Global Instance Permutation_NoDup' :
 Proper (@Permutation A ==> iff) (@NoDup A).

Lemma Permutation_pigeonhole_rel (R : B -> A -> Prop) (l1 : list B) l2 : Forall (fun b => Exists (R b) l2) l1 -> length l2 < length l1 -> exists b b' (l3 : list B), Permutation l1 (b :: b' :: l3) /\ exists a, In a l2 /\ R b a /\ R b' a.