
theorem
  for X be RealNormSpace, R,S be Subset of X
  st R is dense & S is dense open
  holds R /\ S is dense
  proof
    let X be RealNormSpace, R,S be Subset of X;
    reconsider R1 = R, S1 = S as Subset of LinearTopSpaceNorm X
    by NORMSP_2:def 4;
    assume R is dense & S is dense open; then
    R1 is dense & S1 is dense & S1 is open by EQCL2,NORMSP_2:33; then
    R1 /\ S1 is dense by TOPS_1:47;
    hence R /\ S is dense by EQCL2;
  end;
