
theorem Th10:
  for V being RealUnitarySpace, W being Subspace of V, u,v being
  VECTOR of V, w1,w2 being VECTOR of W st w1 = v & w2 = u holds w1 - w2 = v - u
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let u,v be VECTOR of V;
  let w1,w2 be VECTOR of W;
  assume that
A1: w1 = v and
A2: w2 = u;
  - w2 = - u by A2,Th9;
  hence thesis by A1,Th6;
end;
