General documentation

index
foundational types

Library

AdeleRingLocallyCompact (file)
Algebra
Field
Subfield
Order
GroupWithZero
Canonical
WithZero
Ring
Equiv
Analysis
NormedSpace
Completion
FromLocalClassFieldTheory
LocalClassFieldTheory
NumberTheory
NumberField
AdeleRing
Completion
InfiniteAdeleRing
RingTheory
DedekindDomain
AdicValuation
Factorization
FiniteAdeleRing
FinsetAdeleRing
Ideal
Quotient
Topology
Algebra
UniformRing
Instances
Real
UniformSpace
Basic
Aesop (file)
Builder (file)
Apply
Basic
Cases
Constructors
Default
Forward
NormSimp
Tactic
Unfold
BuiltinRules (file)
ApplyHyps
Assumption
DestructProducts
Ext
Intros
Split
Subst
Frontend (file)
Extension (file)
Init
Attribute
Basic
Command
RuleExpr
Saturate
Tactic
Index (file)
Basic
Options (file)
Internal
Public
Rule (file)
Basic
Name
RuleSet (file)
Filter
Member
Name
RuleTac (file)
Forward (file)
Basic
Apply
Basic
Cases
ElabRuleTerm
Preprocess
Tactic
Script
Check
CtorNames
GoalWithMVars
Main
OptimizeSyntax
SScript
ScriptM
SpecificTactics
Step
StructureDynamic
StructureStatic
Tactic
TacticState
UScript
UScriptToSScript
Util
Search
Expansion (file)
Basic
Norm
Simp
Queue (file)
Class
ExpandSafePrefix
Main
RuleSelection
SearchM
Stats
Basic
Extension
Report
Tree (file)
AddRapp
Check
Data
ExtractProof
ExtractScript
Free
RunMetaM
State
Tracing
Traversal
TreeM
UnsafeQueue
Util
Tactic (file)
Ext
Unfold
Basic
EqualUpToIds
UnionFind
UnorderedArraySet
Check
Constants
ElabM
Exception
Main
Nanos
Percent
RulePattern
Saturate
Tracing
Batteries
Classes
BEq
Order
RatCast
SatisfiesM
CodeAction (file)
Attr
Basic
Deprecated
Misc
Control
ForInStep
Basic
Lemmas
Nondet
Basic
Data
Array
Init
Lemmas
Basic
Lemmas
Match
Merge
Monadic
BinomialHeap
Basic
Fin
Basic
Lemmas
HashMap
Basic
WF
Int
DivMod
Order
List
Init
Attach
Lemmas
Basic
Count
EraseIdx
Lemmas
Pairwise
Perm
MLList
Basic
Heartbeats
Nat
Basic
Gcd
Lemmas
RBMap
Alter
Basic
WF
Rat
Basic
Lemmas
String (file)
Basic
Lemmas
Matcher
Sum
Basic
Lemmas
AssocList
Char
DList
LazyList
Thunk
UInt
Lean
Meta
AssertHypotheses
Basic
Clear
DiscrTree
Expr
Inaccessible
InstantiateMVars
SavedState
UnusedNames
AttributeExtra
Except
Expr
Float
HashSet
MonadBacktrack
NameMap
NameMapAttribute
PersistentHashMap
PersistentHashSet
Position
SMap
Syntax
TagAttribute
Linter (file)
UnnecessarySeqFocus
UnreachableTactic
Tactic
Lint (file)
Basic
Frontend
Misc
Simp
TypeClass
Alias
Basic
Classical
Congr
Exact
Init
OpenPrivate
PermuteGoals
SeqFocus
SqueezeScope
Unreachable
Where
Util
Cache
ExtendedBinder
LibraryNote
ProofWanted
Logic
WF
ImportGraph
Imports
RequiredModules
Init (file)
Control (file)
Lawful (file)
Basic
Instances
Basic
EState
Except
ExceptCps
Id
Option
Reader
State
StateCps
StateRef
Data (file)
Array (file)
Subarray (file)
Split
Basic
BasicAux
BinSearch
DecidableEq
InsertionSort
Lemmas
Mem
QSort
BitVec (file)
Basic
Bitblast
Folds
Lemmas
ByteArray (file)
Basic
Char (file)
Basic
Lemmas
Fin (file)
Basic
Fold
Iterate
Lemmas
Log2
FloatArray (file)
Basic
Format (file)
Basic
Instances
Macro
Syntax
Int (file)
Bitwise (file)
Lemmas
Basic
DivMod
DivModLemmas
Gcd
Lemmas
Order
Pow
List (file)
Basic
BasicAux
Control
Impl
Lemmas
Notation
TakeDrop
Nat (file)
Bitwise (file)
Basic
Lemmas
Basic
Compare
Control
Div
Dvd
Gcd
Lcm
Lemmas
Linear
Log2
MinMax
Mod
Power2
SOM
Simproc
Option (file)
Basic
BasicAux
Instances
Lemmas
String (file)
Basic
Extra
Lemmas
ToString (file)
Basic
Macro
UInt (file)
Basic
Lemmas
Log2
AC
Basic
Bool
Cast
Channel
Float
Hashable
OfScientific
Ord
Prod
Queue
Random
Range
Repr
Stream
Sum
Grind (file)
Cases
Lemmas
Norm
Tactics
Omega (file)
Coeffs
Constraint
Int
IntList
LinearCombo
Logic
System (file)
FilePath
IO
IOError
Mutex
Platform
Promise
ST
Uri
BinderPredicates
ByCases
Classical
Coe
Conv
Core
Dynamic
Ext
GetElem
Guard
Hints
MacroTrace
Meta
MetaTypes
Notation
NotationExtra
Prelude
PropLemmas
RCases
ShareCommon
SimpLemmas
Simproc
SizeOf
SizeOfLemmas
Tactics
TacticsExtra
Util
WF
WFTactics
Lake (file)
Build (file)
Actions
Basic
Common
Data
Executable
Facets
Fetch
Imports
Index
Info
Job
Key
Library
Module
Package
Run
Store
Targets
Topological
Trace
CLI
Actions
Build
Error
Config (file)
Context
Defaults
Dependency
Env
ExternLib
ExternLibConfig
FacetConfig
Glob
InstallPath
LeanConfig
LeanExe
LeanExeConfig
LeanLib
LeanLibConfig
Module
Monad
Opaque
Package
Script
TargetConfig
Workspace
WorkspaceConfig
DSL (file)
Attributes
AttributesCore
Config
DeclUtil
Extensions
Meta
Package
Require
Script
Targets
Load
Config
Toml (file)
Data
DateTime
Dict
Value
Elab (file)
Expression
Value
Grammar
Load
ParserUtil
Util
Binder
Casing
Compare
Cycle
DRBMap
EStateT
EquipT
Error
Exit
Family
FilePath
Git
IO
JsonObject
Lift
List
Lock
Log
Message
Name
