General documentation
index
foundational types
Library
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
Tactic
Index (
file
)
Basic
Options (
file
)
Internal
Public
Rule (
file
)
Basic
Name
RuleSet (
file
)
Filter
Member
Name
RuleTac (
file
)
Apply
Basic
Cases
ElabRuleTerm
Forward
Preprocess
Tactic
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
Basic
EqualUpToIds
Tactic
UnionFind
UnorderedArraySet
Check
Constants
ElabM
Exception
Main
Nanos
Percent
RulePattern
Script
Tracing
ImportGraph
Imports
RequiredModules
Init (
file
)
Control (
file
)
Basic
EState
Except
ExceptCps
Id
Lawful
Option
Reader
State
StateCps
StateRef
Data (
file
)
Array (
file
)
Basic
BasicAux
BinSearch
DecidableEq
InsertionSort
Lemmas
Mem
QSort
Subarray
BitVec (
file
)
Basic
Bitblast
Folds
Lemmas
ByteArray (
file
)
Basic
Char (
file
)
Basic
Fin (
file
)
Basic
Fold
Iterate
Lemmas
Log2
FloatArray (
file
)
Basic
Format (
file
)
Basic
Instances
Macro
Syntax
Int (
file
)
Basic
Bitwise
DivMod
DivModLemmas
Gcd
Lemmas
Order
List (
file
)
Basic
BasicAux
Control
Lemmas
Nat (
file
)
Bitwise (
file
)
Basic
Lemmas
Basic
Control
Div
Dvd
Gcd
Lemmas
Linear
Log2
MinMax
Mod
Power2
SOM
Option (
file
)
Basic
BasicAux
Instances
Lemmas
String (
file
)
Basic
Extra
ToString (
file
)
Basic
Macro
UInt (
file
)
Basic
Log2
AC
Basic
Bool
Cast
Channel
Float
Hashable
OfScientific
Ord
Prod
Queue
Random
Range
Repr
Stream
Sum
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
Guard
Hints
Meta
MetaTypes
Notation
NotationExtra
Prelude
PropLemmas
RCases
ShareCommon
SimpLemmas
Simproc
SizeOf
SizeOfLemmas
Tactics
TacticsExtra
Util
WF
WFTactics
Lake (
file
)
Build (
file
)
Actions
Common
Context
Data
Executable
Facets
Imports
Index
Info
Job
Key
Library
Module
Monad
Package
Store
Targets
Topological
Trace
CLI
Actions
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
Config
DeclUtil
Extensions
Meta
Package
Require
Script
Targets
Load
Config
Util
Async
Binder
Casing
Compare
Cycle
DRBMap
EStateT
EquipT
Error
Exit
Family
Git
Lift
List
Log
Name
NativeLib
Opaque
OptionIO
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
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
PackDomain
PackMutual
Preprocess
Rel
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
ElabTerm
Ext
FalseOrByContra
Generalize
Guard
Induction
Injection
LibrarySearch
Location
Match
Meta
NormCast
RCases
Repeat
Rewrite
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
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
Linter (
file
)
Basic
Builtin
Deprecated
MissingDocs
UnusedVariables
Util
Meta (
file
)
Match (
file
)
MatcherApp
Basic
Transform
Basic
CaseArraySizes
CaseValues
Match
MatchEqs
MatchEqsExt
MatchPatternAttr
MatcherInfo
Value
Tactic (
file
)
AC (
file
)
Main
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
Main
RegisterCommand
Rewrite
SimpAll
SimpCongrTheorems
SimpTheorems
Simproc
Types
Acyclic
Apply
Assert
Assumption
AuxLemma
Backtrack
Cases
Cleanup
Clear
Congr
Constructor
Contradiction
Delta
ElimInfo
FVarSubst
Generalize
IndependentOf
Induction
Injection
Intro
LibrarySearch
NormCast
Refl
Rename
Repeat
Replace
Revert
Rewrite
SolveByElim
Split
SplitIf
Subst
Symm
TryThis
Unfold
UnifyEq
Util
ACLt
AbstractMVars
AbstractNestedProofs
AppBuilder
Basic
Check
Closure
Coe
CoeAttr
