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 uniq_perm_eq s1 s2 : uniq s1 -> uniq s2 -> s1 =i s2 -> perm_eq s1 s2.