reserve T for non empty TopSpace,
  X,Z for Subset of T;
reserve x,y for Element of OpenClosedSet(T);

theorem
  for x,y be Element of LattStr(#OpenClosedSet(T),T_join T,T_meet T#),
  x9,y9 be Element of OpenClosedSet(T)
  st x=x9 & y=y9 holds x"/\"y = x9 /\ y9 by Def3;
