Ltac hypInv :=
      try (match goal with
          | [H: Some _ = Some _ |-_ ] => inversion H; clear H; subst
      end); try pairInv.Fixpoint lookupIndex (A : Set)(eqd : eq_dec A)(ls : list A)(a : A) def :=
  match ls with
    | nil => def
    | a' :: ls' =>
      if (eqd a a') then O else S (lookupIndex eqd ls' a def)
  end.

Theorem map_ext_in : forall (A B : Set)(ls : list A)(f1 f2 : A -> B), (forall a, In a ls -> f1 a = f2 a) -> map f1 ls = map f2 ls.