
theorem
  for X be RealNormSpace, A,B being Subset of X
  holds Cl(A \/ B) = Cl A \/ Cl B
  proof
    let X be RealNormSpace, A,B be Subset of X;
    reconsider A1 = A, B1 = B as Subset of LinearTopSpaceNorm X
    by NORMSP_2:def 4;
    A1: Cl A1 = Cl A by EQCL1;
    A2: Cl B1 = Cl B by EQCL1;
    Cl (A1 \/ B1) = Cl (A \/ B) by EQCL1;
    hence thesis by A1,A2,PRE_TOPC:20;
  end;
