WikiLeanAbout & method

Wikidata concept links

Every Wikipedia mathematics concept WikiLean has matched to a formalized declaration in Mathlib4, keyed by its Wikidata item. This is the dataset behind a proposed Wikidata property, “formalized as (Lean/Mathlib)” — the goal is for these links to live in Wikidata itself, queryable via SPARQL and maintainable by the community. ← back to all articles

199 concepts 2271 formalized declarations
Download the dataset as RDF Turtle: wikilean.ttl (predicate wl:formalizedAs + rdfs:seeAlso into the Mathlib docs).
WikidataConceptMathlib declaration(s)
Q2040zero_add, mul_zero, Nat.zero_le, Even.zero, Ideal.bot_prime, add_zero, sub_zero, inv_zero, pow_zero, Finset.prod_empty, Nat.factorial_zero, Cardinal.mk_eq_zero, Ordinal.bot_eq_zero, Zero, Pi.zero_apply, CategoryTheory.Limits.IsZero, zero_div, neg_zero
Q1991Nat.succ, one_mul, one_pow, MulOneClass, IsUnit, Nat.factorial_one, Finset.prod_empty, unitInterval, IsProbabilityMeasure
Q2002Nat.succ, Nat.Prime.even_iff, even_iff_two_dvd, ZMod.instField, ZMod.intCast_zmod_eq_zero_iff_dvd, CharTwo.add_self_eq_zero, Function.Involutive
Q2024Nat.sum_four_squares, IsKleinFour
Q181296Abelian groupCommGroup, PUnit.commGroup, Int.instAddCommGroup, IsCyclic.commGroup, NonUnitalNonAssocRing, instCommGroupUnits, Subgroup.normal_of_isMulCommutative, Subgroup.toCommGroup, CommGroup.is_simple_iff_prime_card, forget₂AddCommGroupIsEquivalence, AddCommGroup.toIntModule, AddCommGroup.equiv_free_prod_directSum_zmod, AddMonoidHom.add, Module.rank, Module.rank_eq_zero_iff_isTorsion, Subgroup.center, Subgroup.center_eq_top_iff, commGroupOfCyclicCenterQuotient, AddCommGroup.equiv_directSum_zmod_of_finite, isCyclic_of_prime_card, IsPGroup.commutative_of_card_eq_prime_sq, ZMod.chineseRemainder, AddGroup.FG, FreeAbelianGroup.lift, Module.Basis.SmithNormalForm, Int.instIsAddCyclic, DivisibleBy, Monoid.IsTorsion, Monoid.IsTorsionFree, Submodule.instIsTorsionFree, AddCommGrpCat.instAbelian
Q180969Algebraic geometryMvPolynomial, MvPolynomial.zeroLocus, MvPolynomial.vanishingIdeal, PrimeSpectrum.zariskiTopology, MvPolynomial.vanishingIdeal_zeroLocus_eq_radical, MvPolynomial.isNoetherianRing, IsIrreducible, TopologicalSpace.NoetherianSpace.exists_finset_irreducible, PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime, ContinuousMap.exists_restrict_eq, AlgebraicGeometry.Scheme.functionField, AlgebraicGeometry.Scheme.RationalMap, Projectivization, ProjectiveSpectrum.zeroLocus, AlgebraicGeometry.Scheme, AlgebraicGeometry.AffineScheme.equivCommRingCat
Q2553675Algebraic K-theoryMatrix.transvection
Q168817Algebraic numberIsAlgebraic, isAlgebraic_int, algebraicClosure, Transcendental, isAlgebraic_rat, GaussianInt, Real.isAlgebraic_cos_rat_mul_pi, IsFractionRing.isAlgebraic_iff, minpoly, Algebraic.countable, IntermediateField.adjoin.finiteDimensional, IntermediateField.finiteDimensional_adjoin, Subalgebra.algebraicClosure, algebraicClosure.isAlgClosure, IsIntegral, integralClosure, NumberField.RingOfIntegers
Q613048Algebraic number theoryPythagoreanTriple, NumberField.Units.exist_unique_eq_mul_prod, Real.exists_int_int_abs_mul_sub_le, Ideal, Prime, Associated, UniqueFactorizationMonoid, Irreducible, Ideal.uniqueFactorizationMonoid, Nat.Prime.sq_add_sq, FractionalIdeal, ClassGroup, NumberField.classNumber, NumberField.InfinitePlace.IsReal, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, NumberField.mixedEmbedding, NumberField.mixedEmbedding.mixedSpace, NumberField.discr, padicNorm, Rat.AbsoluteValue.equiv_real_or_padic, NumberField.FinitePlace, NumberField.AdeleRing, Int.isUnit_iff, NumberField.Units.regulator, NumberField.dedekindZeta, IsDedekindDomain.HeightOneSpectrum.adicCompletion, NumberField.RingOfIntegers.instFintypeClassGroup, legendreSym.quadratic_reciprocity, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT
Q212803Algebraic topologysubgroupIsFreeOfIsFree, HomotopyGroup, FundamentalGroup, singularHomologyFunctor, HomologicalComplex.homology, IsManifold, Geometry.SimplicialComplex, CWComplex, AddCommGroup.equiv_free_prod_directSum_zmod, Complex.isAlgClosed
Q648995Algebraic varietyMvPolynomial.vanishingIdeal_zeroLocus_eq_radical, MvPolynomial.zeroLocus, MvPolynomial.vanishingIdeal, ProjectiveSpectrum.zeroLocus, WeierstrassCurve.IsElliptic, AlgebraicGeometry.Scheme
Q8366AlgorithmList.mergeSort
Q333464Analysis of algorithmsAsymptotics.IsBigO
Q58413Ancient Greek mathematicsEuclideanGeometry.Sphere.thales_theorem, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, irrational_sqrt_natCast_iff, Nat.gcd, Nat.exists_infinite_primes, Even.mul_right, Int.ModEq, DedekindCut
Q11352AngleEuclideanGeometry.angle, Orientation.oangle, EuclideanGeometry.angle_add_of_ne_of_ne, Sbtw.oangle_eq_left_right, EuclideanGeometry.angle_add_angle_add_angle_eq_pi, Real.Angle.angle_eq_iff_two_pi_dvd_sub, InnerProductGeometry.cos_angle, InnerProductGeometry.angle
Q11205ArithmeticNat, Int, Cardinal, Ordinal, Rat, Irrational, Real, MulOneClass, mul_inv_cancel, CommMagma, Semigroup, Add, Finset.sum, sub_eq_add_neg, add_zero, add_comm, Mul, div_eq_mul_inv, mul_one, mul_comm, Monoid.npow, Real.rpow, Real.log, nsmul_eq_mul, npowBinRec, Nat.primeFactorsList_unique, Nat.exists_infinite_primes, FermatLastTheorem, div_add_div_same, div_mul_div_comm, Real.rpow_pos_of_pos, round, ZMod, Matrix, Nat.zero, Nat.succ, Nat.succ_injective, Nat.succ_ne_zero, Nat.rec
Q755991Atiyah–Singer index theoremIsManifold, ContMDiffVectorBundle
Q17736AxiomFirstOrder.Language.Theory, ConditionallyCompleteLinearOrderedField.uniqueOrderRingIso, FirstOrder.Language.Theory.exists_elementaryEmbedding_card_eq
Q220680Banach fixed-point theoremContractingWith, ContractingWith.exists_fixedPoint, ContractingWith.apriori_dist_iterate_fixedPoint_le, LipschitzWith, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, HasStrictFDerivAt.toOpenPartialHomeomorph, ContractingWith.isFixedPt_fixedPoint_iterate
Q182505Bayes' theoremProbabilityTheory.cond_eq_inv_mul_cond_mul, ProbabilityTheory.cond, ProbabilityTheory.cond_mul_eq_inter, ProbabilityTheory.posterior_eq_withDensity, MeasureTheory.Measure.withDensity_rnDeriv_eq
Q4907197Bijection, injection and surjectionFunction.Injective, Function.Surjective, Function.Bijective, Function.injective_iff_hasLeftInverse, Equiv.ofInjective, Function.Injective.comp, Function.Embedding.injective, Function.surjective_iff_hasRightInverse, Setoid.quotientKerEquivOfSurjective, Function.Surjective.comp, Function.bijective_iff_has_inverse, Function.Bijective.comp, Equiv.Perm.permGroup, Cardinal.eq, Cardinal.le_def, Function.bijective_id, Real.expOrderIso, Set.image_preimage_subset, CategoryTheory.Types.mono_iff_injective
Q185547Binomial distributionProbabilityTheory.binomial, PMF.bernoulli, PMF.binomial_one_eq_bernoulli, PMF.binomial_apply, ProbabilityTheory.tendsto_choose_mul_pow_of_tendsto_mul_atTop
Q4973304Boolean algebra (structure)DistribLattice.booleanAlgebraOfComplemented, BooleanAlgebra.toBooleanRing, BooleanAlgebra, PUnit.instBooleanAlgebra, inf_eq_left, BooleanAlgebra.toBoundedOrder, compl_unique, OrderDual.instBooleanAlgebra, Bool.instBooleanAlgebra, Set.instBooleanAlgebra, TopologicalSpace.Clopens.instBooleanAlgebra, instBooleanAlgebraSubtypeIsIdempotentElem, BoundedLatticeHom, map_compl', OrderIso, BooleanRing.toBooleanAlgebra, boolRingCatEquivBoolAlg, Order.Ideal, Order.Ideal.IsPrime, Order.Ideal.IsMaximal, Order.Ideal.IsPrime.isMaximal, Order.PFilter, Ultrafilter.exists_le, GeneralizedBooleanAlgebra
Q1144897Brouwer fixed-point theoremexists_mem_Icc_isFixedPt_of_mapsTo
Q214728Bézier curveAffineMap.lineMap, AffineMap.lineMap_apply_module, bernsteinPolynomial
