reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;
reserve US for UniformSpace;
reserve R for Relation of X;

theorem
  for SF being upper Subset-Family of [:X,X:],R being Relation of X  st
  R in SF & SF = rho(R) & meet SF in SF holds rho(meet SF) = SF
  by Th29,Th30;
