The "usual" difference is that a lemma is a minor theorem usually towards proving a more significant theorem. Whereas a corollary is an "easy" or "evident" consequence of another theorem (or lemma).
A lemma is often invoked several times in the proof of a theorem. So its proof is treated separately, and thus the 'main' proof is significantly shorter, easier to read, and easier to verify in terms of correctness.
Lemma - technical result used in the proof of the theorem, which is claimed as original and proved, but the main interest in which lies its use in the proof of one or more theorems.
As per title, what is a "lemma"? How is it different from "theorem"? ASAIK, I have to prove a self-proposed theorem in my paper. Do I also have to provide the proof for a self-proposed lemma?
So Zorn's lemma is a lemma ONLY BECAUSE we assume the Axiom of Choice rather than Zorn's lemma as an axiom of standard set theory: it is a lemma only because of how we choose to organize mathematics.
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