Q263809C*-algebraCStarAlgebra, ZeroAtInftyContinuousMap.instNonUnitalCommCStarAlgebra, CStarRing.norm_star_mul_self, StarAlgHom, NonUnitalStarAlgHom.norm_apply_le, StarAlgEquiv, StarSubalgebra.cstarAlgebra, IsSelfAdjoint, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, CStarAlgebra.increasingApproximateUnit, Matrix.instCStarRing, ContinuousLinearMap.instCStarAlgebra, gelfandStarTransform, VonNeumannAlgebra
Q729471Cantor's diagonal argumentUncountable, Function.cantor_surjective, Cardinal.not_countable_real, Cardinal.cantorFunction_injective, Cardinal.cantor, Cardinal.le_def, Function.Embedding.schroeder_bernstein, ComputablePred.halting_problem
Q4049983CardinalityCardinal.mk, Cardinal.eq, Set, Cardinal.aleph0, Function.Injective, Function.Surjective, Function.Bijective, Cardinal.le_def, schroeder_bernstein, Ordinal.type, WellOrderingRel, Countable, Set.Countable, Rat, Cardinal.mkRat, IsAlgebraic, Transcendental, Algebraic.countable, Uncountable, Cardinal.not_countable_real, Cardinal.mk_set_nat, Cardinal.mk_real, Cardinal.cantor, Cardinal, Nat.card, Finite.injective_iff_surjective, Cardinal.add_def, Cardinal.mk_prod, Finset.inclusion_exclusion_card_biUnion, Finite, Cardinal.aleph, Ordinal, Ordinal.omega0, Ordinal.omega, Cardinal.aleph_succ, Cardinal.mem_range_aleph_iff, Cardinal.mul_def, Cardinal.sum_lt_prod, Cardinal.add_eq_self, Cardinal.mk_arrow, Cardinal.power_zero, Cardinal.mk_set, not_small_cardinal, Real, Cardinal.continuum, Cardinal.mk_Ioo_real, Real.tanOrderIso, cantorSet, Cardinal.continuum_power_aleph0, Cardinal.aleph0_lt_continuum, Cardinal.beth, ZFSet.omega, ZFSet.powerset, ZFSet.choice, Cardinal.IsInaccessible, ZFSet.vonNeumann, Finset.card_lt_card
Q22952648Cardinality of the continuumCardinal.continuum, Cardinal.mk_set_nat, Cardinal.eq, Cardinal.mk_Ioo_real, Cardinal.not_countable_real, Cardinal.cantor, Function.Embedding.schroeder_bernstein, Cardinal.mk_real, Cardinal.continuum_power_aleph0, Cardinal.beth, Cardinal.sum_lt_prod, Algebraic.cardinalMk_of_countable_of_charZero
Q719395Category (mathematics)CategoryTheory.Category, CategoryTheory.Functor, Quiver.Hom, CategoryTheory.SmallCategory, CategoryTheory.LocallySmall, CategoryTheory.types, CategoryTheory.RelCat, CategoryTheory.Discrete, Preorder.smallCategory, Quiver.IsThin, CategoryTheory.SingleObj, CategoryTheory.Iso, CategoryTheory.Groupoid, FundamentalGroupoid, CategoryTheory.Paths, Preord, CategoryTheory.ConcreteCategory, GrpCat, Ab, CategoryTheory.Cat, CategoryTheory.Functor.category, CategoryTheory.Category.opposite, CategoryTheory.prod, CategoryTheory.Quotient, CategoryTheory.Over, CategoryTheory.Under, CategoryTheory.Localization, CategoryTheory.Mono, CategoryTheory.Epi, CategoryTheory.IsSplitEpi, CategoryTheory.IsSplitMono, CategoryTheory.IsIso, CategoryTheory.End, CategoryTheory.End.monoid, CategoryTheory.Aut, CategoryTheory.IsSplitEpi.epi, CategoryTheory.Preadditive, CategoryTheory.Abelian, AddCommGrpCat, CategoryTheory.EnrichedCategory, CategoryTheory.Limits.HasLimits, CategoryTheory.Limits.Types.hasLimitsOfSize, CategoryTheory.CartesianClosed
Q656772Cayley–Hamilton theoremMatrix.aeval_self_charpoly, Matrix.charpoly, Matrix.pow_eq_aeval_mod_charpoly, Matrix.minpoly_dvd_charpoly, Matrix.charpoly_fin_two, Matrix.adjugate, Polynomial.div_modByMonic_unique, Submodule.eq_bot_of_le_smul_of_le_jacobson_bot
Q166314Chaos theoryMulAction.IsTopologicallyTransitive
Q193878Chinese remainder theoremNat.chineseRemainderOfFinset, ZMod.chineseRemainder, Nat.chineseRemainder_modEq_unique, Ideal.quotientInfToPiQuotient_surj, Nat.chineseRemainder, Nat.chineseRemainderOfList, Ideal.quotientInfRingEquivPiQuotient, Lagrange.interpolate, Nat.chineseRemainder', Ideal.isCoprime_iff_exists, Ideal.prod_eq_iInf_of_pairwise_isCoprime, CompleteOrthogonalIdempotents, linearIndependent_monoidHom
Q5150824Combinatorial designConfiguration.ProjectivePlane, Configuration.HasLines.card_le
Q848569Complete metric spaceCompleteSpace, CauchySeq, IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosed, IsClosed.isComplete, Real.instCompleteSpace, Pi.complete, BoundedContinuousFunction.instCompleteSpace, Padic.instCompleteSpace, IsCompact.isComplete, isCompact_iff_totallyBounded_isComplete, ProperSpace.isCompact_closedBall, IsComplete.isClosed, BaireSpace.of_completelyPseudoMetrizable, ContractingWith.fixedPoint, HasStrictFDerivAt.toOpenPartialHomeomorph, UniformSpace.Completion, Completion.extension_unique, AbstractCompletion.compareEquiv, Completion.instPseudoMetricSpace, Completion.coe_isometry, Real.equivCauchy, Padic, UniformSpace.Completion.instNormedSpace, UniformSpace.Completion.innerProductSpace, IsCompletelyMetrizableSpace, PolishSpace, IsTopologicalGroup.completeSpace_rightUniformSpace_iff_leftUniformSpace, Cauchy
Q1148456Computable functionComputable, Nat.Partrec, ComputablePred, REPred, Language, Nat.Primrec.add, Computable.comp, ack, ComputableIn
Q205084Computational complexity theoryTuring.TM2ComputableInPolyTime, Turing.TM0.Machine
Q319141ConjectureFermatLastTheorem, SimplyConnectedSpace.nonempty_homeomorph_sphere_three, ContinuousMap.HomotopyEquiv.nonempty_homeomorph_sphere, RiemannHypothesis
Q208416Continuum hypothesisCardinal.sum_lt_prod, Cardinal.eq, Cardinal.mkRat, Cardinal.aleph0_lt_continuum, Cardinal.aleph_one_le_iff, Cardinal.power_le_power_left
Q193657Convex setConvex, convexHull, ConvexOn, convex_iff_add_mem, Convex.affine_image, Convex.isPathConnected, StrictConvex, AbsConvex, convex_iff_ordConnected, Convex.sum_mem, Finset.centerMass, convex_empty, convex_sInter, DirectedOn.convex_sUnion, IsExtreme, Set.extremePoints, closure_convexHull_extremePoints, StrictConvexSpace.extremePoints_closedBall_eq_sphere, Convex.closure, Convex.add_smul, convexHull_min, Set.add, Set.addMonoid, convexHull_add, convexHull_sum, convexHullAddMonoidHom, IsCompact.add, IsClosed.add_left_of_isCompact, StarConvex, Convex.starConvex, Set.OrdConnected, Convexity.ConvexSpace
Q66707394Countable setSet.Countable, Denumerable, Function.cantor_surjective, countable_iff_exists_injective, countable_iff_exists_surjective, Uncountable, Infinite, Equiv, Cardinal.eq, Cardinal.not_countable_real, Cardinal.mk_real, Set.Finite.countable, Set.countable_infinite_iff_nonempty_denumerable, Denumerable.prod, Algebraic.countable, Subtype.countable, Set.Countable.mono, Set.Countable.prod, Denumerable.int, Set.Countable.union, Set.countable_iUnion, denumerableList, Set.countable_setOf_finite_subset, Function.Injective.countable, Cardinal.cantor, IsWellOrder
Q7874246Coxeter groupCoxeterMatrix.Group, CoxeterSystem, CoxeterSystem.simple_mul_simple_self, CoxeterMatrix, CoxeterSystem.length, CoxeterSystem.IsReduced, CoxeterSystem.lengthParity
Q190556De Moivre's formulaComplex.cos_add_sin_mul_I_pow, Complex.exp_mul_I, Complex.cos_three_mul, Polynomial.Chebyshev.T_complex_cos
Q1058314DiffeomorphismDiffeomorph, Diffeomorph.toHomeomorph, IsLocalDiffeomorph, IsImmersion
Q628007Difference engineshift_eq_sum_fwdDiff_iter, Polynomial.fwdDiff_iter_degree_eq_factorial, AnalyticAt, taylorWithin, Lagrange.interpolate
Q149999Differential calculusderiv, HasDerivAt, deriv_pow, hasFDerivAt_iff_isLittleO, IsLocalExtr.deriv_eq_zero, exists_deriv_eq_zero, exists_deriv_eq_slope, is_const_of_deriv_eq_zero, taylor_mean_remainder_lagrange, isLocalMax_of_deriv, isLocalMin_of_deriv_deriv_pos, IsLocalExtr.fderiv_eq_zero, ImplicitFunctionData.implicitFunction, HasStrictFDerivAt.to_localInverse
Q11214Differential equationHarmonicAt
Q188444Differential geometryIsRiemannianManifold, LieGroup, GroupLieAlgebra
Q2502381Differential geometry of surfacesContDiffOn, EuclideanSpace.instIsManifoldSphere, VectorField.mlieBracket, RiemannianMetric, pathELength_comp_of_monotoneOn, EuclideanGeometry.law_cos
