% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_82__5333502_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:10.309

% Could-be-implicit typings (22)
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thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
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thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
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thf(ty_n_t__Value__Oval, type,
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thf(ty_n_t__Expr__Obop, type,
    bop : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (53)
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Conform_Ohconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
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thf(sy_c_Conform_Olconf_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    lconf_485928294t_char : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_val) > (list_char > option_ty) > $o).
thf(sy_c_Expr_Oexp_OBinOp_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OBlock_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Expr_Oexp_OLAss_001t__List__Olist_It__String__Ochar_J, type,
    lAss_list_char : list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OSeq_001t__List__Olist_It__String__Ochar_J, type,
    seq_list_char : exp_list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_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_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_If_001t__Option__Ooption_It__Value__Oval_J, type,
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thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Objects_Ohext, type,
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thf(sy_c_Option_Ooption_ONone_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Value__Oval, type,
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thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J, type,
    produc746553401on_val : (list_char > option_val) > (list_char > option_val) > produc1335728385on_val).
thf(sy_c_Product__Type_OPair_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,
    produc52622304on_val : (nat > option2118145160on_val) > (list_char > option_val) > produc515445032on_val).
thf(sy_c_Product__Type_OPair_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,
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thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001t__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,
    produc2106877847on_val : produc515445032on_val > produc515445032on_val > produc744932519on_val).
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).
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    produc564964183on_val : produc1172664615on_val > produc1172664615on_val > produc1161703655on_val).
thf(sy_c_Product__Type_Ocurry_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_001_Eo, type,
    produc761261956_val_o : (produc515445032on_val > $o) > (nat > option2118145160on_val) > (list_char > option_val) > $o).
thf(sy_c_Product__Type_Ocurry_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_001_Eo, type,
    produc699483184_val_o : (produc1097884484on_val > $o) > exp_list_char > produc515445032on_val > $o).
thf(sy_c_Product__Type_Ocurry_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_001_Eo, type,
    produc360843917_val_o : (produc1172664615on_val > $o) > produc1097884484on_val > produc1097884484on_val > $o).
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    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oassigned, type,
    assigned : list_char > exp_list_char > $o).
thf(sy_c_SmallStep_Ored, type,
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thf(sy_c_SmallStep_Oredp, type,
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    transi100378922on_val : set_Pr1368603847on_val > set_Pr1368603847on_val).
thf(sy_c_WellTypeRT_OWTrt, type,
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thf(sy_c_Wfrec_Osame__fst_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,
    same_f1752972725on_val : ((nat > option2118145160on_val) > $o) > ((nat > option2118145160on_val) > set_Pr1104486497on_val) > set_Pr148564103on_val).
thf(sy_c_Wfrec_Osame__fst_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,
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thf(sy_c_Wfrec_Osame__fst_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,
    same_f962657004on_val : (produc1097884484on_val > $o) > (produc1097884484on_val > set_Pr1189492743on_val) > set_Pr1368603847on_val).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
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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,
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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).
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    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_H____, type,
    t : ty).
thf(sy_v_T____, type,
    t2 : ty).
thf(sy_v_V____, type,
    v : list_char).
thf(sy_v_e_Ha____, type,
    e_a : exp_list_char).
