc1246629324on_val))). % hp_def
thf(fact_14_Red__preserves__sconf, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3)))))))). % Red_preserves_sconf
thf(fact_15_subject__reduction, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ S2) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => (?[T3 : ty]: ((wTrt @ P @ (hp @ S3) @ E @ E4 @ T3) & (widen_917054840t_char @ P @ T3 @ T)))))))))). % subject_reduction
thf(fact_16_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts : list_ty, Us : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Us) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us)))))). % widens_trans
thf(fact_17_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => ((wTrt @ P @ (hp @ S2) @ E @ E2 @ T) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % red_preserves_sconf
thf(fact_18_CondReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E4 @ E_1 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondReds
thf(fact_19_red__reds_OCondRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (cond_list_char @ E4 @ E_1 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.CondRed
thf(fact_20_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_21_rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Ax @ Ay) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ A @ B)) @ (transi100378922on_val @ R)) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_22_rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((P @ Ax @ Ay) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Ax @ Ay) @ (produc52622304on_val @ A @ B)) @ (transi432893227on_val @ R)) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_23_rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Ax @ Ay) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ A @ B)) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((P @ A @ B) => (P @ Aa @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_24_converse__rtranclE2, axiom,
    ((![Xa2 : produc1097884484on_val, Xb2 : produc1097884484on_val, Za : produc1097884484on_val, Zb : produc1097884484on_val, R : set_Pr1368603847on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa2 @ Xb2) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R)) => ((~ (((produc1069526295on_val @ Xa2 @ Xb2) = (produc1069526295on_val @ Za @ Zb)))) => (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Xa2 @ Xb2) @ (produc1069526295on_val @ A @ B)) @ R) => (~ ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Za @ Zb)) @ (transi100378922on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_25_converse__rtranclE2, axiom,
    ((![Xa2 : nat > option2118145160on_val, Xb2 : list_char > option_val, Za : nat > option2118145160on_val, Zb : list_char > option_val, R : set_Pr148564103on_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa2 @ Xb2) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R)) => ((~ (((produc52622304on_val @ Xa2 @ Xb2) = (produc52622304on_val @ Za @ Zb)))) => (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Xa2 @ Xb2) @ (produc52622304on_val @ A @ B)) @ R) => (~ ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Za @ Zb)) @ (transi432893227on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_26_converse__rtranclE2, axiom,
    ((![Xa2 : exp_list_char, Xb2 : produc515445032on_val, Za : exp_list_char, Zb : produc515445032on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa2 @ Xb2) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R)) => ((~ (((produc2023458740on_val @ Xa2 @ Xb2) = (produc2023458740on_val @ Za @ Zb)))) => (~ ((![A : exp_list_char, B : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Xa2 @ Xb2) @ (produc2023458740on_val @ A @ B)) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Za @ Zb)) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE2
thf(fact_27_converse__rtrancl__induct2, axiom,
    ((![Ax : produc1097884484on_val, Ay : produc1097884484on_val, Bx : produc1097884484on_val, By : produc1097884484on_val, R : set_Pr1368603847on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Ax @ Ay) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Bx @ By) => ((![A : produc1097884484on_val, B : produc1097884484on_val, Aa : produc1097884484on_val, Ba : produc1097884484on_val]: ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ A @ B) @ (produc1069526295on_val @ Aa @ Ba)) @ R) => ((member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ Aa @ Ba) @ (produc1069526295on_val @ Bx @ By)) @ (transi100378922on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_28_converse__rtrancl__induct2, axiom,
