% 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_467__5339388_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:22:04.794

% Could-be-implicit typings (29)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_J_J, type,
    set_Pr1301890247on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_J, type,
    produc1428501223on_val : $tType).
thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr1368603847on_val : $tType).
thf(ty_n_t__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,
    produc1161703655on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_J, type,
    set_Pr208351751on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    produc655058983on_val : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    set_Pr1189492743on_val : $tType).
thf(ty_n_t__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,
    produc1172664615on_val : $tType).
thf(ty_n_t__Set__Oset_It__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_J, type,
    set_Pr148564103on_val : $tType).
thf(ty_n_t__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,
    produc744932519on_val : $tType).
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Type__Oty_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__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_J_J_J_J_J_J_J_J, type,
    list_P1234162913t_char : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    set_Pr1511552798on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    produc335961278on_val : $tType).
thf(ty_n_t__Set__Oset_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_J, type,
    set_Pr556513572on_val : $tType).
thf(ty_n_t__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,
    produc1097884484on_val : $tType).
thf(ty_n_t__Set__Oset_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_J, type,
    set_Pr723149704on_val : $tType).
thf(ty_n_t__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,
    produc515445032on_val : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Product____Type__Oprod_It__List__Olist_It__Type__Oty_J_Mt__Product____Type__Oprod_It__Type__Oty_Mt__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_J_J_J, type,
    produc1259892823t_char : $tType).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    option2118145160on_val : $tType).
thf(ty_n_t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    list_exp_list_char : $tType).
thf(ty_n_t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    exp_list_char : $tType).
thf(ty_n_t__Option__Ooption_It__Value__Oval_J, type,
    option_val : $tType).
thf(ty_n_t__Option__Ooption_It__Type__Oty_J, type,
    option_ty : $tType).
thf(ty_n_t__List__Olist_It__String__Ochar_J, type,
    list_char : $tType).
thf(ty_n_t__List__Olist_It__Value__Oval_J, type,
    list_val : $tType).
thf(ty_n_t__List__Olist_It__Type__Oty_J, type,
    list_ty : $tType).
thf(ty_n_t__Value__Oval, type,
    val : $tType).
thf(ty_n_t__Type__Oty, type,
    ty : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (72)
thf(sy_c_BigStep_Oeval, type,
    eval : list_P1234162913t_char > exp_list_char > produc515445032on_val > exp_list_char > produc515445032on_val > $o).
thf(sy_c_BigStep_Oevals, type,
    evals : list_P1234162913t_char > list_exp_list_char > produc515445032on_val > list_exp_list_char > produc515445032on_val > $o).
thf(sy_c_BigStep_Ofinal_001t__List__Olist_It__String__Ochar_J, type,
    final_list_char : exp_list_char > $o).
thf(sy_c_BigStep_Ofinals_001t__List__Olist_It__String__Ochar_J, type,
    finals_list_char : list_exp_list_char > $o).
thf(sy_c_Conform_Oconf_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,
    conf_P93989998t_char : list_P1234162913t_char > (nat > option2118145160on_val) > val > ty > $o).
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,
    hconf_1244167010t_char : list_P1234162913t_char > (nat > option2118145160on_val) > $o).
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_OCall_001t__List__Olist_It__String__Ochar_J, type,
    call_list_char : exp_list_char > list_char > list_exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OCast_001t__List__Olist_It__String__Ochar_J, type,
    cast_list_char : list_char > exp_list_char > exp_list_char).
thf(sy_c_Expr_Oexp_OVal_001t__List__Olist_It__String__Ochar_J, type,
    val_list_char : val > exp_list_char).
thf(sy_c_Expr_Oexp_Othrow_001t__List__Olist_It__String__Ochar_J, type,
    throw_list_char : exp_list_char > exp_list_char).
thf(sy_c_JWellForm_Owf__J__mdecl, type,
    wf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_List_Oappend_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    append_exp_list_char : list_exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    cons_exp_list_char : exp_list_char > list_exp_list_char > list_exp_list_char).
thf(sy_c_List_Olist_OCons_001t__Type__Oty, type,
    cons_ty : ty > list_ty > list_ty).
thf(sy_c_List_Olist_ONil_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    nil_exp_list_char : list_exp_list_char).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a1702871623t_char : (exp_list_char > exp_list_char > $o) > list_exp_list_char > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_001t__Type__Oty, type,
    list_a295513531har_ty : (exp_list_char > ty > $o) > list_exp_list_char > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    list_a212154379t_char : (ty > exp_list_char > $o) > list_ty > list_exp_list_char > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Type__Oty_001t__Type__Oty, type,
    list_all2_ty_ty : (ty > ty > $o) > list_ty > list_ty > $o).
thf(sy_c_List_Olist_Olist__all2_001t__Value__Oval_001t__Type__Oty, type,
    list_all2_val_ty : (val > ty > $o) > list_val > list_ty > $o).
thf(sy_c_List_Olist_Omap_001t__Value__Oval_001t__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J, type,
    map_va1515327237t_char : (val > exp_list_char) > list_val > list_exp_list_char).
thf(sy_c_Map_Omap__add_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
    map_ad1615113112ar_val : (list_char > option_val) > (list_char > option_val) > list_char > option_val).
thf(sy_c_Objects_Ohext, type,
    hext : (nat > option2118145160on_val) > (nat > option2118145160on_val) > $o).
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,
    produc2023458740on_val : exp_list_char > produc515445032on_val > produc1097884484on_val).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    produc1725134254on_val : list_exp_list_char > produc515445032on_val > produc335961278on_val).
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).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    produc245869591on_val : produc335961278on_val > produc335961278on_val > produc655058983on_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_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    produc1802175319on_val : produc655058983on_val > produc655058983on_val > produc1428501223on_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_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    collec105960082on_val : (produc655058983on_val > $o) > set_Pr208351751on_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_SmallStep_Oreds, type,
    reds : list_P1234162913t_char > set_Pr208351751on_val).
thf(sy_c_SmallStep_Oredsp, type,
    redsp : list_P1234162913t_char > list_exp_list_char > produc515445032on_val > list_exp_list_char > produc515445032on_val > $o).
thf(sy_c_State_Ohp, type,
    hp : produc515445032on_val > nat > option2118145160on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    transi432893227on_val : set_Pr148564103on_val > set_Pr148564103on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    transi111096263on_val : set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    transi325225921on_val : set_Pr208351751on_val > set_Pr208351751on_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_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    transi159622442on_val : set_Pr1301890247on_val > set_Pr1301890247on_val).
thf(sy_c_TypeRel_Owiden_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    widen_917054840t_char : list_P1234162913t_char > ty > ty > $o).
thf(sy_c_TypeSafe__Mirabelle__osrwgqrerx_Osconf, type,
    typeSa1777264139_sconf : list_P1234162913t_char > (list_char > option_ty) > produc515445032on_val > $o).
thf(sy_c_Type_Oty_ONT, type,
    nt : ty).
thf(sy_c_Value_Oval_ONull, type,
    null : val).
thf(sy_c_WWellForm_Owwf__J__mdecl, type,
    wwf_J_mdecl : list_P1234162913t_char > list_char > produc1259892823t_char > $o).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_WellTypeRT_OWTrt, type,
    wTrt : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > exp_list_char > ty > $o).