thf(sy_v_ea____, type,
    ea : exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
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thf(sy_v_la____, type,
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% Relevant facts (163)
thf(fact_0_BlockRedNone_Ohyps_I3_J, axiom,
    (((l_a @ v) = none_val))). % BlockRedNone.hyps(3)
thf(fact_1_BlockRedNone_Ohyps_I4_J, axiom,
    ((~ ((assigned @ v @ ea))))). % BlockRedNone.hyps(4)
thf(fact_2_BlockRedNone_Ohyps_I1_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))). % BlockRedNone.hyps(1)
thf(fact_3_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_4_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : 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 @ X))))). % prod_induct4
thf(fact_5_fun__upd__upd, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, Z : option_val]: ((fun_up1252458416on_val @ (fun_up1252458416on_val @ F @ X @ Y) @ X @ Z) = (fun_up1252458416on_val @ F @ X @ Z))))). % fun_upd_upd
thf(fact_6_fun__upd__triv, axiom,
    ((![F : list_char > option_val, X : list_char]: ((fun_up1252458416on_val @ F @ X @ (F @ X)) = F)))). % fun_upd_triv
thf(fact_7_fun__upd__apply, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[X2 : list_char]: (^[Y2 : option_val]: (^[Z2 : list_char]: (if_option_val @ (Z2 = X2) @ Y2 @ (F2 @ Z2))))))))). % fun_upd_apply
thf(fact_8_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_9_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_10_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_11_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_12_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_13_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_14_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_15_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_16_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_17_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_18_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_19_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_20_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_21_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_22_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_23_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_24_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_25_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_26_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X3 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_27_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X3 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_28_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X3 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X3 @ Y3)))))). % surj_pair
thf(fact_29_fun__upd__idem__iff, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = F) = ((F @ X) = Y))))). % fun_upd_idem_iff
thf(fact_30_fun__upd__twist, axiom,
    ((![A2 : list_char, C2 : list_char, M : list_char > option_val, B2 : option_val, D2 : option_val]: ((~ ((A2 = C2))) => ((fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ A2 @ B2) @ C2 @ D2) = (fun_up1252458416on_val @ (fun_up1252458416on_val @ M @ C2 @ D2) @ A2 @ B2)))))). % fun_upd_twist
thf(fact_31_fun__upd__other, axiom,
    ((![Z : list_char, X : list_char, F : list_char > option_val, Y : option_val]: ((~ ((Z = X))) => ((fun_up1252458416on_val @ F @ X @ Y @ Z) = (F @ Z)))))). % fun_upd_other
thf(fact_32_fun__upd__same, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: ((fun_up1252458416on_val @ F @ X @ Y @ X) = Y)))). % fun_upd_same
thf(fact_33_fun__upd__idem, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val]: (((F @ X) = Y) => ((fun_up1252458416on_val @ F @ X @ Y) = F))))). % fun_upd_idem
thf(fact_34_fun__upd__eqD, axiom,
    ((![F : list_char > option_val, X : list_char, Y : option_val, G : list_char > option_val, Z : option_val]: (((fun_up1252458416on_val @ F @ X @ Y) = (fun_up1252458416on_val @ G @ X @ Z)) => (Y = Z))))). % fun_upd_eqD
thf(fact_35_fun__upd__def, axiom,
    ((fun_up1252458416on_val = (^[F2 : list_char > option_val]: (^[A4 : list_char]: (^[B4 : option_val]: (^[X2 : list_char]: (if_option_val @ (X2 = A4) @ B4 @ (F2 @ X2))))))))). % fun_upd_def
thf(fact_36_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_37_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_38_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_39_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_40_BlockRedNone_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, T : ty]: ((wTrt @ p @ ha @ E @ ea @ T) => ((lconf_485928294t_char @ p @ ha @ (fun_up1252458416on_val @ la @ v @ none_val) @ E) => (lconf_485928294t_char @ p @ h_a @ l_a @ E)))))). % BlockRedNone.hyps(2)
thf(fact_41_red__reds_OBlockRedNone, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val))) @ (produc2023458740on_val @ E3 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E2))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ (block_list_char @ V @ T @ E3) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V))))) @ (red @ P)))))))). % red_reds.BlockRedNone
thf(fact_42_same__fstI, axiom,
    ((![P : (nat > option2118145160on_val) > $o, X : nat > option2118145160on_val, Y4 : list_char > option_val, Y : list_char > option_val, R : (nat > option2118145160on_val) > set_Pr1104486497on_val]: ((P @ X) => ((member1177709994on_val @ (produc746553401on_val @ Y4 @ Y) @ (R @ X)) => (member2027247312on_val @ (produc2106877847on_val @ (produc52622304on_val @ X @ Y4) @ (produc52622304on_val @ X @ Y)) @ (same_f1752972725on_val @ P @ R))))))). % same_fstI
