induction n...
simpl.
congruence.
Qed.
Hint Immediate length_repeat.
Instance map_ext_eq_mor A B: Proper (@ext_eq A B ==> ext_eq) map.
repeat intro.
apply map_ext.
assumption.
Qed.

Lemma concat_nil X (l: list (list X)): (forall x, In x l -> x = nil) -> concat l = nil.
Proof with intuition.