Q272621Dirac equationRepresentation
Q1195339Directed acyclic graphSimpleGraph.hasse, Quiver.Arborescence
Q20968946Discrete calculusslope, BoxIntegral.integralSum, intervalIntegral.integral_eq_sub_of_hasDerivAt, Finset.sum_range_sub, fwdDiff, fwdDiff_const, fwdDiff_add, fwdDiff_smul, Geometry.SimplicialComplex, AlgebraicTopology.AlternatingFaceMapComplex.objD, HomologicalComplex.cycles, HomologicalComplex.d_comp_d, ChainComplex, HomologicalComplex.Hom, CochainComplex, groupCohomology.cocycles
Q121416Discrete mathematicspeirce
Q865811Distribution (mathematical analysis)Distribution, TestFunction, Distribution.delta, TemperedDistribution.toTemperedDistribution_dirac_eq_delta, Distribution.lineDerivCLM, HasCompactSupport, MeasureTheory.LocallyIntegrable, ae_eq_of_integral_contDiff_smul_eq, LineDeriv.iteratedLineDerivOp, Distribution.IsVanishingOn, Distribution.dsupport, TemperedDistribution, SchwartzMap, SchwartzMap.seminorm, SchwartzMap.fourierTransformCLM, TemperedDistribution.derivCLM, Function.HasTemperateGrowth.toTemperedDistribution, TemperedDistribution.instFourierTransform, FourierTransform.fourierCLE
Q752487Dual spaceModule.Dual, StrongDual, Module.Dual.eval, Basis.dualBasis, Basis.dualBasis_apply_self, Module.lift_rank_lt_rank_dual, Module.rank_dual_eq_card_dual_of_aleph0_le_rank, LinearMap.BilinForm.toDual, Module.evalEquiv, LinearMap.dualMap, Module.Dual.transpose_apply, LinearMap.toMatrix_transpose, Submodule.dualAnnihilator, Submodule.dualAnnihilator_sup_eq, Module.dualAnnihilator_gc, Submodule.dualQuotEquivDualAnnihilator, Module.dualProdDualEquivDual, LinearMap.toContinuousLinearMap, ContinuousLinearMap.toNormedAddCommGroup, WeakDual, InnerProductSpace.toDual, RealRMK.integral_rieszMeasure, NormedSpace.inclusionInDoubleDual, NormedSpace.inclusionInDoubleDualLi
Q211294Elementary algebrapow_zero, add_comm, left_distrib, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, mul_lt_mul_of_neg_left, eq_equivalence, Eq.subst, lt_trans, ge_iff_le, mul_eq_zero, quadratic_eq_zero_iff, Real.rpow_inv_natCast_pow
Q268493Elliptic curveWeierstrassCurve.Affine.Nonsingular, WeierstrassCurve.IsShortNF, WeierstrassCurve.Affine.Point.instAddCommGroup, WeierstrassCurve.Affine.Point.neg, WeierstrassCurve.Affine.Point.add, WeierstrassCurve.Affine.Point, WeierstrassCurve.Affine.Point.map, WeierstrassCurve.Affine.slope_of_X_ne, WeierstrassCurve.Affine.negY, WeierstrassCurve.Affine.slope_of_Y_ne, WeierstrassCurve.Affine.slope, WeierstrassCurve.LFunction, WeierstrassCurve.exists_variableChange_isShortNF, WeierstrassCurve.exists_variableChange_isCharThreeNF, WeierstrassCurve.exists_variableChange_isCharTwoNF, PeriodPair.derivWeierstrassP_sq, PeriodPair.weierstrassP_add_coe, WeierstrassCurve.exists_variableChange_of_j_eq, PeriodPair.g₂
Q1332450Elliptic geometryProjectivization.equivSubmodule
Q842346Equality (mathematics)Eq, Ne, Eq.refl, Eq.symm, Eq.trans, Eq.subst, congrArg, BEq, funext, rfl, Set.ext, setOf, Set.ext_iff, Prod.ext_iff, FP.Float, Equivalence, Setoid.isPartition_classes, Setoid.bot_def, Con, CategoryTheory.Iso, Equiv, MulEquiv, zmodMulEquivOfGenerator, LinearEquiv.nonempty_equiv_iff_rank_eq, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, EuclideanSpace.volume_ball, Similar
Q230848Euclidean algorithmEuclideanDomain.gcd, Nat.gcd_sub_self_left, Int.gcd_eq_gcd_ab, Nat.gcd, Nat.Coprime, Nat.dvd_gcd, Nat.factorization_gcd, Int.gcd_least_linear, Nat.gcd_rec, Nat.gcd_comm, EuclideanDomain.div_add_mod, Int.ediv_emod_unique, Nat.xgcd, EuclideanDomain.gcd_eq_gcd_ab, span_gcd, IsPrincipalIdealRing, Nat.gcd_eq_gcd_ab, Nat.Prime.dvd_mul, Nat.Coprime.mul_right, Nat.factorization_inj, Int.gcd_dvd_iff, ZMod.instField, ZMod.unitOfCoprime, ZMod.chineseRemainder, EuclideanDomain, GenContFract.terminates_iff_rat, Polynomial.instEuclideanDomain, EuclideanDomain.gcd_dvd_left, GaussianInt, PrincipalIdealRing.to_uniqueFactorizationMonoid, Zsqrtd.norm, EuclideanDomain.to_principal_ideal_domain, Zsqrtd, Nat.sum_four_squares
Q162886Euclidean geometryEuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, Nat.exists_infinite_primes, EuclideanGeometry.angle_eq_angle_of_dist_eq, EuclideanGeometry.angle_add_angle_add_angle_eq_pi, EuclideanGeometry.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter, EuclideanGeometry.side_side_side, EuclideanGeometry.similar_of_angle_angle, MeasureTheory.Measure.addHaar_smul, Congruent, Similar, EuclideanSpace.dist_eq, and_not_self_iff, em
Q168698Exponential functionReal.exp, Real.exp_add, Real.tendsto_exp_div_pow_atTop, Real.exp_pos, Real.hasDerivAt_exp, Real.exp_log, Complex.exp, Complex.isCauSeq_norm_exp, Real.tendsto_one_add_div_pow_exp, Real.exp_neg, Real.exp_strictMono, Real.rpow, Complex.analyticOnNhd_cexp, Complex.tendsto_one_add_div_pow_exp, Complex.exp_add, Complex.exp_log, Complex.exp_periodic, Complex.exp_conj, Complex.norm_exp, Complex.exp_mul_I, Complex.exp_eq_exp_re_mul_sin_add_cos, Complex.two_cos, NormedSpace.exp, NormedSpace.isUnit_exp
Q5446431Fibred categoryCategoryTheory.Functor.Fiber, CategoryTheory.Functor.IsStronglyCartesian, CategoryTheory.Functor.IsPreFibered.pullbackObj, CategoryTheory.Functor.IsStronglyCartesian.isIso_of_base_isIso, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso, CategoryTheory.BasedCategory, CategoryTheory.BasedCategory.bicategory, CategoryTheory.Functor.IsFibered, CategoryTheory.Pseudofunctor.CoGrothendieck.forget, CategoryTheory.Functor.IsStronglyCocartesian
Q4055684First-order logicFirstOrder.Language, FirstOrder.Language.Theory, FirstOrder.Language.Structure, FirstOrder.Language.Term, FirstOrder.Language.Relations, FirstOrder.Language.Functions, FirstOrder.Language.Constants, FirstOrder.Language.BoundedFormula, FirstOrder.Language.BoundedFormula.IsAtomic, FirstOrder.Language.BoundedFormula.freeVarFinset, FirstOrder.Language.Sentence, FirstOrder.Language.BoundedFormula.Realize, FirstOrder.Language.Theory.IsSatisfiable, FirstOrder.Language.Theory.ModelsBoundedFormula, FirstOrder.Language.Theory.Model, FirstOrder.Language.Term.bdEqual, FirstOrder.Language.exists_elementarySubstructure_card_eq, FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable, FirstOrder.Language.Theory.exists_model_card_eq, ExistsUnique
Q976981FormulaEuclideanSpace.volume_ball, FirstOrder.Language.BoundedFormula
Q184410Four color theoremSimpleGraph.degree, SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom
Q1365258Fourier analysisMeasureTheory.Integrable.fourier_inversion, VectorFourier.fourierIntegral, MeasureTheory.Lp.fourierTransformₗᵢ, hasDerivAt_exp, Real.fourier_mul_convolution_eq, Real.fourierIntegral, Real.fourierIntegralInv, AddCircle.hasSum_fourier_series_of_summable, Real.tsum_eq_tsum_fourier_of_rpow_decay, ZMod.dft, ZMod.invDFT_def
Q81392FractalMeasureTheory.dimH, NowhereDifferentiable.exists_uniformContinuous_and_not_differentiableAt, cantorSet
Q864475FunctorCategoryTheory.Functor, CategoryTheory.Functor.op, CategoryTheory.prod, CategoryTheory.Functor.map_isIso, CategoryTheory.Functor.comp, CategoryTheory.SingleObj, TopCat.Presheaf, CategoryTheory.Functor.const, CategoryTheory.Functor.id, CategoryTheory.Functor.diag, CategoryTheory.Limits.lim, CategoryTheory.MonoidalCategory.tensor, CategoryTheory.forget, MonCat.free, CategoryTheory.Functor.hom, CategoryTheory.Functor.IsRepresentable, CategoryTheory.Functor.category
Q44455Game theorySion.exists_isSaddlePointOn
