Goal:
    A : Type  d : A
  ============================
   (∀ (i : nat) (v : A),
      nth i [] d = v
      → (nth_error [] i = Some v) + (nth_error [] i = None ∧ v = d))


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 ])