thf(sy_c_WellTypeRT_OWTrts, type,
    wTrts : list_P1234162913t_char > (nat > option2118145160on_val) > (list_char > option_ty) > list_exp_list_char > list_ty > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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,
    member184158439on_val : produc335961278on_val > set_Pr1511552798on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member2027247312on_val : produc744932519on_val > set_Pr148564103on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J, type,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_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_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_Mt__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_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_J_J, type,
    member1743964944on_val : produc1428501223on_val > set_Pr1301890247on_val > $o).
thf(sy_v_E____, type,
    e : list_char > option_ty).
thf(sy_v_M____, type,
    m : list_char).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_T____, type,
    t : ty).
thf(sy_v_Us____, type,
    us : list_ty).
thf(sy_v_es_Ha____, type,
    es_a : list_exp_list_char).
thf(sy_v_esa____, type,
    esa : list_exp_list_char).
thf(sy_v_h_Ha____, type,
    h_a : nat > option2118145160on_val).
thf(sy_v_ha____, type,
    ha : nat > option2118145160on_val).
thf(sy_v_l_Ha____, type,
    l_a : list_char > option_val).
thf(sy_v_la____, type,
    la : list_char > option_val).
thf(sy_v_thesis____, type,
    thesis : $o).
thf(sy_v_v____, type,
    v : val).

% Relevant facts (219)
thf(fact_0__092_060open_062_092_060exists_062Usa_O_AP_ME_Mh_H_A_092_060turnstile_062_Aes_H_A_091_058_093_AUsa_A_092_060and_062_AP_A_092_060turnstile_062_AUsa_A_091_092_060le_062_093_AUs_092_060close_062, axiom,
    ((?[Us : list_ty]: ((wTrts @ p @ h_a @ e @ es_a @ Us) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Us @ us))))). % \<open>\<exists>Usa. P,E,h' \<turnstile> es' [:] Usa \<and> P \<turnstile> Usa [\<le>] Us\<close>
thf(fact_1_wtes, axiom,
    ((wTrts @ p @ ha @ e @ esa @ us))). % wtes
thf(fact_2_widens__refl, axiom,
    ((![P : list_P1234162913t_char, Xs : list_ty]: (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Xs)))). % widens_refl
thf(fact_3_widens__trans, axiom,
    ((![P : list_P1234162913t_char, Ss : list_ty, Ts : list_ty, Us2 : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Us2) => (list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ss @ Us2)))))). % widens_trans
thf(fact_4_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_5_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_6_widen__refl, axiom,
    ((![P : list_P1234162913t_char, T : ty]: (widen_917054840t_char @ P @ T @ T)))). % widen_refl
thf(fact_7_list__all2__eq, axiom,
    (((^[Y : list_ty]: (^[Z : list_ty]: (Y = Z))) = (list_all2_ty_ty @ (^[Y : ty]: (^[Z : ty]: (Y = Z))))))). % list_all2_eq
thf(fact_8_list__all2__mono, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Ys : list_ty, Q : ty > ty > $o]: ((list_all2_ty_ty @ P @ Xs @ Ys) => ((![Xs2 : ty, Ys2 : ty]: ((P @ Xs2 @ Ys2) => (Q @ Xs2 @ Ys2))) => (list_all2_ty_ty @ Q @ Xs @ Ys)))))). % list_all2_mono
thf(fact_9_list__all2__refl, axiom,
    ((![P : ty > ty > $o, Xs : list_ty]: ((![X : ty]: (P @ X @ X)) => (list_all2_ty_ty @ P @ Xs @ Xs))))). % list_all2_refl
thf(fact_10_list__all2__trans, axiom,
    ((![P1 : ty > ty > $o, P2 : ty > ty > $o, P3 : ty > ty > $o, As : list_ty, Bs : list_ty, Cs : list_ty]: ((![A : ty, B : ty, C : ty]: ((P1 @ A @ B) => ((P2 @ B @ C) => (P3 @ A @ C)))) => ((list_all2_ty_ty @ P1 @ As @ Bs) => ((list_all2_ty_ty @ P2 @ Bs @ Cs) => (list_all2_ty_ty @ P3 @ As @ Cs))))))). % list_all2_trans
thf(fact_11_list_Orel__eq, axiom,
    (((list_all2_ty_ty @ (^[Y : ty]: (^[Z : ty]: (Y = Z)))) = (^[Y : list_ty]: (^[Z : list_ty]: (Y = Z)))))). % list.rel_eq
thf(fact_12_list__all2__antisym, axiom,
    ((![P : ty > ty > $o, Q : ty > ty > $o, Xs : list_ty, Ys : list_ty]: ((![X : ty, Y2 : ty]: ((P @ X @ Y2) => ((Q @ Y2 @ X) => (X = Y2)))) => ((list_all2_ty_ty @ P @ Xs @ Ys) => ((list_all2_ty_ty @ Q @ Ys @ Xs) => (Xs = Ys))))))). % list_all2_antisym
thf(fact_13_list_Orel__refl, axiom,
    ((![Ra : ty > ty > $o, X2 : list_ty]: ((![X : ty]: (Ra @ X @ X)) => (list_all2_ty_ty @ Ra @ X2 @ X2))))). % list.rel_refl
thf(fact_14_IH, axiom,
    ((![E : list_char > option_ty, Ts : list_ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrts @ p @ ha @ E @ esa @ Ts) => (?[Us : list_ty]: ((wTrts @ p @ h_a @ E @ es_a @ Us) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Us @ Ts)))))))). % IH
thf(fact_15_CallParams_Ohyps_I2_J, axiom,
    ((![E : list_char > option_ty, Ts : list_ty]: ((typeSa1777264139_sconf @ p @ E @ (produc52622304on_val @ ha @ la)) => ((wTrts @ p @ ha @ E @ esa @ Ts) => (?[Ts2 : list_ty]: ((wTrts @ p @ h_a @ E @ es_a @ Ts2) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Ts2 @ Ts)))))))). % CallParams.hyps(2)
thf(fact_16_conf, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % conf
thf(fact_17_widens__Cons, axiom,
    ((![P : list_P1234162913t_char, X2 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ (cons_ty @ X2 @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((widen_917054840t_char @ P @ X2 @ Z2)) & ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Xs @ Zs))))))))))). % widens_Cons
thf(fact_18_reds, axiom,
    ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ esa @ (produc52622304on_val @ ha @ la)) @ (produc1725134254on_val @ es_a @ (produc52622304on_val @ h_a @ l_a))) @ (reds @ p)))). % reds
thf(fact_19_wf__prog__wwf__prog, axiom,
    ((![P : list_P1234162913t_char]: ((wf_pro1229751607t_char @ wf_J_mdecl @ P) => (wf_pro1229751607t_char @ wwf_J_mdecl @ P))))). % wf_prog_wwf_prog
thf(fact_20_null, axiom,
    ((wTrt @ p @ ha @ e @ (val_list_char @ v) @ nt))). % null
thf(fact_21_wt, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ (val_list_char @ v) @ m @ esa) @ t))). % wt
thf(fact_22_confs__widens, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, Vs : list_val, Ts : list_ty, Ts3 : list_ty]: ((list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts) => ((list_all2_ty_ty @ (widen_917054840t_char @ P) @ Ts @ Ts3) => (list_all2_val_ty @ (conf_P93989998t_char @ P @ H) @ Vs @ Ts3)))))). % confs_widens
thf(fact_23_CallParams_Oprems_I1_J, axiom,
    ((typeSa1777264139_sconf @ p @ e @ (produc52622304on_val @ ha @ la)))). % CallParams.prems(1)
thf(fact_24_list_Oinject, axiom,
    ((![X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X22) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_25_list_Oinject, axiom,
    ((![X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: (((cons_ty @ X21 @ X22) = (cons_ty @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_26_CallParams_Oprems_I2_J, axiom,
    ((wTrt @ p @ ha @ e @ (call_list_char @ (val_list_char @ v) @ m @ esa) @ t))). % CallParams.prems(2)
thf(fact_27_not__Cons__self2, axiom,
    ((![X2 : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X2 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_28_not__Cons__self2, axiom,
    ((![X2 : ty, Xs : list_ty]: (~ (((cons_ty @ X2 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_29_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_30_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a1702871623t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_31_list_Orel__inject_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, X22 : list_exp_list_char, Y21 : ty, Y22 : list_ty]: ((list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a295513531har_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_32_list_Orel__inject_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, X22 : list_ty, Y21 : exp_list_char, Y22 : list_exp_list_char]: ((list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_a212154379t_char @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_33_list_Orel__inject_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, X22 : list_ty, Y21 : ty, Y22 : list_ty]: ((list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22)) = (((R @ X21 @ Y21)) & ((list_all2_ty_ty @ R @ X22 @ Y22))))))). % list.rel_inject(2)
