intros.
simpl in |- *.
elim (omit_removes v i j).
intros.
exists x; auto with algebra.
Qed.

Lemma seqsum_is_elt_plus_omitseq :
forall (n : Nat) (M : abelian_monoid) (s : seq n M) (i : fin n),
sum s =' s i +' sum (omit s i) in _.