Q621550General topologyTopologicalSpace, IsOpen, TopologicalSpace.IsTopologicalBasis, instTopologicalSpaceSubtype, instTopologicalSpaceProd, TopologicalSpace.coinduced, DiscreteTopology, IndiscreteTopology, CofiniteTopology, Real.pseudoMetricSpace, PseudoMetricSpace, PrimeSpectrum.zariskiTopology, sierpinskiSpace, OrderTopology, ContinuousAt, continuous_of_discreteTopology, continuousAt_def, Continuous.tendsto, SeqContinuous, Continuous.seqContinuous, continuous_iff_seqContinuous, continuous_iff_continuousAt, closure, continuous_iff_image_closure_subset_closure_image, Continuous.comp, IsCompact.image, IsConnected.image, IsPathConnected.image, IsLindelof.image, ContinuousOn.isSeparable_image, TopologicalSpace.le_def, continuous_id_iff_le, IsOpenMap, Homeomorph, Continuous.homeoOfEquivCompactToT2, TopologicalSpace.induced, CompactSpace, IsCompact, isCompact_Icc, isCompact_iff_isClosed_bounded, IsCompact.isClosed, IsCompact.tendsto_subseq, exists_embedding_euclidean_of_compact, ConnectedSpace, isPreconnected_iff_subset_of_disjoint, isPreconnected_Icc, IsPreconnected.image, connectedComponent, connectedComponentSetoid, TotallyDisconnectedSpace, TotallySeparatedSpace, TotallySeparatedSpace.totallyDisconnectedSpace, Path, pathComponent, PathConnectedSpace, PathConnectedSpace.connectedSpace, Pi.topologicalSpace, IsTopologicalBasis.prod, isCompact_pi_infinite, T0Space, T1Space, T2Space, T25Space, RegularSpace, CompletelyRegularSpace, NormalSpace, exists_continuous_zero_one_of_isClosed, CompletelyNormalSpace, PerfectlyNormalSpace, ContinuousMap.exists_restrict_eq, SequentialSpace, FirstCountableTopology, SecondCountableTopology, SeparableSpace, LindelofSpace, SigmaCompactSpace, FirstCountableTopology.frechetUrysohnSpace, SecondCountableTopology.to_firstCountableTopology, IsSigmaCompact.isLindelof, UniformSpace.firstCountableTopology, MetricSpace, EMetric.instParacompactSpace, metrizableSpace_of_t3_secondCountable, dense_sInter_of_isOpen, IsOpen.baireSpace, TopologicalSpace.MetrizableSpace
Q213488GeodesicManifold.pathELength, Manifold.riemannianEDist
Q2662474Geometric group theorySimpleGraph.mulCayley, Int.instAddCommGroup, FreeGroup, Monoid.CoprodI, Equiv.Perm, CoxeterSystem
Q8087GeometryChartedSpace, IsManifold, InnerProductGeometry.angle, EuclideanGeometry.angle, EuclideanSpace.dist_eq, MetricSpace, MeasureTheory.Measure, Similar, MvPolynomial.vanishingIdeal_zeroLocus_eq_radical, Convex
Q504843Graph coloringSimpleGraph.Coloring, SimpleGraph.Colorable, SimpleGraph.chromaticNumber, SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable, SimpleGraph.Coloring.colorClass, SimpleGraph.partitionable_iff_colorable, SimpleGraph.chromaticNumber_le_card, SimpleGraph.chromaticNumber_eq_one_iff, SimpleGraph.chromaticNumber_top, SimpleGraph.isBipartite_iff_exists_isBipartiteWith, SimpleGraph.IsClique.card_le_chromaticNumber, SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom
Q131476Graph theorySimpleGraph, Quiver, Graph, SimpleGraph.Coloring, SimpleGraph.isTuranMaximal_iff_nonempty_iso_turanGraph, SimpleGraph.szemeredi_regularity, SimpleGraph.IsTree, SimpleGraph.incMatrix, SimpleGraph.adjMatrix, SimpleGraph.degMatrix, SimpleGraph.lapMatrix
Q131752Greatest common divisorGCDMonoid.gcd, Nat.gcd, Int.gcd, EuclideanDomain.gcd_zero_right, gcd_eq_zero_iff, dvd_gcd_iff, Nat.Coprime, Nat.gcd_mul_lcm, Nat.factorization_gcd, Nat.gcd_sub_self_left, EuclideanDomain.gcd_val, EuclideanDomain.gcd_self, Int.gcd_eq_gcd_ab, IsCoprime.dvd_of_dvd_mul_right, Nat.gcd_mul_left, Nat.gcd_add_mul_right_left, Nat.gcd_div, Nat.coprime_div_gcd_div_gcd, gcd_comm, gcd_assoc, Nat.Coprime.gcd_mul, gcd_mul_lcm, Nat.totient_gcd_mul_totient_mul, GCDMonoid, UniqueFactorizationMonoid.toGCDMonoid, EuclideanDomain.gcd, span_gcd
Q288465Group actionMulAction, Representation, Equiv.Perm.applyMulAction, FaithfulSMul, MulAction.IsPretransitive, MulAction.IsMultiplyPretransitive, Equiv.Perm.isMultiplyPretransitive, MulAction.IsPreprimitive, ProperlyDiscontinuousSMul, ContinuousSMul, ProperSMul, IsSemisimpleRepresentation, MulAction.orbit, MulAction.orbitRel, MulAction.pretransitive_iff_subsingleton_quotient, MulAction.orbitRel.Quotient, MulAction.IsInvariantBlock, MulAction.IsFixedBlock.orbit, MulAction.fixedPoints, MulAction.fixedBy, MulAction.stabilizer, MulAction.stabilizer_smul_eq_stabilizer_map_conj, MulAction.orbitEquivQuotientStabilizer, MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group, Monoid.toMulAction, MulAction.quotient, ConjAct, Units.instMulAction, LinearEquiv.applyDistribMulAction, CategoryTheory.Action, AlgEquiv.applyMulSemiringAction, Flow, Set.mulAction, CategoryTheory.ActionCategory, MulActionHom, CategoryTheory.actionAsFunctor
Q1055807Group representationAction.ρAut, Representation, Action.IsContinuous, MonoidHom.ker, Representation.IntertwiningMap, Representation.Equiv, Subrepresentation, Representation.IsIrreducible, Representation.IsSemisimpleRepresentation, MulAction, MulAction.bijective, Action.functorCategoryEquivalence, Rep
Q200787Gödel's incompleteness theoremsFirstOrder.Language.Theory.IsComplete, FirstOrder.Field.ACF_isComplete, Nat.Partrec.Code.halting_problem
Q326908Hausdorff spaceSeparatedNhds, T2Space, R1Space, R1Space.t2Space_iff_t0Space, SeparationQuotient.t2Space_iff, t2_iff_isClosed_diagonal, t2Space_of_metrizableSpace, CofiniteTopology.instT1Space, PseudoMetrizableSpace.regularSpace, Prod.t2Space, T2Space.t1Space, R1Space.instR0Space, R1Space.quasiSober, IsCompact.isClosed, SeparatedNhds.of_isCompact_isCompact, NormalSpace.of_compactSpace_r1Space, t2Space_iff_of_isOpenQuotientMap, isClosed_eq, Continuous.ext_on, T2Space.r1Space, instRegularSpaceOfWeaklyLocallyCompactSpaceOfR1Space, CompleteSpace, ContinuousMap.instCommCStarAlgebra
Q273167Hilbert's problemsMeasureTheory.IsProbabilityMeasure, RiemannHypothesis
Q5018842History of algebraleft_distrib, mul_comm, mul_self_sub_mul_self, add_sq, Nat.chineseRemainder, Polynomial, sq_add_sq_mul, quadratic_eq_zero_iff, PythagoreanTriple, Pell.IsFundamental.eq_zpow_or_neg_zpow, quadratic_ne_zero_of_discrim_ne_sq, Matrix.det, Complex.exists_root, isSolvable_gal_of_irreducible, intermediateFieldEquivSubgroup
Q2393733History of geometryEuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two
Q3893386History of mathematical notationInnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq', Nat.Prime.dvd_mul, Nat.fib, Matrix.cramer, Field, Cardinal.aleph
Q185264History of mathematicsnorm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, Nat.Perfect, quadratic_eq_zero_iff, EuclideanGeometry.thales_theorem, irrational_sqrt_two, Nat.exists_infinite_primes, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, Nat.choose_succ_succ, add_pow, Nat.fib, Real.sin, Zsqrtd.norm_mul, exists_hasDerivAt_eq_slope, Pell.exists_of_not_isSquare, Real.tendsto_sum_pi_div_four, Real.hasSum_arctan, Real.hasSum_cos, Real.cos_eq_tsum, Complex, Complex.I, Complex.exists_root, legendreSym.quadratic_reciprocity, ChartedSpace, Module, Quaternion, BooleanAlgebra, isSolvable_gal_of_irreducible, ZFSet, Padic, MeasureTheory.IsProbabilityMeasure, MeasureTheory.lintegral, Hyperreal, LucasLehmer.lucas_lehmer_sufficiency
Q5870804History of the function conceptDifferentiable, Continuous, BooleanRing, Classical.epsilon, Partrec, halting_problem, ZFSet.sep, ZFSet.pair
Q5887297Hom functorCategoryTheory.LocallySmall, CategoryTheory.coyoneda, CategoryTheory.yoneda, CategoryTheory.Functor.hom, CategoryTheory.yonedaEquiv, CategoryTheory.MonoidalClosed.internalHom, CategoryTheory.MonoidalClosed, CategoryTheory.ihom.adjunction, CategoryTheory.ihom, CategoryTheory.Functor.IsRepresentable, CategoryTheory.Profunctor.id, CategoryTheory.Adjunction.rightAdjoint_preservesLimits, CategoryTheory.projective_iff_preservesEpimorphisms_coyoneda_obj, TensorProduct.lift.equiv