thf(fact_34_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > exp_list_char > $o, X21 : exp_list_char, Y21 : exp_list_char, X22 : list_exp_list_char, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a1702871623t_char @ R @ X22 @ Y22) => (list_a1702871623t_char @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_35_list_Orel__intros_I2_J, axiom,
    ((![R : exp_list_char > ty > $o, X21 : exp_list_char, Y21 : ty, X22 : list_exp_list_char, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_a295513531har_ty @ R @ X22 @ Y22) => (list_a295513531har_ty @ R @ (cons_exp_list_char @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_36_list_Orel__intros_I2_J, axiom,
    ((![R : ty > exp_list_char > $o, X21 : ty, Y21 : exp_list_char, X22 : list_ty, Y22 : list_exp_list_char]: ((R @ X21 @ Y21) => ((list_a212154379t_char @ R @ X22 @ Y22) => (list_a212154379t_char @ R @ (cons_ty @ X21 @ X22) @ (cons_exp_list_char @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_37_list_Orel__intros_I2_J, axiom,
    ((![R : ty > ty > $o, X21 : ty, Y21 : ty, X22 : list_ty, Y22 : list_ty]: ((R @ X21 @ Y21) => ((list_all2_ty_ty @ R @ X22 @ Y22) => (list_all2_ty_ty @ R @ (cons_ty @ X21 @ X22) @ (cons_ty @ Y21 @ Y22))))))). % list.rel_intros(2)
thf(fact_38_list__all2__Cons, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X2 : exp_list_char, Xs : list_exp_list_char, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X2 @ Xs) @ (cons_exp_list_char @ Y3 @ Ys)) = (((P @ X2 @ Y3)) & ((list_a1702871623t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_39_list__all2__Cons, axiom,
    ((![P : exp_list_char > ty > $o, X2 : exp_list_char, Xs : list_exp_list_char, Y3 : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X2 @ Xs) @ (cons_ty @ Y3 @ Ys)) = (((P @ X2 @ Y3)) & ((list_a295513531har_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_40_list__all2__Cons, axiom,
    ((![P : ty > exp_list_char > $o, X2 : ty, Xs : list_ty, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X2 @ Xs) @ (cons_exp_list_char @ Y3 @ Ys)) = (((P @ X2 @ Y3)) & ((list_a212154379t_char @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_41_list__all2__Cons, axiom,
    ((![P : ty > ty > $o, X2 : ty, Xs : list_ty, Y3 : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X2 @ Xs) @ (cons_ty @ Y3 @ Ys)) = (((P @ X2 @ Y3)) & ((list_all2_ty_ty @ P @ Xs @ Ys))))))). % list_all2_Cons
thf(fact_42_list__all2__Cons1, axiom,
    ((![P : exp_list_char > exp_list_char > $o, X2 : exp_list_char, Xs : list_exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ (cons_exp_list_char @ X2 @ Xs) @ Ys) = (?[Z2 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z2 @ Zs))) & ((((P @ X2 @ Z2)) & ((list_a1702871623t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_43_list__all2__Cons1, axiom,
    ((![P : exp_list_char > ty > $o, X2 : exp_list_char, Xs : list_exp_list_char, Ys : list_ty]: ((list_a295513531har_ty @ P @ (cons_exp_list_char @ X2 @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((P @ X2 @ Z2)) & ((list_a295513531har_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_44_list__all2__Cons1, axiom,
    ((![P : ty > exp_list_char > $o, X2 : ty, Xs : list_ty, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ (cons_ty @ X2 @ Xs) @ Ys) = (?[Z2 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Ys = (cons_exp_list_char @ Z2 @ Zs))) & ((((P @ X2 @ Z2)) & ((list_a212154379t_char @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_45_list__all2__Cons1, axiom,
    ((![P : ty > ty > $o, X2 : ty, Xs : list_ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ (cons_ty @ X2 @ Xs) @ Ys) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Ys = (cons_ty @ Z2 @ Zs))) & ((((P @ X2 @ Z2)) & ((list_all2_ty_ty @ P @ Xs @ Zs))))))))))). % list_all2_Cons1
thf(fact_46_list__all2__Cons2, axiom,
    ((![P : exp_list_char > exp_list_char > $o, Xs : list_exp_list_char, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a1702871623t_char @ P @ Xs @ (cons_exp_list_char @ Y3 @ Ys)) = (?[Z2 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z2 @ Zs))) & ((((P @ Z2 @ Y3)) & ((list_a1702871623t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_47_list__all2__Cons2, axiom,
    ((![P : ty > exp_list_char > $o, Xs : list_ty, Y3 : exp_list_char, Ys : list_exp_list_char]: ((list_a212154379t_char @ P @ Xs @ (cons_exp_list_char @ Y3 @ Ys)) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z2 @ Zs))) & ((((P @ Z2 @ Y3)) & ((list_a212154379t_char @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_48_list__all2__Cons2, axiom,
    ((![P : exp_list_char > ty > $o, Xs : list_exp_list_char, Y3 : ty, Ys : list_ty]: ((list_a295513531har_ty @ P @ Xs @ (cons_ty @ Y3 @ Ys)) = (?[Z2 : exp_list_char]: (?[Zs : list_exp_list_char]: (((Xs = (cons_exp_list_char @ Z2 @ Zs))) & ((((P @ Z2 @ Y3)) & ((list_a295513531har_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_49_list__all2__Cons2, axiom,
    ((![P : ty > ty > $o, Xs : list_ty, Y3 : ty, Ys : list_ty]: ((list_all2_ty_ty @ P @ Xs @ (cons_ty @ Y3 @ Ys)) = (?[Z2 : ty]: (?[Zs : list_ty]: (((Xs = (cons_ty @ Z2 @ Zs))) & ((((P @ Z2 @ Y3)) & ((list_all2_ty_ty @ P @ Zs @ Ys))))))))))). % list_all2_Cons2
thf(fact_50_wf__mdecl__wwf__mdecl, axiom,
    ((![P : list_P1234162913t_char, C2 : list_char, Md : produc1259892823t_char]: ((wf_J_mdecl @ P @ C2 @ Md) => (wwf_J_mdecl @ P @ C2 @ Md))))). % wf_mdecl_wwf_mdecl
thf(fact_51_WTrtCallNT, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, Es : list_exp_list_char, Ts : list_ty, M : list_char, T : ty]: ((wTrt @ P @ H @ E @ E2 @ nt) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrt @ P @ H @ E @ (call_list_char @ E2 @ M @ Es) @ T)))))). % WTrtCallNT
thf(fact_52_prod__induct4, axiom,
    ((![P : produc655058983on_val > $o, X2 : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X2))))). % prod_induct4
thf(fact_53_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X2))))). % prod_induct4
thf(fact_54_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X23 : list_char > option_val, Y1 : nat > option2118145160on_val, Y23 : list_char > option_val]: (((produc52622304on_val @ X1 @ X23) = (produc52622304on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_55_prod_Oinject, axiom,
    ((![X1 : produc335961278on_val, X23 : produc335961278on_val, Y1 : produc335961278on_val, Y23 : produc335961278on_val]: (((produc245869591on_val @ X1 @ X23) = (produc245869591on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_56_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X23 : produc515445032on_val, Y1 : list_exp_list_char, Y23 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X23) = (produc1725134254on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_57_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X23 : produc1097884484on_val, Y1 : produc1097884484on_val, Y23 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X23) = (produc1069526295on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_58_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X23 : produc515445032on_val, Y1 : exp_list_char, Y23 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X23) = (produc2023458740on_val @ Y1 @ Y23)) = (((X1 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_59_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_60_old_Oprod_Oinject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_61_old_Oprod_Oinject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) = (((A2 = A3)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_62_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_63_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_64_WTrtCons, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, E2 : exp_list_char, T : ty, Es : list_exp_list_char, Ts : list_ty]: ((wTrt @ P @ H @ E @ E2 @ T) => ((wTrts @ P @ H @ E @ Es @ Ts) => (wTrts @ P @ H @ E @ (cons_exp_list_char @ E2 @ Es) @ (cons_ty @ T @ Ts))))))). % WTrtCons
