induction n1; intuition; simpl in *.
Qed.

Theorem shiftOut_plus_if :
forall n1 n2 s s' s'' b1 b2,
shiftOut s n1 = Some (b1, s') ->
shiftOut s' n2 = Some (b2, s'') ->
shiftOut s (n1 + n2) = Some (Vector.append b1 b2, s'').