reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;

theorem Th37:
  for A, B being Subset of Y holds MaxADSet(A /\ B) c= MaxADSet(A)
  /\ MaxADSet(B)
proof
  let A, B be Subset of Y;
A1: MaxADSet(A /\ B) c= MaxADSet(B) by Th31,XBOOLE_1:17;
  MaxADSet(A /\ B) c= MaxADSet(A) by Th31,XBOOLE_1:17;
  hence thesis by A1,XBOOLE_1:19;
end;
