theorem, lemma, axiom, corollary - arcturus9/useful-link GitHub Wiki

axiom(공리, 사실로 받아들인것)

• which is accepted as true for that particular branch

theorem(정리, 사실임이 증명된것)

• which has been proved to be true from whichever axioms relevant to that particular branch

lemma(부명제, 정리를 증명하는 과정에서 증명된 것)

• which is proven during the course of reaching the proof of a theorem
• logically there is no qualitative difference between a lemma and a theorem
• lemma is seen more as a stepping-stone than a theorem

corollary(귀결)

• which is a direct result, or a direct application, of another proof.

statement(서술)

• which has objective and logical meaning

proposition(문제/명제, 사실인지 조사할 대상)

• which is offered up for investigation as to its truth or falsehood

https://www.quora.com/What-are-the-differences-between-theorems-definitions-axioms-lemmas-corollaries-propositions-and-statements