    ((![Ax : nat > option2118145160on_val, Ay : list_char > option_val, Bx : nat > option2118145160on_val, By : list_char > option_val, R : 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 @ R)) => ((P @ Bx @ By) => ((![A : nat > option2118145160on_val, B : list_char > option_val, Aa : nat > option2118145160on_val, Ba : list_char > option_val]: ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ A @ B) @ (produc52622304on_val @ Aa @ Ba)) @ R) => ((member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ Aa @ Ba) @ (produc52622304on_val @ Bx @ By)) @ (transi432893227on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_29_converse__rtrancl__induct2, axiom,
    ((![Ax : exp_list_char, Ay : produc515445032on_val, Bx : exp_list_char, By : produc515445032on_val, R : set_Pr1189492743on_val, P : exp_list_char > produc515445032on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Ax @ Ay) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Bx @ By) => ((![A : exp_list_char, B : produc515445032on_val, Aa : exp_list_char, Ba : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ A @ B) @ (produc2023458740on_val @ Aa @ Ba)) @ R) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ Aa @ Ba) @ (produc2023458740on_val @ Bx @ By)) @ (transi111096263on_val @ R)) => ((P @ Aa @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_30_prod__cases4, axiom,
    ((![Y2 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y2 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
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_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_34_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y22 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X2 = Y22))))))). % prod.inject
thf(fact_35_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y22 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X2 = Y22))))))). % prod.inject
thf(fact_36_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y22 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y22)) = (((X1 = Y1)) & ((X2 = Y22))))))). % prod.inject
thf(fact_37_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R) => (member354538064on_val @ P2 @ (transi111096263on_val @ R)))))). % r_into_rtrancl
thf(fact_38_rtrancl__idemp, axiom,
    ((![R : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R)) = (transi111096263on_val @ R))))). % rtrancl_idemp
thf(fact_39_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, R2 : 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 @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E5 : exp_list_char, H3 : nat > option2118145160on_val, L3 : list_char > option_val]: (R2 @ E5 @ H3 @ L3 @ E5 @ H3 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_12 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E6 : exp_list_char, H4 : nat > option2118145160on_val, L4 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_0 @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E_12 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R2 @ E_12 @ H_1 @ L_1 @ E6 @ H4 @ L4) => (R2 @ E_0 @ H_0 @ L_0 @ E6 @ H4 @ L4)))) => (R2 @ E2 @ H @ L @ E4 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_40_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : 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 @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_41_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_42_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_43_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_44_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y2 = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_45_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y2 = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_46_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y2 = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_47_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_48_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_49_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_50_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_51_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_52_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P2))))). % prod_cases
thf(fact_53_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_54_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_55_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_56_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_57_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X4))))). % prod_induct3
thf(fact_58_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X4 : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X4))))). % prod_induct3
thf(fact_59_prod__cases3, axiom,
    ((![Y2 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y2 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_60_prod__cases3, axiom,
    ((![Y2 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y2 = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_61_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R))))))). % converse_rtrancl_into_rtrancl
