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_filter s1 s2 P : perm_eq s1 s2 -> perm_eq (filter P s1) (filter P s2).