# Formatting an implication cycle proof

Some theorems/lemmata/propositions start with "If [...] then the following are equivalent:". After this, an enumeration (i), (ii), (iii) follows.

The proof is usually done in an "implication cycle": first prove (i)⇒(ii), then (ii)⇒(iii) and (iii)⇒(i).

The question is: What's the right method to use for such proofs?

1. Is there some kind of environment aside the obvious, like "\begin{description}"?
2. Best would be if the references (and labels) are created automatically.
3. Additionally, does this method also automatically change the numbering, for example if I change "(i)" to "A."?
• Please have you tried anything or the image is a scan of a textbook? – Sebastiano Sep 5 '18 at 10:24
• The image is a scan from a textbook. – quiliup Sep 5 '18 at 10:30
• This is about style, so off-topic for the site. I'd avoid the quotes and the colon, but that's just personal preference. – egreg Sep 5 '18 at 10:59
• @egreg You are right at some point. My question is about style, but not only. My purpose is to find an easy way tackling the points 2 and 3, maybe there is a package I don't know about. If you still convinced the question shouldn't belong here, explain please, where to ask... I'd avoid the quotes and colons too; the images do not show, what I want to achieve, but what I noticed is the way of handling the problem at the moment. – quiliup Sep 5 '18 at 11:11
• Out of the box, latex can us \label on the lemma parts, and \ref in the proof parts. Getting the implication to appear would be more difficult and probably not worth the trouble. Especially since some proofs don't prove a cycle, but instead prove that (i) and (iii) are each equal to (ii). For example, this image isn't proving (iii) => (i). – Teepeemm Sep 5 '18 at 11:33