thf(fact_62_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_63_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_64_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_65_converse__rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ B2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((member354538064on_val @ (produc1069526295on_val @ Z @ B2) @ (transi111096263on_val @ R)) => ((P @ Z) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_66_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc1097884484on_val, R : set_Pr1189492743on_val]: (member354538064on_val @ (produc1069526295on_val @ A2 @ A2) @ (transi111096263on_val @ R))))). % rtrancl.rtrancl_refl
thf(fact_67_converse__rtranclE, axiom,
    ((![X4 : produc1097884484on_val, Z2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R)) => ((~ ((X4 = Z2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z2) @ (transi111096263on_val @ R))))))))))))). % converse_rtranclE
thf(fact_68_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X2) @ (transi111096263on_val @ R)) => ((![A : produc1097884484on_val]: (P @ A @ A)) => ((![A : produc1097884484on_val, B : produc1097884484on_val, C : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A @ B) @ (transi111096263on_val @ R)) => ((P @ A @ B) => ((member354538064on_val @ (produc1069526295on_val @ B @ C) @ R) => (P @ A @ C))))) => (P @ X1 @ X2))))))). % rtrancl.inducts
thf(fact_69_rtrancl__induct, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val, P : produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((P @ A2) => ((![Y3 : produc1097884484on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ R) => ((P @ Y3) => (P @ Z))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_70_rtrancl__trans, axiom,
    ((![X4 : produc1097884484on_val, Y2 : produc1097884484on_val, R : set_Pr1189492743on_val, Z2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y2) @ (transi111096263on_val @ R)) => ((member354538064on_val @ (produc1069526295on_val @ Y2 @ Z2) @ (transi111096263on_val @ R)) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Z2) @ (transi111096263on_val @ R))))))). % rtrancl_trans
thf(fact_71_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R)))))))))))))))). % rtrancl.simps
thf(fact_72_rtrancl_Ocases, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R)) => ((~ ((A22 = A1))) => (~ ((![B : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ B) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ B @ A22) @ R)))))))))))). % rtrancl.cases
thf(fact_73_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R)))))))))))). % rtranclE
thf(fact_74_fst__conv, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val]: ((produc708556547on_val @ (produc1069526295on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_75_fst__conv, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val]: ((produc1141111712on_val @ (produc2023458740on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_76_fst__conv, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val]: ((produc1246629324on_val @ (produc52622304on_val @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_77_fst__eqD, axiom,
    ((![X4 : produc1097884484on_val, Y2 : produc1097884484on_val, A2 : produc1097884484on_val]: (((produc708556547on_val @ (produc1069526295on_val @ X4 @ Y2)) = A2) => (X4 = A2))))). % fst_eqD
thf(fact_78_fst__eqD, axiom,
    ((![X4 : exp_list_char, Y2 : produc515445032on_val, A2 : exp_list_char]: (((produc1141111712on_val @ (produc2023458740on_val @ X4 @ Y2)) = A2) => (X4 = A2))))). % fst_eqD
thf(fact_79_fst__eqD, axiom,
    ((![X4 : nat > option2118145160on_val, Y2 : list_char > option_val, A2 : nat > option2118145160on_val]: (((produc1246629324on_val @ (produc52622304on_val @ X4 @ Y2)) = A2) => (X4 = A2))))). % fst_eqD
thf(fact_80_subject__reduction2, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, E : list_char > option_ty, T : ty]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => ((typeSa1777264139_sconf @ P @ E @ (produc52622304on_val @ H @ L)) => ((wTrt @ P @ H @ E @ E2 @ T) => (?[T3 : ty]: ((wTrt @ P @ H2 @ E @ E4 @ T3) & (widen_917054840t_char @ P @ T3 @ T)))))))))). % subject_reduction2
thf(fact_81_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X4 : 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 @ X4))))). % prod_induct4
thf(fact_82_exp_Oinject_I12_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, Y121 : exp_list_char, Y122 : exp_list_char, Y123 : exp_list_char]: (((cond_list_char @ X121 @ X122 @ X123) = (cond_list_char @ Y121 @ Y122 @ Y123)) = (((X121 = Y121)) & ((((X122 = Y122)) & ((X123 = Y123))))))))). % exp.inject(12)
thf(fact_83_eq__fst__iff, axiom,
    ((![A2 : produc1097884484on_val, P2 : produc1172664615on_val]: ((A2 = (produc708556547on_val @ P2)) = (?[B4 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_84_eq__fst__iff, axiom,