NativeLib
Opaque
OrdHashSet
OrderedTagAttribute
Proc
RBArray
Store
StoreInsts
Sugar
Task
Version
Lean (file)
Compiler (file)
IR (file)
Basic
Borrow
Boxing
Checker
CompilerM
CtorLayout
ElimDeadBranches
ElimDeadVars
EmitC
EmitUtil
ExpandResetReuse
Format
FreeVars
LiveVars
NormIds
PushProj
RC
ResetReuse
SimpCase
Sorry
UnboxResult
LCNF (file)
Simp (file)
Basic
Config
ConstantFold
DefaultAlt
DiscrM
FunDeclInfo
InlineCandidate
InlineProj
JpCases
Main
SimpM
SimpValue
Used
AlphaEqv
AuxDeclCache
BaseTypes
Basic
Bind
CSE
Check
Closure
CompatibleTypes
CompilerM
ConfigOptions
DeclHash
DependsOn
ElimDead
ElimDeadBranches
FVarUtil
FixedParams
FloatLetIn
ForEachExpr
InferType
Internalize
JoinPoints
LCtx
LambdaLifting
Level
Main
MonadScope
MonoTypes
OtherDecl
PassManager
Passes
PhaseExt
PrettyPrinter
PullFunDecls
PullLetDecls
ReduceArity
ReduceJpArity
Renaming
ScopeM
SpecInfo
Specialize
Testing
ToDecl
ToExpr
ToLCNF
ToMono
Types
Util
AtMostOnce
BorrowedAnnotation
CSimpAttr
ClosedTermCache
ConstFolding
ExportAttr
ExternAttr
FFI
ImplementedByAttr
InitAttr
InlineAttrs
Main
NameMangling
NeverExtractAttr
NoncomputableAttr
Old
Options
Specialize
Data (file)
Json (file)
Basic
Elab
FromToJson
Parser
Printer
Stream
Lsp (file)
Basic
Capabilities
Client
CodeActions
Communication
Diagnostics
Extra
InitShutdown
Internal
Ipc
LanguageFeatures
TextSync
Utf16
Workspace
Xml (file)
Basic
Parser
Array
AssocList
Format
FuzzyMatching
HashMap
HashSet
JsonRpc
KVMap
LBool
LOption
Name
NameMap
NameTrie
OpenDecl
Options
Parsec
PersistentArray
PersistentHashMap
PersistentHashSet
Position
PrefixTree
RBMap
RBTree
Rat
SMap
SSet
Trie
DocString (file)
Extension
Elab (file)
Deriving (file)
BEq
Basic
DecEq
FromToJson
Hashable
Inhabited
Nonempty
Ord
Repr
SizeOf
TypeName
Util
InfoTree (file)
Main
Types
PreDefinition (file)
Structural (file)
BRecOn
Basic
Eqns
FindRecArg
IndPred
Main
Preprocess
SmartUnfolding
WF (file)
Eqns
Fix
GuessLex
Ite
Main
PackMutual
Preprocess
Rel
TerminationArgument
TerminationHint
Basic
Eqns
Main
MkInhabitant
Quotation (file)
Precheck
Util
Tactic (file)
Conv (file)
Basic
Change
Congr
Delta
Pattern
Rewrite
Simp
Unfold
Omega (file)
Core
Frontend
MinNatAbs
OmegaM
Basic
BuiltinTactic
Cache
Calc
Change
Config
Congr
Delta
Doc
ElabTerm
Ext
FalseOrByContra
Generalize
Guard
Induction
Injection
LibrarySearch
Location
Match
Meta
NormCast
RCases
Repeat
Rewrite
Rewrites
Rfl
ShowTerm
Simp
SimpTrace
Simpa
Simproc
SolveByElim
Split
Symm
Unfold
App
Arg
Attributes
AutoBound
AuxDef
BinderPredicates
Binders
BindersUtil
BuiltinCommand
BuiltinNotation
BuiltinTerm
Calc
CheckTactic
Command
ComputedFields
Config
DeclModifiers
DeclNameGen
DeclUtil
Declaration
DeclarationRange
DefView
Do
ElabRules
Eval
Exception
Extra
Frontend
GenInjective
GuardMsgs
Import
Inductive
InheritDoc
LetRec
Level
Macro
MacroArgUtil
MacroRules
Match
MatchAltView
MatchExpr
Mixfix
MutualDef
Notation
Open
ParseImportsFast
PatternVar
Print
RecAppSyntax
SetOption
StructInst
Structure
Syntax
SyntheticMVars
Term
Util
Language
Basic
Lean
Linter (file)
Basic
Builtin
ConstructorAsVariable
Deprecated
MissingDocs
UnusedVariables
Util
Meta (file)
ArgsPacker (file)
Basic
Constructions (file)
BRecOn
RecOn
Match (file)
MatcherApp
Basic
Transform
Basic
CaseArraySizes
CaseValues
Match
MatchEqs
MatchEqsExt
MatchPatternAttr
MatcherInfo
Value
Tactic (file)
AC (file)
Main
Grind (file)
Attr
Cases
Core
Injection
Preprocessor
RevertAll
Types
Util
LinearArith (file)
Nat (file)
Basic
Simp
Solver
Basic
Main
Simp
Solver
Simp (file)
BuiltinSimprocs (file)
BitVec
Char
Core
Fin
Int
Nat
String
UInt
Util
Attr
Diagnostics
Main
RegisterCommand
Rewrite
SimpAll
SimpCongrTheorems
SimpTheorems
Simproc
Types
Acyclic
Apply
Assert
Assumption
AuxLemma
Backtrack
Cases
Cleanup
Clear
Congr
Constructor
Contradiction
Delta
ElimInfo
FVarSubst
FunInd
Generalize
IndependentOf
Induction
Injection
Intro
LibrarySearch
NormCast
Refl
Rename
Repeat
Replace
Revert
Rewrite
Rewrites
Rfl
SolveByElim
Split
SplitIf
Subst
Symm
TryThis
Unfold
UnifyEq
Util
ACLt
AbstractMVars
AbstractNestedProofs
AppBuilder
Basic
Canonicalizer
Check
CheckTactic
Closure
Coe
CoeAttr
CollectFVars
CollectMVars
CompletionName
CongrTheorems
CtorRecognizer
DecLevel
Diagnostics
DiscrTree
DiscrTreeTypes
Eqns
Eval
ExprDefEq
ExprLens
ExprTraverse
ForEachExpr
FunInfo
GeneralizeTelescope
GeneralizeVars
GetUnfoldableConst
GlobalInstances
IndPredBelow
Inductive
InferType
Injective
Instances
Iterator
KAbstract
KExprMap
LazyDiscrTree
LevelDefEq
LitValues
MatchUtil
NatInstTesters
Offset
PPGoal
RecursorInfo
Reduce
ReduceEval
SizeOf
Structure
SynthInstance
Transform
TransparencyMode
UnificationHint
WHNF
Parser (file)
Tactic (file)
Doc
Attr
Basic
Command
Do
Extension
Extra
Level
Module
