This question is regarding an answer to the question below:
Expectation regarding Brownian Motion
This is a formula regarding getting expectation under the topic of Brownian Motion. $ \begin{align*} E[W(s)W(t)] &=E[W(s)(W(t)−W(s))+W(s)^2]\\ &=E[W(s)]E[W(t)−W(s)]+E[W(s)^2]\\ &=0+s =\min(s,t). \end{align*} $
One of Michael Hardy's comment is: "The step that says $E[W(s)(W(t)−W(s))]=E[W(s)]E[W(t)−W(s)]$ depends on an assumption that $t>s$."
So, finally, my question is how does the assumption $t>s$ play out in the $E[W(s)(W(t)−W(s))]=E[W(s)]E[W(t)−W(s)]?$
What if $t\leq s$?
Thanks a lot! Love the smart math stack exchange crowd!