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Lift.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.Order.Filter.Prod import Mathlib.Order.ConditionallyCompleteLattice.Basic import Mathlib.Order.Filter.Finite import Mathlib.Order.Filter.Bases.Basic /...
DilationEquiv.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.MetricSpace.Dilation /-! # Dilation equivalence In this file we define `DilationEquiv X Y`, a type of bundled equivalences between `X` and...
Icc.lean
/- Copyright (c) 2025 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.InnerProductSpace.Calculus import Mathlib.Geometry.Manifold.ContMDiff.Basic import Mathlib.Geometry.Manifold.Instances.Real import Mathl...
Card.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Pointwise.Set.Scalar import Mathlib.Algebra.GroupWithZero.Action.Basic import Mathlib.SetTheory.Cardinal.Finite /-! # Cardinality of sets un...
StandardSmoothCotangent.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.LinearAlgebra.Basis.Exact import Mathlib.RingTheory.Extension.Cotangent.Basic import Mathlib.RingTheory.Smooth.StandardSmooth import Mathlib.RingTh...
Noetherian.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Subobject.ArtinianObject import Mathlib.CategoryTheory.Subobject.NoetherianObject /-! # Artinian and noetherian categories An artinian cat...
AbstractFuncEq.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.MellinTransform /-! # Abstract functional equations for Mellin transforms This file formalises a general version of an argument used to pro...
countalg.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 ss...
Star.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Topology.Algebra.Constructions import Mathlib.Topology.ContinuousMap.Defs import Mathlib.Algebra.Star.Basic /-! # Continuity of `star` This file defines th...
ssrfun.v
From mathcomp Require Import ssreflect. From Corelib Require Export ssrfun. From mathcomp Require Export ssrnotations. #[export] Set Warnings "-overwriting-delimiting-key". (* remove above line when requiring Rocq >= 9.0 *) Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (***********...
Gaussian.lean
/- Copyright (c) 2023 Luke Mantle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Luke Mantle, Jake Levinson -/ import Mathlib.RingTheory.Polynomial.Hermite.Basic import Mathlib.Analysis.Calculus.Deriv.Add import Mathlib.Analysis.Calculus.Deriv.Polynomial import Mathli...
mxrepresentation.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...
Submonoid.lean
/- Copyright (c) 2021 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Algebra.Group.Submonoid.Defs import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic import Mathlib.Order.Interval.Set.Defs /-! # The submonoid of ...
Associated.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 -/ import Mathlib.Algebra.GroupWithZero.Associated import Mathlib.Algebra.Order.Monoid.Canonical.Defs /-! # Associated, prime, and irreducible elements....
Compact.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, Yury Kudryashov -/ import Mathlib.Order.Filter.Tendsto import Mathlib.Data.Set.Accumulate import Mathlib.Topology.Bornology.Basic import Mathlib.Topolog...
Units.lean
/- Copyright (c) 2020 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Topology.Algebra.Ring.Ideal import Mathlib.RingTheory.Ideal.Nonunits /-! # The group of units of a com...
Determinant.lean
/- Copyright (c) 2022 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Alex J. Best -/ import Mathlib.LinearAlgebra.Determinant import Mathlib.LinearAlgebra.FreeModule.Finite.Basic /-! # Determinants in free (finite) modules Quite a lot of our...
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...
Induced.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Shift.CommShift /-! # Shift induced from a category to another In this file, we introduce a sufficient condition on a functor `F : C ⥤ D` so tha...
GetAllModules.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kim Morrison, Damiano Testa -/ import Mathlib.Init import Lean.Util.Path /-! # Utility functions for finding all `.lean` files or modules in a project. TODO: `getLean...
convert2.lean
import Mathlib.Algebra.BigOperators.Ring.List import Mathlib.Algebra.Ring.Nat import Mathlib.Tactic.Convert set_option linter.unreachableTactic false -- Prior to https://github.com/leanprover-community/mathlib4/pull/7945 this failed with `(kernel) declaration has metavariables '_example'`. /-- error: maximum recursio...
SmallDegreeVieta.lean
/- Copyright (c) 2025 Qinchuan Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Qinchuan Zhang -/ import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.LinearCombination import Mathlib.RingTheory.Polynomial.Vieta /-! # Vieta's Formula for polynomial of small degr...
DistLat.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Category.Lat /-! # The category of distributive lattices This file defines `DistLat`, the category of distributive lattices. Note that [`DistLat`]...
Split.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.BoxIntegral.Partition.Basic /-! # Split a box along one or more hyperplanes ## Main definitions A hyperplane `{x : ι → ℝ | x i = a}` spli...
