theorem Th104:
 for I being set, f being non-empty ManySortedSet of I
 for s being f-compatible ManySortedSet of I
  holds s in product f
 proof let I be set, f be non-empty ManySortedSet of I;
  let s be f-compatible ManySortedSet of I;
A1: dom s = I by PARTFUN1:def 2 .= dom f by PARTFUN1:def 2;
   then for x being object st x in dom f holds s.x in f.x by FUNCT_1:def 14;
  hence s in product f by A1,Th9;
 end;