thf(fact_65_mem__Collect__eq, axiom,
    ((![A2 : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A2 @ (collec105960082on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_66_mem__Collect__eq, axiom,
    ((![A2 : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A2 @ (collec2055896722on_val @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_67_Collect__mem__eq, axiom,
    ((![A4 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_68_Collect__mem__eq, axiom,
    ((![A4 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_69_surj__pair, axiom,
    ((![P4 : produc515445032on_val]: (?[X : nat > option2118145160on_val, Y2 : list_char > option_val]: (P4 = (produc52622304on_val @ X @ Y2)))))). % surj_pair
thf(fact_70_surj__pair, axiom,
    ((![P4 : produc655058983on_val]: (?[X : produc335961278on_val, Y2 : produc335961278on_val]: (P4 = (produc245869591on_val @ X @ Y2)))))). % surj_pair
thf(fact_71_surj__pair, axiom,
    ((![P4 : produc335961278on_val]: (?[X : list_exp_list_char, Y2 : produc515445032on_val]: (P4 = (produc1725134254on_val @ X @ Y2)))))). % surj_pair
thf(fact_72_surj__pair, axiom,
    ((![P4 : produc1172664615on_val]: (?[X : produc1097884484on_val, Y2 : produc1097884484on_val]: (P4 = (produc1069526295on_val @ X @ Y2)))))). % surj_pair
thf(fact_73_surj__pair, axiom,
    ((![P4 : produc1097884484on_val]: (?[X : exp_list_char, Y2 : produc515445032on_val]: (P4 = (produc2023458740on_val @ X @ Y2)))))). % surj_pair
thf(fact_74_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P4 : produc515445032on_val]: ((![A : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_75_prod__cases, axiom,
    ((![P : produc655058983on_val > $o, P4 : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_76_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P4 : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_77_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P4 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_78_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P4 : produc1097884484on_val]: ((![A : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A @ B))) => (P @ P4))))). % prod_cases
thf(fact_79_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_80_Pair__inject, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, A3 : produc335961278on_val, B3 : produc335961278on_val]: (((produc245869591on_val @ A2 @ B2) = (produc245869591on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_81_Pair__inject, axiom,
    ((![A2 : list_exp_list_char, B2 : produc515445032on_val, A3 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A2 @ B2) = (produc1725134254on_val @ A3 @ B3)) => (~ (((A2 = A3) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_82_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_83_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_84_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc515445032on_val]: (~ ((![A : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y3 = (produc52622304on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_85_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : produc335961278on_val]: (~ ((Y3 = (produc245869591on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_86_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : produc515445032on_val]: (~ ((Y3 = (produc1725134254on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_87_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y3 = (produc1069526295on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_88_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : produc515445032on_val]: (~ ((Y3 = (produc2023458740on_val @ A @ B)))))))))). % old.prod.exhaust
thf(fact_89_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_90_old_Oprod_Oinducts, axiom,
    ((![P : produc655058983on_val > $o, Prod : produc655058983on_val]: ((![A : produc335961278on_val, B : produc335961278on_val]: (P @ (produc245869591on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_91_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_92_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_93_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_94_prod__cases3, axiom,
    ((![Y3 : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (~ ((Y3 = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C))))))))))). % prod_cases3
thf(fact_95_prod__cases3, axiom,
    ((![Y3 : produc335961278on_val]: (~ ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_96_prod__cases3, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y3 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_97_prod__cases3, axiom,
    ((![Y3 : produc1097884484on_val]: (~ ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y3 = (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_98_prod__induct3, axiom,
    ((![P : produc655058983on_val > $o, X2 : produc655058983on_val]: ((![A : produc335961278on_val, B : list_exp_list_char, C : produc515445032on_val]: (P @ (produc245869591on_val @ A @ (produc1725134254on_val @ B @ C)))) => (P @ X2))))). % prod_induct3
thf(fact_99_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X2 : produc335961278on_val]: ((![A : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X2))))). % prod_induct3
thf(fact_100_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X2 : produc1172664615on_val]: ((![A : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ C)))) => (P @ X2))))). % prod_induct3
thf(fact_101_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X2 : produc1097884484on_val]: ((![A : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A @ (produc52622304on_val @ B @ C)))) => (P @ X2))))). % prod_induct3
thf(fact_102_prod__cases4, axiom,
    ((![Y3 : produc655058983on_val]: (~ ((![A : produc335961278on_val, B : list_exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y3 = (produc245869591on_val @ A @ (produc1725134254on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_103_prod__cases4, axiom,
    ((![Y3 : produc1172664615on_val]: (~ ((![A : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y3 = (produc1069526295on_val @ A @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_104_red__reds_OListRed2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (reds @ P)))))). % red_reds.ListRed2
thf(fact_105_exp_Oinject_I9_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, Y91 : exp_list_char, Y92 : list_char, Y93 : list_exp_list_char]: (((call_list_char @ X91 @ X92 @ X93) = (call_list_char @ Y91 @ Y92 @ Y93)) = (((X91 = Y91)) & ((((X92 = Y92)) & ((X93 = Y93))))))))). % exp.inject(9)
thf(fact_106_calculation, axiom,
    ((v = null))). % calculation
thf(fact_107_reds__preserves__hconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((hconf_1244167010t_char @ P @ H) => (hconf_1244167010t_char @ P @ H2))))))). % reds_preserves_hconf
thf(fact_108_reds__preserves__lconf, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => ((wTrts @ P @ H @ E @ Es @ Ts) => ((lconf_485928294t_char @ P @ H @ L @ E) => (lconf_485928294t_char @ P @ H2 @ L2 @ E))))))). % reds_preserves_lconf
