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