Hi Solomon, I don't think we should reduce head coverings to submission, nor reduce submission to something done in worship. There will still be a creational hierarchy in the new heavens and the new earth, and men will still lead; but because the church herself will have reached eschatological fulfillment, shining forth as the glory of Christ, I think it follows that women will shine forth in the heavenly court without need of a covering any more. This doesn't eliminate submission, since the church will still submit to Christ, of course!