thf(fact_43_same__fstI, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Y4 : produc515445032on_val, Y : produc515445032on_val, R : exp_list_char > set_Pr148564103on_val]: ((P @ X) => ((member2027247312on_val @ (produc2106877847on_val @ Y4 @ Y) @ (R @ X)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X @ Y4) @ (produc2023458740on_val @ X @ Y)) @ (same_f366220041on_val @ P @ R))))))). % same_fstI
thf(fact_44_same__fstI, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val, Y4 : produc1097884484on_val, Y : produc1097884484on_val, R : produc1097884484on_val > set_Pr1189492743on_val]: ((P @ X) => ((member354538064on_val @ (produc1069526295on_val @ Y4 @ Y) @ (R @ X)) => (member208988944on_val @ (produc564964183on_val @ (produc1069526295on_val @ X @ Y4) @ (produc1069526295on_val @ X @ Y)) @ (same_f962657004on_val @ P @ R))))))). % same_fstI
thf(fact_45_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_46_BlockRedNone_Oprems_I2_J, axiom,
    ((lconf_485928294t_char @ p @ ha @ la @ e))). % BlockRedNone.prems(2)
thf(fact_47_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S : produc1097884484on_val, R : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S) @ R) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_48_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S : produc515445032on_val, R : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S) @ R) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_49_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S : list_char > option_val, R : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S) @ R) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_50_curryI, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((F @ (produc1069526295on_val @ A2 @ B2)) => (produc360843917_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_51_curryI, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((F @ (produc2023458740on_val @ A2 @ B2)) => (produc699483184_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_52_curryI, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((F @ (produc52622304on_val @ A2 @ B2)) => (produc761261956_val_o @ F @ A2 @ B2))))). % curryI
thf(fact_53_BlockRedNone_Oprems_I1_J, axiom,
    ((wTrt @ p @ ha @ e @ (block_list_char @ v @ t2 @ ea) @ t))). % BlockRedNone.prems(1)
thf(fact_54_curryD, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc360843917_val_o @ F @ A2 @ B2) => (F @ (produc1069526295on_val @ A2 @ B2)))))). % curryD
thf(fact_55_curryD, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryD
thf(fact_56_curryD, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryD
thf(fact_57_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_58_Collect__mem__eq, axiom,
    ((![A5 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X2 : produc1172664615on_val]: (member354538064on_val @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_59_curryE, axiom,
    ((![F : produc1172664615on_val > $o, A2 : produc1097884484on_val, B2 : produc1097884484on_val]: ((produc360843917_val_o @ F @ A2 @ B2) => (F @ (produc1069526295on_val @ A2 @ B2)))))). % curryE
thf(fact_60_curryE, axiom,
    ((![F : produc1097884484on_val > $o, A2 : exp_list_char, B2 : produc515445032on_val]: ((produc699483184_val_o @ F @ A2 @ B2) => (F @ (produc2023458740on_val @ A2 @ B2)))))). % curryE
thf(fact_61_curryE, axiom,
    ((![F : produc515445032on_val > $o, A2 : nat > option2118145160on_val, B2 : list_char > option_val]: ((produc761261956_val_o @ F @ A2 @ B2) => (F @ (produc52622304on_val @ A2 @ B2)))))). % curryE
thf(fact_62_lconf__empty, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty]: (lconf_485928294t_char @ P @ H @ (^[X2 : list_char]: none_val) @ E)))). % lconf_empty
thf(fact_63_empty__upd__none, axiom,
    ((![X : list_char]: ((fun_up1252458416on_val @ (^[X2 : list_char]: none_val) @ X @ none_val) = (^[X2 : list_char]: none_val))))). % empty_upd_none
thf(fact_64_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_65_exp_Oinject_I10_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, Y101 : list_char, Y102 : ty, Y103 : exp_list_char]: (((block_list_char @ X101 @ X102 @ X103) = (block_list_char @ Y101 @ Y102 @ Y103)) = (((X101 = Y101)) & ((((X102 = Y102)) & ((X103 = Y103))))))))). % exp.inject(10)
thf(fact_66_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_67_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_68_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H3 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H3) => (hext @ H @ H3)))))). % hext_trans
thf(fact_69_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_70_redp__redsp_OBlockRedNone, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, V : list_char, E3 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, T : ty]: ((redp @ P @ E2 @ (produc52622304on_val @ H @ (fun_up1252458416on_val @ L @ V @ none_val)) @ E3 @ (produc52622304on_val @ H2 @ L2)) => (((L2 @ V) = none_val) => ((~ ((assigned @ V @ E2))) => (redp @ P @ (block_list_char @ V @ T @ E2) @ (produc52622304on_val @ H @ L) @ (block_list_char @ V @ T @ E3) @ (produc52622304on_val @ H2 @ (fun_up1252458416on_val @ L2 @ V @ (L @ V)))))))))). % redp_redsp.BlockRedNone
