reserve T for TopSpace,
  A, B for Subset of T;

theorem :: Theorem 3
  A is regular_open iff A is supercondensed & A is open
proof
  thus A is regular_open implies A is supercondensed & A is open
  proof
    assume A is regular_open;
    then
A1: Int Cl A = A by TOPS_1:def 8;
    thus thesis by A1;
  end;
  assume that
A2: A is supercondensed and
A3: A is open;
  Int Cl A = Int A by A2;
  hence thesis by A3,TOPS_1:23;
end;
