(* 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 uniq_size_uniq s1 s2 :
uniq s1 -> s1 =i s2 -> uniq s2 = (size s2 == size s1).