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;
reserve A,B for set;

theorem Th57:
  sproduct {} = {{}}
proof
  sproduct {} c= PFuncs({},{}) by Th55,RELAT_1:38,ZFMISC_1:2;
  hence sproduct {} c= {{}} by PARTFUN1:48;
  let x be object;
  assume x in {{}};
  then x = {} by TARSKI:def 1;
  hence thesis by Th50;
end;
