filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
numdomain.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import ssrAC div fintyp... |
LinearPMap.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.LinearAlgebra.LinearPMap
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Partially defined linear operators over topological vector spaces
We define bas... |
Groupoid.lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.CategoryTheory.Closed.Monoidal
import Mathlib.CategoryTheory.Functor.Currying
import Mathlib.CategoryTheory.Monoidal.FunctorCategory
/-!
# Functors ... |
Set.lean | /-
Copyright (c) 2022 Ian Benway. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ian Benway
-/
import Mathlib.Tactic.Set
import Mathlib.Tactic.Basic
import Mathlib.Util.SleepHeartbeats
import Qq
example (x : Nat) (h : x = x) : x = x := by
set! p := h
set q : x = ... |
ScottTopology.lean | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Order.ScottContinuity
import Mathlib.Topology.Order.UpperLowerSetTopology
/-!
# Scott topology
This file introduces the Scott topology on a p... |
Notation.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
import Mathlib.Algebra.Group.Fin.Tuple
import Mathlib.Data.Matrix.RowCol
import Mathlib.Data.Fin.VecNotation
import Mathlib.Tactic.FinCases
import Mathlib.Alge... |
ContinuousEval.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Hom.ContinuousEvalConst
import Mathlib.Topology.ContinuousMap.Defs
/-!
# Bundled maps with evaluation continuous in both variables
In this... |
FiniteDimensional.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.FiniteDimensional.Defs
import Mathlib.LinearAlgebra.FreeModule... |
Shrink.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Group.Action.TransferInstance
import Mathlib.Logic.Small.Defs
import Mathlib.Tactic.SuppressCompilation
/-!
# Transfer group structures from `α` t... |
GeomSum.lean | import Mathlib.Algebra.Group.NatPowAssoc
import Mathlib.Algebra.Order.Field.GeomSum
import Mathlib.Algebra.Order.Ring.GeomSum
import Mathlib.Algebra.Ring.Regular
import Mathlib.Tactic.Abel
import Mathlib.Tactic.Positivity.Basic
deprecated_module (since := "2025-06-19")
|
ApproximateUnit.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Topology.Algebra.Monoid
/-! # Approximate units
An *approximate unit* is a filter `l` such that multiplication on the left (or right) by `m : α`
tends ... |
Basic.lean | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
import Mathlib.RingTheory.LocalRing.RingHom.Basic
import Mathlib.GroupTheory.Torsion
/-!
# Units of a numbe... |
Subsingleton.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Data.Set.Insert
import Mathlib.Tactic.ByContra
/-!
# Subsingleton
Defines the predicate `Subsingleton s : Prop`, saying that `s` has... |
GCDMonoid.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet
import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors
/... |
Density.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Field.Rat
import Mathlib.Data.Fintype.Card
import Mathlib.Data.NNRat.Order
import Mathlib.Data.Rat.Cast.CharZero
import Mathlib.Tactic.Positi... |
Cardinality.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.LinearAlgebra.Basis.Cardinality
import Mathlib.LinearAlgebra.DFinsupp
import Mathlib.LinearAlgebra.Isomorphisms
import Mathlib.LinearAlgebra.StdBasis
i... |
Multiequalizer.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
/-!
# Preservation of multicoequalizers
Let `J : MultispanShape` and `d : MultispanIndex J C`.
If `F : C ⥤ D`, we d... |
SecondInter.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Geometry.Euclidean.Sphere.Basic
/-!
# Second intersection of a sphere and a line
This file defines and proves basic results about the second intersection... |
AsLimit.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Category.LightProfinite.Basic
/-!
# Light profinite sets as limits of finite sets.
We show that any light profinite set is isomorphic to ... |
Isometry.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Fintype.Lattice
import Mathlib.Data.Fintype.Sum
import Mathlib.Topology.Homeomorph.Lemmas
import Mathlib.Topology.MetricSpace.Antilipschitz
... |
binomial.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import div fintype tuple ... |
Birthday.lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Algebra.Order.Group.OrderIso
import Mathlib.SetTheory.Game.Ordinal
import Mathlib.SetTheory.Ordinal.NaturalOps
import Mathlib.T... |
Quaternion.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Eric Wieser
-/
import Mathlib.Algebra.Quaternion
import Mathlib.Analysis.InnerProductSpace.Continuous
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.To... |
Etale.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.AlgebraicGeometry.Morphisms.Etale
import Mathlib.AlgebraicGeometry.PullbackCarrier
import Mathlib.AlgebraicGeometry.Sites.BigZariski
import Mathlib... |
PushforwardContinuous.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward
import Mathlib.Algebra.Category.ModuleCat.Sheaf
import Mathlib.CategoryTheory.Sites.Over
/-!
