I am trying to prove that Einstein Sum $$S_{es}(a,b) = \frac{a+b}{1+ab}$$ is an s-norm operator. But, i got struggle on proving its monotonicity, i.e
If $a\leq c$ and $b \leq d$ then $s_{es}(a,b) \leq s_{es}(c,d)$.
So, i want to prove prove that if $0 \leq a, b, c, d \leq 1$ such that $a\leq c$ and $b \leq d$ then
$$\frac{a+b}{1+ab} \leq \frac{c+d}{1+cd}$$
I've tried to work backward, but got no result. Any suggestion?