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.
0/1 Sorting lemma (comparison-exchange algorithms)
Abel's lemma (mathematical series)
Abhyankar's lemma (algebraic geometry)
Archimedes's lemmas (euclidean geometry)
Artin–Rees lemma (commutative algebra)
Aubin–Lions lemma
Barbalat's lemma (dynamical systems)
Basic perturbation lemma (computer science, algebra)
Berge's lemma (graph theory)
Bézout's lemma (number theory)
Bhaskara's lemma (Diophantine equations)
Blichfeldt's lemma
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)
Doob–Dynkin lemma (probability 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
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's 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)
Grönwall's inequality Grönwall's lemma (inequalities)
Gromov's convex integration lemma
Gross's integration lemma
Grothendieck lemma (differential forms)
Handshaking lemma (graph theory)
Hardy–Littlewood lemma (differentiation)
Harmonic series summation lemma
Haruki's lemma (plane geometry)
Hartogs's lemma (several complex variables)
Hayashi's connecting lemma
Hensel's lemma (commutative rings)
Higman's lemma (order theory)
Hindley–Rosen lemma
Hopf lemma
Horseshoe lemma (homological algebra)
Hotelling's lemma (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
Itô's lemma (stochastic calculus)
Johnson–Lindenstrauss lemma (Euclidean geometry)
Jónsson's lemma
Jordan's lemma (complex analysis)
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
Kőnig'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's lemma
Little's lemma (queuing theory)
Littlewood–Offord lemma (combinatorics)
Łojasiewicz factorization lemma
Lovász local lemma (probability theory)
Malliavin's absolute continuity lemma (measure 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)
Mother's Note lemma
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)
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
Prime avoidance 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)
Stechkin's lemma (functional and numerical analysis)
Stein's lemma (probability theory)
Stewart–Walker lemma (tensors)
Switching lemma (computational complexity theory)
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
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)
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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