Goal:
  
  A : Type
  B : Type
  f : nat → A → B
  n : nat
  k : nat
  a : A
  l : list A
  IHl : ∀ n k : nat,
          nth_error (mapi_rec f l k) n =
          option_map (f (n + k)) (nth_error l n)
  ============================
   (option_map (f (S n + k)) (nth_error l n) =
    option_map (f (S (n + k))) (nth_error l n))


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 ])