CollectFVars
CollectMVars
CompletionName
CongrTheorems
Constructions
CtorRecognizer
DecLevel
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
Offset
PPGoal
RecursorInfo
Reduce
ReduceEval
SizeOf
Structure
SynthInstance
Transform
TransparencyMode
UnificationHint
WHNF
Parser (
file
)
Attr
Basic
Command
Do
Extension
Extra
Level
Module
StrInterpolation
Syntax
Tactic
Term
Types
ParserCompiler (
file
)
Attribute
PrettyPrinter (
file
)
Delaborator (
file
)
Basic
Builtins
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
FileSetupInfo
FindExpr
FindLevelMVar
FindMVar
FoldConsts
ForEachExpr
ForEachExprWhere
HasConstCache
Heartbeats
InstantiateLevelParams
LakePath
LeanOptions
MonadBacktrack
MonadCache
OccursCheck
PPExt
Path
Paths
Profile
PtrSet
RecDepth
Recognizers
ReplaceExpr
ReplaceLevel
SCC
ShareCommon
Sorry
TestExtern
Trace
Widget (
file
)
Basic
Diff
InteractiveCode
InteractiveDiagnostic
InteractiveGoal
TaggedText
Types
UserWidget
Attributes
AuxRecursor
Class
CoreM
Declaration
DeclarationRange
DocString
Environment
Eval
Exception
Expr
HeadIndex
Hygiene
ImportingFlag
InternalExceptionId
KeyedDeclsAttribute
LabelAttribute
LazyInitExtension
Level
LoadDynlib
LocalContext
Log
Message
MetavarContext
Modifiers
MonadEnv
ProjFns
ReducibilityAttrs
ResolveName
Runtime
ScopedEnvExtension
Structure
SubExpr
Syntax
ToExpr
LeanAPAP
Extras
BSG
Mathlib
Algebra
Algebra
Basic
Field
Defs
Group
AddChar
Order
Field
Basic
Module
Defs
Analysis
InnerProductSpace
PiL2
NormedSpace
PiLp
Combinatorics
Additive
Energy
Data
Fintype
Pi
NNRat
Defs
Lemmas
Rat
Cast
CharZero
ZMod
Basic
Tactic
Positivity
Prereqs
AddChar
Basic
Circle
PontryaginDuality
Discrete
Convolution
Basic
Compact
Norm
Order
DFT
Basic
Compact
LpNorm
Basic
Compact
Expect
Basic
Complex
Density
Indicator
Translate
Mathlib
Algebra
Algebra
Subalgebra
Basic
Operations
Pointwise
Prod
Tower
Basic
Bilinear
Defs
Equiv
Hom
NonUnitalHom
NonUnitalSubalgebra
Operations
Opposite
Pi
Prod
RestrictScalars
Tower
BigOperators
List
Basic
Lemmas
Multiset
Basic
Lemmas
Associated
Basic
Fin
Finprod
Finsupp
Intervals
Module
NatAntidiagonal
Option
Pi
Ring
RingEquiv
WithTop
Category
GroupCat
Abelian
Basic
Colimits
EpiMono
EquivalenceGroupAddGroup
FilteredColimits
ForgetCorepresentable
Kernels
Limits
Preadditive
ZModuleEquivalence
ModuleCat
Abelian
Basic
Biproducts
Colimits
EpiMono
Kernels
Limits
MonCat
Basic
FilteredColimits
Limits
CharP
Algebra
Basic
ExpChar
Invertible
Reduced
Two
CharZero
Defs
Lemmas
Quotient
DirectSum
Basic
Decomposition
Finsupp
Module
Divisibility
Basic
Units
EuclideanDomain
Basic
Defs
Instances
Field
Basic
Defs
Equiv
IsField
Opposite
FreeMonoid
Basic
Function
Finite
Indicator
Support
GCDMonoid
Basic
Finset
Multiset
Nat
Group
Commute
Basic
Defs
Hom
Units
Equiv
Basic
TypeTags
Hom
Basic
CompTypeclasses
Defs
End
Instances
Pi
Basic
Lemmas
Semiconj
Basic
Defs
Units
Units (
file
)
Equiv
Hom
WithOne
Defs
AddChar
Aut
Basic
Center
Centralizer
Commutator
Conj
ConjFinite
Defs
Embedding
Ext
InjSurj
Int
Nat
Opposite
OrderSynonym
Prod
TypeTags
ULift
UniqueProds
GroupPower
Basic
CovariantClass
Hom
IterateHom
NegOnePow
Order
Ring
GroupRingAction
Basic
Subobjects
GroupWithZero
Units
Basic
Equiv
Lemmas
Basic
Bitwise
Commute
Defs
Divisibility
Hom
InjSurj
NeZero
NonZeroDivisors
Pi
Power
Semiconj
