reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;

theorem
  {} in rng F iff Product F = 0
proof
  thus {} in rng F implies Product F = 0 by Th26,CARD_1:27;
  assume Product F = 0;
  then product F = {};
  hence thesis by Th26;
end;
