reserve X for TopSpace;
reserve C for Subset of X;
reserve A, B for Subset of X;

theorem
  A is open & A is closed implies Int Cl A = Cl Int A
proof
  assume that
A1: A is open and
A2: A is closed;
A3: Cl A = A by A2,PRE_TOPC:22;
  Int A = A by A1,TOPS_1:23;
  hence thesis by A3;
end;
