List of lemmas

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.

This list is incomplete; you can help by expanding it.

0 to 9

• 0/1 Sorting lemma (comparison-exchange algorithms)

A to E

• Abel's lemma (mathematical series)
• Abhyankar's lemma (algebraic geometry)
• Archimedes' lemmas (euclidean geometry)
• Artin–Rees lemma (commutative algebra) named after Emil Artin and Elmer Rees
• Aubin–Lions lemma
• Barbalat's lemma (dynamical systems)
• Basic perturbation lemma (computer science, algebra)
• Berge's lemma (graph theory) named after Claude Berge
• Bézout's lemma (number theory)
• Bhaskara's lemma (Diophantine equations)
• Borel's lemma (partial differential equations)
• Borel–Cantelli lemma (probability theory)
• Bounding lemmas, of which there are several
• Bramble–Hilbert lemma (numerical analysis)
• Brezis–Lions lemma
• Burnside's lemma also known as the Cauchy–Frobenius lemma (group theory)
• Céa's lemma (numerical analysis)
• Closed map lemma (topology)
• Closeness lemma (functions)
• Commutation lemmas, of which there are several
• Composition lemmas, of which there are several
• Cotlar–Stein lemma (functional analysis)
• Couchman's lemma (set theory)
• Counting lemmas, of which there are several
• Cousin's lemma (integrals)
• Covering lemma (set theory)
• Craig interpolation lemma (mathematical logic)
• Crossing lemma (knot theory, graph theory)
• Danielson–Lanczos lemma (Fourier transforms)
• Davis–Figiel–Johnson–Pelczynski factorization lemma
• Dehn's lemma (geometric topology)
• Delta lemma (set theory)
• Deny–Lions lemma
• Diagonal lemma (mathematical logic)
• Dickson's lemma (combinatorics)
• Dobrushin's lemma (point process theory)
• Dwork's lemma (number theory)
• Dynkin lemma (set theory)
• Ehrling's lemma (functional analysis)
• Ellis–Numakura lemma (topological semigroups)
• Estimation lemma (contour integrals)
• Euclid's lemma (number theory)
• Expander mixing lemma (graph theory)
• Expansion lemmas, of which there are several

F to J

• Factorization lemma (measure theory)
• Farkas's lemma (linear programming)
• Fatou's lemma (measure theory)
• Feinstein's fundamental lemma (probability theory)
• Fekete's lemma (mathematical analysis)
• Feld–Tai lemma (electromagnetism)
• Finsler's lemma (control theory)
• Fitting lemma (abstract algebra)
• Five lemma (homological algebra)
• Fixed-point lemma for normal functions (axiomatic set theory)
• Fodor's lemma (set theory)
• Forking lemma (cryptography)
• Frattini's lemma (finite groups)
• Friedrichs' lemma
• Frostman's lemma (geometric measure theory)
• Fundamental lemma (Langlands program)
• Fundamental lemma of calculus of variations
• Fundamental lemma of interpolation theory (numerical analysis)
• Fundamental lemma of sieve theory (sieve theory)
• Gauss's lemmas (polynomials | number theory | Riemannian geometry)
• Glivenko–Cantelli lemma (statistics)
• Gödel's diagonal lemma (mathematical logic)
• Goursat's lemma (algebra)
• Gronwall's inequality Gronwall's lemma (inequalities)
• Gromov's convex integration lemma
• Gross's integration lemma
• Grothendieck lemma (differential forms) named after Alexander Grothendieck
• Handshaking lemma (graph theory)
• Hardy–Littlewood lemma (differentiation)
• Harmonic series summation lemma
• Haruki's lemma (plane geometry)
• Hartogs' lemma (several complex variables)
• Hayashi's connecting lemma
• Hensel's lemma (commutative rings)
• Higman's lemma (order theory)
• Hindley–Rosen lemma
• Horseshoe lemma (homological algebra)
• Hotelling's lemma (envelope theory microeconomics)
• Hua's lemma (analytic number theory)
• Huet's strong confluence lemma
• Injective test lemma (homological algebra)
• Integration lemmas, of which there are several
• Iteration lemmas, of which there are several
• Itō's lemma (stochastic calculus)
• Johnson–Lindenstrauss lemma (Euclidean geometry)
• Jordan's lemma (complex analysis)

