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 Th51:
  product f c= sproduct f
proof
  let x be object;
  assume x in product f;
  then ex g st x = g & dom g = dom f &
  for x being object st x in dom f holds g.x in f.x by Def5;
  hence thesis by Def9;
end;
