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Lemma (mathematics)

Definition

In mathematics and other fields, a lemma is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however, a lemma can also turn out to be more important than originally thought.

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Abstract logic Ackermann set theory Aleph number Algebraic logic Alphabet (formal languages)Ancient Greek Argument Argument mapping Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Bijection Binary operation Boolean algebra Boolean algebras canonically defined Boolean function Burnside's lemma Bézout's identity Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Carl Friedrich Gauss Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Co-premise Codomain Compactness theorem Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable set Concrete category Conservative extension Consistency Constructible universe Construction of the 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(disambiguation)General set theory Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Inference Inference objection Infinite-valued logic Infinite set Informal logic Information theory Inhabited set Injective function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism Itô's lemma Jordan's lemma Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Lemma (morphology)Lindström's theorem List of Hilbert systems List of axioms List of first-order theories List of formal systems List of lemmas List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Lovász local lemma Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Mathematical logic Mathematical object Mathematical proof Mathematics Metalanguage Minimal axioms for Boolean algebra Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Nakayama's lemma Natural deduction Negation New Foundations Noether normalization lemma Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Objection (argument)Open formula Operation (mathematics)Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Partition of a set Peano axioms Philosophy Philosophy of mathematics PlanetMath Poincaré lemma Porism Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Proof of impossibility Proof theory Proposition Propositional calculus Propositional formula Propositional variable Quantifier (logic)Quantifier rank Recursion Recursive set Relation (mathematics)Reverse mathematics Riesz's lemma Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Schur's lemma Schwarz's lemma Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Skolem arithmetic Small cancellation theory Society for Industrial and Applied Mathematics Soundness Spectrum of a sentence Spectrum of a theory Sperner's lemma Square of opposition Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Three-valued logic Timeline of mathematical logic Transfer principle Transitive set True arithmetic Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Urelement Urysohn's lemma Validity (logic)Variable (mathematics)Venn diagram Vitali covering lemma Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Yoneda lemma Zariski's lemma Zermelo–Fraenkel set theory Zorn's lemma

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