reserve T for TopSpace;
reserve T for non empty TopSpace;
reserve F for Subset-Family of T;
reserve T for non empty TopSpace;

theorem
  for A, B being Subset of T st A is closed_condensed & B is
  closed_condensed holds Int A c= Int B iff A c= B
proof
  let A, B be Subset of T;
  assume that
A1: A is closed_condensed and
A2: B is closed_condensed;
  thus Int A c= Int B implies A c= B
  proof
    assume Int A c= Int B;
    then
A3: Cl Int A c= Cl Int B by PRE_TOPC:19;
    Cl Int A = A by A1,TOPS_1:def 7;
    hence thesis by A2,A3,TOPS_1:def 7;
  end;
  thus thesis by TOPS_1:19;
end;
