reserve A,X for non empty set;
reserve f for PartFunc of [:X,X:],REAL;
reserve a for Real;

theorem
  for X being non empty set, f being PartFunc of [:X,X:],REAL,
      R being Equivalence_Relation of X st R = low_toler(f,0)[*] &
  f is nonnegative Reflexive discerning holds Class R = SmallestPartition X
  by Th24;
