intros k l; split; intros [y H].
- exists y...
- induction H as [a l eq|a l H IH].
+ destruct a as [k' y'].
exists y'...
+ destruct IH as [e H0].
exists e...
Qed.

Lemma In_inv : forall k k' e l, In k ((k',e) :: l) -> eq k k' \/ In k l.