Q579978Homological algebraChainComplex, HomologicalComplex.d, HomologicalComplex.homology, HomologicalComplex.Acyclic, singularChainComplexFunctor, CategoryTheory.ShortComplex.Exact, CategoryTheory.ShortComplex.ShortExact, CategoryTheory.Abelian.isIso_of_epi_of_isIso_of_isIso_of_mono, CategoryTheory.ShortComplex.SnakeInput.snake_lemma, CategoryTheory.Abelian, CategoryTheory.Functor.rightDerived, Ext, CategoryTheory.Tor, CategoryTheory.SpectralSequence, singularHomologyFunctor, HomologicalComplex.Hom, HomologicalComplex.QuasiIso, HomologicalComplex.homologyFunctor, CategoryTheory.ShortComplex.ShortExact.δ
Q215111Homomorphismmap_one, MulHom, MonoidHom, RingHom, NonUnitalRingHom, LinearMap, AlgHom, Matrix.scalar, MulEquiv, CategoryTheory.Iso, EquivLike.bijective, MulEquiv.ofBijective, Homeomorph, Monoid.End, Monoid.End.instMonoid, Module.End.instRing, MulAut, LinearMap.GeneralLinearGroup, CategoryTheory.mono_iff_injective, CategoryTheory.Mono, CategoryTheory.SplitMono, CategoryTheory.IsSplitMono.mono, CategoryTheory.ConcreteCategory.mono_of_injective, CategoryTheory.epi_iff_surjective, CategoryTheory.Epi, IsLocalization.epi, CategoryTheory.SplitEpi, CategoryTheory.SplitEpi.epi, Con.ker, Con.quotientKerEquivRange, QuotientGroup.con_ker_eq_conKer, FirstOrder.Language.Hom, SimpleGraph.Hom
Q1279571Indian mathematicsEuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, PythagoreanTriple, Nat.choose_succ_succ, Nat.sum_range_choose, Nat.factorial, Real.sin, Real.pi_gt_d4, Real.sin_sq_add_cos_sq, mul_zero, quadratic_eq_zero_iff, sq_add_mul_sq_mul_sq_add_mul_sq, Real.deriv_sin, exists_deriv_eq_zero, Real.pi_gt_d6, mul_self_eq_mul_self_iff, Real.sin_add, Real.hasSum_sin, tsum_geometric_of_lt_one, Real.hasSum_arctan, Real.tendsto_sum_pi_div_four, exists_hasDerivAt_eq_slope
Q131222Information theoryReal.negMulLog_zero, Real.binEntropy, Real.binEntropy_le_log_two, InformationTheory.klDiv
Q12503IntegerInt, Denumerable.int, Int.instCommRing, Int.instAddCommGroup, CommRingCat.zIsInitial, RingHom.injective_int, instIsAddCyclicInt, intCyclicAddEquiv, Int.instCommMonoid, Int.instIsDomain, Int.not_isField, Rat.isFractionRing, Int.ediv_emod_unique'', Int.euclideanDomain, Nat.primeFactorsList_unique, Int.instLinearOrder, Int.instIsStrictOrderedRing, sub_eq_add_neg, Equiv.intEquivNat, Cardinal.mk_int, Function.Bijective
Q187631InterpolationAffineMap.lineMap, AffineMap.lineMap_apply_ring, Lagrange.interpolate, Lagrange.eq_interpolate_iff
Q16743426Introduction to gauge theoryCircle.instCommGroup, CommGroup, Group, Int.instAddCommGroup
Q838495Jordan normal formModule.End.genEigenspace, Module.End.maxGenEigenspaceIndex, Module.End.exists_isNilpotent_isSemisimple, spectrum.map_polynomial_aeval_of_degree_pos, Matrix.charpoly_units_conj, LinearMap.aeval_self_charpoly, minpoly, IsCompactOperator.hasEigenvalue_iff_mem_spectrum
Q1765138Kerala school of astronomy and mathematicstsum_geometric_of_lt_one, Real.hasSum_sin, Real.hasSum_cos, Real.tendsto_sum_pi_div_four, Real.deriv_sin
Q11476KinematicsIsometry, Matrix.mem_orthogonalGroup_iff'
Q1225713Krull dimensionringKrullDim, ringKrullDim_eq_zero_of_field, Ring.krullDimLE_zero_and_isLocalRing_tfae, RelSeries.length, Ideal.primeHeight, Ideal.primeHeight_eq_zero_iff, Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim, Ideal.finiteHeight_of_isNoetherianRing, Ideal.height_le_iff_exists_minimalPrimes, Ideal.height, PrimeSpectrum.topologicalKrullDim_eq_ringKrullDim, MvPolynomial.ringKrullDim_of_isNoetherianRing, Polynomial.ringKrullDim_of_isNoetherianRing, IsPrincipalIdealRing.ringKrullDim_eq_one, Ring.KrullDimLE.isField_of_isDomain, ringKrullDim_eq_bot_of_subsingleton, ringKrullDim_nonneg_of_nontrivial, isArtinianRing_iff_isNoetherianRing_krullDimLE_zero, Module.supportDim
Q199691Laplace transformProbabilityTheory.mgf
Q484637Linear equationAffineMap
Q202843Linear programmingIsMinOn.of_isLocalMin_of_convex_univ
Q8078Logicem, inf_sup_left
Q1166618Mathematical logicMetric.continuousAt_iff, Cardinal.not_countable_real, Function.cantor_surjective, exists_wellFoundedLT, ZFSet.isOrdinal_notMem_univ, FirstOrder.Language.exists_elementarySubstructure_card_eq, FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable, FirstOrder.Language, ZFSet, Classical.axiomOfChoice, FirstOrder.Language.Theory, ComputablePred.halting_problem
Q141495Mathematical optimizationIsMinOn, IsLocalMin, IsMinOn.of_isLocalMin_of_convex_univ, IsCompact.exists_isMinOn, LowerSemicontinuousOn.exists_isMinOn, IsLocalExtr.hasDerivAt_eq_zero, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d
Q156495Mathematical physicsintervalIntegral.integral_eq_sub_of_hasDerivAt, IsLocalExtr.deriv_eq_zero, fourierCoeff, IsRiemannianManifold, HilbertSpace, spectrum
Q395MathematicsFermatLastTheorem, Module, BooleanAlgebra, Function.cantor_surjective, Module.Flat.of_free, Nat.exists_infinite_primes
Q1045555Maximum likelihood estimationProbabilityTheory.multivariateGaussian
Q51501Maxwell's equationsgradient, hasDerivAt_integral_of_dominated_loc_of_lip
Q2796622MeanFinset.centroid, Real.geom_mean_le_arith_mean, Finset.affineCombination, MeasureTheory.average
Q226995MedianConvexOn.map_integral_le
Q464794Minkowski spaceLinearMap.BilinForm.IsOrtho, LinearMap.BilinForm.toDual, LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot
Q467606Model theoryFirstOrder.Language.BoundedFormula, FirstOrder.Language.Sentence, FirstOrder.Language.Theory, FirstOrder.Language.Theory.IsSatisfiable, FirstOrder.Language.Theory.IsComplete, FirstOrder.Language.completeTheory, FirstOrder.Language, FirstOrder.Language.Structure, FirstOrder.Language.Theory.Model, FirstOrder.Language.Substructure, FirstOrder.Language.ElementarySubstructure, FirstOrder.Language.ElementarySubstructure.theory_model_iff, FirstOrder.Language.ElementaryEmbedding, FirstOrder.Language.Embedding.toHom, FirstOrder.Language.LHom.reduct, FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable, FirstOrder.Language.exists_elementarySubstructure_card_eq, FirstOrder.Language.Theory.exists_large_model_of_infinite_model, Set.Definable, FirstOrder.Language.Substructure.isElementary_of_exists, Set.DefinableFun, FirstOrder.Language.Theory.typeOf, FirstOrder.Language.Theory.CompleteType, FirstOrder.Language.DefinableSet.instBooleanAlgebra, FirstOrder.Language.Theory.CompleteType.instCompactSpace, FirstOrder.Language.Ultraproduct.structure, FirstOrder.Language.Ultraproduct.sentence_realize, Cardinal.Categorical, Order.iso_of_countable_dense, FirstOrder.Language.IsFraisseLimit
Q18848Module (mathematics)Module, Module.AEval, AddCommGroup.uniqueIntModule, Module.Free, Pi.module, Submodule, MulOpposite, Module.compHom, Submodule.span, Submodule.instIsModularLattice, LinearMap, LinearEquiv, LinearMap.ker, LinearMap.quotKerEquivRange, ModuleCat.abelian, Module.Finite, Module.Projective, Module.Injective, Module.Flat, IsSimpleModule, IsSemisimpleModule, FaithfulSMul, Module.IsTorsionFree, IsNoetherian, IsArtinian, SetLike.GradedSMul, Representation, Module.toAddMonoidEnd, SheafOfModules
Q232207Monte Carlo methodProbabilityTheory.strong_law_ae
Q190529Nicolas Bourbakione_add_one_eq_two, Set.empty_def, Function.Bijective, Metric.ball
Q233858Non-Euclidean geometryCircle, DualNumber
Q617295Nondeterministic finite automatonDFA, NFA, DFA.toNFA_correct, NFA.toDFA_correct, NFA.accepts, NFA.accepts_iff_exists_path, NFA.evalFrom, DFA.toNFA, εNFA, εNFA.εClosure, εNFA.evalFrom, εNFA.accepts, εNFA.toNFA_correct, εNFA.toNFA_evalFrom_match, Language.IsRegular.add, Language.IsRegular.inf, Language.IsRegular.compl
Q12479Number theoryInt, PythagoreanTriple, Mul, Dvd.dvd, Nat.div_add_mod, Nat.three_dvd_iff, Nat.gcd, Nat.Coprime, EuclideanDomain.gcd, GenContFract, Nat.Prime, Nat.exists_infinite_primes, Nat.factorization, Nat.primeFactorsList, Nat.Prime.dvd_mul, Nat.primeFactorsList_unique, ZMod, Int.ModEq, ZMod.pow_card, Nat.ModEq.pow_totient, Filter.Tendsto, Complex.I, Complex.re, Nat.primeCounting, riemannZeta, riemannZeta_eulerProduct, RiemannHypothesis, Ideal.IsPrime, dedekindZeta, IsAlgebraic, NumberField, IsAbelianGalois, Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, Transcendental
