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

theorem
  {SmallestPartition A} is Classification of A
proof
  SmallestPartition A in PARTITIONS(A) by PARTIT1:def 3;
  then reconsider S = {SmallestPartition A} as Subset of PARTITIONS(A) by
ZFMISC_1:31;
  S is Classification of A
  proof
    let X,Y be a_partition of A;
    assume that
A1: X in S and
A2: Y in S;
    X = SmallestPartition A by A1,TARSKI:def 1;
    hence thesis by A2,TARSKI:def 1;
  end;
  hence thesis;
end;
