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

theorem
  for S being Subset of PARTITIONS(A) st S = {{A},SmallestPartition A}
  holds S is Strong_Classification of A
proof
  let S be Subset of PARTITIONS(A) such that
A1: S = {{A},SmallestPartition A};
A2: SmallestPartition A in S by A1,TARSKI:def 2;
  S is Classification of A & {A} in S by A1,Th14,TARSKI:def 2;
  hence thesis by A2,Def2;
end;