Q11216Numerical analysisLagrange.interpolate, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt
Q82990Numerical digitNat.ofDigits, Nat.ofDigits_eq_sum_mapIdx
Q753445Numerical integrationtrapezoidal_integral, MeasureTheory.integral_prod
Q541182Numerical methods for ordinary differential equationsIsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt
Q131030Operator (mathematics)Module.End, LinearMap, LinearMap.toMatrix, lp, ContinuousLinearMap.toNormedRing, ContinuousLinearMap, ContinuousLinearMap.addCommGroup, gradient, LinearMap.GeneralLinearGroup, Matrix.orthogonalGroup, Matrix.specialOrthogonalGroup, VectorFourier.fourierIntegral
Q191780Ordinal numberOrdinal, InitialSeg.total, IsWellOrder, Ordinal.type, Ordinal.omega0, Ordinal.lt_wf, OrderIso, Ordinal.isEquivalent, ZFSet.omega, ZFSet.IsOrdinal, ZFSet.IsOrdinal.mem, ZFSet.IsOrdinal.subset_iff_eq_or_mem, Ordinal.bddAbove_of_small, Order.lt_succ, not_small_ordinal, Ordinal.type_eq, Ordinal.zero_or_succ_or_isSuccLimit, Ordinal.zero_le, Order.succ, Order.IsSuccLimit, Ordinal.isSuccLimit_iff, IsSuccPrelimit.sSup_Iio, Ordinal.omega0_le_of_isSuccLimit, Ordinal.le_iSup, Order.IsNormal, Ordinal.induction, Ordinal.limitRecOn, Ordinal.instPow, Ordinal.not_bddAbove_fp, Ordinal.enumOrd, Ordinal.isPrincipal_add_iff_add_lt_ne_self, Ordinal.epsilon, Ordinal.CNF, Cardinal.ord, Ordinal.isSuccLimit_ord, Ordinal.omega, Ordinal.cof, Ordinal.cof_eq_aleph0_of_isSuccLimit, Ordinal.cof_succ, Ordinal.cof_ord_cof, IsCofinal, Ordinal.IsAcc, Ordinal.isClosed_iff_iSup, Ordinal.epsilon_zero_eq_nfp, derivedSet
Q1783179Orthogonal groupMatrix.orthogonalGroup, Matrix.specialOrthogonalGroup, Matrix.mem_orthogonalGroup_iff, LinearIsometryEquiv.instGroup, AffineIsometryEquiv.instGroup, Matrix.det_of_mem_unitary, Matrix.mem_specialOrthogonalGroup_iff, Submodule.reflection, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, QuadraticForm.equivalent_of_isAlgClosed, char_dvd_card_solutions_of_sum_lt, LieAlgebra.Orthogonal.so, LinearIsometry.isConformalMap, pinGroup, spinGroup
Q333871Orthogonal matrixMatrix.orthogonalGroup, Matrix.mem_orthogonalGroup_iff, Matrix.specialOrthogonalGroup, Matrix.permMatrix_one, Equiv.swap, Matrix.det_of_mem_unitary, Matrix.det_permutation, LieAlgebra.Orthogonal.so, exp_mem_unitary_of_mem_skewAdjoint, Matrix.IsHermitian.spectral_theorem
Q746242P versus NP problemComputablePred.halting_problem
Q48297ParabolaAffineMap
Q1413083ParameterReal.logb, Nat.descFactorial, circleMap, ProbabilityTheory.poissonPMF, ProbabilityTheory.gaussianReal
Q1187620Perfect graphSimpleGraph.IsClique, SimpleGraph.cliqueNum, SimpleGraph.Coloring, SimpleGraph.chromaticNumber, SimpleGraph.cliqueNum_le_chromaticNumber, PartialOrder, IncompRel, IsChain, IsAntichain
Q161519PermutationFintype.card_perm, Equiv.Perm, Equiv.permGroup, Equiv.Perm.one_def, Equiv.Perm.cycleFactorsFinset_noncommProd, Equiv.Perm.IsCycle, Function.IsFixedPt, derangements, Equiv.swap, Equiv.Perm.Disjoint.commute, Equiv.Perm.formPerm_reverse, Equiv.Perm.mul_apply, Equiv.trans, Fintype.card_embedding_eq, descPochhammer, Finset.powersetCard, Finset.card_powersetCard, Nat.choose, Fintype.card_pi_const, Equiv.Perm.cycleType, Equiv.Perm.card_of_cycleType, IsConj, Equiv.Perm.isConj_iff_cycleType_eq, orderOf, Equiv.Perm.lcm_cycleType, Equiv.Perm.truncSwapFactors, Equiv.Perm.sign, Matrix.det_permutation, Equiv.Perm.permMatrix, Matrix.permMatrixHom
Q530152Picard–Lindelöf theoremIsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, IsPicardLindelof.picard_eq_of_hasDerivAt, ODE.picard, ContractingWith.tendsto_iterate_fixedPoint, ContractingWith.exists_fixedPoint, IsPicardLindelof.FunSpace.exists_contractingWith_iterate_next, IsPicardLindelof.FunSpace.dist_iterate_next_apply_le, ContractingWith.isFixedPt_fixedPoint_iterate, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt
Q188276Pigeonhole principleFintype.exists_ne_map_eq_of_card_lt, Fintype.exists_lt_card_fiber_of_mul_lt_card, Function.Embedding.isEmpty_of_card_lt, AddCircle.denseRange_zsmul_coe_iff, Finite.exists_ne_map_eq_of_infinite, Fintype.exists_card_fiber_le_of_card_le_mul, Finset.exists_ne_map_eq_of_card_lt_of_maps_to, Fintype.card_le_of_injective, Fintype.card_le_of_surjective, Fintype.exists_le_card_fiber_of_mul_le_card, Fintype.exists_card_fiber_lt_of_card_lt_mul, Cardinal.le_def, Cardinal.exists_uncountable_fiber, Cardinal.infinite_pigeonhole
Q205692Poisson distributionpoissonMeasure, poissonMeasure_singleton, tendsto_choose_mul_pow_of_tendsto_mul_atTop
Q206925Power seriesFormalMultilinearSeries, Polynomial.taylor, tsum_geometric_of_norm_lt_one, NormedSpace.exp_eq_tsum, Real.sin_eq_tsum, FormalMultilinearSeries.radius, FormalMultilinearSeries.radius_inv_eq_limsup, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, FormalMultilinearSeries.summable_norm_apply, Real.tendsto_tsum_powerSeries_nhdsWithin_lt, HasFPowerSeriesOnBall.add, FormalMultilinearSeries.min_radius_le_radius_add, AnalyticAt.mul, tsum_mul_tsum_eq_tsum_sum_antidiagonal, PowerSeries.inv, HasFPowerSeriesOnBall.fderiv, AnalyticAt, FormalMultilinearSeries.analyticOnNhd, DifferentiableOn.analyticAt, AnalyticAt.contDiffAt, HasFPowerSeriesOnBall.factorial_smul, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, AnalyticOnNhd.eqOn_of_preconnected_of_eventuallyEq, PowerSeries.mk, FormalMultilinearSeries.hasFPowerSeriesOnBall, PowerSeries, MvPowerSeries, PowerSeries.order
Q915906Presentation of a groupPresentedGroup, FreeGroup, Group.IsFinitelyPresented
Q863912Prime idealIdeal.IsPrime, Ideal.span_singleton_prime, Nat.Prime.dvd_mul, PrimeSpectrum, AlgebraicGeometry.AffineScheme, Ideal.IsPrime.mul_notMem, Ideal.primeCompl, PrincipalIdealRing.isMaximal_of_irreducible, Polynomial.irreducible_of_eisenstein_criterion, Ideal.IsMaximal, Ideal.IsMaximal.isPrime, Ideal.IsPrime.isMaximal_of_ne_bot, MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton, Ideal.Quotient.isDomain_iff_prime, Ideal.isPrime_bot, PrimeSpectrum.instIsEmpty, Ideal.exists_maximal, Ideal.isPrime_of_maximally_disjoint, Ideal.IsPrime.comap, Ideal.IsMinimalPrime, minimalPrimes.equivIrreducibleComponents, UniqueFactorizationMonoid.iff_exists_prime_mem_of_isPrime, PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime, AlgebraicGeometry.Scheme, exists_le_isAssociatedPrime_of_isNoetherianRing, Ideal.subset_union_prime, Ideal.IsPrime.inf_le', Ideal.IsOka.isPrime_of_maximal_not, Ideal.isOka_isPrincipal
Q207522Probability density functionMeasureTheory.pdf, MeasureTheory.HasPDF, MeasureTheory.withDensity_eq_iff_of_sigmaFinite, MeasureTheory.pdf.IsUniform.pdf_eq, ProbabilityTheory.gaussianPDFReal, MeasureTheory.pdf.integral_mul_eq_integral, MeasureTheory.noAtoms_withDensity, MeasureTheory.pdf.indepFun_iff_pdf_prod_eq_pdf_mul_pdf, MeasureTheory.pdf.integral_pdf_smul, ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf
Q7246880Probability interpretationsMeasureTheory.uniformOn_univ, ProbabilityTheory.strong_law_ae
Q623472Probability spaceMeasureTheory.IsProbabilityMeasure, MeasurableSpace, MeasurableSet, MeasureTheory.ProbabilityMeasure, MeasureTheory.MeasureSpace, MeasurableSet.iInter, PMF, MeasureTheory.Measure.IsComplete, Measurable, MeasureTheory.Measure.map, MeasurableSpace.measurableSet_top, MeasureTheory.borel, ProbabilityTheory.cond, ProbabilityTheory.cond_isProbabilityMeasure, ProbabilityTheory.IndepSet, ProbabilityTheory.IndepFun, Disjoint, MeasureTheory.measure_union, Set.inter
