
theorem Th37:
  for V being RealUnitarySpace, W being Subspace of V, v being
  VECTOR of V holds v in v + W
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let v be VECTOR of V;
  v + 0.V = v & 0.V in W by Th11,RLVECT_1:4;
  hence thesis;
end;
