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Defs.lean
/- Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Lutz -/ import Mathlib.FieldTheory.IntermediateField.Basic /-! # Adjoining Elements to Fields In this file we introduce the notion of adjoinin...
Basic.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.Data.Vector.Defs import Mathlib.Data.List.Nodup import Mathlib.Data.List.OfFn import Mathlib.Data.List.Scan import Mathlib.Control.Applicative import M...
archimedean.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 or...
Equalizers.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Preser...
MyhillNerode.lean
/- Copyright (c) 2024 Google. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Wong -/ import Mathlib.Computability.DFA import Mathlib.Data.Set.Finite.Basic /-! # Myhill–Nerode theorem This file proves the Myhill–Nerode theorem using left quotients. Given a lang...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
Completeness.lean
/- Copyright (c) 2023 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Normed.Group.Uniform import Mathlib.Analysis.SpecificLimits.Basic /-! # Completeness of normed groups This file includes a completeness c...
CastCard.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 -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Int.Cast.Basic /-! # Cardinality of a finite set and subtraction This file contains res...
Prime.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, Anne Baanen -/ import Mathlib.Algebra.BigOperators.Group.List.Lemmas import Mathlib.Algebra.GroupWithZero.Associated /-! # Products of lists of prime e...
orderedzmod.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...
Basic.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Order.Filter.CountableInter import Mathlib.Topology.Closure /-! # `Gδ` sets In this file we define `Gδ` sets and prove their b...
CancelDenoms.lean
import Mathlib.Tactic.CancelDenoms.Core import Mathlib.Tactic.NormNum.Ineq
Equiv.lean
/- Copyright (c) 2024 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.RingTheory.Coalgebra.Hom /-! # Isomorphisms of `R`-coalgebras This file defines bundled isomorphisms of `R`-coalgebras. We simply mimic the ear...
finfun.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 tuple. ...
Finset.lean
/- Copyright (c) 2021 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.Algebra.GroupWithZero.Basic import Mathlib.Algebra.Group.Pointwise.Finset.Basic /-! # Pointwise operations of finsets in a gro...
EventuallyConstant.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.CategoryTheory.Filtered.Basic import Mathlib.CategoryTheory.Limits.HasLimits /-! # Limits of eventually constant functors If `F : J ⥤ C` is a functor from a co...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
ssrbool.v
From mathcomp Require Import ssreflect ssrfun. From Corelib Require Export ssrbool. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (**********************) (* not yet backported *) (**********************) Lemma homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT] [aP : pred ...
Prod.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Oliver Nash -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Union /-! # Finsets in product types This file defines finset constru...
rat.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 prime fintype fi...
OfMinimal.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.Dynamics.Ergodic.Action.Regular import Mathlib.MeasureTheory.Measure.ContinuousPreimage import Mathlib.MeasureTheory.Measure.Haar.Unique /-! # Ergod...
WLOG.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Johan Commelin, Reid Barton, Thomas Murrills -/ import Mathlib.Tactic.Core import Lean.Meta.Tactic.Cases /-! # Without loss of generality tactic The ...
Field.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fangming Li, Jujian Zhang -/ import Mathlib.RingTheory.KrullDimension.Basic /-! # The Krull dimension of a field This file proves that the Krull dimension of a field is zero. -/ open ...
Cartesian.lean
/- Copyright (c) 2020 Bhavik Mehta, Edward Ayers, Thomas Read. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Edward Ayers, Thomas Read -/ import Mathlib.CategoryTheory.Closed.Monoidal import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic /-! # Cartesia...
Basic.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.CategoryTheory.Limits.Shapes.FiniteLimits import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.MorphismProperty.Composition i...
Opposite.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.Opposite import Mathlib.Algebra.Order.Monoid.Defs /-! # Order instances for `MulOpposite`/`AddOpposite` This files transfers order instance...
Gaussian.lean
import Mathlib.Probability.Distributions.Gaussian.Real deprecated_module (since := "2025-05-16")
Equiv.lean
/- Copyright (c) 2021 Shing Tak Lam. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam -/ import Mathlib.Topology.Homotopy.Basic /-! # Homotopy equivalences between topological spaces In this file, we define homotopy equivalences between topological space...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
HierarchyDesign.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Eric Wieser -/ import Mathlib.Init import Batteries.Util.LibraryNote /-! # Documentation of the algebraic hierarchy A library note giving advice on modifying the algebrai...