Q5862903Probability theoryMeasurableSet, IsProbabilityMeasure, ProbabilityMeasure, ProbabilityTheory.uniformOn, PMF, PMF.toMeasure_apply, ProbabilityTheory.cdf, ProbabilityTheory.monotone_cdf, MeasureTheory.pdf, ProbabilityTheory.cdf_measure_stieltjesFunction, MeasureTheory.Measure, MeasureTheory.Measure.rnDeriv, MeasureTheory.TendstoInDistribution, MeasureTheory.TendstoInMeasure, MeasureTheory.TendstoInMeasure.tendstoInDistribution, ProbabilityTheory.strong_law_ae, ProbabilityTheory.tendstoInDistribution_inv_sqrt_mul_sum_sub
Q942423Projective moduleModule.Projective, Module.Projective.of_free, Module.projective_lifting_property, Module.Projective.iff_split_of_projective, Module.Projective.iff_split, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj, Module.projective_def, Module.Projective.of_split, Module.Free.of_divisionRing, Module.projective_of_isSemisimpleRing, Module.Flat.of_projective, Module.Flat.projective_of_finitePresentation, CategoryTheory.ProjectiveResolution, ModuleCat.enoughProjectives, CategoryTheory.projectiveDimension, CategoryTheory.projective_iff_hasProjectiveDimensionLT_one, Module.projective_of_isLocalizedModule, Module.freeLocus_eq_univ_iff, Module.rankAtStalk, Module.isLocallyConstant_rankAtStalk
Q877775Projective spaceProjectivization.equivSubmodule, projectivizationSetoid, Projectivization, Projectivization.Subspace, Projectivization.Subspace.instInfSet, Projectivization.Subspace.span, Projectivization.Independent, Complex.exists_root, AlgebraicGeometry.Proj, littleWedderburn, Projectivization.map, Matrix.ProjGenLinGroup, Module.Grassmannian
Q837863Pure mathematicsirrational_sqrt_two
Q15909572Quadratic formulaquadratic_eq_zero_iff, discrim
Q472883Quadratic reciprocitylegendreSym.quadratic_reciprocity, legendreSym.quadratic_reciprocity_one_mod_four, legendreSym.quadratic_reciprocity_three_mod_four, ZMod.exists_sq_eq_neg_one_iff, ZMod.exists_sq_eq_two_iff, legendreSym.at_neg_one, ZMod.pow_card_sub_one_eq_one, legendreSym, ZMod.exists_sq_eq_neg_two_iff, jacobiSym.quadratic_reciprocity, jacobiSym
Q918099Ramsey's theoremFinite.exists_infinite_fiber
Q23937546Real projective lineProjectivization, Projectivization.equivSubmodule, projectivizationSetoid, Matrix.op_smul_eq_vecMul, Projectivization.generalLinearGroup_smul_def, Matrix.ProjGenLinGroup, OnePoint.smul_some_eq_ite
Q7322955Ricci calculusTensorProduct.contractLeft, Basis.ext_elem_iff, MultilinearMap.alternatization, fderiv_mul, CovariantDerivative, IsCovariantDerivativeOn.leibniz, extDeriv, VectorField.mlieBracket_self, Matrix.one_apply, CovariantDerivative.torsion
Q825857Riemann sphereonePointEquivSphereOfFinrankEq, OnePoint.equivProjectivization, stereographic, MeromorphicOn, MDifferentiable.exists_eq_const_of_compactSpace
Q753035Riemann surfaceMDifferentiable.comp, MDifferentiable.exists_eq_const_of_compactSpace
Q187235Riemann zeta functionriemannZeta, differentiableAt_riemannZeta, riemannZeta_residue_one, riemannZeta_eulerProduct_tprod, Nat.exists_infinite_primes, not_summable_one_div_on_primes, riemannZeta_one_sub, completedRiemannZeta_one_sub, RiemannHypothesis, riemannZeta_ne_zero_of_one_le_re, riemannZeta_two_mul_nat, riemannZeta_two, riemannZeta_neg_nat_eq_bernoulli, riemannZeta_neg_two_mul_nat_add_one, riemannZeta_zero, LSeries_zeta_mul_Lseries_moebius, mellin, hurwitzZeta
Q1208658Ring theoryCommRing, IsDomain, IsPrincipalIdealRing, EuclideanDomain, MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton, PrimeSpectrum, Module, Matrix.instRing, IsSimpleRing.exists_ringEquiv_matrix_divisionRing, jacobson_density, IsSemiprimaryRing.isNoetherian_iff_isArtinian, littleWedderburn, ringKrullDim, MvPolynomial.ringKrullDim_of_isNoetherianRing, IsMoritaEquivalent, CommRing.Pic, Ring.jacobson, Quaternion, MvPolynomial.IsSymmetric, MvPolynomial.esymmAlgEquiv
Q534131Root systemRootPairing.IsRootSystem, RootPairing.IsCrystallographic, RootPairing.IsReduced, RootPairing.IsIrreducible, RootPairing.Equiv, RootPairing.rootSpan, RootPairing.weylGroup, LieAlgebra.IsKilling.rootSystem, RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed, RootPairing.Base, RootPairing.Base.toWeightBasis, RootPairing.coroot, RootPairing.flip, RootPairing.flip_flip, RootPairing.Base.flip, LieAlgebra.IsKilling.isSimple_iff_isIrreducible, RootPairing.InvariantForm.exists_apply_eq_or
Q6500908Self-adjoint operatorIsSelfAdjoint, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, LinearPMap.graph, LinearPMap.adjoint, LinearMap.IsSymmetric, LinearPMap.IsSelfAdjoint, LinearMap.IsSymmetric.continuous, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, realPart_add_I_smul_imaginaryPart, ContinuousLinearMap.IsPositive.isSelfAdjoint, LinearMap.IsSymmetric.norm_eq_iSup_rayleighQuotient, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zero, resolventSet, spectrum, IsSelfAdjoint.val_re_map_spectrum, QuasispectrumRestricts.isSelfAdjoint, LinearMap.IsSymmetric.eigenvectorBasis, cfc, MeasureTheory.Measure.MutuallySingular
Q12482Set theoryCardinal, Cardinal.not_countable_real, Cardinal.cantor, Ordinal, Set.Mem, Set.Subset, Set.ssubset_iff_subset_ne, Set.union, Set.inter, Set.diff, Set.compl, symmDiff, Set.prod, Set.instEmptyCollectionSet, Set.powerset, ZFSet.rank
Q331350SimplexAffine.Simplex, Affine.Simplex.mkOfPoint, stdSimplex_fin_two, Affine.Triangle, stdSimplex, Geometry.SimplicialComplex, AbstractSimplicialComplex, Affine.Simplex.face, single_mem_stdSimplex, AffineBasis.coord, stdSimplex_unique, Basis.addHaar_parallelepiped, TopCat.toSSetObjEquiv, CategoryTheory.SimplicialObject
Q420904Singular value decompositionLinearMap.singularValues, LinearMap.card_support_singularValues, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Matrix.IsHermitian.spectral_theorem, Matrix.frobenius_norm_def
Q190667Slide ruleReal.log_mul, quadratic_eq_zero_iff, Real.logb, div_add_one
Q133327SpacetimeEuclideanSpace.dist_eq, Isometry.dist_eq, IsRiemannianManifold
Q3503315Spectral sequenceCategoryTheory.CohomologicalSpectralSequence, CategoryTheory.SpectralSequence.page, CategoryTheory.SpectralSequence, CategoryTheory.SpectralSequence.Hom, HomologicalComplex₂, HomologicalComplex₂.total, CategoryTheory.CohomologicalSpectralSequenceNat
Q1425077Spectral theoremMatrix.IsHermitian.spectral_theorem, LinearMap.IsSymmetric, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, Module.End.HasEigenvector, LinearMap.IsSymmetric.direct_sum_isInternal, Module.End.eigenspace, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, IsStarNormal, ContinuousLinearMap.orthogonalComplement_iSup_eigenspaces_eq_bot, cfc
Q2409122Spectral theoryresolventSet, spectrum, resolvent, Module.End.HasEigenvalue.mem_spectrum, IsSelfAdjoint.mem_spectrum_eq_re, InnerProductSpace.rankOne, Module.End.HasEigenvalue, OrthonormalBasis.sum_rankOne_eq_id, OrthonormalBasis.sum_repr', IsSelfAdjoint.hasEigenvector_of_isMaxOn
Q203218Spherical coordinate systemMetric.sphere
Q164Squareirrational_sqrt_two, IsSquare, DihedralGroup, norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two
Q389813Square root of 2Real.sqrt, irrational_sqrt_two, irrational_sqrt_natCast_iff, Real.cos_pi_div_four
Q193394Squaring the circleEuclideanSpace.volume_ball_fin_two, intermediate_value_Icc, integral_inv, irrational_pi
Q7598372Standard probability spaceMeasureTheory.Measure.map, MeasurableSpace.CountablySeparated, MeasurableSpace.CountablyGenerated, MeasureTheory.Measure.condKernel
Q2500758Stationary pointIsLocalMin, IsLocalMax, IsLocalExtr, IsExtrOn, IsLocalExtr.deriv_eq_zero, isLocalMin_of_deriv_deriv_pos
Q80918Stirling numberNat.stirlingFirst, Nat.stirlingSecond, descPochhammer_zero, Ring.descPochhammer_eq_factorial_smul_choose
Q484298Surface (topology)chartAt, ModelWithCorners.IsBoundaryPoint, ModelWithCorners.IsInteriorPoint, SmoothBumpCovering.exists_embedding_euclidean_of_compact
