Assalamu Alaikum,
If you mean, women can be banned because of lewdness, I support that, and that hadith you have quoted also points out to the same. My point was, praying in the same room in itself is not lewdness. As I can see from your mail, you do not think, the demand to pray in the same room in itself is lewd, we are now on the same page. The argument about different levels of imaan was shallow though.