StrInterpolation
Syntax
Term
Types
ParserCompiler (file)
Attribute
PrettyPrinter (file)
Delaborator (file)
Attributes
Basic
Builtins
FieldNotation
Options
SubExpr
TopDownAnalyze
Basic
Formatter
Parenthesizer
Server (file)
CodeActions (file)
Attr
Basic
Provider
FileWorker (file)
RequestHandling
SetupFile
Utils
WidgetRequests
Rpc (file)
Basic
Deriving
RequestHandling
AsyncList
Completion
CompletionItemData
FileSource
GoTo
ImportCompletion
InfoUtils
References
Requests
Snapshots
Utils
Watchdog
Util (file)
CollectFVars
CollectLevelParams
CollectMVars
Diff
FileSetupInfo
FindExpr
FindLevelMVar
FindMVar
FoldConsts
ForEachExpr
ForEachExprWhere
HasConstCache
Heartbeats
InstantiateLevelParams
LakePath
LeanOptions
MonadBacktrack
MonadCache
OccursCheck
PPExt
Path
Paths
Profile
Profiler
PtrSet
RecDepth
Recognizers
ReplaceExpr
ReplaceLevel
SCC
ShareCommon
Sorry
TestExtern
Trace
Widget (file)
Basic
Diff
InteractiveCode
InteractiveDiagnostic
InteractiveGoal
TaggedText
Types
UserWidget
AddDecl
Attributes
AuxRecursor
BuiltinDocAttr
Class
CoreM
Declaration
DeclarationRange
Environment
Eval
Exception
Expr
HeadIndex
Hygiene
ImportingFlag
InternalExceptionId
KeyedDeclsAttribute
LabelAttribute
LazyInitExtension
Level
LoadDynlib
LocalContext
Log
Message
MetavarContext
Modifiers
MonadEnv
ProjFns
ReducibilityAttrs
ReservedNameAction
ResolveName
Runtime
ScopedEnvExtension
Structure
SubExpr
Syntax
ToExpr
Mathlib (file)
Algebra
AddConstMap
Basic
Equiv
Algebra
Hom (file)
Rat
Subalgebra
Basic
Directed
MulOpposite
Operations
Order
Pointwise
Prod
Rank
Tower
Unitization
Basic
Bilinear
Defs
Equiv
Field
NonUnitalHom
NonUnitalSubalgebra
Operations
Opposite
Pi
Prod
Quasispectrum
Rat
RestrictScalars
Spectrum
Tower
Unitization
Associated
Basic
OrderedCommMonoid
BigOperators
Group
Finset
List
Multiset
GroupWithZero
Finset
Ring (file)
List
Multiset
Nat
Associated
Fin
Finprod
Finsupp
Intervals
Module
NatAntidiagonal
Option
Pi
RingEquiv
WithTop
Category
AlgebraCat
Basic
Limits
Monoidal
Symmetric
BialgebraCat
Basic
CoalgebraCat
Basic
ComonEquivalence
FGModuleCat
Basic
Limits
Grp
AB5
Abelian
Adjunctions
Basic
Biproducts
Colimits
EnoughInjectives
EpiMono
EquivalenceGroupAddGroup
FilteredColimits
ForgetCorepresentable
Images
Injective
Kernels
Limits
Preadditive
Subobject
ZModuleEquivalence
Zero
HopfAlgebraCat
Basic
ModuleCat
Differentials
Basic
Presheaf
Monoidal
Basic
Closed
Symmetric
Presheaf (file)
Abelian
ChangeOfRings
Colimits
Limits
Pushforward
Sheafification
Sheafify
Sheaf (file)
Abelian
ChangeOfRings
Colimits
Free
Generators
Limits
PushforwardContinuous
Quasicoherent
Abelian
Adjunctions
Algebra
Basic
Biproducts
ChangeOfRings
Colimits
EpiMono
FilteredColimits
Free
Images
Injective
Kernels
Limits
Products
Projective
Simple
Subobject
Tannaka
MonCat
Adjunctions
Basic
Colimits
FilteredColimits
Limits
Ring
Adjunctions
Basic
Colimits
Constructions
FilteredColimits
Instances
Limits
Semigrp
Basic
BoolRing
GrpWithZero
CharP
Algebra
Basic
CharAndCard
Defs
ExpChar
IntermediateField
Invertible
LocalRing
MixedCharZero
Pi
Quotient
Reduced
Subring
Two
CharZero
Defs
Infinite
Lemmas
Quotient
ContinuedFractions
Computation
ApproximationCorollaries
Approximations
Basic
CorrectnessTerminating
TerminatesIffRat
Translations
Basic
ContinuantsRecurrence
ConvergentsEquiv
Determinant
TerminatedStable
Translations
DirectSum
Algebra
Basic
Decomposition
Finsupp
Internal
LinearMap
Module
Ring
Divisibility
Basic
Prod
Units
EuclideanDomain
Basic
Defs
Field
Int
Field
Basic
Defs
Equiv
IsField
MinimalAxioms
Opposite
Power
Rat
Subfield
ULift
FreeMonoid
Basic
Count
GCDMonoid
Basic
Finset
IntegrallyClosed
Multiset
Nat
Group
Action
Basic
Defs
Opposite
Option
Pi
Prod
Sigma
Sum
Units
Commute
Basic
Defs
Hom
Units
Equiv
Basic
TypeTags
Fin
Basic
Tuple
Hom
Basic
CompTypeclasses
Defs
End
Instances
Invertible
Basic
Defs
Pi
Basic
Lemmas
Semiconj
Basic
Defs
Units
Subgroup
Actions
Basic
Finite
MulOpposite
Order
Pointwise
ZPowers
Submonoid
Basic
DistribMulAction
Membership
MulOpposite
Operations
Pointwise
Units
Subsemigroup
Basic
Membership
Operations
Units (file)
Equiv
Hom
WithOne
Basic
Defs
AddChar
Aut
Basic
Center
Commutator
Conj
ConjFinite
Defs
Embedding
Even
Ext
FiniteSupport
Indicator
InjSurj
Int
MinimalAxioms
Nat
NatPowAssoc
Opposite
PNatPowAssoc
Prod
Support
TypeTags
ULift
UniqueProds
ZeroOne
GroupPower
IterateHom
GroupWithZero
Action
Defs
Opposite
Units
Basic
Equiv
Lemmas
Basic
Center
Commute
Conj
Defs
Divisibility
Hom
Indicator
InjSurj
Invertible
NeZero
NonZeroDivisors
Opposite
Pi
Prod
Semiconj
ULift
WithZero
Homology
DerivedCategory
Basic
ExactFunctor
Ext
HomologySequence
ShortExact
SingleTriangle
Embedding
Basic
Boundary
Extend
IsSupported
Restriction
TruncGE
Factorizations
Basic
