An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. [1]
In mathematics, informal logic and argument mapping, a lemma (plural lemmas or lemmata) is a generally minor, proven proposition which is used as a stepping stone to a larger result. For that reason, it is also known as a “helping theorem” or an “auxiliary theorem”.[2]
A proposition is a statement that is either true or false. In our course, we will usually call a mathematical proposition a theorem. A theorem is a main result. A proposition that is mainly of interest to prove a larger theorem is called a lemma. Some intermediate results are called propositions. Finally, a corollary is a statement that follows easily from a theorem. [3]
[1]: https://en.wikipedia.org/wiki/Axiom[2]: https://en.wikipedia.org/wiki/Lemma_(mathematics)#:~:text=In%20mathematics%2C%20informal%20logic%20and,or%20an%20%22auxiliary%20theorem%22.[3]: http://math.northwestern.edu/~clark/285/handouts/abs-math.pdf