thf(fact_109_exp_Oinject_I3_J, axiom,
    ((![X32 : val, Y32 : val]: (((val_list_char @ X32) = (val_list_char @ Y32)) = (X32 = Y32))))). % exp.inject(3)
thf(fact_110_conf__Null, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, T : ty]: ((conf_P93989998t_char @ P @ H @ null @ T) = (widen_917054840t_char @ P @ nt @ T))))). % conf_Null
thf(fact_111_exp_Odistinct_I65_J, axiom,
    ((![X32 : val, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((val_list_char @ X32) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(65)
thf(fact_112_reds__preserves__sconf, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, E : list_char > option_ty, Ts : list_ty]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => ((wTrts @ P @ (hp @ S2) @ E @ Es @ Ts) => ((typeSa1777264139_sconf @ P @ E @ S2) => (typeSa1777264139_sconf @ P @ E @ S3))))))). % reds_preserves_sconf
thf(fact_113_redsp__reds__eq, axiom,
    ((redsp = (^[P5 : list_P1234162913t_char]: (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (^[Z2 : list_exp_list_char]: (^[Aa : produc515445032on_val]: (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ X3 @ Y4) @ (produc1725134254on_val @ Z2 @ Aa)) @ (reds @ P5)))))))))). % redsp_reds_eq
thf(fact_114_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_115_red__reds_OCallParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (reds @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (red @ P)))))). % red_reds.CallParams
thf(fact_116_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E3 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E4 : exp_list_char]: (?[S5 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E3 @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ E4 @ Es3))) & ((((A42 = S5)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S4) @ (produc2023458740on_val @ E4 @ S5)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S5 : produc515445032on_val]: (?[V2 : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V2) @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A42 = S5)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_117_red__hext__incr, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_118_red__reds_OCallObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E5 @ M @ Es) @ S3)) @ (red @ P)))))). % red_reds.CallObj
thf(fact_119_red__preserves__sconf, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : 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 @ E5 @ 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_120_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_121_WTrts__hext__mono, axiom,
    ((![P : list_P1234162913t_char, H : nat > option2118145160on_val, E : list_char > option_ty, Es : list_exp_list_char, Ts : list_ty, H2 : nat > option2118145160on_val]: ((wTrts @ P @ H @ E @ Es @ Ts) => ((hext @ H @ H2) => (wTrts @ P @ H2 @ E @ Es @ Ts)))))). % WTrts_hext_mono
thf(fact_122_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_123_red__preserves__hconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (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_124_red__preserves__lconf, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (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_125_redp__redsp_OListRed2, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, V : val]: ((redsp @ P @ Es @ S2 @ Es2 @ S3) => (redsp @ P @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2 @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3))))). % redp_redsp.ListRed2
thf(fact_126_red__reds_OListRed1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E5 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_127_reds_Ocases, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) => ((![E6 : exp_list_char, S6 : produc515445032on_val, E7 : exp_list_char, S7 : produc515445032on_val, Es5 : list_exp_list_char]: ((A1 = (cons_exp_list_char @ E6 @ Es5)) => ((A22 = S6) => ((A32 = (cons_exp_list_char @ E7 @ Es5)) => ((A42 = S7) => (~ ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E6 @ S6) @ (produc2023458740on_val @ E7 @ S7)) @ (red @ P))))))))) => (~ ((![Es5 : list_exp_list_char, S6 : produc515445032on_val, Es6 : list_exp_list_char, S7 : produc515445032on_val, V3 : val]: ((A1 = (cons_exp_list_char @ (val_list_char @ V3) @ Es5)) => ((A22 = S6) => ((A32 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6)) => ((A42 = S7) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es5 @ S6) @ (produc1725134254on_val @ Es6 @ S7)) @ (reds @ P)))))))))))))))). % reds.cases
thf(fact_128_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_129_extend__1__evals, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, T3 : produc515445032on_val, Es7 : list_exp_list_char, T4 : produc515445032on_val, Es2 : list_exp_list_char, T5 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ T3) @ (produc1725134254on_val @ Es7 @ T4)) @ (reds @ P)) => ((evals @ P @ Es7 @ T4 @ Es2 @ T5) => (evals @ P @ Es @ T3 @ Es2 @ T5))))))). % extend_1_evals
thf(fact_130_red__reds_ORedCastNull, axiom,
    ((![C2 : list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ (val_list_char @ null)) @ S2) @ (produc2023458740on_val @ (val_list_char @ null) @ S2)) @ (red @ P))))). % red_reds.RedCastNull
thf(fact_131_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ R))) = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_132_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ R))) = (^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_133_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ R))) = (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_134_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ R))) = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_135_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ R))) = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_136_exp_Oinject_I2_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, Y21 : list_char, Y22 : exp_list_char]: (((cast_list_char @ X21 @ X22) = (cast_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % exp.inject(2)
thf(fact_137_exp_Odistinct_I29_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X32 : val]: (~ (((cast_list_char @ X21 @ X22) = (val_list_char @ X32))))))). % exp.distinct(29)
thf(fact_138_exp_Odistinct_I41_J, axiom,
    ((![X21 : list_char, X22 : exp_list_char, X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char]: (~ (((cast_list_char @ X21 @ X22) = (call_list_char @ X91 @ X92 @ X93))))))). % exp.distinct(41)
thf(fact_139_red__reds_OCastRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E5) @ S3)) @ (red @ P)))))). % red_reds.CastRed
thf(fact_140_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_141_evals__hext, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((evals @ P @ Es @ (produc52622304on_val @ H @ L) @ Es2 @ (produc52622304on_val @ H2 @ L2)) => (hext @ H @ H2))))). % evals_hext
thf(fact_142_extend__evals, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es7 : list_exp_list_char, S8 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es7 @ S8)) @ (transi325225921on_val @ (reds @ P))) => ((evals @ P @ Es7 @ S8 @ Es2 @ S3) => (evals @ P @ Es @ S2 @ Es2 @ S3))))))). % extend_evals
thf(fact_143_bigs__by__smalls, axiom,
    ((![P : list_P1234162913t_char, Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((evals @ P @ Es @ S2 @ Es2 @ S3) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P)))))))). % bigs_by_smalls
thf(fact_144_ListReds2, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds2