WithZero
Homology
ShortComplex
Ab
Abelian
Basic
ConcreteCategory
Exact
ExactFunctor
Homology
LeftHomology
Limits
ModuleCat
PreservesHomology
QuasiIso
RightHomology
ShortExact
SnakeLemma
Exact
ExactSequence
ImageToKernel
Invertible
Basic
Defs
GroupWithZero
Ring
Module
LinearMap
Basic
End
Submodule
Basic
Bilinear
Ker
Lattice
LinearMap
Map
Pointwise
Range
RestrictScalars
Basic
BigOperators
DedekindDomain
Defs
Equiv
Hom
MinimalAxioms
Opposites
PID
Pi
Prod
Projective
Torsion
ULift
MonoidAlgebra
Basic
Degree
Division
NoZeroDivisors
Support
MvPolynomial
Basic
CommRing
Degrees
Equiv
Rename
Variables
Order
BigOperators
Group
Finset
List
Multiset
Ring
Finset
List
Multiset
CauSeq
Basic
BigOperators
Completion
Field
Canonical
Basic
Defs
Basic
Defs
InjSurj
Power
Group
Abs
Action
Defs
InjSurj
Instances
Int
Lattice
MinMax
Nat
OrderIso
PosPart
Prod
TypeTags
Units
GroupWithZero
Canonical
Hom
Basic
Monoid
Ring
Interval
Set
Group
Instances
Monoid
Finset
Module
Algebra
Defs
OrderedSMul
Pointwise
Synonym
Monoid
Canonical
Defs
Basic
Defs
Lemmas
MinMax
NatCast
OrderDual
Prod
TypeTags
Units
WithTop
Nonneg
Field
Floor
Ring
Positive
Ring
Ring
Abs
Canonical
CharZero
Defs
InjSurj
Int
Lemmas
Nat
Pow
WithTop
Sub
Canonical
Defs
WithTop
AbsoluteValue
Archimedean
Chebyshev
Floor
Invertible
Kleene
Monovary
Pi
Rearrangement
Support
ToIntervalMod
ZeroLEOne
Polynomial
Degree
Definitions
Lemmas
TrailingDegree
Module
Basic
AlgebraMap
Basic
BigOperators
CancelLeads
Coeff
Derivative
Div
EraseLead
Eval
Expand
FieldDivision
Identities
Induction
Inductions
Laurent
Lifts
Monic
Monomial
Reverse
RingDivision
Splits
Regular
Basic
Pow
SMul
Ring
Divisibility
Basic
Hom
Basic
Defs
AddAut
Aut
Basic
Center
Centralizer
Commute
CompTypeclasses
Defs
Equiv
Fin
Idempotents
InjSurj
Int
Nat
Opposite
OrderSynonym
Pi
Prod
Regular
Semiconj
ULift
Units
Squarefree
Basic
Star
Basic
BigOperators
Center
Module
Order
Pi
Pointwise
Prod
SelfAdjoint
StarAlgHom
Subalgebra
Unitary
AddTorsor
Associated
Bounds
CovariantAndContravariant
DirectLimit
FreeAlgebra
GeomSum
IsPrimePow
ModEq
NeZero
Opposites
PUnitInstances
Parity
Periodic
QuadraticDiscriminant
Quotient
SMulWithZero
AlgebraicGeometry
PrimeSpectrum
Basic
Maximal
Noetherian
Analysis
Asymptotics
AsymptoticEquivalent
Asymptotics
Theta
Calculus
Conformal
NormedSpace
ContDiff
Basic
Defs
RCLike
Deriv
Add
AffineMap
Basic
Comp
Inv
Inverse
Linear
Mul
Pow
Prod
Shift
Slope
ZPow
FDeriv
Add
Basic
Bilinear
Comp
Equiv
Extend
Linear
Measurable
Mul
Prod
RestrictScalars
InverseFunctionTheorem
ApproximatesLinearOn
Deriv
FDeriv
IteratedDeriv
Defs
Lemmas
LocalExtr
Basic
Rolle
FormalMultilinearSeries
MeanValue
TangentCone
Complex
Basic
Circle
Conformal
Isometry
RealDeriv
Convex
Cone
Basic
Extension
SpecificFunctions
Basic
Deriv
Basic
Between
Combination
Deriv
Function
Gauge
Hull
Jensen
Mul
Normed
Segment
Slope
Star
Strict
StrictConvexSpace
Topology
Uniform
InnerProductSpace
Basic
Orthogonal
PiL2
Projection
Symmetric
LocallyConvex
BalancedCoreHull
Basic
Bounded
Polar
WithSeminorms
Normed
Field
Basic
UnitBall
Group
AddCircle
AddTorsor
BallSphere
Basic
Completion
Hom
InfiniteSum
Lemmas
Pointwise
Quotient
Seminorm
Order
Basic
Lattice
MulAction
NormedSpace
HahnBanach
Extension
SeparatingDual
Separation
Multilinear
Basic
Curry
OperatorNorm
Asymptotics
