** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

** word, lexeme, lemma, lexicon, vocabulary, terminology

** Noether normalization lemma

** Schwarz – Ahlfors – Pick theorem, an extension of the Schwarz lemma for hyperbolic manifolds

** Schwarz lemma

** Burnside's lemma, a theorem of group theory

** The Lovász local lemma ( proved in 1975, by László Lovász & P. Erdős )

** Algorithmic Lovász local lemma ( proved in 2009, by Robin Moser and Gábor Tardos )

** Krasner's lemma, in number theory

** Hensel's lemma and Henselian rings, named after Kurt

* Sperner's lemma

Sperner's lemma, from 1928, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.

In mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which follows from it.

Sperner's lemma states that every Sperner coloring ( described below ) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.

* Sperner's lemma

It is sometimes called Sperner's lemma, but that name also refers to another result on coloring.

By contrast, the Brouwer fixed-point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point ( See also Sperner's lemma ).