This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.
Algebra
- Abhyankar's lemma
- Aubin–Lions lemma
- Bergman's diamond lemma
- Fitting lemma
- Injective test lemma
- Hua's lemma (exponential sums)
- Krull's separation lemma
- Schanuel's lemma (projective modules)
- Schwartz–Zippel lemma
- Shapiro's lemma
- Stewart–Walker lemma (tensors)
- Whitehead's lemma (Lie algebras)
- Zariski's lemma
Algebraic geometry
Category theory
A commutative diagram that illustrates the five lemma
Linear algebra
Group theory
- Burnside's lemma also known as the Cauchy–Frobenius lemma
- Frattini's lemma (finite groups)
- Goursat's lemma
- Mautner's lemma (representation theory)
- Ping-pong lemma (geometric group theory)
- Schreier's subgroup lemma
- Schur's lemma (representation theory)
- Zassenhaus lemma
Polynomials
Ring theory and commutative algebra
Universal algebra
Analysis
- Fekete's lemma
- Fundamental lemma of calculus of variations
- Hopf lemma
- Sard's lemma (singularity theory)
- Stechkin's lemma (functional and numerical analysis)
- Vitali covering lemma (real analysis)
- Watson's lemma
Complex analysis
Fourier analysis
Differential equations
Differential forms
Functional analysis
Mathematical series
Numerical analysis
Applied mathematics
diagram of a length-8 fast Fourier transform
- Danielson–Lanczos lemma (Fourier transforms)
- Farkas's lemma (linear programming)
- Feld–Tai lemma (electromagnetism)
- Little's lemma (queuing theory)
- Finsler's lemma
Control theory
Computational complexity theory
Cryptography
Formal languages
- Interchange lemma
- Newman's lemma (term rewriting)
- Ogden's lemma
- Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics
Combinatorics
- Cousin's lemma (integrals)
- Dickson's lemma
- Littlewood–Offord lemma
- Pólya–Burnside lemma
- Sperner's lemma
- Ky Fan lemma (combinatorial geometry)
Graph theory
Order theory
Dynamical systems
Geometry
Euclidean geometry
Hyperbolic geometry
Metric spaces
Riemannian geometry
Mathematical logic
- Craig interpolation lemma
- Diagonal lemma
- Lindenbaum's lemma
- Mostowski collapse lemma
- Teichmüller–Tukey lemma also known as Tukey's lemma
- Zorn's lemma; equivalent to the axiom of choice
Set theory
Number theory
- Bézout's lemma
- Dwork's lemma
- Euclid's lemma
- Gauss's lemma
- Hensel's lemma
- Zolotarev's lemma
- Siegel's lemma (Diophantine approximation)
Analytic number theory
Diophantine equations
Sieve theory
Probability theory
- Borel–Cantelli lemma
- Doob–Dynkin lemma
- Itô's lemma (stochastic calculus)
- Lovász local lemma
- Stein's lemma
- Wald's lemma
Statistics
Measure theory
Topology
Differential topology
Fixed-point theory
An example of a covering described by the Knaster–Kuratowski–Mazurkiewicz lemma
Geometric topology
Topological groups and semigroups
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