Notation perm_eql s1 s2 := (perm_eq s1 =1 perm_eq s2).Notation perm_eqr s1 s2 := (perm_eq^~ s1 =1 perm_eq^~ s2).

Lemma perm_cons x s1 s2 : perm_eq (x :: s1) (x :: s2) = perm_eq s1 s2.