Section Permutation_properties.
Variable A:Type.
Implicit Types a b : A.
Implicit Types l m : list A.
(** Compatibility with others operations on lists *)
Global Instance Permutation_in' :
Proper (Logic.eq ==> @Permutation A ==> iff) (@In A) | 10.
Global Instance Permutation_app' :
Proper (@Permutation A ==> @Permutation A ==> @Permutation A) (@app A) | 10.
Local Hint Resolve Permutation_app_comm : core.
Local Hint Resolve Permutation_cons_app : core.
Local Hint Resolve Permutation_middle : core.
Global Instance Permutation_rev' :
Proper (@Permutation A ==> @Permutation A) (@rev A) | 10.

Theorem Permutation_length : forall (l l' : list A),
Permutation l l' -> length l = length l'.