    ((![A2 : exp_list_char, P2 : produc1097884484on_val]: ((A2 = (produc1141111712on_val @ P2)) = (?[B4 : produc515445032on_val]: (P2 = (produc2023458740on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_85_eq__fst__iff, axiom,
    ((![A2 : nat > option2118145160on_val, P2 : produc515445032on_val]: ((A2 = (produc1246629324on_val @ P2)) = (?[B4 : list_char > option_val]: (P2 = (produc52622304on_val @ A2 @ B4))))))). % eq_fst_iff
thf(fact_86_fstI, axiom,
    ((![X4 : produc1172664615on_val, Y2 : produc1097884484on_val, Z2 : produc1097884484on_val]: ((X4 = (produc1069526295on_val @ Y2 @ Z2)) => ((produc708556547on_val @ X4) = Y2))))). % fstI
thf(fact_87_fstI, axiom,
    ((![X4 : produc1097884484on_val, Y2 : exp_list_char, Z2 : produc515445032on_val]: ((X4 = (produc2023458740on_val @ Y2 @ Z2)) => ((produc1141111712on_val @ X4) = Y2))))). % fstI
thf(fact_88_fstI, axiom,
    ((![X4 : produc515445032on_val, Y2 : nat > option2118145160on_val, Z2 : list_char > option_val]: ((X4 = (produc52622304on_val @ Y2 @ Z2)) => ((produc1246629324on_val @ X4) = Y2))))). % fstI
thf(fact_89_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : 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 @ E4 @ (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_90_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : 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 @ E4 @ (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_91_CondRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_1 : exp_list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ E2 @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CondRedsThrow
thf(fact_92_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_93_exp_Odistinct_I201_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X14 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (throw_list_char @ X14))))))). % exp.distinct(201)
thf(fact_94_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_95_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_96_red__reds_OThrowThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.ThrowThrow
thf(fact_97_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_98_ThrowRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowRedsThrow
thf(fact_99_red__reds_OCondThrow, axiom,
    ((![E2 : exp_list_char, E_1 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cond_list_char @ (throw_list_char @ E2) @ E_1 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CondThrow
thf(fact_100_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_101_WhileRedsThrow, axiom,
    ((![B2 : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ B2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (while_list_char @ B2 @ C2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % WhileRedsThrow
thf(fact_102_FAccRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccRedsThrow
thf(fact_103_CastRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_104_exp_Oinject_I2_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, Y21 : list_char, Y222 : exp_list_char]: (((cast_list_char @ X21 @ X22) = (cast_list_char @ Y21 @ Y222)) = (((X21 = Y21)) & ((X22 = Y222))))))). % exp.inject(2)
thf(fact_105_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_106_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_107_exp_Odistinct_I199_J, axiom,
    ((![X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cond_list_char @ X121 @ X122 @ X123) = (while_list_char @ X131 @ X132))))))). % exp.distinct(199)
thf(fact_108_exp_Odistinct_I47_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(47)
thf(fact_109_exp_Odistinct_I147_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(147)
thf(fact_110_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)
thf(fact_111_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_112_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_113_exp_Odistinct_I51_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X14 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (throw_list_char @ X14))))))). % exp.distinct(51)
thf(fact_114_exp_Odistinct_I49_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (while_list_char @ X131 @ X132))))))). % exp.distinct(49)
thf(fact_115_exp_Odistinct_I37_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((cast_list_char @ X21 @ X22) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(37)
thf(fact_116_red__reds_OCastRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C4 @ E4) @ S3)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_117_red__reds_OFAccRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F @ D2) @ S3)) @ (red @ P)))))). % red_reds.FAccRed
thf(fact_118_red__reds_OCastThrow, axiom,
    ((![C4 : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_119_red__reds_OFAccThrow, axiom,
