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 leq_size_perm s1 s2 : uniq s1 -> {subset s1 <= s2} -> size s2 <= size s1 -> s1 =i s2 /\ size s1 = size s2.