I don't think you mean that. You mean "regeneration precedes believing" don't you?
To have faith IS to be believing. Faith and Belief are synonymns in my view, therefore, one cannot precede the other.
I think you're right. I've been predestined to develop a sinus infection today to God's glory. I think I'll retire now before my mind shuts off totally. (And no wise cracks.) :O)