Goal:
    A : Type  B : Type  f : A → B
  ============================
   ((∀ l : list A, nth_error (map f l) 0 = option_map f (nth_error l 0))
    → ∀ l : list A, nth_error (map f l) 1 = option_map f (nth_error l 1))


DEBUG:Going to execute:
trivial; hnf