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_eq_all s1 s2 P : perm_eq s1 s2 -> all P s1 = all P s2.