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

theorem
  A \/ Cl Int A = the carrier of X implies Cl Int A = the carrier of X
proof
  assume A \/ Cl Int A = the carrier of X;
  then (Int A) \/ (Cl Int A) = the carrier of X by TDLAT_3:4;
  hence thesis by PRE_TOPC:18,XBOOLE_1:12;
end;
