End Palindrome.
Hint Rewrite mapo_app : list.
Definition inter_nonempty X '(G1, G2) :=
exists x, @L X G1 x /\ L G2 x.

Theorem intersect (Sigma : finType) (G : cfg Sigma) :
exists f, PALIN G <-> @inter_nonempty (Gamma Sigma) (f G).