As a non-native English speaker (and writer) I always had the problem of understanding the distinction between a 'Theorem' and a 'Proposition'. When writing papers, I tend to name only the main result(s) 'Theorem', any auxiliary result leading to this Theorem a 'Lemma' (and, sometimes, small observations that are necessary to prove a Lemma are labeled as 'Claim'). I avoid using the term 'Proposition'.

However, sometimes a paper consists of a number important results (which by all means earn to be called 'Theorem') that are combined to obtain a certain main result. Hence, another term such as 'Proposition' might come in handy, yet I don't know whether it suits either the main or the intermediate results.

So, my question is: When to use 'Theorem' and when to use 'Proposition' in a paper?

Theoremis from Greek andPropositionis from Latin, so going to the etymology may help a proper use (which is not necessarily the most popular one). Here's a nice list of mathematical terms etymonline.com/… $\endgroup$1more comment