Something like..
Let h, j, k, and l be scalars, h, j, k, l ∈ R.
If
hv1 + jv2 + kv3 + lv4 = E
hv1 + jv2 + kv3 + lv4 = "ax + by + cz = d"
then S is a spanning set of E?
(in essense are we saying that an addition of planes that have been multiplied by some scalar give us E?) It's a weird concept...