Goal:
  
  A : Type
  B : Type
  f : A → B
  IHn : ∀ l : list A, nth_error (map f l) 0 = option_map f (nth_error l 0)
  ============================
   (∀ (a : A) (l : list A),
      match map f (a :: l) with
      | _ :: x :: _ => Some x
      | _ => None
      end = option_map f match l with
                         | [] => None
                         | x :: _ => Some x
                         end)


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 ])