Different types of mathematical claims

Lemma, proposition, theorem or corollary are different types of mathematical claims with different levels of importance and difficulty. Logically, these claims are same as all of them need a valid proof to be deemed true.

1. Lemma: easily proved and least interesting claim that can be used to prove other claims like proposition or theorem.
2. Proposition: interesting claim; however have lesser importance than theorem.
3. Theorem: most important claim that says something definitive for the subject, hence, often take more effort to prove than a proposition or lemma.
4. Corollary: quick consequence of theorem or proposition that was proved recently in the text.