(* Equality up to permutation *)
Section PermSeq.
Variable T : eqType.
Implicit Type s : seq T.
Definition perm_eq s1 s2 :=
all [pred x | count_mem x s1 == count_mem x s2] (s1 ++ s2).

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