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 Th33:
  Fr(K \/ L) c= Fr K \/ Fr L
proof
  Cl((K`) /\ L`) c= Cl K` by PRE_TOPC:19,XBOOLE_1:17;
  then
A1: Cl((K`) /\ L`) /\ Cl K c= Cl(K`) /\ Cl K by XBOOLE_1:26;
  Cl((K`) /\ L`) c= Cl L` by PRE_TOPC:19,XBOOLE_1:17;
  then
A2: Cl((K`) /\ L`) /\ Cl L c= Cl(L`) /\ Cl L by XBOOLE_1:26;
  Fr(K \/ L) = (Cl K \/ Cl L) /\ Cl((K \/ L)`) by PRE_TOPC:20
    .= Cl((K`) /\ L`) /\ (Cl K \/ Cl L) by XBOOLE_1:53
    .= (Cl((K`) /\ L`) /\ Cl K) \/ (Cl((K`) /\ L`) /\ Cl L) by XBOOLE_1:23;
  hence thesis by A1,A2,XBOOLE_1:13;
end;