HomotopyCategory (file)
DegreewiseSplit
HomComplex
HomComplexShift
HomologicalFunctor
MappingCone
Pretriangulated
Shift
ShiftSequence
ShortExact
SingleFunctors
Triangulated
ShortComplex
Ab
Abelian
Basic
ConcreteCategory
Exact
ExactFunctor
FunctorEquivalence
HomologicalComplex
Homology
LeftHomology
Limits
Linear
ModuleCat
Preadditive
PreservesHomology
QuasiIso
RightHomology
ShortExact
SnakeLemma
Additive
Augment
Bifunctor
BifunctorHomotopy
BifunctorShift
CommSq
ComplexShape
ComplexShapeSigns
ConcreteCategory
DifferentialObject
ExactSequence
Functor
HomologicalBicomplex
HomologicalComplex
HomologicalComplexAbelian
HomologicalComplexBiprod
HomologicalComplexLimits
HomologySequence
HomologySequenceLemmas
Homotopy
HomotopyCofiber
ImageToKernel
Linear
LocalCohomology
Localization
Opposite
QuasiIso
Refinements
Single
SingleHomology
TotalComplex
TotalComplexShift
TotalComplexSymmetry
Jordan
Basic
Lie
Derivation
AdjointAction
Basic
Killing
Semisimple
Basic
Defs
Weights
Basic
Cartan
Chain
Killing
Linear
RootSystem
Abelian
BaseChange
Basic
CartanExists
CartanMatrix
CartanSubalgebra
Character
Classical
DirectSum
Engel
EngelSubalgebra
Free
IdealOperations
InvariantForm
Killing
Matrix
Nilpotent
NonUnitalNonAssocAlgebra
Normalizer
OfAssociative
Quotient
Rank
SkewAdjoint
Sl2
Solvable
Subalgebra
Submodule
TensorProduct
TraceForm
UniversalEnveloping
Module
Equiv
Basic
Defs
LinearMap
Basic
Defs
End
Polynomial
Prod
Rat
Star
Submodule
Basic
Bilinear
EqLocus
Equiv
IterateMapComap
Ker
Lattice
LinearMap
Localization
Map
Order
Pointwise
Range
RestrictScalars
Zlattice
Basic
Covolume
Algebra
Basic
BigOperators
Bimodule
Card
CharacterModule
DedekindDomain
Defs
FinitePresentation
GradedModule
Hom
Injective
LocalizedModule
LocalizedModuleIntegers
MinimalAxioms
Opposites
PID
Pi
PointwisePi
Prod
Projective
Rat
Torsion
ULift
MonoidAlgebra
Basic
Degree
Division
Grading
Ideal
NoZeroDivisors
Support
ToDirectSum
MvPolynomial
Basic
Cardinal
Comap
CommRing
Counit
Degrees
Derivation
Division
Equiv
Expand
Funext
Invertible
Monad
PDeriv
Polynomial
Rename
Supported
Variables
Order
Antidiag
Finsupp
Pi
Prod
BigOperators
Group
Finset
List
Multiset
Ring
Finset
List
Multiset
CauSeq
Basic
BigOperators
Completion
Field
Canonical
Basic
Defs
Unbundled
Basic
Basic
Defs
InjSurj
Pi
Power
Rat
Subfield
Floor (file)
Div
Prime
Group
Unbundled
Abs
Basic
Abs
Action
Basic
Bounds
Cone
Defs
DenselyOrdered
Indicator
InjSurj
Instances
Int
Lattice
MinMax
Nat
OrderIso
PiLex
PosPart
Prod
Synonym
TypeTags
Units
GroupWithZero
Canonical
Synonym
Unbundled
WithZero
Hom
Basic
Monoid
Ring
Interval
Set
Group
Instances
Monoid
Basic
Finset
Multiset
Module
Algebra
Defs
OrderedSMul
Pointwise
Synonym
Monoid
Canonical
Defs
Unbundled
Basic
Defs
ExistsOfLE
MinMax
OrderDual
Pow
WithTop
Basic
Defs
NatCast
OrderDual
Prod
Submonoid
ToMulBot
TypeTags
Units
WithTop
Nonneg
Field
Floor
Module
Ring
Positive
Field
Ring
Ring
Unbundled
Basic
Nonneg
Abs
Basic
Canonical
Cast
Cone
Defs
Finset
InjSurj
Int
Nat
Pow
Prod
Rat
Star
Synonym
WithTop
Sub
Basic
Canonical
Defs
Prod
WithTop
AbsoluteValue
AddGroupWithTop
AddTorsor
Algebra
Archimedean
Chebyshev
CompleteField
EuclideanAbsoluteValue
Invertible
Kleene
Monovary
Pi
Pointwise
Rearrangement
Sum
ToIntervalMod
UpperLower
ZeroLEOne
PUnitInstances
Algebra
Module
Order
Pointwise
Stabilizer
Polynomial
Degree
CardPowDegree
Definitions
Lemmas
TrailingDegree
Module
AEval
Basic
FiniteDimensional
AlgebraMap
Basic
BigOperators
Bivariate
CancelLeads
Cardinal
Coeff
DenomsClearable
Derivation
Derivative
Div
EraseLead
Eval
Expand
FieldDivision
GroupRingAction
HasseDeriv
Identities
Induction
Inductions
Laurent
Lifts
Mirror
Monic
Monomial
PartialFractions
Reverse
RingDivision
Roots
Smeval
SpecificDegree
Splits
Taylor
UnitTrinomial
Regular
Basic
Pow
SMul
Ring
Action
Basic
Field
Group
Invariant
Subobjects
Divisibility
Basic
Lemmas
Hom
Basic
Defs
Semireal
Defs
Subring
Basic
MulOpposite
Order
Pointwise
Units
Subsemiring
Basic
MulOpposite
Order
Pointwise
AddAut
Aut
Basic
BooleanRing
Center
Centralizer
CentroidHom
Commute
CompTypeclasses
Defs
Equiv
Ext
Fin
Idempotents
Identities
InjSurj
Int
Invertible
MinimalAxioms
Nat
NegOnePow
Opposite
Parity
Pi
Prod
Rat
Regular
Semiconj
SumsOfSquares
ULift
Units
WithZero
Squarefree
Basic
Star
Basic
BigOperators
CHSH
Center
Free
Module
NonUnitalSubalgebra
NonUnitalSubsemiring
Order
Pi
Pointwise
Prod
Rat
RingQuot
SelfAdjoint
StarAlgHom
StarRingHom
Subalgebra
Subsemiring
Unitary
Tropical
Basic
BigOperators
Lattice
Vertex
HVertexOperator
AddTorsor
AlgebraicCard
Bounds
CubicDiscriminant
DirectLimit
DualNumber
DualQuaternion
Exact
Expr
Free
FreeAlgebra
FreeNonUnitalNonAssocAlgebra
GeomSum
GradedMonoid
GradedMulAction
HierarchyDesign
IsPrimePow
