Example In_example_2 :
forall n, In n [2; 4] ->
exists n', n = 2 * n'.
(** (Notice the use of the empty pattern to discharge the last case _en passant_.) *)
(** We can also prove more generic, higher-level lemmas about [In].  Note, in the next, how [In] starts out applied to a variable and only gets expanded when we do case analysis on this variable: *)

Lemma In_map :
forall (A B : Type) (f : A -> B) (l : list A) (x : A),
In x l ->
In (f x) (map f l).