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 RS being strict RelStr holds
  UniformSpaceStr2RelStr(RelStr2UniformSpaceStr(RS)) = RS
  proof
    let RS be strict RelStr;
    set US = UniformSpaceStr2RelStr (RelStr2UniformSpaceStr(RS));
    now
      thus the carrier of US = the carrier of RS;
      the InternalRel of US = meet rho(the InternalRel of RS);
      hence the InternalRel of US = the InternalRel of RS by Th28;
    end;
    hence thesis;
  end;
