# Removing countable set in monotone proof

I want to show that if $f:[a,b]\to\mathbb{R}$ is continuous, $N\subseteq [a,b]$ is countable and $\limsup_{x\to a^+}\frac{f(x)-f(a)}{x-a}\geq 0$ on $[a,b]\setminus N$, then $f(x)\geq f(y)$ for all $x,y\in[a,b]$, $x\geq y$.