reserve T for TopSpace;
reserve A,B for Subset of T;

theorem Th1:
  A /\ Int(A` \/ B) c= B
proof
A1: A misses A` by XBOOLE_1:79;
  A /\ (A` \/ B) = (A /\ A`) \/ A /\ B by XBOOLE_1:23
    .= {} \/ A /\ B by A1
    .= A /\ B;
  then
A2: A /\ (A` \/ B)c= B by XBOOLE_1:17;
  A /\ Int(A` \/ B) c= A /\ (A` \/ B) by TOPS_1:16,XBOOLE_1:26;
  hence thesis by A2;
end;
