
theorem Th17:
  for X be RealLinearSpace
  for Y1,Y2 be Subspace of X
  holds RLSp2RVSp(Y1 /\ Y2) = RLSp2RVSp(Y1) /\ RLSp2RVSp(Y2)
  proof
    let X be RealLinearSpace;
    let Y1,Y2 be Subspace of X;
    set Y12 = Y1 /\ Y2;
    the carrier of Y12 = (the carrier of Y1) /\ (the carrier of Y2)
      by RLSUB_2:def 2;
    hence thesis by VECTSP_5:def 2;
  end;
