Goal:
  
  A : Type
  B : Type
  f : A → B
  IHn : nat
  l : ∀ l : list A,
        nth_error (map f l) (S IHn) = option_map f (nth_error l (S IHn))
  ============================
   (∀ (a : A) (l : list A),
      match map f (a :: l) with
      | _ :: _ :: l1 => nth_error l1 IHn
      | _ => None
      end =
      option_map f
        match l with
        | [] => None
        | _ :: l0 => nth_error l0 IHn
        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 ])