intros. simpl. unfold eq_part. intro g. split. simpl. intro H1.
apply Trans with(subtype_elt x1). exact H1. exact H.
simpl. intro H1. apply Trans with(subtype_elt x2). exact H1.
apply Sym. exact H. Qed.

(* Specifications: *)
Lemma stillsurj:forall(E:Setoid)(A:part_set E)
(n:Nat)(v:seq n E)(i j:fin n)
,   A=' seq_set v   ->   ~i=' j   ->   v i=' v j
->   A=' seq_set(omit v i).