thf(fact_71_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: (((^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R))) = (^[X2 : produc1097884484on_val]: (^[Y2 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_72_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S3 : set_Pr556513572on_val]: (((^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ R))) = (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X2 @ Y2) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_73_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S3 : set_Pr723149704on_val]: (((^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ R))) = (^[X2 : nat > option2118145160on_val]: (^[Y2 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X2 @ Y2) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_74_redp__red__eq, axiom,
    ((redp = (^[P3 : list_P1234162913t_char]: (^[X2 : exp_list_char]: (^[Y2 : produc515445032on_val]: (^[Z2 : exp_list_char]: (^[Aa : produc515445032on_val]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ X2 @ Y2) @ (produc2023458740on_val @ Z2 @ Aa)) @ (red @ P3)))))))))). % redp_red_eq
thf(fact_75_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_76_red__reds_ORedBlock, axiom,
    ((![V : list_char, T : ty, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (val_list_char @ U)) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedBlock
thf(fact_77_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, H4 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E4 @ H4 @ L3 @ E4 @ H4 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_02 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E5 : exp_list_char, H5 : 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_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E5 @ H5 @ L4) => (R @ E_0 @ H_0 @ L_02 @ E5 @ H5 @ L4)))) => (R @ E2 @ H @ L @ E3 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_78_BlockRedsFinal, axiom,
    ((![E_02 : exp_list_char, S_0 : produc515445032on_val, E_2 : exp_list_char, H_2 : nat > option2118145160on_val, L_2 : list_char > option_val, P : list_P1234162913t_char, H_02 : nat > option2118145160on_val, L_0 : list_char > option_val, V : list_char, T : ty]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_02 @ S_0) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ L_2))) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E_2) => ((S_0 = (produc52622304on_val @ H_02 @ (fun_up1252458416on_val @ L_0 @ V @ none_val))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ E_02) @ (produc52622304on_val @ H_02 @ L_0)) @ (produc2023458740on_val @ E_2 @ (produc52622304on_val @ H_2 @ (fun_up1252458416on_val @ L_2 @ V @ (L_0 @ V))))) @ (transi111096263on_val @ (red @ P))))))))). % BlockRedsFinal
thf(fact_79_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_80_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_81_map__add__None, axiom,
    ((![M : list_char > option_val, N : list_char > option_val, K : list_char]: (((map_ad1615113112ar_val @ M @ N @ K) = none_val) = ((((N @ K) = none_val)) & (((M @ K) = none_val))))))). % map_add_None
thf(fact_82_map__add__eq__empty__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((map_ad1615113112ar_val @ F @ G) = (^[X2 : list_char]: none_val)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % map_add_eq_empty_iff
thf(fact_83_empty__map__add, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ (^[X2 : list_char]: none_val) @ M) = M)))). % empty_map_add
thf(fact_84_map__add__empty, axiom,
    ((![M : list_char > option_val]: ((map_ad1615113112ar_val @ M @ (^[X2 : list_char]: none_val)) = M)))). % map_add_empty
thf(fact_85_empty__eq__map__add__iff, axiom,
    ((![F : list_char > option_val, G : list_char > option_val]: (((^[X2 : list_char]: none_val) = (map_ad1615113112ar_val @ F @ G)) = (((F = (^[X2 : list_char]: none_val))) & ((G = (^[X2 : list_char]: none_val)))))))). % empty_eq_map_add_iff
thf(fact_86_exp_Odistinct_I67_J, axiom,
    ((![X32 : val, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((val_list_char @ X32) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(67)
thf(fact_87_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_88_redp__redsp_ORedBlock, axiom,
    ((![P : list_P1234162913t_char, V : list_char, T : ty, U : val, S : produc515445032on_val]: (redp @ P @ (block_list_char @ V @ T @ (val_list_char @ U)) @ S @ (val_list_char @ U) @ S)))). % redp_redsp.RedBlock
thf(fact_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_rtrancl__idemp, axiom,
    ((![R2 : set_Pr1189492743on_val]: ((transi111096263on_val @ (transi111096263on_val @ R2)) = (transi111096263on_val @ R2))))). % rtrancl_idemp
thf(fact_99_r__into__rtrancl, axiom,
    ((![P2 : produc1172664615on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ P2 @ R2) => (member354538064on_val @ P2 @ (transi111096263on_val @ R2)))))). % r_into_rtrancl
thf(fact_100_option_Odisc__eq__case_I1_J, axiom,
    ((![Option : option_val]: ((Option = none_val) = (case_option_o_val @ $true @ (^[Uu : val]: $false) @ Option))))). % option.disc_eq_case(1)
thf(fact_101_option_Odisc__eq__case_I2_J, axiom,
    ((![Option : option_val]: ((~ ((Option = none_val))) = (case_option_o_val @ $false @ (^[Uu : val]: $true) @ Option))))). % option.disc_eq_case(2)
thf(fact_102_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_103_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_104_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A4 : produc1097884484on_val]: (((A1 = A4)) & ((A22 = A4))))) | ((?[A4 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A4)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A4 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_105_rtrancl__trans, axiom,
