List of lemmas

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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

• Abhyankar's lemma
• Fundamental lemma (Langlands program)

Category theory

A commutative diagram that illustrates the five lemma

• Five lemma
• Horseshoe lemma
• Nine lemma
• Short five lemma
• Snake lemma
• Splitting lemma

Linear algebra

• Matrix determinant lemma
• Matrix inversion lemma

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

• Gauss's lemma (polynomials)
• Schwartz–Zippel lemma

Ring theory and commutative algebra

• Artin–Rees lemma
• Hensel's lemma (commutative rings)
• Nakayama lemma
• Noether's normalization lemma
• Prime avoidance lemma

Universal algebra

• Jónsson's lemma

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

• Estimation lemma (contour integrals)
• Hartogs's lemma (several complex variables)
• Jordan's lemma
• Lemma on the Logarithmic derivative
• Schwarz lemma

Fourier analysis

• Riemann–Lebesgue lemma

Differential equations

• 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

• Poincaré lemma of closed and exact differential forms

Functional analysis

• Cotlar–Stein lemma
• Ehrling's lemma
• Riesz's lemma

Mathematical series

• Abel's lemma
• Kronecker's lemma

Numerical analysis

• Bramble–Hilbert lemma
• Céa's lemma

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

• Finsler's lemma
• Hautus lemma
• Kalman–Yakubovich–Popov lemma

Computational complexity theory

• Isolation lemma
• Switching lemma

Cryptography

• Forking lemma
• Leftover hash lemma
• Piling-up lemma (linear cryptanalysis)
• Yao's XOR lemma

Formal languages

• Interchange lemma
• Newman's lemma (term rewriting)
• Ogden's lemma
• Pumping lemma sometimes called the Bar-Hillel lemma

Microeconomics

• Hotelling's lemma
• Shephard's lemma

Combinatorics

• Cousin's lemma (integrals)
• Dickson's lemma
• Littlewood–Offord lemma
• Pólya–Burnside lemma
• Sperner's lemma
• Ky Fan lemma (combinatorial geometry)

Graph theory

• Berge's lemma
• Counting lemma
• Crossing lemma
• Expander mixing lemma
• Handshaking lemma
• Kelly's lemma
• Kőnig's lemma
• Szemerédi regularity lemma

Order theory

• Higman's lemma
• Ultrafilter lemma

Dynamical systems

• Barbalat's lemma
• Kac's lemma (ergodic theory)

Geometry

• Shadowing lemma
• Big-little-big lemma (mathematics of paper folding)
• Gordan's lemma
• Hilbert's lemma

Euclidean geometry

• Archimedes's lemmas
• Johnson–Lindenstrauss lemma (Euclidean geometry)

Hyperbolic geometry

• Margulis lemma

Metric spaces

• Lebesgue's number lemma (dimension theory)

Riemannian geometry

• Gauss's lemma (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

• Covering lemma
• Delta lemma
• Dynkin lemma
• Fodor's lemma
• Fixed-point lemma for normal functions (axiomatic set theory)
• Moschovakis coding lemma
• Rasiowa–Sikorski lemma

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

• Hua's lemma
• Vaughan's lemma

Diophantine equations

• Bhaskara's lemma

Sieve theory

• Fundamental lemma of 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

• Glivenko–Cantelli lemma
• Neyman–Pearson lemma
• Robbins lemma

Measure theory

• Factorization lemma
• Fatou's lemma
• Frostman's lemma (geometric measure theory)
• Malliavin's absolute continuity lemma

Topology

• Lindelöf's lemma
• Urysohn's lemma
• Tube lemma

Differential topology

• Morse lemma

Fixed-point theory

An example of a covering described by the Knaster–Kuratowski–Mazurkiewicz lemma

• Knaster–Kuratowski–Mazurkiewicz lemma

Geometric topology

• Dehn's lemma

Topological groups and semigroups

• Ellis–Numakura lemma (topological semigroups)