 However, the extension exists under the additional assumption that for every "y" ∈ "E" there exists "x"∈"F" such that "y" − "x" ∈"K"; in other words, if "E" = "K" + "F".By transfinite induction it is sufficient to consider the case dim "E"/"F" = 1.Choose "y" ∈ "E"\"F".