Whats the difference between theorem, lemma and corollary? Lemma — a minor result whose sole purpose is to help in proving a theorem It is a stepping stone on the path to proving a theorem It is a stepping stone on the path to proving a theorem Very occasionally lemmas can take on a life of their own (Zorn’s lemma, Urysohn’s lemma, Burnside’s lemma, Sperner’s lemma)
Definition: Theorem, Lemma, Proposition, Conjecture and Principle etc. Theorem vs Lemma is totally subjective, but typically lemmas are used as components in the proof of a theorem Propositions are perhaps even weaker, but again, totally subjective A conjecture is a statement which requires proof, should be proven, and is not proven
linear algebra - Steinitz exchange lemma - Mathematics Stack Exchange (Side note: I am teaching linear algebra, and I just lectured on the Steinitz Exchange Lemma, with the consequence that every linearly independent subset in a subspace of $\mathbb{R}^n$ is contained in a basis and any two bases of a subspace have the same number of elements
Lemma Proposition Theorem, which one should we pick? 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 Corollary - a specialization of a just presented theorem, in terms more likely to be useful in practice, or of intuitive interest
如何理解Yoneda lemma（米田引理）的重要性？ - 知乎 定理（Yoneda Lemma）：设 C 是一个局部小范畴，则对于任意的函子： F:C\rightarrow Set 和 C 中任意对象 c ，存在从 Nat(hom_{C}(c,-),F) 到 Fc 的双射。 （即函子 Hom_{C}(c,-) 到函子 F 的自然变换可以与集合 Fc 中的元素一一对应起来。
Terminology: Difference between Lemma, Theorem, Definition, Hypothesis . . . Lemma - This is a property that one can derive or prove which is usually technical in nature and is not of primary importance to the overall body of knowledge one is trying to develop Usually lemmas are there as precursors to larger results that one wants to obtain, or introduce a new technique or tool that one can use over and over again