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
edit- 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
editCategory theory
editLinear algebra
editGroup theory
edit- 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
editRing theory and commutative algebra
edit- Artin–Rees lemma
- Hensel's lemma (commutative rings)
- Nakayama lemma
- Noether's normalization lemma
- Prime avoidance lemma
Universal algebra
editAnalysis
edit- 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
edit- Estimation lemma (contour integrals)
- Hartogs's lemma (several complex variables)
- Jordan's lemma
- Lemma on the Logarithmic derivative
- Schwarz lemma
Fourier analysis
editDifferential equations
edit- Borel's lemma (partial differential equations)
- Grönwall's lemma
- Lax–Milgram lemma
- Pugh's closing lemma
- Weyl's lemma (Laplace equation) (partial differential equations)
Differential forms
editFunctional analysis
editMathematical series
editNumerical analysis
editApplied mathematics
edit- Danielson–Lanczos lemma (Fourier transforms)
- Farkas's lemma (linear programming)
- Feld–Tai lemma (electromagnetism)
- Little's lemma (queuing theory)
- Finsler's lemma
Control theory
editComputational complexity theory
editCryptography
editFormal languages
edit- Interchange lemma
- Newman's lemma (term rewriting)
- Ogden's lemma
- Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics
editCombinatorics
edit- Cousin's lemma (integrals)
- Dickson's lemma
- Littlewood–Offord lemma
- Pólya–Burnside lemma
- Sperner's lemma
- Ky Fan lemma (combinatorial geometry)
Graph theory
edit- Berge's lemma
- Counting lemma
- Crossing lemma
- Expander mixing lemma
- Handshaking lemma
- Kelly's lemma
- Kőnig's lemma
- Szemerédi regularity lemma
Order theory
editDynamical systems
editGeometry
editEuclidean geometry
editHyperbolic geometry
editMetric spaces
editRiemannian geometry
editMathematical logic
edit- 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
editNumber theory
edit- 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
editDiophantine equations
editSieve theory
editProbability theory
edit- Borel–Cantelli lemma
- Doob–Dynkin lemma
- Itô's lemma (stochastic calculus)
- Lovász local lemma
- Stein's lemma
- Wald's lemma