Over.lean
import Mathlib.CategoryTheory.Monoidal.Cartesian.Over deprecated_module (since := "2025-05-15")
Set.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.Set.Image import Mathlib.Order.TypeTags /-! # `Set.range` on `WithBot` and `WithTop` -/ open Set variable {α β : Type*} theorem WithBot.ran...
Action.lean
/- Copyright (c) 2020 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn -/ import Mathlib.CategoryTheory.Elements import Mathlib.CategoryTheory.IsConnected import Mathlib.CategoryTheory.SingleObj import Mathlib.GroupTheory.GroupAction.Quotient impor...
Neighborhoods.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, Jeremy Avigad -/ import Mathlib.Order.Filter.AtTopBot.Basic import Mathlib.Topology.Closure /-! # Neighborhoods in topological spaces Each point `x` o...
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.Field.TransferInstance import Mathlib.Logic.Small.Defs import Mathlib.Tactic.SuppressCompilation /-! # Transfer field structures from `α` to `Shri...
numfield.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...
toAdditiveIrredDef.lean
import Mathlib.Tactic.IrreducibleDef import Mathlib.Algebra.Group.Defs set_option autoImplicit true @[to_additive] irreducible_def mul_conj [Group G] (a b : G) := a⁻¹ * b * a example [AddGroup A] (a b : A) : add_conj a b = (-a) + b + a := add_conj_def a b
LogDeriv.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv import Mathlib.Analysis.Calculus.LogDeriv...
Pairwise.lean
/- Copyright (c) 2025 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.List.Pairwise import Mathlib.Data.Multiset.Defs /-! # Pairwise relations on a multiset This file provides basic results about `Multiset.Pairwise` (d...
PosLog.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.SpecialFunctions.Log.Basic /-! # The Positive Part of the Logarithm This file defines the function `Real.posLog = r ↦ max 0 (log r)` and int...
Subalgebra.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Jireh Loreaux -/ import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.Algebra.Tower import Mathlib.Algebra.Star.Module import Mathlib.Algebra.Star.NonUn...
Rat.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Field.Rat import Mathlib.Algebra.Order.Nonneg.Field import Mathlib.Algebra.Order.Ring.Rat /-! # The rational numbers form a li...
LieGroup.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri -/ import Mathlib.Geometry.Manifold.Algebra.Monoid /-! # Lie groups A Lie group is a group that is also a `C^n` manifold, in which the group operations of multipli...
Opposite.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Shift.Adjunction import Mathlib.CategoryTheory.Preadditive.Opposite /-! # The (naive) shift on the opposite category If `C` is a category equipp...
TautoSet.lean
/- Copyright (c) 2025 Lenny Taelman. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lenny Taelman -/ import Mathlib.Tactic.TautoSet variable {α : Type} {A B C D E : Set α} example (h : B ∪ C ⊆ A ∪ A) : B ⊆ A := by tauto_set example (h : B ∩ B ∩ C ⊇ A) : A ⊆ B := by...
Continuity.lean
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic import Mathlib.Topology.Basic import Mathlib.Topology.ContinuousMap.Basic set_option autoImplicit true section basic variable [TopologicalSpace W] [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z] variable {I : Type _} {X' : I → Type _} [∀ i, T...
classfun.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...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
DeprecateTo.lean
import Mathlib.Tactic.DeprecateTo import Mathlib.Tactic.ToAdditive /-- info: * Pairings: #[(new_name_mul, mul_easy_deprecated), (new_name_add, add_easy_deprecated)] Try this: /-- I also have a doc-string -/ @[to_additive /-- With its additive doc-string -/ ] theorem new_name_mul : True := .intro @[deprecated (...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
DirectLimit.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Gabin Kolly -/ import Mathlib.Data.Finite.Sum import Mathlib.Data.Fintype.Order import Mathlib.ModelTheory.FinitelyGenerated import Mathlib.ModelTheory.Quotients import...
MaricaSchoenheim.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.Combinatorics.SetFamily.FourFunctions import Mathlib.Data.Nat.Squarefree /-! # The Marica-Schönheim special case of Graham's conjecture Graham's conjectu...
Basic.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme import Mathlib.AlgebraicGeometry.AffineScheme import Mathlib.AlgebraicGeometry.Gluing /-! # Basic properties of...
finfield.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 div tupl...
UniformSpace.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Patrick Massot, Kim Morrison -/ import Mathlib.CategoryTheory.Adjunction.Reflective import Mathlib.CategoryTheory.Monad.Limits import Mathlib.Topology.Category.TopCat.Basic ...
MellinEqDirichlet.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.SpecialFunctions.Gamma.Deligne /-! # Dirichlet series as Mellin transforms Here we prove general results of the form "the Mellin transform o...