Q229102Surjective functionFunction.Surjective, Function.surjective_id, Real.log_surjective, Prod.fst_surjective, Function.Bijective, Function.RightInverse, Function.surjective_iff_hasRightInverse, Set.image_preimage_eq, Function.injective_comp_right_iff_surjective, CategoryTheory.Types.epi_iff_surjective, CategoryTheory.IsSplitEpi.epi, CategoryTheory.SplitEpi.section_, CategoryTheory.IsSplitEpi, Cardinal.mk_le_of_surjective, Fintype.injective_iff_surjective_of_equiv, Function.Surjective.comp, Set.rangeFactorization_surjective, Setoid.quotientKerEquivOfSurjective
Q849512Symmetric groupEquiv.Perm, Fintype.card_perm, Equiv.Perm.subgroupOfMulAction, Equiv.permUnique, Equiv.Perm.permGroup, Equiv.Perm.mul_apply, Equiv.Perm.IsSwap, Equiv.Perm.closure_isSwap, Equiv.Perm.sign, Equiv.Perm.sign_prod_list_swap, Equiv.Perm.sign_mul, alternatingGroup, Equiv.Perm.alternatingGroup.index_eq_two, Equiv.Perm.mclosure_swap_castSucc_succ, Equiv.Perm.IsCycle, Equiv.Perm.IsCycle.orderOf, Equiv.Perm.card_support_eq_two, Equiv.Perm.Disjoint, Equiv.Perm.Disjoint.commute, Equiv.Perm.truncCycleFactors, Fin.revPerm, Fin.rev_rev, Equiv.Perm.isConj_iff_cycleType_eq, Equiv.Perm.partition, Equiv.Perm.fin_5_not_solvable, Equiv.Perm.alternatingGroup.isSimpleGroup, Subgroup, Equiv.Perm.isCoatom_stabilizer, Sylow.isPGroup', IteratedWreathProduct, MulAction.IsPretransitive, Polynomial.Gal.galAction_isPretransitive, Subgroup.zpowers, Equiv.Perm.lcm_cycleType, MonoidAlgebra.instIsSemisimpleModule (Maschke)
Q21030012Symmetry (geometry)MulAction.stabilizer, AffineIsometryEquiv.pointReflection
Q2431134Symmetry in mathematicsFunction.Even, Function.Odd, Matrix.IsSymm, Matrix.IsSymm.apply, Matrix.isSymm_diagonal, Matrix.isHermitian_iff_isSymmetric, Equiv.Perm, Fintype.card_perm, MvPolynomial.IsSymmetric, MvPolynomial.esymmAlgHom_surjective, SymmetricPower, Polynomial.Gal.galActionHom, CategoryTheory.Aut, MulAut, LinearMap.GeneralLinearGroup, RingAut, LinearMap.BilinForm.IsAlt.neg_eq, Symmetric, Isometry, Congruent
Q11203System of linear equationsMatrix.mulVec_eq_sum, Matrix.mulVec, Matrix.mulVec_cramer, Matrix.inv_mulVec_eq_vec, Matrix.mulVec_zero, Matrix.mulVec_add, Matrix.mulVecLin, LinearMap.sub_mem_ker_iff, LinearMap.mem_range
Q746550Tangent bundleTangentBundle, Bundle.TotalSpace.mk, Bundle.TotalSpace.proj, ContMDiff.contMDiff_tangentMap, tangentBundleCore, TangentSpace.vectorBundle, ContMDiffSection
Q909601Tangent spaceTangentSpace, range_mfderiv_coe_sphere, TangentBundle, ContMDiff, ContMDiffMap.algebra, Derivation, Derivation.map_algebraMap, PointDerivation, NormedSpace.fromTangentSpace, lineDeriv, tangentMap
Q1137206Taylor's theoremtaylor_mean_remainder_lagrange, hasDerivAt_iff_isLittleO, taylorWithinEval, taylor_isLittleO, taylorWithin, taylor_mean_remainder, taylor_integral_remainder, taylor_mean_remainder_bound, exists_taylor_mean_remainder_bound, AnalyticAt, FormalMultilinearSeries.radius_inv_eq_limsup, HasFPowerSeriesOnBall.tendstoUniformlyOn, expNegInvGlue.not_analyticAt_zero, DifferentiableOn.analyticOnNhd, Complex.circleIntegral_div_sub_of_differentiable_on_off_countable, DifferentiableOn.contDiffOn, Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le, HasFDerivAt, fderiv
Q214856TessellationDiscreteTiling.Prototile
Q65943TheoremEuclideanGeometry.angle_add_angle_add_angle_eq_pi, FermatLastTheorem, even_iff_two_dvd, FirstOrder.Language.Theory, FirstOrder.Language.Sentence
Q1154787Theta functionjacobiTheta₂, jacobiTheta₂_add_left', jacobiTheta₂_add_left, jacobiTheta_S_smul, jacobiTheta₂_functional_equation, Complex.betaIntegral, Complex.betaIntegral_eq_Gamma_mul_div, Nat.Partition, Nat.Partition.hasProd_powerSeriesMk_card_restricted, pentagonal, Nat.Partition.distincts, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted
Q2393193Time complexityTuring.TM2ComputableInPolyTime
Q737279Timeline of mathematicsirrational_sqrt_two, Nat.exists_infinite_primes, ZMod.chineseRemainder, Real.sin, sq_add_sq_mul_sq_add_sq, EuclideanSpace.volume_ball, Real.arctan, add_pow, fermatLastTheoremThree, EuclideanGeometry.law_sin, Nat.rec, Real.sin_add, pow_eq_pow_iff_of_ne_zero, exists_deriv_eq_zero, Complex.hasSum_arctan, exists_deriv_eq_slope, intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le, Real.hasSum_pow_div_log_of_abs_lt_1, taylor_mean_remainder_lagrange, deriv.lhopital_zero_nhds, bernoulli, taylorWithin, Complex.cos_add_sin_mul_I_pow, ProbabilityTheory.gaussianReal, hasSum_zeta_two, ProbabilityTheory.cond_eq_inv_mul_cond_mul, irrational_pi, MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable, Complex.exists_root, intermediate_value_Icc, Metric.tendsto_nhds_nhds, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, Nat.infinite_setOf_prime_and_eq_mod, TendstoUniformly, Quaternion, BooleanAlgebra, IsRiemannianManifold, RiemannHypothesis, Cardinal.not_countable_real, CommRing, MeasureTheory.IsProbabilityMeasure, Computable
Q42989TopologyTopologicalSpace, Homeomorph, ContinuousMap.HomotopyEquiv, IsOpen, IsClosed, IsClopen, TopologicalSpace.OpenNhds, Continuous, ChartedSpace, IsCompact, IsConnected, MetricSpace, Metric.isOpen_iff, subgroupIsFreeOfIsFree, CategoryTheory.GrothendieckTopology
Q173091Transcendental numberTranscendental, Transcendental.irrational, transcendental_liouvilleNumber, Liouville, Liouville.transcendental, Algebraic.countable
Q208216Triangle inequalitydist_triangle, norm_add_le, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, dist_le_range_sum_dist, sameRay_iff_norm_add, Real.norm_eq_abs, PiLp.norm_eq_sum, EuclideanSpace.norm_eq, norm_inner_eq_norm_iff, Real.Lp_add_le, Filter.Tendsto.cauchySeq, abs_norm_sub_norm_le, lipschitzWith_one_norm
Q8084TrigonometryReal.sin, Real.cos, Real.tan, Real.cos_pi_div_two_sub, Circle, Real.arctan, Complex.hasSum_sin, Complex.exp_mul_I, EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, Real.sin_sq_add_cos_sq, Complex.sin
Q163310Turing machineTuring.TM0.Machine, ComputablePred.halting_problem, Turing.TM0.Cfg
Q658429Vector bundleVectorBundle, Bundle.Trivial.vectorBundle, tangentBundleCore, FiberBundle, Bundle.Trivialization, Bundle.Trivial, VectorBundleCore.coordChange, FiberBundleCore.coordChange_comp, FiberBundleCore.fiberBundle, VectorBundle.prod, Bundle.ContinuousLinearMap.vectorBundle, VectorBundle.pullback, RiemannianBundle, ContMDiffVectorBundle
Q200802Vector calculuscrossProduct, triple_product_eq_det, MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le, HasFDerivAt, IsLocalExtr.fderiv_eq_zero, EuclideanSpace, TangentBundle
Q1970172Von Neumann algebraVonNeumannAlgebra, WStarAlgebra, IsStarProjection
Q37172WavefourierIntegral_gaussian
Q831390WaveletMeasureTheory.Lp
Q659746Well-orderIsWellOrder, WellOrder, WellFounded.has_min, SuccOrder.ofLinearWellFoundedLT, WellFoundedLT.conditionallyCompleteLinearOrderBot, isWellOrder_lt, Ordinal.type, exists_wellFoundedLT, WellFoundedLT.induction, type_nat_lt, PrincipalSeg.ofElement, InitialSeg.isLowerSet_range, ZFSet.IsOrdinal, PrincipalSeg.irrefl, InitialSeg.total, InitialSeg.image_Iio, Ordinal, Preorder.topology, IsCofinal, Ordinal.type_fintype
Q576728Winding numberFundamentalGroup
Q3573180YuktibhāṣāReal.hasSum_arctan, Real.tendsto_sum_pi_div_four, Real.pi_lt_d20, Real.hasSum_sin, Real.cos_add, taylor_mean_remainder_lagrange
Q290810Zorn's lemmazorn_le, IsChain.exists_maxChain, PartialOrder, GE.ge, LinearOrder, Subtype.partialOrder, IsChain, IsMax, upperBounds, exists_maximal_of_chains_bounded, zorn_le_nonempty_Ici₀, Module.Basis.exists_basis, Ideal.exists_maximal, isCompact_univ_pi, ChainCompletePartialOrder.nonempty_fixedPoints_of_inflationary, exists_extension_of_le_sublinear, Ultrafilter.exists_le