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_2 : forall k k' e e' l,
InA eqk (k, e) ((k', e') :: l) -> ~ eq k k' -> InA eqk (k, e) l.