theorem
 for I being set, f being non-empty I-defined Function
 for p being f-compatible I-defined Function
  ex s being Element of product f st p c= s
proof let I be set;
  let f be non-empty I-defined Function,
  p be f-compatible I-defined Function;
  reconsider p as Element of sproduct f by Th100;
  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;
