reserve TS for 1-sorted,
  K, Q for Subset of TS;
reserve TS for TopSpace,
  GX for TopStruct,
  x for set,
  P, Q for Subset of TS,
  K , L for Subset of TS,
  R, S for Subset of GX,
  T, W for Subset of GX;

theorem Th19:
  T c= W implies Int T c= Int W
proof
  assume T c= W;
  then W` c= T` by SUBSET_1:12;
  then Cl W` c= Cl T` by PRE_TOPC:19;
  hence thesis by SUBSET_1:12;
end;
