theorem
  not (ex x st x in dom f & f.x is Function) implies uncurry f = {} &
  uncurry' f = {}
proof
  assume
A1: not (ex x st x in dom f & f.x is Function);
A2: now
    set t = the Element of dom uncurry f;
    assume dom uncurry f <> {};
    then ex x,g,y st t = [x,y] & x in dom f & g = f.x & y in dom g by Def2;
    hence contradiction by A1;
  end;
  hence uncurry f = {};
  thus thesis by A2,Th1,RELAT_1:41;
end;
