theorem Thm23:
  for x be non empty set holds
    product <*x*> = the set of all <*y*> where y is Element of x
  proof
    let x be non empty set;
A1: rng <*x*> = {x} & <*x*>.1 = x by FINSEQ_1:38; then
    {} in rng <*x*> implies {} = x; then
    <*x*> is non-empty 1-element FinSequence by RELAT_1:def 9;
    hence thesis by A1,Thm21;
  end;