thf(fact_145_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_146_converse__rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R2 : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Bx @ By) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa2 : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa2 @ Ba)) @ R2) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Aa2 @ Ba) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_147_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_148_converse__rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Bx @ By) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa2 : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa2 @ Ba)) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Aa2 @ Ba) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Aa2 @ Ba) => (P @ A @ B))))) => (P @ Ax @ Ay))))))). % converse_rtrancl_induct2
thf(fact_149_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_150_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_151_converse__rtranclE2, axiom,
    ((![Xa : produc335961278on_val, Xb : produc335961278on_val, Za : produc335961278on_val, Zb : produc335961278on_val, R2 : set_Pr1301890247on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2)) => ((~ (((produc245869591on_val @ Xa @ Xb) = (produc245869591on_val @ Za @ Zb)))) => (~ ((![A : produc335961278on_val, B : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Xa @ Xb) @ (produc245869591on_val @ A @ B)) @ R2) => (~ ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Za @ Zb)) @ (transi159622442on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_152_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_153_converse__rtranclE2, axiom,
    ((![Xa : list_exp_list_char, Xb : produc515445032on_val, Za : list_exp_list_char, Zb : produc515445032on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2)) => ((~ (((produc1725134254on_val @ Xa @ Xb) = (produc1725134254on_val @ Za @ Zb)))) => (~ ((![A : list_exp_list_char, B : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Xa @ Xb) @ (produc1725134254on_val @ A @ B)) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Za @ Zb)) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE2
thf(fact_154_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_155_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_156_rtrancl__induct2, axiom,
    ((![Ax : produc335961278on_val, Ay : produc335961278on_val, Bx : produc335961278on_val, By : produc335961278on_val, R2 : set_Pr1301890247on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ Bx @ By)) @ (transi159622442on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : produc335961278on_val, B : produc335961278on_val, Aa2 : produc335961278on_val, Ba : produc335961278on_val]: ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ Ax @ Ay) @ (produc245869591on_val @ A @ B)) @ (transi159622442on_val @ R2)) => ((member1743964944on_val @ (produc1802175319on_val @ (produc245869591on_val @ A @ B) @ (produc245869591on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_157_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_158_rtrancl__induct2, axiom,
    ((![Ax : list_exp_list_char, Ay : produc515445032on_val, Bx : list_exp_list_char, By : produc515445032on_val, R2 : set_Pr208351751on_val, P : list_exp_list_char > produc515445032on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ Bx @ By)) @ (transi325225921on_val @ R2)) => ((P @ Ax @ Ay) => ((![A : list_exp_list_char, B : produc515445032on_val, Aa2 : list_exp_list_char, Ba : produc515445032on_val]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Ax @ Ay) @ (produc1725134254on_val @ A @ B)) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A @ B) @ (produc1725134254on_val @ Aa2 @ Ba)) @ R2) => ((P @ A @ B) => (P @ Aa2 @ Ba))))) => (P @ Bx @ By))))))). % rtrancl_induct2
thf(fact_159_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_160_converse__rtrancl__induct__red, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (transi111096263on_val @ (red @ P))) => ((![E6 : exp_list_char, H4 : nat > option2118145160on_val, L3 : list_char > option_val]: (R @ E6 @ H4 @ L3 @ E6 @ H4 @ L3)) => ((![E_0 : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E_1 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, E7 : 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_0)) @ (produc2023458740on_val @ E_1 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => ((R @ E_1 @ H_1 @ L_1 @ E7 @ H5 @ L4) => (R @ E_0 @ H_0 @ L_0 @ E7 @ H5 @ L4)))) => (R @ E2 @ H @ L @ E5 @ H2 @ L2))))))). % converse_rtrancl_induct_red
thf(fact_161_CallRedsObj, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ E5 @ M @ Es) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsObj
thf(fact_162_CastReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (cast_list_char @ C2 @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastReds
thf(fact_163_CastRedsNull, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ (val_list_char @ null) @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (val_list_char @ null) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsNull
thf(fact_164_rtranclE, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y2) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y2 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_165_rtranclE, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((~ ((A2 = B2))) => (~ ((![Y2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y2) @ (transi111096263on_val @ R2)) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y2 @ B2) @ R2)))))))))))). % rtranclE
thf(fact_166_rtrancl_Ocases, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) => ((~ ((A22 = A1))) => (~ ((![B : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ B) @ (transi325225921on_val @ R2)) => (~ ((member1689761872on_val @ (produc245869591on_val @ B @ A22) @ R2)))))))))))). % rtrancl.cases
thf(fact_167_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_168_rtrancl_Osimps, axiom,
    ((![A1 : produc335961278on_val, A22 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ A1 @ A22) @ (transi325225921on_val @ R2)) = (((?[A5 : produc335961278on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc335961278on_val]: (?[B4 : produc335961278on_val]: (?[C3 : produc335961278on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member1689761872on_val @ (produc245869591on_val @ A5 @ B4) @ (transi325225921on_val @ R2))) & ((member1689761872on_val @ (produc245869591on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_169_rtrancl_Osimps, axiom,
    ((![A1 : produc1097884484on_val, A22 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ A1 @ A22) @ (transi111096263on_val @ R2)) = (((?[A5 : produc1097884484on_val]: (((A1 = A5)) & ((A22 = A5))))) | ((?[A5 : produc1097884484on_val]: (?[B4 : produc1097884484on_val]: (?[C3 : produc1097884484on_val]: (((A1 = A5)) & ((((A22 = C3)) & ((((member354538064on_val @ (produc1069526295on_val @ A5 @ B4) @ (transi111096263on_val @ R2))) & ((member354538064on_val @ (produc1069526295on_val @ B4 @ C3) @ R2)))))))))))))))). % rtrancl.simps
thf(fact_170_rtrancl__trans, axiom,
    ((![X2 : produc335961278on_val, Y3 : produc335961278on_val, R2 : set_Pr208351751on_val, Z3 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X2 @ Y3) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y3 @ Z3) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ X2 @ Z3) @ (transi325225921on_val @ R2))))))). % rtrancl_trans
thf(fact_171_rtrancl__trans, axiom,
    ((![X2 : produc1097884484on_val, Y3 : produc1097884484on_val, R2 : set_Pr1189492743on_val, Z3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X2 @ Y3) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y3 @ Z3) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ X2 @ Z3) @ (transi111096263on_val @ R2))))))). % rtrancl_trans