Encode.lean
/- Copyright (c) 2024 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid -/ import Mathlib.Lean.Meta.RefinedDiscrTree.Basic import Lean.Meta.DiscrTree /-! # Encoding an `Expr` as a sequence of `Key`s We compute the encoding of an expres...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
Set.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Floris van Doorn -/ import Mathlib.Algebra.Ring.Defs import Mathlib.Algebra.Group.Pointwise.Set.Basic /-! # Pointwise operations of sets in a ring This file proves pr...
Algebra.lean
/- Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Lutz -/ import Mathlib.FieldTheory.Finiteness import Mathlib.FieldTheory.IntermediateField.Adjoin.Defs import Mathlib.FieldTheory.IntermediateFi...
CardinalArrow.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.CategoryTheory.Comma.Arrow import Mathlib.CategoryTheory.FinCategory.Basic import Mathlib.CategoryTheory.EssentiallySmall import Mathlib.Data.Set.Finite.Basic i...
Basic.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.Ring.Divisibility.Lemmas import Mathlib.Algebra.Lie.Nilpotent import Mathlib.Algebra.Lie.Engel import Mathlib.LinearAlgebra.Eigenspace.Pi import Math...
mxabelem.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...
IO.lean
/- Copyright (c) 2023 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Jon Eugster -/ import Std.Data.TreeSet import Cache.Lean variable {α : Type} open Lean namespace Cache.IO open System (FilePath) /-- Target directory for build fil...
VanKampen.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Adjunction.FullyFaithful import Mathlib.CategoryTheory.Adjunction.Limits import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Ma...
Basic.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Group.Equiv.Opposite import Mathlib.Algebra.Group.Finsupp import Mathlib.Algebra.Group.Pi.Lemmas import Mathlib.Algebra.Group.Pointwise.Finset.Ba...
Adj.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.Bicategory.Adjunction.Mate import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor /-! # The bicategory of adjunctions in a bicategory Gi...
RingHomProperties.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Category.Ring.Constructions import Mathlib.Algebra.Category.Ring.Colimits import Mathlib.CategoryTheory.Iso import Mathlib.CategoryTheory.MorphismPro...
Untilt.lean
/- Copyright (c) 2025 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiedong Jiang -/ import Mathlib.NumberTheory.Basic import Mathlib.RingTheory.AdicCompletion.Basic import Mathlib.RingTheory.Perfection /-! # Untilt Function In this file, we define t...
CombinedProducts.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.CategoryTheory.Limits.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts /-! # Constructors for combining (co)fans We pro...
Subtype.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Logic.Function.Basic import Mathlib.Tactic.AdaptationNote import Mathlib.Tactic.Simps.Basic /-! # Subtypes This file provides basic API for subtypes,...
mxpoly.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 choice seq. From mathcomp Require Import div fintype tupl...
CoverPreserving.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Functor.Flat import Mathlib.CategoryTheory.Sites.Continuous import Mathlib.Tactic.ApplyFun /-! # Cover-preserving functors between sites. In ...
Finite.lean
/- Copyright (c) 2025 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Divisibility.Basic import Mathlib.Data.Fintype.Defs /-! # Divisibility in finite types -/ variable {M : Type*} [Semigroup M] instance [Fint...
Basic.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.RCLike.Basic import Mathlib.Data.Complex.BigOperators import Mathlib.Data.Complex.Module import Mathlib.Data.Complex.Order import Mathli...
Test.lean
/- Copyright (c) 2025 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Mathlib.Init import Qq import Mathlib.Util.AssertExists /-- warning: Module MathlibTest.DirectoryDependencyLinter.Test depends on Mathlib.Util.AssertExist...
Orthogonality.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.FieldTheory.Finite.Basic import Mathlib.NumberTheory.DirichletCharacter.Basic import Mathlib.NumberTheory.MulChar.Duality /-! # Orthogonality relations ...
Linear.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.FunctorCategory import Mathlib.CategoryTheory.Linear.Basic import Mathlib.CategoryTheory.Center.Basic /-! # Center of a linear catego...
UniformConvergence.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, David Loeffler -/ import Mathlib.Analysis.NormedSpace.FunctionSeries import Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs import Mathlib.NumberTheory.Modular...