Closure.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, Jeremy Avigad -/ import Mathlib.Order.Filter.Lift import Mathlib.Topology.Basic /-! # Interior, closure and frontier of a set This file provides lemma...
nilpotent.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 path. From mathcomp Require Import fintype div bigop prime finset fingroup morphism. Fro...
Associator.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 -/ import Mathlib.Algebra.Algebra.Hom import Mathlib.LinearAlgebra.TensorProduct.Basic /-! # Associators and unitors for tensor products of modules over a commuta...
Rank.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.SetTheory.Ordinal.Family /-! # Rank in a well-founded relation For `r` a well-founded relation, `IsWellFounded.rank r a` is recursively defined as the le...
IsPoly.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Robert Y. Lewis -/ import Mathlib.Algebra.MvPolynomial.Funext import Mathlib.Algebra.Ring.ULift import Mathlib.RingTheory.WittVector.Basic /-! # The `IsPoly` predicate ...
RestrictScalars.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Andrew Yang, Johannes Hölzl, Kevin Buzzard, Yury Kudryashov -/ import Mathlib.Algebra.Module.End import Mathlib.Algebra....
Oscillation.lean
/- Copyright (c) 2024 James Sundstrom. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: James Sundstrom -/ import Mathlib.Data.ENNReal.Real import Mathlib.Order.WellFoundedSet import Mathlib.Topology.EMetricSpace.Diam /-! # Oscillation In this file we define the oscill...
GaloisClosure.lean
/- Copyright (c) 2024 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan, Yuyang Zhao -/ import Mathlib.FieldTheory.Normal.Closure import Mathlib.FieldTheory.SeparableClosure /-! # Main definitions and results In a field extension `K/k` * `Fin...
Free.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.Algebra.FreeNonUnitalNonAssocAlgebra import Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra import Mathlib.Algebra.Lie.UniversalEnveloping import Mathlib.GroupT...
intdiv.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 choice fintype...
LiftingProperties.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.Preadditive.Projective.Basic import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty /-! # Characterization of projective objects in terms...
Limits.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta, Jack McKoen -/ import Mathlib.CategoryTheory.Monad.Adjunction import Mathlib.CategoryTheory.Adjunction.Limits import Mathlib.CategoryTheory.Limits.Shapes.IsTe...
Pointwise.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Jujian Zhang -/ import Mathlib.Algebra.GroupWithZero.Subgroup import Mathlib.Algebra.Order.Group.Action import Mathlib.LinearAlgebra.Finsupp.Supported import Mathlib.LinearAl...
Constructions.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.InnerProductSpace.Harmonic.Basic import Mathlib.Analysis.Calculus.ContDiff.RestrictScalars import Mathlib.Analysis.SpecialFunctions.Complex.An...
mxrepresentation.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...
Check.lean
import Mathlib.Tactic.Check /- Override metavariable delaborator for natural metavariables to print `?m` instead of including a unique number, for `#guard_msgs`. -/ open Lean PrettyPrinter Delaborator in @[delab mvar] def delabMVar : Delab := do let kind ← (← SubExpr.getExpr).mvarId!.getKind unless kind.isNatural d...
DivisionRing.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison, Chris Hughes, Anne Baanen, Junyan Xu -/ import Mathlib.LinearAlgebra.Basis.VectorSpace import Mathlib.LinearAlgebra.Dimensi...
Cofiltered.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang -/ import Mathlib.Topology.Category.TopCat.Limits.Basic import Mathlib.CategoryTheory.Filtered.Basic /-! # Cofiltered limits in...
falgebra.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 choice fintype div...
Conditional.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Independence.Kernel import Mathlib.Probability.Kernel.Condexp /-! # Conditional Independence We define conditional independence of sets/σ-alg...
PythagoreanTriples.lean
/- Copyright (c) 2020 Paul van Wamelen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul van Wamelen -/ import Mathlib.Data.Int.NatPrime import Mathlib.Data.ZMod.Basic import Mathlib.RingTheory.Int.Basic import Mathlib.Tactic.FieldSimp /-! # Pythagorean Triples Th...
Arctan.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex /-! # The `arctan` function. Inequalit...
BicategoricalComp.lean
/- Copyright (c) 2022 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.CategoryTheory.Bicategory.Basic /-! # Bicategorical composition `⊗≫` (composition up to associators) We provide `f ⊗≫ g`, the `bicategoricalComp` operation...
Commute.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.Algebra.GroupWithZero.Semiconj import Mathlib.Algebra.Group.Commute.Units import Mathlib.Tactic.Nontriviality /-! # Lemmas about commuting elements in...
