
theorem
  for f being Function, A, B being set, i, j being object
  st i in dom f & j in dom f & A c= f.i & B c= f.j
  holds product(f +* (i,j) --> (A,B)) c= product f
proof
  let f be Function, A, B be set, i, j be object;
  assume A1: i in dom f & j in dom f & A c= f.i & B c= f.j;
  then product f = product(f +* (i,j) --> (f.i,f.j)) by Th11;
  hence thesis by A1, Th31;
end;
