theorem
  for f being non-empty Function
  for p being Element of sproduct f
  ex s being Element of product f st p c= s
proof
  let f be non-empty Function,
  p be Element of sproduct f;
  set h = the Element of product f;
  reconsider s = h +* p as Element of product f by Th53;
  take s;
  thus thesis by FUNCT_4:25;
end;