    ((![E2 : exp_list_char, F : list_char, D2 : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ (throw_list_char @ E2) @ F @ D2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.FAccThrow
thf(fact_120_CastReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C4 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C4 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_121_FAccReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, F : list_char, D2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (fAcc_list_char @ E2 @ F @ D2) @ S2) @ (produc2023458740on_val @ (fAcc_list_char @ E4 @ F @ D2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % FAccReds
thf(fact_122_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E4 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, L_02 : list_char > option_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E4 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
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_map__le__map__add, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: (map_le_list_char_ty @ F2 @ (map_add_list_char_ty @ G @ F2))))). % map_le_map_add
thf(fact_125_map__le__map__add, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: (map_le_list_char_val @ F2 @ (map_ad1615113112ar_val @ G @ F2))))). % map_le_map_add
thf(fact_126_map__add__le__mapE, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty, H : list_char > option_ty]: ((map_le_list_char_ty @ (map_add_list_char_ty @ F2 @ G) @ H) => (map_le_list_char_ty @ G @ H))))). % map_add_le_mapE
thf(fact_127_map__add__le__mapE, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val, H : list_char > option_val]: ((map_le_list_char_val @ (map_ad1615113112ar_val @ F2 @ G) @ H) => (map_le_list_char_val @ G @ H))))). % map_add_le_mapE
thf(fact_128_map__le__refl, axiom,
    ((![F2 : list_char > option_ty]: (map_le_list_char_ty @ F2 @ F2)))). % map_le_refl
thf(fact_129_map__le__trans, axiom,
    ((![M1 : list_char > option_ty, M2 : list_char > option_ty, M3 : list_char > option_ty]: ((map_le_list_char_ty @ M1 @ M2) => ((map_le_list_char_ty @ M2 @ M3) => (map_le_list_char_ty @ M1 @ M3)))))). % map_le_trans
thf(fact_130_map__le__antisym, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ G) => ((map_le_list_char_ty @ G @ F2) => (F2 = G)))))). % map_le_antisym
thf(fact_131_map__le__iff__map__add__commute, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ (map_add_list_char_ty @ F2 @ G)) = ((map_add_list_char_ty @ F2 @ G) = (map_add_list_char_ty @ G @ F2)))))). % map_le_iff_map_add_commute
thf(fact_132_map__le__iff__map__add__commute, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ (map_ad1615113112ar_val @ F2 @ G)) = ((map_ad1615113112ar_val @ F2 @ G) = (map_ad1615113112ar_val @ G @ F2)))))). % map_le_iff_map_add_commute
thf(fact_133_map__add__subsumed2, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ G) => ((map_add_list_char_ty @ G @ F2) = G))))). % map_add_subsumed2
thf(fact_134_map__add__subsumed2, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ G) => ((map_ad1615113112ar_val @ G @ F2) = G))))). % map_add_subsumed2
thf(fact_135_map__add__subsumed1, axiom,
    ((![F2 : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ G) => ((map_add_list_char_ty @ F2 @ G) = G))))). % map_add_subsumed1
thf(fact_136_map__add__subsumed1, axiom,
    ((![F2 : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ G) => ((map_ad1615113112ar_val @ F2 @ G) = G))))). % map_add_subsumed1
thf(fact_137_map__add__le__mapI, axiom,
    ((![F2 : list_char > option_ty, H : list_char > option_ty, G : list_char > option_ty]: ((map_le_list_char_ty @ F2 @ H) => ((map_le_list_char_ty @ G @ H) => (map_le_list_char_ty @ (map_add_list_char_ty @ F2 @ G) @ H)))))). % map_add_le_mapI
thf(fact_138_map__add__le__mapI, axiom,
    ((![F2 : list_char > option_val, H : list_char > option_val, G : list_char > option_val]: ((map_le_list_char_val @ F2 @ H) => ((map_le_list_char_val @ G @ H) => (map_le_list_char_val @ (map_ad1615113112ar_val @ F2 @ G) @ H)))))). % map_add_le_mapI
thf(fact_139_BinOpRedsThrow1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOpRedsThrow1
thf(fact_140_SeqRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqRedsThrow
thf(fact_141_LAssRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsThrow
thf(fact_142_exp_Oinject_I11_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, Y111 : exp_list_char, Y112 : exp_list_char]: (((seq_list_char @ X111 @ X112) = (seq_list_char @ Y111 @ Y112)) = (((X111 = Y111)) & ((X112 = Y112))))))). % exp.inject(11)
thf(fact_143_exp_Oinject_I6_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, Y61 : list_char, Y62 : exp_list_char]: (((lAss_list_char @ X61 @ X62) = (lAss_list_char @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % exp.inject(6)
