I was wondering if a poset is separative if
$ p \Vdash q \in \dot{G} ~~ \Rightarrow p \leq q$
I think it's clear that $ p, q \in G $ and hence are compatible but I am not seeing why ( if it's true ) $ p \leq q$. I don't know if perhaps we can use separativity( i.e. that $ p \not\leq q \Rightarrow \exists r \leq p $ such that $ r \bot q$ ). That said I wanted to use this to find a dense subset that is perhaps predense below $ q$ and that must contain $p$ so that we can reach a contradiction using separativity and the definition of Genericity. I don't see how yet though.
Thanks for any thoughts/help!