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_ind_bis :
forall P : list A -> list A -> Prop,
P [] [] ->
(forall x l l', Permutation l l' -> P l l' -> P (x :: l) (x :: l')) ->
(forall x y l l', Permutation l l' -> P l l' -> P (y :: x :: l) (x :: y :: l')) ->
(forall l l' l'', Permutation l l' -> P l l' -> Permutation l' l'' -> P l' l'' -> P l l'') ->
forall l l', Permutation l l' -> P l l'.