thf(fact_144_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_145_exp_Odistinct_I193_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (while_list_char @ X131 @ X132))))))). % exp.distinct(193)
thf(fact_146_exp_Odistinct_I145_J, axiom,
    ((![X71 : exp_list_char, X72 : list_char, X73 : list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((fAcc_list_char @ X71 @ X72 @ X73) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(145)
thf(fact_147_exp_Odistinct_I133_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X131 : exp_list_char, X132 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (while_list_char @ X131 @ X132))))))). % exp.distinct(133)
thf(fact_148_exp_Odistinct_I121_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X71 : exp_list_char, X72 : list_char, X73 : list_char]: (~ (((lAss_list_char @ X61 @ X62) = (fAcc_list_char @ X71 @ X72 @ X73))))))). % exp.distinct(121)
thf(fact_149_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_150_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_151_exp_Odistinct_I45_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(45)
thf(fact_152_exp_Odistinct_I35_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X61 : list_char, X62 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(35)
thf(fact_153_exp_Odistinct_I31_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(31)
thf(fact_154_exp_Odistinct_I93_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(93)
thf(fact_155_exp_Odistinct_I131_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(131)
thf(fact_156_exp_Odistinct_I191_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X121 : exp_list_char, X122 : exp_list_char, X123 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (cond_list_char @ X121 @ X122 @ X123))))))). % exp.distinct(191)
thf(fact_157_exp_Odistinct_I129_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(129)
thf(fact_158_exp_Odistinct_I91_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(91)
thf(fact_159_exp_Odistinct_I81_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X61 : list_char, X62 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (lAss_list_char @ X61 @ X62))))))). % exp.distinct(81)
thf(fact_160_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_1 : exp_list_char, T_12 : ty, E_2 : exp_list_char, T_22 : ty]: ((wTrt @ P @ H @ E @ E_1 @ T_12) => ((wTrt @ P @ H @ E @ E_2 @ T_22) => (wTrt @ P @ H @ E @ (seq_list_char @ E_1 @ E_2) @ T_22)))))). % WTrtSeq
thf(fact_161_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_162_exp_Odistinct_I135_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X14 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (throw_list_char @ X14))))))). % exp.distinct(135)
thf(fact_163_exp_Odistinct_I195_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X14 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (throw_list_char @ X14))))))). % exp.distinct(195)
thf(fact_164_red__reds_OLAssRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E4) @ S3)) @ (red @ P)))))). % red_reds.LAssRed
thf(fact_165_red__reds_OSeqRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S3)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_166_red__reds_OBinOpRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E4 @ Bop @ E_2) @ S3)) @ (red @ P)))))). % red_reds.BinOpRed1
thf(fact_167_red__reds_OLAssThrow, axiom,
    ((![V2 : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.LAssThrow
thf(fact_168_red__reds_OSeqThrow, axiom,
    ((![E2 : exp_list_char, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (throw_list_char @ E2) @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.SeqThrow
thf(fact_169_red__reds_OBinOpThrow1, axiom,
    ((![E2 : exp_list_char, Bop : bop, E_2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ (throw_list_char @ E2) @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.BinOpThrow1
thf(fact_170_LAssReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E2) @ S2) @ (produc2023458740on_val @ (lAss_list_char @ V2 @ E4) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % LAssReds
thf(fact_171_SeqReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2) @ (produc2023458740on_val @ (seq_list_char @ E4 @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_172_BinOp1Reds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E4 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Bop : bop, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E4 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (binOp_list_char @ E2 @ Bop @ E_2) @ S2) @ (produc2023458740on_val @ (binOp_list_char @ E4 @ Bop @ E_2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % BinOp1Reds

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[T4 : ty]: ((widen_917054840t_char @ p @ T4 @ t) & (wTrt @ p @ (hp @ s2) @ e @ e3 @ T4))))).