# Pushforward of sh... |
Grassmannian.lean | /-
Copyright (c) 2025 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.RingTheory.Spectrum.Prime.FreeLocus
/-!
# Grassmannians
## Main definitions
- `Module.Grassmannian`: `G(k, M; R)` is the `k`ᵗʰ Grassmannian of the `R`-module... |
AlgebraicallyClosed.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity
import Mathlib.NumberTheory.Cyclotomic.Basic
/-!
# Instances for HasEnoughRootsOfUnity
We provide an instanc... |
Compare.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Ordering.Basic
import Mathlib.Order.Synonym
/-!
# Comparison
This file provides basic results about orderings and comparison in linear orders.
... |
Grade.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Set.Finite.Basic
import Mathlib.Order.Atoms
import Mathlib.Order.Grade
import Mathlib.Order.Nat
/-!
# Finsets and multisets form a graded order
This... |
Init.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Init
import Aesop
/-!
# Matroid Rule Set
This module defines the `Matroid` Aesop rule set which is used by the
`aesop_mat` tactic. Aesop rule sets only b... |
Erased.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Logic.Equiv.Defs
/-!
# A type for VM-erased data
This file defines a type `Erased α` which is classically isomorphic to `α`,
but erased in the VM. Th... |
Epi.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
import Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective
import Mathlib.CategoryTheory.Sites.EpiMono
... |
Ulift.lean | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
import Mathlib.Algebra.Category.Grp.LargeColimits
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.Algebra.Module.CharacterModule
import Mathlib.CategoryTheory.L... |
vector.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop fi... |
Basic.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
import Mathlib.Geometry.Euclidean.PerpBisector
import Mathlib.Algebra.QuadraticDiscriminant
/-!
# Euclidean spaces
This file makes some definitions and... |
SeparatingDual.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.NormedSpace.HahnBanach.Extension
import Mathlib.Analysis.NormedSpace.HahnBanach.Separation
import Mathlib.Analysis.NormedSpace.Multiline... |
ZeroLEOne.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Order.Basic
/-!
# Typeclass expressing `0 ≤ 1`.
-/
variable {α : Type*}
open Function
/-- Typeclas... |
Relation.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Order.SuccPred.Archimedean
/-!
# Relations on types with a `SuccOrder`
This file contains properties about relations on types with a `SuccOrder`
... |
matrix.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype finfun f... |
Limits.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Category.CompHausLike.Limits
import Mathlib.Topology.Category.LightProfinite.Basic
/-!
# Explicit limits and colimits
This file applies ... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
Pi.lean | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.MeasureTheory.Integral.Prod
/-!
# Integration with respect to a finite product of measures
On a finite product of measure spaces, we show that a produc... |
ssrnotations.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
(******************************************************************************)
(* - Reserved notation for various arithmetic and algebraic operations: ... |
IndObject.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.FinallySmall
import Mathlib.CategoryTheory.Limits.Presheaf
import Mathlib.CategoryTheory.Filtered.Small
import Mathlib.CategoryTheo... |
Basic.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.Dual.Lemmas
/-!
# Perfect pairings of modules
A perfect pairing of two (left) modules may be defined either as:
1. A bilinear map `M × N → R`... |
ZGroup.lean | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.FieldTheory.Finite.Basic
import Mathlib.GroupTheory.Abelianization.Finite
import Mathlib.GroupTheory.Nilpotent
import Mathlib.GroupTheory.SchurZassen... |
OfNat.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Init
/-! # The `ofNat()` macro -/
/--
This macro is a shorthand for `OfNat.ofNat` combined with `no_index`.
When writing lemmas about `OfNat.ofNat`, the t... |
AbsConvex.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
import Mathlib.Analysis.Convex.TotallyBounded
/-!
# Absolutely convex sets
A set `s` in an commutative monoid `E` i... |
maximal.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import div fintype finfun bigop finset prime binomial.
Fro... |
Colon.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Ring.Action.Pointwise.Set
import Mathlib.LinearAlgebra.Quotient.Defs
import Mathlib.RingTheory.Ideal.Maps
/-!
# The colon ideal
This file defines `Subm... |
Lemmas.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov
-/
import Mathlib.Analysis.Asymptotics.Defs
import Mathlib.Analysis.Normed.Group.Bounded
import Mathlib.Analysis.Normed.Group.InfiniteSum
import Mathlib.A... |
SimplyConnected.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps
import Mathlib.Topology.Homotopy.Contractible
import Mathlib.CategoryTheory.PUnit
import Math... |
gfunctor.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype.
