theorem Th127:
  product <*D1,D2,D3*> = the set of all <*d1,d2,d3*>
proof
  thus product <*D1,D2,D3*> c= the set of all <*d1,d2,d3*>
  proof
    let a be object;
    assume a in product <*D1,D2,D3*>;
    then ex x,y,z st x in D1 & y in D2 & z in D3 & a = <*x,y,z*> by Th123;
    hence thesis;
  end;
  let a be object;
  assume a in the set of all  <*d1,d2,d3*>;
  then ex d1,d2,d3 st a = <*d1,d2,d3*>;
  hence thesis by Th123;
end;
