reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;

theorem Th49:
  g in sproduct f implies dom g c= dom f &
  for x st x in dom g holds g.x in f.x
proof
  assume g in sproduct f;
  then ex h st g = h & dom h c= dom f &
  for x being object st x in dom h holds h.x in f.x by Def9;
  hence thesis;
end;