From mathcomp Require Import bigop finset fingroup morphism automorphism.
From math... |
LocallyConstant.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Topology.LocallyConstant.Algebra
import Mathlib.Topology.ContinuousMap.Basic
import Mathlib.Topology.ContinuousMap.Algebra
/-!
# The algebra morphism from l... |
Irrational.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Rat
import Mathlib.Data.Nat.Prime.Int
import Mathlib.Data.Rat.Sqrt
imp... |
RadonNikodym.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Probability.Kernel.Disintegration.Density
import Mathlib.Probability.Kernel.WithDensity
/-!
# Radon-Nikodym derivative and Lebesgue decomposition for kern... |
InjSurj.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Yury Kudryashov, Neil Strickland
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Algebra.Opposites
import Mathlib.Algebra.GroupWit... |
Multiset.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.GCDMonoid.Basic
import Mathlib.Algebra.Order.Group.Multiset
import Mathlib.Data.Multiset.FinsetOps
import Mathlib.Data.Multiset.Fold
/-!
# GCD... |
numdomain.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import ssrAC div fintyp... |
fingraph.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat.
From mathcomp Require Import seq path fintype.
(******************************************... |
LinearMap.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Module.LinearMap.End
import Mathlib.Algebra.Module.Submodule.Defs
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
/-!
# Linear maps in... |
Interval.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Embedding
import Mathlib.Algebra.Ring.CharZero
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Algebra.Order.Group.Unbundled.Int
import M... |
Quotient.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, David Kurniadi Angdinata, Devon Tuma, Riccardo Brasca
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.Eval.SMul
import Mathlib.GroupTheory.GroupAction.... |
CorrectnessTerminating.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Translations
import Mathlib.Algebra.ContinuedFractions.TerminatedStable
import Mathlib.Algebra.ContinuedFrac... |
Completion.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Robert Y. Lewis
-/
import Mathlib.Algebra.Order.CauSeq.Basic
import Mathlib.Algebra.Ring.Action.Rat
import Mathlib.Tactic.FastInstance
/-!
# Cauchy completion
This fi... |
Impartial.lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import Mathlib.SetTheory.Game.Basic
import Mathlib.Tactic.NthRewrite
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module
"This module is now at `Combinatoria... |
Addition.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Miyahara Kō
-/
import Mathlib.Data.Option.Defs
import Mathlib.Tactic.CC.MkProof
/-!
# Process when an new equation is added to a congruence closure
-/
unive... |
Basic.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Countable.Defs
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.Data.ENat.Defs
import Mathlib.Logic.Equiv.Nat
/-!
# Countable types
In this ... |
ProdAssoc.lean | import Mathlib.Tactic.ProdAssoc
variable {α β γ δ : Type*}
example : (α × β) × (γ × δ) ≃ α × (β × γ) × δ := by
exact (prod_assoc% : (α × β) × (γ × δ) ≃ α × (β × γ) × δ)
example : (α × β) × (γ × δ) ≃ α × (β × γ) × δ := prod_assoc%
example : (α × β) × (γ × δ) ≃ α × (β × γ) × δ :=
(prod_assoc% : _ ≃ α × β × γ × δ)... |
Hahn.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.MeasureTheory.VectorMeasure.Basic
import Mathlib.Order.SymmDiff
/-!
# Hahn decomposition
This file proves the Hahn decomposition theorem (signed version). ... |
QExpansion.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.Complex.TaylorSeries
import Mathlib.Analysis.Complex.UpperHalfPlane.Exp
import Mathlib.NumberTheory.ModularForms.Basic
import Mathlib.NumberTh... |
Invariants.lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.RepresentationTheory.Basic
import Mathlib.RepresentationTheory.FDRep
/-!
# Subspace of invariants a group representation
This file introduces the s... |
LSum.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.BigOperators.GroupWithZero.Action
import Mathlib.Algebra.Module.Equiv.Basic
import Mathlib.Algebra.Module.Submodule.LinearMap
import Mathlib.Li... |
FunctorToTypes.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.Types
import Mathlib.Data.Set.Basic
/-!
# The functor from `Set X` to types
Given `X : Type u`, ... |
Continuous.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic
import Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving
import Mathlib.Topology.Alg... |
Defs.lean | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Field.Defs
/-!
