
theorem LMQ07:
  for V be RealLinearSpace, W be Subspace of V holds
  for x be object holds x is Point of VectQuot(V,W)
    iff ex v be Point of V st x = v + W
  proof
    let V be RealLinearSpace, W be Subspace of V;
    let x be object;
    A1: x in the carrier of VectQuot (V,W)
      iff x in CosetSet(V,W) by LMQ06;
    (ex A be Coset of W st x = A)
      iff ex v be Point of V st x = v + W
    proof
      thus (ex A be Coset of W st x = A) implies
      ex v be Point of V st x = v + W by RLSUB_1:def 6;
      assume ex v be Point of V st x = v + W; then
      x is Coset of W by RLSUB_1:def 6;
      hence thesis;
    end;
    hence thesis by A1;
  end;