Strong.lean
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax deprecated_module (since := "2025-05-11")
TotalComplexShift.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.Homology.HomotopyCategory.Shift import Mathlib.Algebra.Homology.TotalComplex /-! # Behaviour of the total complex with respect to shifts There are two ...
LocalContext.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.Init import Lean.LocalContext /-! # Additional methods about `LocalContext` -/ namespace Lean.LocalContext universe u v variable {m : Type u → Type v} [...
MatrixPolynomialAlgebra.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Data.Matrix.Basis import Mathlib.Data.Matrix.Composition import Mathlib.RingTheory.MatrixAlgebra import Mathlib.RingTheory.PolynomialAlgebra /-! # Algebra...
primitive_action.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 div seq fintype tuple finset. From mathcomp Require Import fin...
polydiv.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ssralg poly. (**********************...
CompleteLatticeIntervals.lean
/- Copyright (c) 2022 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Order.ConditionallyCompleteLattice.Basic import Mathlib.Order.LatticeIntervals import Mathlib.Order.Interval.Set.OrdConnected /-! # Subtypes of cond...
Semantics.lean
/- Copyright (c) 2021 Aaron Anderson, Jesse Michael Han, Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn -/ import Mathlib.Data.Finset.Basic import Mathlib.ModelTheory.Syntax import Mathlib.Data.List....
Order.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kenny Lau -/ import Mathlib.Algebra.CharP.Defs import Mathlib.RingTheory.Multiplicity import Mathlib.RingTheory.PowerSeries.Basic /-! # Formal power series (in one va...
Basic.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.RingTheory.Nilpotent.Basic import Mathlib.RingTheory.UniqueFactorizationDomain.GCDMonoid import Mathlib.RingTheory.UniqueFactorizationDomain.Multiplici...
Card.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.Finset.Card import Mathlib.Data.Fintype.Basic /-! # Cardinalities of finite types This file defines the cardinality `Fintype.card α` as the numb...
QuaternionBasis.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.Quaternion import Mathlib.Tactic.Ring /-! # Basis on a quaternion-like algebra ## Main definition...
Classical.lean
/- Copyright (c) 2020 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Data.Matrix.Basis import Mathlib.Data.Matrix.DMatrix import Mathlib.Algebra.Lie.Abelian import Mathlib.LinearAlgebra.Matrix.Trace import Mathlib.Algebra.Lie....
fast_instance.lean
import Mathlib.Tactic.FastInstance import Mathlib.Logic.Function.Defs import Mathlib.Tactic.Spread namespace testing set_option autoImplicit false -- For debugging: --set_option trace.Elab.fast_instance true /-! Testing a diamond: CommSemigroup -/ class Mul (α : Type*) where mul : α → α → α class Semigroup (α : ...
Infinite.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Data.Nat.Factorial.Basic import Mathlib.Data.Nat.Prime.Defs import Mathlib.Order.Bounds.Basic /-! ## Notable ...
PDeriv.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam, Yury Kudryashov -/ import Mathlib.Algebra.MvPolynomial.Derivation import Mathlib.Algebra.MvPolynomial.Variables /-! # Partial derivatives of polynomials This file defi...
mxalgebra.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 b...
Coverage.lean
/- Copyright (c) 2023 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Sites.Sheaf import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq /-! # Coverages A coverage `K` on a category `C` is a set of presieve...
SlashActions.lean
/- Copyright (c) 2022 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs import Mathlib.LinearAlgebra.Matrix.SpecialLi...
Products.lean
/- Copyright (c) 2020 Kim Morrison, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.Products import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # Preserving products Construc...
UniformField.lean
/- Copyright (c) 2019 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.RingTheory.SimpleRing.Basic import Mathlib.Topology.Algebra.Field import Mathlib.Topology.Algebra.UniformRing /-! # Completion of topological fields ...
CoverEntropy.lean
/- Copyright (c) 2024 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine, Pietro Monticone -/ import Mathlib.Analysis.Asymptotics.ExpGrowth import Mathlib.Data.ENat.Lattice import Mathlib.Data.Real.ENatENNReal import Mathlib.Dynamics.Topologi...
presentation.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. From mathcomp Require Import fintype finset fingroup morphism. (**********************...
Cat.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.CategoryTheory.ConcreteCategory.Bundled import Mathlib.CategoryTheory.Discrete.Basic import Mathlib.CategoryTheory.Types import Mathlib.CategoryTheor...
Nat.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.Order.Group.Nat import Mathlib.Algebra.Order.GroupWithZero...
Defs.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov, Kim Morrison -/ import Mathlib.Data.Finsupp.SMul /-! # Monoid algebras When the domain of a `Finsupp` has a multiplicative or additive structure, we ...