
theorem Th9:
  for V being RealUnitarySpace, W being Subspace of V, v being
  VECTOR of V, w being VECTOR of W st w = v holds - v = - w
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let v be VECTOR of V;
  let w be VECTOR of W;
A1: - v = (- 1) * v & - w = (- 1) * w by RLVECT_1:16;
  assume w = v;
  hence thesis by A1,Th7;
end;
