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 edit
Category theory edit
Linear algebra edit
Group 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 edit
Ring theory and commutative algebra edit
- Artin–Rees lemma
- Hensel's lemma (commutative rings)
- Nakayama lemma
- Noether's normalization lemma
- Prime avoidance lemma
Universal algebra edit
Analysis 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 edit
Differential 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 edit
Functional analysis edit
Mathematical series edit
Numerical analysis edit
Applied 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 edit
Computational complexity theory edit
Cryptography edit
Formal languages edit
- Interchange lemma
- Newman's lemma (term rewriting)
- Ogden's lemma
- Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics edit
Combinatorics 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 edit
Dynamical systems edit
Geometry edit
Euclidean geometry edit
Hyperbolic geometry edit
Metric spaces edit
Riemannian geometry edit
Mathematical 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 edit
Number 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 edit
Diophantine equations edit
Sieve theory edit
Probability theory edit
- Borel–Cantelli lemma
- Doob–Dynkin lemma
- Itô's lemma (stochastic calculus)
- Lovász local lemma
- Stein's lemma
- Wald's lemma