
theorem Th6:
  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
A1: v = w1 & u = w2;
  w1 + w2 = ((the addF of V)||the carrier of W).[w1,w2] by Def1;
  hence thesis by A1,FUNCT_1:49;
end;