LinearRecurrence
ModEq
NeZero
Opposites
PEmptyInstances
Periodic
QuadraticDiscriminant
Quandle
Quaternion
QuaternionBasis
Quotient
RingQuot
SMulWithZero
Symmetrized
TrivSqZeroExt
AlgebraicGeometry
Cover
Open
EllipticCurve
DivisionPolynomial
Basic
Degree
Affine
Group
Jacobian
Projective
Weierstrass
Modules
Presheaf
Sheaf
Tilde
Morphisms
Affine
Basic
ClosedImmersion
Constructors
FiniteType
IsIso
OpenImmersion
QuasiCompact
QuasiSeparated
RingHomProperties
Separated
UnderlyingMap
UniversallyClosed
PrimeSpectrum
Basic
IsOpenComapC
Maximal
Module
Noetherian
TensorProduct
ProjectiveSpectrum
Scheme
StructureSheaf
Topology
Sites
BigZariski
AffineScheme
FunctionField
GammaSpecAdjunction
Gluing
GluingOneHypercover
Limits
Noetherian
OpenImmersion
Properties
Pullbacks
Restrict
Scheme
Spec
Stalk
StructureSheaf
AlgebraicTopology
DoldKan
Compatibility
Decomposition
Degeneracies
Equivalence
EquivalenceAdditive
EquivalencePseudoabelian
Faces
FunctorGamma
FunctorN
GammaCompN
Homotopies
HomotopyEquivalence
NCompGamma
NReflectsIso
Normalized
Notations
PInfty
Projections
SplitSimplicialObject
FundamentalGroupoid
Basic
FundamentalGroup
InducedMaps
PUnit
Product
SimplyConnected
SimplicialCategory
Basic
SimplicialSet (file)
Monoidal
AlternatingFaceMapComplex
CechNerve
ExtraDegeneracy
KanComplex
MooreComplex
Nerve
Quasicategory
SimplexCategory
SimplicialObject
SingularSet
SplitSimplicialObject
TopologicalSimplex
Analysis
Analytic
Basic
CPolynomial
Composition
Constructions
Inverse
IsolatedZeros
Linear
Meromorphic
Polynomial
RadiusLiminf
Uniqueness
Asymptotics
AsymptoticEquivalent
Asymptotics
SpecificAsymptotics
SuperpolynomialDecay
Theta
BoxIntegral
Box
Basic
SubboxInduction
Partition
Additive
Basic
Filter
Measure
Split
SubboxInduction
Tagged
Basic
DivergenceTheorem
Integrability
Calculus
AddTorsor
AffineMap
Coord
BumpFunction
Basic
Convolution
FiniteDimension
InnerProduct
Normed
Conformal
InnerProduct
NormedSpace
ContDiff
Basic
Bounds
Defs
FiniteDimension
RCLike
Deriv
Add
AffineMap
Basic
Comp
Inv
Inverse
Linear
Mul
Pi
Polynomial
Pow
Prod
Shift
Slope
Star
Support
ZPow
FDeriv
Add
Analytic
Basic
Bilinear
Comp
Equiv
Extend
Linear
Measurable
Mul
Pi
Prod
RestrictScalars
Star
Symmetric
Gradient
Basic
InverseFunctionTheorem
ApproximatesLinearOn
ContDiff
Deriv
FDeriv
FiniteDimensional
IteratedDeriv
Defs
Lemmas
LineDeriv
Basic
IntegrationByParts
Measurable
QuadraticMap
LocalExtr
Basic
LineDeriv
Polynomial
Rolle
Darboux
DiffContOnCl
Dslope
FormalMultilinearSeries
Implicit
LHopital
LagrangeMultipliers
MeanValue
Monotone
ParametricIntegral
ParametricIntervalIntegral
Rademacher
SmoothSeries
TangentCone
Taylor
UniformLimitsDeriv
Complex
Polynomial
Basic
UnitTrinomial
UnitDisc
Basic
UpperHalfPlane
Basic
Exp
FunctionsBoundedAtInfty
Manifold
Metric
Topology
AbelLimit
AbsMax
Angle
Arg
Asymptotics
Basic
CauchyIntegral
Circle
Conformal
Convex
Hadamard
HalfPlane
Isometry
Liouville
LocallyUniformLimit
OpenMapping
OperatorNorm
PhragmenLindelof
ReImTopology
RealDeriv
RemovableSingularity
Schwarz
TaylorSeries
Tietze
Convex
Cone
Basic
Closure
Extension
InnerDual
Pointed
Proper
SimplicialComplex
Basic
SpecificFunctions
Basic
Deriv
Pow
AmpleSet
Basic
Between
Body
Caratheodory
Combination
Complex
Contractible
Deriv
EGauge
Exposed
Extrema
Extreme
Function
Gauge
GaugeRescale
Hull
Independent
Integral
Intrinsic
Jensen
Join
KreinMilman
Measure
Mul
Normed
PartitionOfUnity
Quasiconvex
Radon
Segment
Side
Slope
Star
StoneSeparation
Strict
StrictConvexBetween
StrictConvexSpace
Strong
Topology
Uniform
CstarAlgebra
ContinuousFunctionalCalculus
Basic
Instances
NonUnital
Order
Restrict
Unique
Unital
Unitary
Basic
Exponential
GelfandDuality
Matrix
Multiplier
Spectrum
Unitization
Distribution
AEEqOfIntegralContDiff
FourierSchwartz
SchwartzSpace
Fourier
AddCircle
FourierTransform
FourierTransformDeriv
Inversion
PoissonSummation
RiemannLebesgueLemma
ZMod
FunctionalSpaces
SobolevInequality
InnerProductSpace
Adjoint
Basic
Calculus
ConformalLinearMap
Dual
EuclideanDist
GramSchmidtOrtho
LaxMilgram
LinearPMap
MeanErgodic
NormPow
OfNorm
Orientation
Orthogonal
PiL2
Positive
ProdL2
Projection
Rayleigh
Spectrum
Symmetric
TwoDim
WeakOperatorTopology
l2Space
LocallyConvex
AbsConvex
BalancedCoreHull
Barrelled
Basic
Bounded
ContinuousOfBounded
Polar
StrongTopology
WeakDual
WithSeminorms
Normed
Algebra
Basic
Spectrum
TrivSqZeroExt
Unitization
UnitizationL1
Field
Basic
InfiniteSum
UnitBall
Group
SemiNormedGrp (file)
Completion
Kernels
AddCircle
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BallSphere
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Bounded
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Completeness
Completion
Constructions
ControlledClosure
Hom
