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.

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)