
theorem Th38:
  for f being Function, X, Y being set, i being object st i in dom f & X c= Y
  holds product(f +* (i,X)) c= product(f +* (i,Y))
proof
  let f be Function, X, Y be set, i be object;
  assume A1: i in dom f & X c= Y;
  then f +* (i,X) = f +* (i .--> X) & f +* (i,Y) = f +* (i .--> Y)
    by FUNCT_7:def 3;
  hence thesis by A1, Th27;
end;