HomCompletion
InfiniteSum
Int
Lemmas
Pointwise
Quotient
Rat
Seminorm
Submodule
Tannery
Uniform
ZeroAtInfty
Lp
LpEquiv
PiLp
ProdLp
WithLp
lpSpace
Module
Basic
Complemented
Completion
Dual
FiniteDimension
Ray
Span
WeakDual
Operator
Banach
BanachSteinhaus
BoundedLinearMaps
Compact
ContinuousLinearMap
LinearIsometry
WeakOperatorTopology
Order
Basic
Lattice
UpperLower
Ring
Seminorm
SeminormFromBounded
Units
MulAction
NormedSpace
HahnBanach
Extension
SeparatingDual
Separation
Multilinear
Basic
Curry
OperatorNorm
Asymptotics
Basic
Bilinear
Completeness
Mul
NNNorm
NormedSpace
Prod
PiTensorProduct
InjectiveSeminorm
ProjectiveSeminorm
AddTorsor
AddTorsorBases
AffineIsometry
BallAction
ConformalLinearMap
Connected
ContinuousAffineMap
DualNumber
ENorm
Exponential
Extend
Extr
FunctionSeries
HomeomorphBall
IndicatorFunction
Int
MStructure
MatrixExponential
MazurUlam
Pointwise
QuaternionExponential
RCLike
Real
RieszLemma
SphereNormEquiv
ODE
Gronwall
PicardLindelof
RCLike
Basic
Lemmas
SpecialFunctions
Complex
Analytic
Arctan
Arg
Circle
Log
LogBounds
LogDeriv
ContinuousFunctionalCalculus
ExpLog
Gamma
Basic
Beta
BohrMollerup
Deligne
Gaussian
FourierTransform
GaussianIntegral
PoissonSummation
Log
Base
Basic
Deriv
ENNRealLog
ENNRealLogExp
ERealExp
Monotone
NegMulLog
Pow
Asymptotics
Complex
Continuity
Deriv
Integral
NNReal
Real
Trigonometric
Angle
Arctan
ArctanDeriv
Basic
Bounds
Chebyshev
Complex
ComplexDeriv
Cotangent
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EulerSineProd
Inverse
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Series
Arsinh
Bernstein
CompareExp
Exp
ExpDeriv
Exponential
ImproperIntegrals
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JapaneseBracket
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PolarCoord
PolynomialExp
Polynomials
SmoothTransition
Sqrt
Stirling
SpecificLimits
Basic
FloorPow
Normed
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VonNeumannAlgebra
Basic
BoundedVariation
ConstantSpeed
Convolution
Hofer
Matrix
MeanInequalities
MeanInequalitiesPow
MellinInversion
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Oscillation
PSeries
PSeriesComplex
Quaternion
Seminorm
Subadditive
SumIntegralComparisons
SumOverResidueClass
CategoryTheory
Abelian
DiagramLemmas
Four
Basic
EpiWithInjectiveKernel
Exact
Ext
FunctorCategory
Generator
Images
Injective
InjectiveResolution
LeftDerived
NonPreadditive
Opposite
Projective
ProjectiveResolution
Pseudoelements
Refinements
RightDerived
Subobject
Transfer
Adjunction
AdjointFunctorTheorems
Basic
Comma
Evaluation
FullyFaithful
Lifting
Limits
Mates
Opposites
Over
Reflective
Restrict
Unique
Whiskering
Bicategory
Functor
Lax
Oplax
Prelax
Pseudofunctor
Kan
Adjunction
HasKan
IsKan
NaturalTransformation
Oplax
Strong
Adjunction
Basic
Coherence
End
Extension
Free
FunctorBicategory
LocallyDiscrete
SingleObj
Strict
Category
Cat (file)
Limit
Basic
Bipointed
Factorisation
GaloisConnection
Grpd
Init
KleisliCat
Pairwise
PartialFun
Pointed
Preorder
Quiv
RelCat
TwoP
ULift
ChosenFiniteProducts (file)
FunctorCategory
Closed
Cartesian
Functor
FunctorCategory
Ideal
Monoidal
Types
Zero
Comma
Arrow
Basic
Over
Presheaf
StructuredArrow
ConcreteCategory
Basic
Bundled
BundledHom
Elementwise
EpiMono
ReflectsIso
UnbundledHom
Dialectica
Basic
Monoidal
EffectiveEpi
Basic
Comp
Coproduct
Enough
Extensive
Preserves
RegularEpi
Endofunctor
Algebra
Enriched
Basic
FiberedCategory
BasedCategory
Cartesian
HomLift
Filtered
Basic
Connected
Final
Small
FinCategory
AsType
Basic
Functor
Derived
RightDerived
KanExtension
Adjunction
Basic
Pointwise
Basic
Category
Const
Currying
EpiMono
Flat
FullyFaithful
Functorial
Hom
OfSequence
ReflectsIso
Trifunctor
Galois
Basic
Decomposition
Examples
GaloisObjects
Prorepresentability
GradedObject (file)
Associator
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Monoidal
Single
Trifunctor
Unitor
Groupoid (file)
Basic
FreeGroupoid
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VertexGroup
GuitartExact
Basic
VerticalComposition
Idempotents
Basic
Biproducts
FunctorCategories
FunctorExtension
HomologicalComplex
Karoubi
KaroubiKaroubi
SimplicialObject
LiftingProperties
Adjunction
Basic
Limits
Constructions
Over
Basic
Connected
Products
BinaryProducts
EpiMono
Equalizers
Filtered
FiniteProductsOfBinaryProducts
LimitsOfProductsAndEqualizers
Pullbacks
WeaklyInitial
ZeroObjects
Final (file)
ParallelPair
Indization
IndObject
Preserves
Shapes
BinaryProducts
Biproducts
Equalizers
Images
Kernels
Products
Pullbacks
Terminal
Zero
Basic
Filtered
Finite
FunctorCategory
Limits
Opposites
Ulift
Shapes
NormalMono
Basic
Equalizers
Pullback
Assoc
CommSq
Cospan
HasPullback
Iso
Mono
Pasting
PullbackCone
Square
BinaryProducts
Biproducts
CombinedProducts
