Global Instance Permutation_length' :
Proper (@Permutation A ==> Logic.eq) (@length A) | 10.
Global Instance Permutation_Forall (P : A -> Prop) :
Proper ((@Permutation A) ==> Basics.impl) (Forall P).
Global Instance Permutation_Exists (P : A -> Prop) :
Proper ((@Permutation A) ==> Basics.impl) (Exists P).

Lemma Permutation_Forall2 (P : A -> B -> Prop) :
forall l1 l1' (l2 : list B), Permutation l1 l1' -> Forall2 P l1 l2 ->
exists l2' : list B, Permutation l2 l2' /\ Forall2 P l1' l2'.