# Linear ordered (semi)fields
A ... |
integral_char.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
positivity.lean | import Mathlib.Tactic.Positivity
import Mathlib.Data.Complex.Trigonometric
import Mathlib.Data.Real.Sqrt
import Mathlib.Data.ENNReal.Basic
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Analysis.SpecialFuncti... |
Powerset.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kyle Miller
-/
import Mathlib.Data.Finset.Powerset
import Mathlib.Data.Set.Finite.Basic
/-!
# Finiteness of the powerset of a finite set
## Implementa... |
Limit.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Order.SetIsMax
import Mathlib.Order.SuccPred.Limit
/-!
# Limit elements in Set.Ici
If `J` is a linearly ordered type, `j : J`,
and `m : Set.Ici j` is successor... |
SupIndep.lean | /-
Copyright (c) 2021 Aaron Anderson, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Kevin Buzzard, Yaël Dillies, Eric Wieser
-/
import Mathlib.Data.Finset.Lattice.Union
import Mathlib.Data.Finset.Pairwise
import Mathlib.Data.Finset.Prod
i... |
SeparableDegree.lean | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.FieldTheory.Separable
/-!
# Separable degree
This file contains basics about the separable degree of a polynom... |
Satisfiability.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.ModelTheory.Ultraproducts
import Mathlib.ModelTheory.Bundled
import Mathlib.ModelTheory.Skolem
import Mathlib.Order.Filter.AtTopBot.Basic
/-!
# First-... |
Basic.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Richard Hill, Andrew Yang
-/
import Mathlib.Algebra.Category.ModuleCat.Colimits
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.Topology.Algebra.Module.ModuleTopology
impo... |
WithWeakNamespace.lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Daniel Selsam, Gabriel Ebner
-/
import Mathlib.Init
/-!
# Defines `with_weak_namespace` command.
Changes the current namespace without causing scoped things t... |
Basic.lean | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.RingTheory.Invariant.Defs
import Mathlib.RingTheory.IntegralClosure.IntegralRestrict
/-!
# Invariant Extensions of Rings
Given an extension of ring... |
Equiv.lean | import Mathlib.Data.Int.Order.Units
import Mathlib.GroupTheory.Perm.Finite
example : orderOf (-1 : ℤˣ) = 2 :=
orderOf_eq_prime (Int.units_sq _) (by decide)
|
CompletelyRegular.lean | /-
Copyright (c) 2023 Matias Heikkilä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matias Heikkilä
-/
import Mathlib.Topology.UrysohnsLemma
import Mathlib.Topology.UnitInterval
import Mathlib.Topology.Compactification.StoneCech
import Mathlib.Topology.Order.Lattice
... |
HomologicalBicomplex.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou
-/
import Mathlib.Algebra.Homology.HomologicalComplex
/-!
# Bicomplexes
Given a category `C` with zero morphisms and two complex shapes
`c₁ : ComplexShape I₁` a... |
Counting.lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Combinatorics.SimpleGraph.Clique
import Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform
import Mathlib.Data.Real.Basic
imp... |
Bilipschitz.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Topology.MetricSpace.Antilipschitz
import Mathlib.Topology.MetricSpace.Lipschitz
/-! # Bilipschitz equivalence
A common pattern in Mathlib is to replac... |
fraction.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq.
From mathcomp Require Import ssrAC choice tuple ... |
PolarCoord.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Function.Jacobian
import Mathlib.MeasureTheory.Measure.Lebesgue.Complex
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deri... |
Index.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.BigOperators.GroupWithZero.Finset
import Mathlib.Algebra.GroupWithZero.Subgroup
import Mathlib.Data.Finite.Card
import Mathlib.Data.Finite.Pr... |
interval_inference.v | (* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice.
From mathcomp Require Import order ssralg ssrnum ssrint interval.
(**md********************************************************... |
OpenMapping.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Baire.Lemmas
import Mathlib.Topology.Algebra.Group.Pointwise
/-! # Open mapping theorem for morphisms of topological groups
We prove t... |
Defs.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
import Mathlib.Algebra.Regular.Basic
import Mathlib.Data.F... |
Semiring.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Kappelmann
-/
import Mathlib.Algebra.Order.Floor.Defs
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.Tactic.Linarith
/-!
# Lemmas on `Nat.floor` and `Na... |
choice.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(**************************************************... |
LapMatrix.lean | /-
Copyright (c) 2023 Adrian Wüthrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adrian Wüthrich
-/
import Mathlib.Combinatorics.SimpleGraph.AdjMatrix
import Mathlib.LinearAlgebra.Matrix.PosDef
/-!
# Laplacian Matrix
This module defines the Laplacian matrix of a... |
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