ConcreteCategory
Countable
Diagonal
DisjointCoproduct
Equalizers
Equivalence
FiniteLimits
FiniteProducts
FunctorCategory
FunctorToTypes
Images
KernelPair
Kernels
Multiequalizer
Products
Reflexive
RegularMono
SingleObj
SplitCoequalizer
SplitEqualizer
StrictInitial
StrongEpi
Terminal
Types
WideEqualizers
WidePullbacks
ZeroMorphisms
ZeroObjects
Bicones
ColimitLimit
Comma
ConcreteCategory
ConeCategory
Cones
Connected
Creates
Elements
EpiMono
EssentiallySmall
ExactFunctor
Filtered
FilteredColimitCommutesFiniteLimit
FinallySmall
FintypeCat
Fubini
FullSubcategory
FunctorCategory
FunctorToTypes
HasLimits
IndYoneda
IsConnected
IsLimit
Lattice
MonoCoprod
Opposites
Over
Pi
Presheaf
SmallComplete
Types
TypesFiltered
Unit
VanKampen
Yoneda
Linear
Basic
FunctorCategory
LinearFunctor
Yoneda
Localization
CalculusOfFractions (file)
ComposableArrows
Fractions
Preadditive
DerivabilityStructure
Basic
Constructor
Adjunction
Bousfield
Composition
Construction
Equivalence
FiniteProducts
HasLocalization
HomEquiv
LocalizerMorphism
Opposite
Pi
Predicate
Prod
Resolution
SmallHom
SmallShiftedHom
StructuredArrow
Triangulated
Monad
Adjunction
Algebra
Basic
Coequalizer
Equalizer
EquivMon
Kleisli
Limits
Monadicity
Products
Types
Monoidal
Braided
Basic
Opposite
Cartesian
Comon_
Free
Basic
Coherence
Internal
FunctorCategory
Limits
Module
Types
OfChosenFiniteProducts
Basic
Symmetric
Rigid
Basic
FunctorCategory
OfEquivalence
Types
Basic
Coyoneda
Symmetric
Bimod
Bimon_
Category
Center
CoherenceLemmas
CommMon_
Comon_
Conv
Discrete
End
Functor
FunctorCategory
Functorial
Limits
Linear
Mod_
Mon_
NaturalTransformation
OfHasFiniteProducts
Opposite
Preadditive
Skeleton
Subcategory
Tor
Transport
MorphismProperty
Basic
Composition
Concrete
Factorization
IsInvertedBy
Limits
Pi
Basic
Preadditive
Yoneda
Basic
Injective
Limits
Projective
AdditiveFunctor
Basic
Biproducts
EilenbergMoore
EndoFunctor
FunctorCategory
Generator
HomOrthogonal
Injective
InjectiveResolution
LeftExact
Mat
OfBiproducts
Opposite
Projective
ProjectiveResolution
Schur
SingleObj
Products
Associator
Basic
Bifunctor
Unitor
Quotient (file)
Linear
Preadditive
Shift
Basic
CommShift
Induced
InducedShiftSequence
Localization
Opposite
Predicate
Pullback
Quotient
ShiftSequence
ShiftedHom
SingleFunctors
Sigma
Basic
Sites
Coherent
Basic
CoherentSheaves
CoherentTopology
Comparison
Equivalence
ExtensiveSheaves
ExtensiveTopology
LocallySurjective
ReflectsPrecoherent
ReflectsPreregular
RegularSheaves
RegularTopology
SheafComparison
NonabelianCohomology
H1
SheafCohomology
Basic
Abelian
Adjunction
Canonical
Closed
CompatiblePlus
CompatibleSheafification
ConcreteSheafification
ConstantSheaf
Continuous
CoverLifting
CoverPreserving
Coverage
CoversTop
DenseSubsite
Discrete
EffectiveEpimorphic
EpiMono
EqualizerSheafCondition
Equivalence
Grothendieck
InducedTopology
IsSheafFor
IsSheafOneHypercover
LeftExact
Limits
Localization
LocallyBijective
LocallyFullyFaithful
LocallyInjective
LocallySurjective
MayerVietorisSquare
OneHypercover
Over
Plus
Preserves
PreservesLocallyBijective
PreservesSheafification
Pretopology
Pullback
Sheaf
SheafHom
SheafOfTypes
Sheafification
Sieves
Spaces
Subsheaf
Types
Whiskering
SmallObject
Construction
Iteration
Subobject
Basic
Comma
FactorThru
Lattice
Limits
MonoOver
Types
WellPowered
Sums
Associator
Basic
Triangulated
TStructure
Basic
Basic
Functor
HomologicalFunctor
Opposite
Pretriangulated
Rotate
Subcategory
TriangleShift
Triangulated
Yoneda
Action
Adhesive
Balanced
CatCommSq
ClosedUnderIsomorphisms
CofilteredSystem
CommSq
ComposableArrows
Conj
ConnectedComponents
Core
Countable
DifferentialObject
DiscreteCategory
Elements
Elementwise
Endomorphism
EpiMono
EqToHom
Equivalence
EssentialImage
EssentiallySmall
Extensive
FintypeCat
FullSubcategory
Generator
GlueData
Grothendieck
IsConnected
Iso
IsomorphismClasses
NatIso
NatTrans
Noetherian
Opposites
PEmpty
PUnit
PathCategory
Simple
SingleObj
Skeletal
Square
Subterminal
Thin
Types
UnivLE
Whiskering
WithTerminal
Yoneda
Combinatorics
Additive
AP
Three
Behrend
Defs
Corner
Defs
Roth
Dissociation
ETransform
Energy
ErdosGinzburgZiv
FreimanHom
PluenneckeRuzsa
RuzsaCovering
Derangements
Basic
Exponential
Finite
Enumerative
Catalan
Composition
DoubleCounting
Partition
Hall
Basic
Finite
Optimization
ValuedCSP
Quiver
Arborescence
Basic
Cast
ConnectedComponent
Covering
Path
Push
SingleObj
Subquiver
Symmetric
SetFamily
Compression
Down
UV
AhlswedeZhang
CauchyDavenport
FourFunctions
HarrisKleitman
Intersecting
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LYM
Shadow
Shatter
SimpleGraph
Connectivity (file)
Subgraph
WalkCounting
Ends
Defs
Properties
Regularity
Bound
Chunk
Energy
Equitabilise
Increment
Lemma
Uniform
Triangle
Basic
Counting