Basic
Bilinear
Completeness
Mul
NNNorm
NormedSpace
Star
Basic
AddTorsor
AffineIsometry
Banach
Basic
BoundedLinearMaps
Completion
ConformalLinearMap
ContinuousLinearMap
Dual
Extend
FiniteDimension
IndicatorFunction
LinearIsometry
PiLp
Pointwise
RCLike
Ray
Real
RieszLemma
Span
Units
WithLp
RCLike
Basic
Lemmas
SpecialFunctions
Complex
Arg
Log
LogDeriv
Log
Base
Basic
Deriv
Pow
Asymptotics
Complex
Continuity
Deriv
NNReal
Real
Trigonometric
Angle
Arctan
ArctanDeriv
Basic
Bounds
Complex
ComplexDeriv
Deriv
Inverse
Exp
ExpDeriv
Integrals
NonIntegrable
Sqrt
SpecificLimits
Basic
Normed
MeanInequalities
MeanInequalitiesPow
Seminorm
SumIntegralComparisons
CategoryTheory
Abelian
Basic
Exact
FunctorCategory
Images
NonPreadditive
Opposite
Refinements
Adjunction
Basic
Comma
FullyFaithful
Limits
Opposites
Reflective
Restrict
Bicategory
Basic
Strict
Category
Basic
Cat
Init
Preorder
ULift
Comma
Arrow
Basic
Over
StructuredArrow
ConcreteCategory
Basic
Bundled
BundledHom
Elementwise
ReflectsIso
Filtered
Basic
FinCategory
AsType
Basic
Functor
Basic
Category
Const
Currying
EpiMono
FullyFaithful
Hom
ReflectsIso
LiftingProperties
Adjunction
Basic
Limits
Constructions
BinaryProducts
EpiMono
Equalizers
FiniteProductsOfBinaryProducts
LimitsOfProductsAndEqualizers
Pullbacks
Preserves
Shapes
BinaryProducts
Biproducts
Equalizers
Kernels
Products
Pullbacks
Terminal
Zero
Basic
Filtered
Finite
Limits
Shapes
NormalMono
Basic
Equalizers
BinaryProducts
Biproducts
ConcreteCategory
Equalizers
Equivalence
FiniteLimits
FiniteProducts
FunctorCategory
Images
Kernels
Multiequalizer
Products
Pullbacks
RegularMono
SplitCoequalizer
StrongEpi
Terminal
Types
WidePullbacks
ZeroMorphisms
ZeroObjects
Comma
ConcreteCategory
ConeCategory
Cones
Creates
ExactFunctor
Filtered
FunctorCategory
HasLimits
IsLimit
Opposites
Over
Types
TypesFiltered
Unit
Yoneda
Linear
Basic
MorphismProperty
Basic
Pi
Basic
Preadditive
AdditiveFunctor
Basic
Biproducts
FunctorCategory
Injective
LeftExact
Opposite
Projective
Products
Basic
Subobject
Basic
FactorThru
Lattice
Limits
MonoOver
WellPowered
Balanced
CommSq
ComposableArrows
Conj
DiscreteCategory
Endomorphism
EpiMono
EqToHom
Equivalence
EssentialImage
EssentiallySmall
FullSubcategory
Groupoid
Iso
IsomorphismClasses
NatIso
NatTrans
Opposites
PEmpty
PUnit
Skeletal
Thin
Types
Whiskering
Yoneda
Combinatorics
Additive
ETransform
Energy
PluenneckeRuzsa
RuzsaCovering
Enumerative
Composition
DoubleCounting
Partition
Quiver
Basic
Path
Push
Symmetric
SetFamily
CauchyDavenport
Control
Monad
Basic
Traversable
Basic
Instances
Lemmas
Applicative
Basic
Bifunctor
EquivFunctor
Functor
ULift
Data
Array
Defs
Bool
Basic
Set
Complex
Abs
Basic
BigOperators
Cardinality
Exponential
Module
Order
Countable
Basic
Defs
DFinsupp
Basic
Encodable
ENNReal
Basic
Inv
Operations
Real
ENat
Basic
Lattice
Fin
Tuple
Basic
Basic
Interval
OrderHom
VecNotation
Finite
Basic
Card
Defs
Set
Finset
Antidiagonal
Attr
Basic
Card
Fin
Fold
Functor
Image
Lattice
NAry
NatAntidiagonal
NoncommProd
Option
Order
Pairwise
Pi
Piecewise
Pointwise
Powerset
Preimage
Prod
Sigma
Sort
Sum
Union
Update
Finsupp
Antidiagonal
Basic
Defs
Encodable
Fin
Fintype
Indicator
Multiset
Order
ToDFinsupp
Fintype
Basic
BigOperators
Card
Fin
Lattice
List
Option
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