Axiom: a proposition and principle that has been tested by human long-term practice and does not need other judgments to prove.

Theorem: A proposition or formula that can be proved theoretically as a principle or law. The difference between theorems and axioms is that axioms exist naturally. The theorem is further proved according to the axiom.

Lemma: It is regarded as equivalent to theorem, which means it can be used as theorem. .

Assertion: The result of simple guess based on known axioms or theorems has not been systematically proved, or the proof method itself has not been found, but the actual result is consistent. Of course, the result may or may not be right.