    ((![X : produc1097884484on_val, Y : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y @ Z) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_106_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) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((P @ Y3) => (P @ Z3))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_107_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_108_converse__rtranclE, axiom,
    ((![X : produc1097884484on_val, Z : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Z) @ (transi111096263on_val @ R2)) => ((~ ((X = Z))) => (~ ((![Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X @ Y3) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_109_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_110_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) => ((![Y3 : produc1097884484on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z3 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z3) => (P @ Y3))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_111_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_112_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C2) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C2) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_113_TryRedsVal, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, V2 : val, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V : list_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ S2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ E2 @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % TryRedsVal
thf(fact_114_BinOp2Reds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V2 : 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 @ V2) @ Bop @ E2) @ S) @ (produc2023458740on_val @ (binOp_list_char @ (val_list_char @ V2) @ Bop @ E3) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % BinOp2Reds
thf(fact_115_SeqReds2, axiom,
    ((![E_12 : exp_list_char, S_0 : produc515445032on_val, V_1 : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char, E_22 : exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_12 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V_1) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E_2 @ S_1) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E_12 @ E_2) @ S_0) @ (produc2023458740on_val @ E_22 @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % SeqReds2
thf(fact_116_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_117_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_118_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_119_exp_Odistinct_I55_J, axiom,
    ((![X32 : val, X41 : exp_list_char, X42 : bop, X43 : exp_list_char]: (~ (((val_list_char @ X32) = (binOp_list_char @ X41 @ X42 @ X43))))))). % exp.distinct(55)
thf(fact_120_exp_Odistinct_I69_J, axiom,
    ((![X32 : val, X111 : exp_list_char, X112 : exp_list_char]: (~ (((val_list_char @ X32) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(69)
thf(fact_121_exp_Odistinct_I77_J, axiom,
    ((![X32 : val, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((val_list_char @ X32) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(77)
thf(fact_122_redp__redsp_OSeqRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, E_2 : exp_list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (seq_list_char @ E2 @ E_2) @ S @ (seq_list_char @ E3 @ E_2) @ S2))))). % redp_redsp.SeqRed
thf(fact_123_WTrtSeq, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E_12 : exp_list_char, T_1 : ty, E_2 : exp_list_char, T_2 : ty]: ((wTrt @ P @ H @ E @ E_12 @ T_1) => ((wTrt @ P @ H @ E @ E_2 @ T_2) => (wTrt @ P @ H @ E @ (seq_list_char @ E_12 @ E_2) @ T_2)))))). % WTrtSeq
thf(fact_124_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_125_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_126_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_127_exp_Odistinct_I197_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((seq_list_char @ X111 @ X112) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(197)
thf(fact_128_exp_Odistinct_I181_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, X111 : exp_list_char, X112 : exp_list_char]: (~ (((block_list_char @ X101 @ X102 @ X103) = (seq_list_char @ X111 @ X112))))))). % exp.distinct(181)
thf(fact_129_exp_Odistinct_I89_J, axiom,
    ((![X41 : exp_list_char, X42 : bop, X43 : exp_list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((binOp_list_char @ X41 @ X42 @ X43) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(89)
thf(fact_130_exp_Odistinct_I189_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((block_list_char @ X101 @ X102 @ X103) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(189)
thf(fact_131_redp__redsp_OTryRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, C4 : list_char, V : list_char, E_2 : exp_list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (tryCatch_list_char @ E2 @ C4 @ V @ E_2) @ S @ (tryCatch_list_char @ E3 @ C4 @ V @ E_2) @ S2))))). % redp_redsp.TryRed
thf(fact_132_redp__redsp_ORedSeq, axiom,
    ((![P : list_P1234162913t_char, V2 : val, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S @ E_2 @ S)))). % redp_redsp.RedSeq
thf(fact_133_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_134_redp__redsp_ORedTry, axiom,
