Goal:
    A : Type  B : Type  f : A → B
  ============================
   ((∀ l : list A, nth_error (map f l) 0 = option_map f (nth_error l 0))
    → ∀ l : list A, nth_error (map f l) 1 = option_map f (nth_error l 1))


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 ])