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 catCA_perm_ind P : (forall s1 s2 s3, P (s1 ++ s2 ++ s3) -> P (s2 ++ s1 ++ s3)) -> (forall s1 s2, perm_eq s1 s2 -> P s1 -> P s2).