reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;

theorem Th33:
  for A being Subset of X holds
    ([:A,A:] \/ [:X \ A,X \ A:])~ = [:A,A:] \/ [:X \ A,X \ A:]
  proof
    let A be Subset of X;
    [:A,A:]~ = [:A,A:] & [:X\A,X\A:]~ = [:X\A,X\A:] by SYSREL:5;
    hence thesis by RELAT_1:23;
  end;
