reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;
reserve X for non empty set,
  x for Element of X;
reserve F for Part-Family of X;

theorem
  {} is a_partition of {}
proof
  reconsider A = {} as Subset-Family of {} by XBOOLE_1:2;
  union A = {} & for a be Subset of {} st a in A holds a<>{} & for b be
  Subset of {} st b in A holds a = b or a misses b;
  hence thesis by Def4;
end;
