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;
