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
Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Yoneda 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 the 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
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
Knaster–Kuratowski–Mazurkiewicz lemma
Geometric topology Dehn's lemma
Topological groups and semigroups Ellis–Numakura lemma (topological semigroups)