    ((![P : list_P1234162913t_char, V2 : val, C4 : list_char, V : list_char, E_2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (tryCatch_list_char @ (val_list_char @ V2) @ C4 @ V @ E_2) @ S @ (val_list_char @ V2) @ S)))). % redp_redsp.RedTry
thf(fact_135_red__reds_OSeqRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_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 @ (seq_list_char @ E2 @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_136_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_137_red__reds_OTryRed, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V : 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 @ (tryCatch_list_char @ E2 @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (tryCatch_list_char @ E3 @ C4 @ V @ E_2) @ S2)) @ (red @ P)))))). % red_reds.TryRed
thf(fact_138_red__reds_ORedSeq, axiom,
    ((![V2 : val, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ (val_list_char @ V2) @ E_2) @ S) @ (produc2023458740on_val @ E_2 @ S)) @ (red @ P))))). % red_reds.RedSeq
thf(fact_139_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_140_SeqReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_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 @ (seq_list_char @ E2 @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E3 @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % SeqReds
thf(fact_141_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_142_red__reds_ORedTry, axiom,
    ((![V2 : val, C4 : list_char, V : list_char, E_2 : exp_list_char, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (tryCatch_list_char @ (val_list_char @ V2) @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (val_list_char @ V2) @ S)) @ (red @ P))))). % red_reds.RedTry
thf(fact_143_TryReds, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, C4 : list_char, V : 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 @ (tryCatch_list_char @ E2 @ C4 @ V @ E_2) @ S) @ (produc2023458740on_val @ (tryCatch_list_char @ E3 @ C4 @ V @ E_2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % TryReds
thf(fact_144_BinOpRedsThrow2, axiom,
    ((![E_12 : 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_12 @ 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_12 @ Bop @ E_2) @ S_0) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % BinOpRedsThrow2
thf(fact_145_red__reds_ORedInitBlock, axiom,
    ((![V : list_char, T : ty, V2 : val, U : val, S : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (block_list_char @ V @ T @ (seq_list_char @ (lAss_list_char @ V @ (val_list_char @ V2)) @ (val_list_char @ U))) @ S) @ (produc2023458740on_val @ (val_list_char @ U) @ S)) @ (red @ P))))). % red_reds.RedInitBlock
thf(fact_146_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_147_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_148_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_149_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_150_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_151_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_152_exp_Odistinct_I137_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(137)
thf(fact_153_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_154_exp_Odistinct_I209_J, axiom,
    ((![X14 : exp_list_char, X151 : exp_list_char, X152 : list_char, X153 : list_char, X154 : exp_list_char]: (~ (((throw_list_char @ X14) = (tryCatch_list_char @ X151 @ X152 @ X153 @ X154))))))). % exp.distinct(209)
thf(fact_155_LAssRedsThrow, axiom,
    ((![E2 : exp_list_char, S : produc515445032on_val, A2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, V : 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 @ (lAss_list_char @ V @ E2) @ S) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S2)) @ (transi111096263on_val @ (red @ P))))))). % LAssRedsThrow
thf(fact_156_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_157_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_158_exp_Odistinct_I187_J, axiom,
    ((![X101 : list_char, X102 : ty, X103 : exp_list_char, X14 : exp_list_char]: (~ (((block_list_char @ X101 @ X102 @ X103) = (throw_list_char @ X14))))))). % exp.distinct(187)
thf(fact_159_exp_Odistinct_I127_J, axiom,
    ((![X61 : list_char, X62 : exp_list_char, X101 : list_char, X102 : ty, X103 : exp_list_char]: (~ (((lAss_list_char @ X61 @ X62) = (block_list_char @ X101 @ X102 @ X103))))))). % exp.distinct(127)
thf(fact_160_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_161_redp__redsp_OLAssThrow, axiom,
    ((![P : list_P1234162913t_char, V : list_char, E2 : exp_list_char, S : produc515445032on_val]: (redp @ P @ (lAss_list_char @ V @ (throw_list_char @ E2)) @ S @ (throw_list_char @ E2) @ S)))). % redp_redsp.LAssThrow
thf(fact_162_redp__redsp_OLAssRed, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S : produc515445032on_val, E3 : exp_list_char, S2 : produc515445032on_val, V : list_char]: ((redp @ P @ E2 @ S @ E3 @ S2) => (redp @ P @ (lAss_list_char @ V @ E2) @ S @ (lAss_list_char @ V @ E3) @ S2))))). % redp_redsp.LAssRed

% Helper facts (3)
thf(help_If_3_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Option__Ooption_It__Value__Oval_J_T, axiom,
    ((![X : option_val, Y : option_val]: ((if_option_val @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ ha @ (fun_up1252458416on_val @ la @ v @ none_val))) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ h_a @ l_a))) @ (red @ p)))).
