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)
  ============================
   (∀ v : A, hd = v → (Some hd = Some v) + (Some hd = None ∧ v = d))


DEBUG:Going to execute:
trivial; hnf; intros