Yes it is completely normal and it is a good sign. Most of us LBS cling to the old relationship hoping our now changed spouses will return to normal. We deal with a ton of crazy disrespectful behavior and hope that our kind loving spouse will return. As we improve ourselves and make a new life for ourself we can detach more. We realize that unless the walk away spouse makes changes to themselves, that we do not want an R with them.
Short version: you are detaching well. Keep it up bud.