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.Condensed.Light.Module /-! # Limits in categories of light condensed objects This file adds some instances for limits in light condensed sets and...
IntervalSucc.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.Pairwise.Basic import Mathlib.Data.Set.Lattice import Mathlib.Order.SuccPred.Archimedean /-! # Intervals `Ixx (f x) (f (Order.succ x))` In...
Matrix.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Heather Macbeth -/ import Mathlib.Data.Matrix.Defs import Mathlib.Topology.Algebra.IsUniformGroup.Basic import Mathlib.Topology.UniformSpace.Pi /-! # Uniform space structure...
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. (**********************...
Basic.lean
/- Copyright (c) 2021 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Module.ULift import Mathlib.Data.Finsupp.Fintype import Mathlib.LinearAlgebra.Basis.Basic import Mathlib....
Lasker.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Order.Irreducible import Mathlib.RingTheory.Ideal.Colon import Mathlib.RingTheory.Ideal.IsPrimary import Mathlib.RingTheory.Noetherian.Defs /-! # La...
Finset.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Pi import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Pointwise.Finset.Scalar ...
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. (**************************************************...
Compact.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Yury Kudryashov -/ import Mathlib.Topology.Algebra.Support import Mathlib.Topology.Order.IntermediateValue import Mathlib.Topology.Order.IsLUB import Mathlib.Topology.O...
Vector.lean
/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Data.Fintype.Vector /-! # Finiteness of vector types -/ variable {α : Type*} instance List.Vector.finite [Finite α] {n : ℕ} : Finite (Vector α n) := by ...
Initialize.lean
/- Copyright (c) 2024 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid -/ import Mathlib.Lean.Meta.RefinedDiscrTree.Basic import Lean.Meta.CompletionName /-! # Constructing a RefinedDiscrTree `RefinedDiscrTree` is lazy, so to add an e...
Quotient.lean
/- Copyright (c) 2025 Christian Merten, Yi Song, Sihan Su. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Yi Song, Sihan Su -/ import Mathlib.LinearAlgebra.TensorProduct.Quotient import Mathlib.RingTheory.Ideal.Quotient.Operations import Mathlib.RingT...
Map.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 -/ import Mathlib.MeasureTheory.MeasurableSpace.Embedding import Mathlib.MeasureTheory.Measure.MeasureSpace /-! # Pushforward of a measure In this file...
Monoidal.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.CategoryTheory.Monoidal.Transport import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic import Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat impo...
IsometricSMul.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.Algebra.GroupWithZero.Pointwise.Set.Basic import Mathlib.Algebra.Ring.Pointwise.Set import Mathlib.Topology.Algebra.ConstMulAction import Mathlib.Top...
Factors.lean
/- Copyright (c) 2021 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Eric Wieser -/ import Mathlib.Data.Nat.Factors import Mathlib.Tactic.NormNum.Prime /-! # `simproc` for `Nat.primeFactorsList` Note that since `norm_num` can only prod...
mxpoly.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 choice seq. From mathcomp Require Import div fintype tupl...
Principal.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Sara Rousta -/ import Mathlib.Order.Interval.Set.OrderIso import Mathlib.Order.UpperLower.CompleteLattice /-! # Principal upper/lower sets The results in thi...
Instances.lean
/- Copyright (c) 2025 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Order.CompletePartialOrder import Mathlib.RingTheory.DedekindDomain.PID import Mathlib.FieldTheory.Separabl...
finmodule.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...
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.Data.Finset.Grade import Mathlib.Data.Finset.Powerset import Mathlib.Order.Interval.Finset.Basic /-! # Intervals of finsets as finsets This file provides...
MulOpposite.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.Algebra.Ring.Subsemiring.MulOpposite import Mathlib.Algebra.Ring.Subring.Basic /-! # Subring of opposite rings For every ring `R`, we construct an equivalence betwe...
Karoubi.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Idempotents.Basic import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor import Mathlib.CategoryTheory.Equivalence /-! # The Karoubi envelope ...
mod_cases.lean
import Mathlib.Tactic.ModCases private axiom test_sorry : ∀ {a}, a example (n : ℤ) : 3 ∣ n ^ 3 - n := by mod_cases n % 3 · guard_hyp H :ₛ n ≡ 0 [ZMOD 3]; guard_target = 3 ∣ n ^ 3 - n; exact test_sorry · guard_hyp H :ₛ n ≡ 1 [ZMOD 3]; guard_target = 3 ∣ n ^ 3 - n; exact test_sorry · guard_hyp H :ₛ n ≡ 2 [ZMOD 3...
sesquilinear.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup. From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector. (************************************************...
