Goal:
    A : Type  B : Type  f : A → B
  ============================
   (∀ (a : A) (l : list A),
      nth_error (map f (a :: l)) 0 = option_map f (nth_error (a :: l) 0))


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