thf(fact_172_rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ A2) => ((![Y2 : produc335961278on_val, Z4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ Y2) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ Y2 @ Z4) @ R2) => ((P @ Y2) => (P @ Z4))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_173_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) => ((![Y2 : produc1097884484on_val, Z4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ Y2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ Y2 @ Z4) @ R2) => ((P @ Y2) => (P @ Z4))))) => (P @ B2))))))). % rtrancl_induct
thf(fact_174_rtrancl_Oinducts, axiom,
    ((![X1 : produc335961278on_val, X23 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ X1 @ X23) @ (transi325225921on_val @ R2)) => ((![A : produc335961278on_val]: (P @ A @ A)) => ((![A : produc335961278on_val, B : produc335961278on_val, C : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A @ B) @ (transi325225921on_val @ R2)) => ((P @ A @ B) => ((member1689761872on_val @ (produc245869591on_val @ B @ C) @ R2) => (P @ A @ C))))) => (P @ X1 @ X23))))))). % rtrancl.inducts
thf(fact_175_rtrancl_Oinducts, axiom,
    ((![X1 : produc1097884484on_val, X23 : produc1097884484on_val, R2 : set_Pr1189492743on_val, P : produc1097884484on_val > produc1097884484on_val > $o]: ((member354538064on_val @ (produc1069526295on_val @ X1 @ X23) @ (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 @ X23))))))). % rtrancl.inducts
thf(fact_176_converse__rtranclE, axiom,
    ((![X2 : produc335961278on_val, Z3 : produc335961278on_val, R2 : set_Pr208351751on_val]: ((member1689761872on_val @ (produc245869591on_val @ X2 @ Z3) @ (transi325225921on_val @ R2)) => ((~ ((X2 = Z3))) => (~ ((![Y2 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ X2 @ Y2) @ R2) => (~ ((member1689761872on_val @ (produc245869591on_val @ Y2 @ Z3) @ (transi325225921on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_177_converse__rtranclE, axiom,
    ((![X2 : produc1097884484on_val, Z3 : produc1097884484on_val, R2 : set_Pr1189492743on_val]: ((member354538064on_val @ (produc1069526295on_val @ X2 @ Z3) @ (transi111096263on_val @ R2)) => ((~ ((X2 = Z3))) => (~ ((![Y2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X2 @ Y2) @ R2) => (~ ((member354538064on_val @ (produc1069526295on_val @ Y2 @ Z3) @ (transi111096263on_val @ R2))))))))))))). % converse_rtranclE
thf(fact_178_rtrancl_Ortrancl__refl, axiom,
    ((![A2 : produc335961278on_val, R2 : set_Pr208351751on_val]: (member1689761872on_val @ (produc245869591on_val @ A2 @ A2) @ (transi325225921on_val @ R2))))). % rtrancl.rtrancl_refl
thf(fact_179_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_180_converse__rtrancl__induct, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, P : produc335961278on_val > $o]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((P @ B2) => ((![Y2 : produc335961278on_val, Z4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ Y2 @ Z4) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ Z4 @ B2) @ (transi325225921on_val @ R2)) => ((P @ Z4) => (P @ Y2))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_181_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) => ((![Y2 : produc1097884484on_val, Z4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ Y2 @ Z4) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ Z4 @ B2) @ (transi111096263on_val @ R2)) => ((P @ Z4) => (P @ Y2))))) => (P @ A2))))))). % converse_rtrancl_induct
thf(fact_182_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, C4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ (transi325225921on_val @ R2)) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C4) @ R2) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C4) @ (transi325225921on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_183_rtrancl_Ortrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ (transi111096263on_val @ R2)) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C4) @ R2) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C4) @ (transi111096263on_val @ R2))))))). % rtrancl.rtrancl_into_rtrancl
thf(fact_184_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc335961278on_val, B2 : produc335961278on_val, R2 : set_Pr208351751on_val, C4 : produc335961278on_val]: ((member1689761872on_val @ (produc245869591on_val @ A2 @ B2) @ R2) => ((member1689761872on_val @ (produc245869591on_val @ B2 @ C4) @ (transi325225921on_val @ R2)) => (member1689761872on_val @ (produc245869591on_val @ A2 @ C4) @ (transi325225921on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_185_converse__rtrancl__into__rtrancl, axiom,
    ((![A2 : produc1097884484on_val, B2 : produc1097884484on_val, R2 : set_Pr1189492743on_val, C4 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ A2 @ B2) @ R2) => ((member354538064on_val @ (produc1069526295on_val @ B2 @ C4) @ (transi111096263on_val @ R2)) => (member354538064on_val @ (produc1069526295on_val @ A2 @ C4) @ (transi111096263on_val @ R2))))))). % converse_rtrancl_into_rtrancl
thf(fact_186_ListReds1, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E5 @ Es) @ S3)) @ (transi325225921on_val @ (reds @ P))))))). % ListReds1
thf(fact_187_ListRedsVal, axiom,
    ((![E2 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S_0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ Es2 @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S_0) @ (produc1725134254on_val @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)) @ (transi325225921on_val @ (reds @ P)))))))). % ListRedsVal
thf(fact_188_CallRedsParams, axiom,
    ((![Es : list_exp_list_char, S2 : produc515445032on_val, Es2 : list_exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, V : val, M : list_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S2) @ (produc1725134254on_val @ Es2 @ S3)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es) @ S2) @ (produc2023458740on_val @ (call_list_char @ (val_list_char @ V) @ M @ Es2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsParams
thf(fact_189_extend__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E8 : exp_list_char, S8 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E8 @ S8)) @ (transi111096263on_val @ (red @ P))) => ((eval @ P @ E8 @ S8 @ E5 @ S3) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % extend_eval
thf(fact_190_big__by__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S2 @ E5 @ S3) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P)))))))). % big_by_small
thf(fact_191_extend__1__eval, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E8 : exp_list_char, S8 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E8 @ S8)) @ (red @ P)) => ((eval @ P @ E8 @ S8 @ E5 @ S3) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % extend_1_eval
thf(fact_192_Val, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val]: (eval @ P @ (val_list_char @ V) @ S2 @ (val_list_char @ V) @ S2)))). % Val
thf(fact_193_eval__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, V : val, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((eval @ P @ (val_list_char @ V) @ S2 @ E5 @ S3) => (~ (((E5 = (val_list_char @ V)) => (~ ((S3 = S2)))))))))). % eval_cases(2)
thf(fact_194_eval__hext, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val]: ((eval @ P @ E2 @ (produc52622304on_val @ H @ L) @ E5 @ (produc52622304on_val @ H2 @ L2)) => (hext @ H @ H2))))). % eval_hext
thf(fact_195_CastNull, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, S_1 : produc515445032on_val, C2 : list_char]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ null) @ S_1) => (eval @ P @ (cast_list_char @ C2 @ E2) @ S_0 @ (val_list_char @ null) @ S_1))))). % CastNull
