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).

Theorem Permutation_nil_app_cons : forall (l l' : list A) (x : A),
~ Permutation nil (l++x::l').