I'm writing a paper on the topic of data clustering, in which i use a specific optimization model to increase the clustering accuracy.
Generally speaking, in a part of the paper i presented a lemma which proves that how the objective of my optimization framework is directly linked to the accuracy of the obtained clusters.
This lemma is important as it provides the required mathematical conditions for the validity of my model. Also, i used the lemma to support the rationality/motivation behind my specific model design and the observed performance increase in the implementations.
But i heard that if there is no theorem to come after the lemma, using a lemma is not sensible. Does it mean that it's better to present it as a theorem instead of a lemma? Or i'd have to present the above math in the body of the paper without using lemma/theorem?
Well, my personal preference is to use definition/lemma/theorems where i can in the paper to make it mathematically more clear and easy to follow.
If the lemma is not generic, ie does not have so importance in general I think you should keep the line lemma- theorem. Otherwise you can keep your lemma under the name of $proposition$