NormTrace.lean
/- Copyright (c) 2023 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.Localization.Module import Mathlib.RingTheory.Norm.Basic import Mathlib.RingTheory.Discriminant /-! # Field/algebra norm / trace and localizatio...
End.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.Algebra.Group.Defs import Mathlib.Order.RelIso.Basic /-! # Relation isomorphisms form a group -/ assert_not_exists MulAction MonoidWithZero variable...
Smooth.lean
/- Copyright (c) 2023 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Adam Topaz -/ import Mathlib.Algebra.Category.Ring.Colimits import Mathlib.Algebra.Category.Ring.FilteredColimits import Mathlib.Algebra.Category.Ring.Limits import M...
MulCoeff.lean
/- Copyright (c) 2022 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Heather Macbeth -/ import Mathlib.Algebra.MvPolynomial.Supported import Mathlib.RingTheory.WittVector.Truncated /-! # Leading terms of Witt vector multiplication Th...
NCompGamma.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.DoldKan.GammaCompN import Mathlib.AlgebraicTopology.DoldKan.NReflectsIso /-! The unit isomorphism of the Dold-Kan equivalence In order to con...
Defs.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Batteries.Data.DList.Basic import Mathlib.Data.WSeq.Basic /-! # Miscellaneous definitions concerning weak sequences These definitions, as well as thos...
Basic.lean
/- Copyright (c) 2024 Yaël Dillies, Kin Yau James Wong. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Kin Yau James Wong, Rémy Degenne -/ import Mathlib.MeasureTheory.Function.AEEqOfLIntegral import Mathlib.Probability.Kernel.Composition.MeasureCompProd ...
DeprecatedModule.lean
/- Copyright (c) 2025 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Std.Time.Format import Mathlib.Init /-! # The `deprecated.module` linter The `deprecated.module` linter emits a warning when a file that has been renamed or s...
Product.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.CategoryTheory.Groupoid import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic import Mathlib.Topology.Category.TopCat.Limits.Products impo...
separable.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 div. From mathcomp Require Import choice fintype tupl...
gseries.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 bigop finset fingroup morphism. From mathcomp...
Basic.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, Minchao Wu, Mario Carneiro -/ import Mathlib.Data.Finset.Attach import Mathlib.Data.Finset.Disjoint import Mathlib.Data.Finset.Erase import Mat...
Rat.lean
/- Copyright (c) 2015 Nathaniel Thomas. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Module.Basic import Mathlib.Algebra.NoZeroSMulDivisors.Basic import Mathlib.Algebra.Field.Ra...
Support.lean
/- Copyright (c) 2025 Jon Bannon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Bannon, Jireh Loreaux -/ import Mathlib.MeasureTheory.Measure.OpenPos /-! # Support of a Measure This file develops the theory of the **support** of a measure `μ` on a topological m...
Defs.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Defs /-! # Torsors of additive group actions This file defines torsors of additive group actions. ## Notations Th...
Mon_.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.Algebra.Group.PUnit import Mathlib.CategoryTheory.Monoidal.Braided.Basic import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas import Mathlib.CategoryTheo...
Groupoid.lean
/- Copyright (c) 2018 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Kim Morrison, David Wärn -/ import Mathlib.CategoryTheory.ObjectProperty.FullSubcategory import Mathlib.CategoryTheory.Products.Basic import Mathlib.CategoryTheory.Pi.Basic i...
ColimitLimit.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.CategoryTheory.Limits.Types.Colimits import Mathlib.CategoryTheory.Limits.Types.Limits import Mathlib.CategoryTheory.Functor.Currying import Mathlib.Catego...
InducedTopology.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv /-! # Induced Topology We say that a functor `G : C ⥤ (D, K)` is locally dense if for each covering sieve `T` ...
Finite.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.NormalizedFactors /-! # Finiteness of divisors ## Main results * `UniqueFactoriz...
WithBot.lean
/- Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Andrew Yang -/ import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop import Mathlib.Algebra.Order.SuccPred import Mathlib.Order.SuccPred.WithBot /-! # Algebra...