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;

theorem Th32:
  for P being a_partition of {} holds P = {}
proof
  let P be a_partition of {};
  assume not thesis;
  then consider Z being object such that
A1: Z in P by XBOOLE_0:def 1;
  Z <> {} by A1,Def4;
  hence thesis by A1;
end;
