On this website : https://spinningup.openai.com/en/latest/spinningup/rl_intro3.html#baselines-in-policy-gradients  , they justify the fact that adding a baseline b(s(t)) in the policy gradient doesn't change its gradient by saying that this is "an immediate consequence of the EGLP Lemma". However, I did not manage to prove it with this Lemma, can somebody help me please?

The proof is trivial when b is a constant, but I struggle to derive it whenever b is a fonction of the current state s because you can't take it out of the integral.

On the OpenAI's Spinning Up, they justify the fact that adding a baseline $b(s_t)$ in the policy gradient doesn't change its gradient by saying that this is

an immediate consequence of the EGLP Lemma

However, I did not manage to prove it with this lemma. Can somebody help me, please?

The proof is trivial when $b$ is a constant, but I struggle to derive it whenever $b$ is a function of the current state $s$ because you can't take it out of the integral.