theorem Th100:
 for I being set, f being non-empty I-defined Function
 for p being f-compatible I-defined Function
  holds p in sproduct f
 proof let I be set, f be non-empty I-defined Function;
  let p be f-compatible I-defined Function;
A1: dom p c= dom f by FUNCT_1:105;
   for x being object st x in dom p holds p.x in f.x by FUNCT_1:def 14;
  hence p in sproduct f by A1,Def9;
 end;
