Goal:
    A : Type
  ============================
   (option_map id None = id None)


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | split ]
            | case not_locked_false_eq_true; assumption
            | match goal with
              | H:~ _ |- _ => solve [ case H; trivial ]
              end ])