Removal
Tripartite
Acyclic
AdjMatrix
Basic
Clique
Coloring
ConcreteColorings
Dart
DegreeSum
Density
Finite
Finsubgraph
Girth
Hamiltonian
Hasse
IncMatrix
Init
LapMatrix
Maps
Matching
Metric
Operations
Partition
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StronglyRegular
Subgraph
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Turan
Young
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YoungDiagram
Colex
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Pigeonhole
Schnirelmann
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AkraBazzi
AkraBazzi
GrowsPolynomially
Ackermann
ContextFreeGrammar
DFA
Encoding
EpsilonNFA
Halting
Language
NFA
Partrec
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Primrec
Reduce
RegularExpressions
TMComputable
TMToPartrec
TuringMachine
Condensed
Light
Basic
Discrete
Explicit
Functors
Module
TopCatAdjunction
TopComparison
Basic
Discrete
Epi
Equivalence
Explicit
Functors
Limits
Module
Solid
TopCatAdjunction
TopComparison
Control
Bitraversable
Basic
Instances
Lemmas
EquivFunctor (file)
Instances
Functor (file)
Multivariate
Monad
Basic
Cont
Writer
Traversable
Basic
Equiv
Instances
Lemmas
Applicative
Basic
Bifunctor
Combinators
Fix
Fold
Lawful
LawfulFix
Random
ULift
ULiftable
Data
Analysis
Filter
Topology
Array
Defs
ExtractLemmas
Lemmas
Bool
AllAny
Basic
Count
Set
Buffer
Basic
Complex
Abs
Basic
BigOperators
Cardinality
Determinant
Exponential
ExponentialBounds
FiniteDimensional
Module
Order
Orientation
Countable
Basic
Defs
Small
DFinsupp
Basic
Encodable
Interval
Lex
Multiset
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WellFounded
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Basic
Inv
Operations
Real
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Basic
Lattice
FP
Basic
Fin
Tuple
Basic
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Curry
Finset
NatAntidiagonal
Reflection
Sort
Basic
Fin2
FlagRange
SuccPred
VecNotation
Finite
Basic
Card
Defs
Set
Finset
Pointwise (file)
Interval
Attr
Basic
Card
Density
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Functor
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Image
Interval
Lattice
MulAntidiagonal
NAry
NatAntidiagonal
NatDivisors
NoncommProd
Option
Order
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Pairwise
Pi
PiInduction
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Antidiagonal
Basic
BigOperators
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Fintype
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Interval
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Basic
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Lattice
List
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Parity
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Pi
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Sigma
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Sum
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Vector
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Int
Cast
Basic
Defs
Field
Lemmas
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Order
Lemmas
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CharZero
ConditionallyCompleteOrder
Defs
GCD
Interval
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Lemmas
Log
ModEq
NatPrime
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Matrix
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Basic
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Composition
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DualNumber
Hadamard
Invertible
Kronecker
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Rank
Reflection
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Matroid
Basic
Closure
Constructions
Dual
IndepAxioms
Init
Map
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Interval
Lattice
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BigOperators
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Basic
Star
Nat
Cast
Order
Basic
Field
Ring
Basic
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Defs
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Synonym
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Choose
Basic
Bounds
Cast
Central
Dvd
Factorization
Lucas
Multinomial
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Factorial
Basic
BigOperators
Cast
DoubleFactorial
SuperFactorial
Factorization
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Defs
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Root
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Basic
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GCD
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BigOperators
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