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 Th32:
  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 /\ L) /\ Cl((K`) \/ L`) by XBOOLE_1:54
    .= Cl(K /\ L) /\ (Cl(K`) \/ Cl L`) by PRE_TOPC:20
    .=(Cl(K /\ L) /\ Cl(K`)) \/ (Cl(K /\ L) /\ Cl(L`)) by XBOOLE_1:23;
  hence thesis by A1,A2,XBOOLE_1:13;
end;
