A.S

I was reviewing some close votes, and this came up: http://math.stackexchange.com/questions/263919/delta-subset-phi-is-a-base-in-a-root-system-imples-delta-vee-subset-ph
So how are we to deal with these questions where--1. old question, perhaps highly upvoted but has no answer, 2. along with newer duplicate question which does have an answer

And step 9 follows by $Y \in F \to \exists x,y: Y = \langle x,y \rangle \land \langle x,y \rangle \in F$
$\to \exists x,y: Y = \langle x,y \rangle \land \langle x,y \rangle \in G$
$\to Y \in G$