K to O

• Kalman–Yakubovich–Popov lemma (system analysis, control theory)
• Kelly's lemma (graph theory)
• Klop's lemma (lambda calculus)
• Knaster–Kuratowski–Mazurkiewicz lemma (fixed-point theory)
• Knuth's 0-1 sorting lemma
• König's lemma (graph theory)
• Kronecker's lemma (infinite sums)
• Krull's separation lemma
• Lambda lemma for normally hyperbolic invariant manifolds (topology)
• Lax–Milgram lemma (differential equations)
• Lebesgue's number lemma (dimension theory)
• Leftover hash-lemma (cryptography)
• Lindelöf's lemma (topology)
• Lindenbaum's lemma (mathematical logic)
• Lions' lemma
• Little's lemma (queuing theory)
• Littlewood–Offord lemma (combinatorics)
• Łojasiewicz factorization lemma
• Lovász local lemma (probability theory)
• Margulis lemma (hyperbolic geometry)
• Matrix determinant lemma (matrix theory)
• Matrix inversion lemma
• Mautner's lemma (representation theory)
• Morse lemma (differential topology)
• Moschovakis' coding lemma (set theory)
• Mostowski collapse lemma (mathematical logic)
• Nakayama lemma (commutative algebra)
• Newman's lemma (term rewriting)
• Neyman–Pearson lemma (statistics)
• Nine lemma (homological algebra)
• Noether's normalization lemma (commutative algebra)
• Ogden's lemma (formal languages)

P to T

• Parallel moves lemma
• Parity lemmas, of which there are several
• Partition lemmas, of which there are several
• Ping-pong lemma (geometric group theory)
• Piling-up lemma (linear cryptanalysis)
• Poincaré lemma of closed and exact differential forms (differential forms)
• Pólya–Burnside lemma
• Pugh's closing lemma
• Pumping lemma (formal languages) sometimes called the Bar-Hillel lemma
• Quantifier reversal lemma
• Racah factorization lemma
• Rasiowa–Sikorski lemma (set theory)
• Recursion lemmas, of which there are several
• Reduction lemmas, of which there are several
• Ricci's lemma (tensors)
• Riemann–Lebesgue lemma (harmonic analysis)
• Rigidity lemma (algebraic geometry)
• Riesz's lemma (functional analysis)
• Robbins lemma (statistics)
• Rouche–Kronecker–Campelli lemma (linear algebra)
• Sard's lemma (mathematical analysis, singularity theory)
• Satisfiability coding lemma
• Schanuel's lemma (projective modules)
• Schreier's subgroup lemma (group theory)
• Schur's lemma (representation theory)
• Schwarz lemma (complex analysis)
• Schwartz–Zippel lemma (polynomials)
• Separation lemmas, of which there are several
• Shadowing lemma (geometry)
• Shephard's lemma (microeconomics)
• Short five lemma (homological algebra)
• Siegel's lemma (Diophantine approximation)
• Snake lemma (homological algebra)
• Sperner's lemma (combinatorics)
• Splitting lemma (homological algebra)
• Stein's lemma (probability theory)
• Stewart–Walker lemma (tensors)
• Szemerédi regularity lemma (graph theory)
• Transformation lemmas, of which there are several
• Tube lemma (topology)
• Tukey's lemma (metamathematics) also known as the Teichmüller–Tukey lemma

U to Z

• Ultrafilter lemma (order theory)
• Uniform bounding lemma
• Urysohn's lemma (general topology)
• Varadhan's integration lemma
• Vaughan's lemma (analytic number theory)
• Verdu–Han lemma (probability theory)
• Vitali covering lemma (real analysis)
• Vizing's adjacency lemma (graph theory)
• Wald's lemma (probability theory)
• Watson's lemma
• Weyl's lemma (Laplace equation) (partial differential equations)
• Whitehead's lemma (Lie algebras)
• Yao's XOR lemma (cryptography)
• Yoneda lemma, (category theory)
• Zassenhaus lemma (group theory)
• Zolotarev's lemma (number theory)
• Zorn's lemma also known as the Kuratowski–Zorn lemma (set theory)