thf(fact_196_eval__evals_OCons, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, Es : list_exp_list_char, Es2 : list_exp_list_char, S_2 : produc515445032on_val]: ((eval @ P @ E2 @ S_0 @ (val_list_char @ V) @ S_1) => ((evals @ P @ Es @ S_1 @ Es2 @ S_2) => (evals @ P @ (cons_exp_list_char @ E2 @ Es) @ S_0 @ (cons_exp_list_char @ (val_list_char @ V) @ Es2) @ S_2)))))). % eval_evals.Cons
thf(fact_197_small__by__big, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => ((final_list_char @ E5) => (eval @ P @ E2 @ S2 @ E5 @ S3))))))). % small_by_big
thf(fact_198_big__iff__small, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val]: ((wf_pro1229751607t_char @ wwf_J_mdecl @ P) => ((eval @ P @ E2 @ S2 @ E5 @ S3) = (((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P)))) & ((final_list_char @ E5)))))))). % big_iff_small
thf(fact_199_not__finals__ConsI, axiom,
    ((![E2 : exp_list_char, Es : list_exp_list_char]: ((~ ((final_list_char @ E2))) => (~ ((finals_list_char @ (cons_exp_list_char @ E2 @ Es)))))))). % not_finals_ConsI
thf(fact_200_Red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (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 @ E5 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (transi111096263on_val @ (red @ P))))))). % Red_lcl_add
thf(fact_201_red__lcl__add, axiom,
    ((![E2 : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E5 : 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 @ E5 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H @ (map_ad1615113112ar_val @ L_02 @ L))) @ (produc2023458740on_val @ E5 @ (produc52622304on_val @ H2 @ (map_ad1615113112ar_val @ L_02 @ L2)))) @ (red @ P)))))). % red_lcl_add
thf(fact_202_CastRedsThrow, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, A2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, C2 : 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 @ C2 @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % CastRedsThrow
thf(fact_203_CallRedsThrowObj, axiom,
    ((![E2 : exp_list_char, S0 : produc515445032on_val, A2 : exp_list_char, S_1 : produc515445032on_val, P : list_P1234162913t_char, M : list_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_1)) @ (transi111096263on_val @ (red @ P))))))). % CallRedsThrowObj
thf(fact_204_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_205_CallObjThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E5 : exp_list_char, S_1 : produc515445032on_val, M : list_char, Ps : list_exp_list_char]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E5) @ S_1) => (eval @ P @ (call_list_char @ E2 @ M @ Ps) @ S_0 @ (throw_list_char @ E5) @ S_1))))). % CallObjThrow
thf(fact_206_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_207_exp_Odistinct_I75_J, axiom,
    ((![X32 : val, X14 : exp_list_char]: (~ (((val_list_char @ X32) = (throw_list_char @ X14))))))). % exp.distinct(75)
thf(fact_208_exp_Odistinct_I177_J, axiom,
    ((![X91 : exp_list_char, X92 : list_char, X93 : list_exp_list_char, X14 : exp_list_char]: (~ (((call_list_char @ X91 @ X92 @ X93) = (throw_list_char @ X14))))))). % exp.distinct(177)
thf(fact_209_red__reds_OThrowRed, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (red @ P)))))). % red_reds.ThrowRed
thf(fact_210_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_211_ConsThrow, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, S_0 : produc515445032on_val, E5 : exp_list_char, S_1 : produc515445032on_val, Es : list_exp_list_char]: ((eval @ P @ E2 @ S_0 @ (throw_list_char @ E5) @ S_1) => (evals @ P @ (cons_exp_list_char @ E2 @ Es) @ S_0 @ (cons_exp_list_char @ (throw_list_char @ E5) @ Es) @ S_1))))). % ConsThrow
thf(fact_212_ThrowReds, axiom,
    ((![E2 : exp_list_char, S2 : produc515445032on_val, E5 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S2) @ (produc2023458740on_val @ E5 @ S3)) @ (transi111096263on_val @ (red @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E5) @ S3)) @ (transi111096263on_val @ (red @ P))))))). % ThrowReds
thf(fact_213_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_214_red__reds_OCallThrowObj, axiom,
    ((![E2 : exp_list_char, M : list_char, Es : list_exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ (throw_list_char @ E2) @ M @ Es) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CallThrowObj
thf(fact_215_red__reds_OCastThrow, axiom,
    ((![C2 : list_char, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char]: (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (cast_list_char @ C2 @ (throw_list_char @ E2)) @ S2) @ (produc2023458740on_val @ (throw_list_char @ E2) @ S2)) @ (red @ P))))). % red_reds.CastThrow
thf(fact_216_evals__cases_I2_J, axiom,
    ((![P : list_P1234162913t_char, E2 : exp_list_char, Es : list_exp_list_char, S2 : produc515445032on_val, E5 : list_exp_list_char, S3 : produc515445032on_val]: ((evals @ P @ (cons_exp_list_char @ E2 @ Es) @ S2 @ E5 @ S3) => ((![V3 : val, S_12 : produc515445032on_val, Es6 : list_exp_list_char]: ((E5 = (cons_exp_list_char @ (val_list_char @ V3) @ Es6)) => ((eval @ P @ E2 @ S2 @ (val_list_char @ V3) @ S_12) => (~ ((evals @ P @ Es @ S_12 @ Es6 @ S3)))))) => (~ ((![E7 : exp_list_char]: ((E5 = (cons_exp_list_char @ (throw_list_char @ E7) @ Es)) => (~ ((eval @ P @ E2 @ S2 @ (throw_list_char @ E7) @ S3)))))))))))). % evals_cases(2)
thf(fact_217_CallRedsThrowParams, axiom,
    ((![E2 : exp_list_char, S0 : produc515445032on_val, V : val, S_1 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char, Vs_1 : list_val, A2 : exp_list_char, Es_2 : list_exp_list_char, S_2 : produc515445032on_val, M : list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E2 @ S0) @ (produc2023458740on_val @ (val_list_char @ V) @ S_1)) @ (transi111096263on_val @ (red @ P))) => ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ S_1) @ (produc1725134254on_val @ (append_exp_list_char @ (map_va1515327237t_char @ val_list_char @ Vs_1) @ (cons_exp_list_char @ (throw_list_char @ A2) @ Es_2)) @ S_2)) @ (transi325225921on_val @ (reds @ P))) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (call_list_char @ E2 @ M @ Es) @ S0) @ (produc2023458740on_val @ (throw_list_char @ A2) @ S_2)) @ (transi111096263on_val @ (red @ P)))))))). % CallRedsThrowParams
thf(fact_218_evals_Osimps, axiom,
    ((evals = (^[P5 : list_P1234162913t_char]: (^[A12 : list_exp_list_char]: (^[A23 : produc515445032on_val]: (^[A33 : list_exp_list_char]: (^[A43 : produc515445032on_val]: (((?[S4 : produc515445032on_val]: (((A12 = nil_exp_list_char)) & ((((A23 = S4)) & ((((A33 = nil_exp_list_char)) & ((A43 = S4))))))))) | ((((?[E3 : exp_list_char]: (?[S_02 : produc515445032on_val]: (?[V2 : val]: (?[S_13 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (?[Es4 : list_exp_list_char]: (?[S_22 : produc515445032on_val]: (((A12 = (cons_exp_list_char @ E3 @ Es3))) & ((((A23 = S_02)) & ((((A33 = (cons_exp_list_char @ (val_list_char @ V2) @ Es4))) & ((((A43 = S_22)) & ((((eval @ P5 @ E3 @ S_02 @ (val_list_char @ V2) @ S_13)) & ((evals @ P5 @ Es3 @ S_13 @ Es4 @ S_22))))))))))))))))))) | ((?[E3 : exp_list_char]: (?[S_02 : produc515445032on_val]: (?[E4 : exp_list_char]: (?[S_13 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A12 = (cons_exp_list_char @ E3 @ Es3))) & ((((A23 = S_02)) & ((((A33 = (cons_exp_list_char @ (throw_list_char @ E4) @ Es3))) & ((((A43 = S_13)) & ((eval @ P5 @ E3 @ S_02 @ (throw_list_char @ E4) @ S_13)))))))))))))))))))))))))). % evals.simps

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![Us3 : list_ty]: (((wTrts @ p @ h_a @ e @ es_a @ Us3) & (list_all2_ty_ty @ (widen_917054840t_char @ p) @ Us3 @ us)) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
