filename
stringlengths
5
42
content
stringlengths
15
319k
Fixed.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Polynomial.GroupRingAction import Mathlib.Algebra.Ring.Action.Field import Mathlib.Algebra.Ring.Action.Invariant import Mathlib.FieldTheory.Finiteness im...
Observe.lean
/- Copyright (c) 2023 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Init import Lean.Meta.Tactic.TryThis import Lean.Elab.Tactic.ElabTerm import Lean.Meta.Tactic.LibrarySearch /-! # The `observe` tactic. `observe hp :...
Reduced.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.RingTheory.LocalProperties.Basic import Mathlib.RingTheory.Nilpotent.Defs /-! # `IsReduced` is a local property In this file, we prove that `IsReduced` is ...
Range.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kenny Lau -/ import Mathlib.Algebra.Group.Int.Defs import Mathlib.Algebra.Order.Group.Unbundled.Basic /-! # Intervals in ℤ This file defines integer ranges. `range m n` is...
Init.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 -/ import Mathlib.Data.Stream.Defs import Mathlib.Logic.Function.Basic import Mathlib.Data.Nat.Basic import Mathlib.Tactic.Common /-! # Streams a.k.a. infinit...
Finite.lean
/- Copyright (c) 2025 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.Matroid.Closure /-! # Finite-rank sets `Matroid.IsRkFinite M X` means that every basis of the set `X` in the matroid `M` is finite, or equivalently...
BigOperators.lean
/- Copyright (c) 2022 Pim Otte. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Pim Otte -/ import Mathlib.Algebra.Order.BigOperators.Ring.Finset import Mathlib.Tactic.Zify /-! # Factorial with big operators This file contains some lemmas on factorials in...
CommGrp_.lean
/- Copyright (c) 2025 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Monoidal.Internal.Types.Grp_ import Mathlib.CategoryTheory.Monoidal.CommGrp_ /-! # `CommGrp_ (Type u) ≌ CommGrp.{u}` The category of int...
Flag.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Patrick Massot -/ import Mathlib.Data.Fin.FlagRange import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.Dual.Basis import Mathlib.RingTheory.SimpleR...
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. (******************************************...
AE.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yury Kudryashov -/ import Mathlib.MeasureTheory.OuterMeasure.Basic /-! # The “almost everywhere” filter of co-null sets. If `μ` is an outer measure or a measure on `α...
FunctorCategory.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.Monoidal.CommMon_ import Mathlib.CategoryTheory.Monoidal.Comon_ import Mathlib.CategoryTheory.Monoidal.FunctorCategory /-! # `Mon_ (C ⥤ D) ...
Limits.lean
/- Copyright (c) 2024 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan, Youle Fang, Jujian Zhang, Yuyang Zhao -/ import Mathlib.CategoryTheory.ConcreteCategory.EpiMono import Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic import Mathlib.Top...
pgroup.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 div. From mathcomp Require Import fintype bigop finset prime fingroup morphism. From mat...
SuccPred.lean
/- Copyright (c) 2025 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Order.SuccPred import Mathlib.Order.Interval.Finset.SuccPred /-! # Finset intervals in an additive successor-predecessor order This file proves r...
Defs.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Geometry.Manifold.IsManifold.ExtChartAt import Mathlib.Geometry.Manifold.LocalInvariantProperties /-! # The derivative of func...
Tor.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.CategoryTheory.Abelian.LeftDerived import Mathlib.CategoryTheory.Monoidal.Preadditive /-! # Tor, the left-derived functor of tensor product We define `To...
Lattice.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Measure.AEMeasurable /-! # Typeclasses for measurability of lattice operations In this file we define classes `MeasurableSup` and `Measurab...
LinearOrder.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, Patrick Massot, Yury Kudryashov, Rémy Degenne -/ import Mathlib.Order.Interval.Set.Basic import Mathlib.Order.MinMax /-! # Interval properties in linea...
Opposite.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.Algebra.MonoidAlgebra.Defs import Mathlib.Algebra.Ring.Opposite import Mathlib.Data.Finsupp.Basic /-! # Monoid algebras...
Intrinsic.lean
/- Copyright (c) 2023 Paul Reichert. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul Reichert, Yaël Dillies -/ import Mathlib.Analysis.Normed.Affine.AddTorsorBases /-! # Intrinsic frontier and interior This file defines the intrinsic frontier, interior and closur...
ShrinkingLemma.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Reid Barton -/ import Mathlib.Topology.Separation.Regular /-! # The shrinking lemma In this file we prove a few versions of the shrinking lemma. The lemma says that...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
polyXY.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 choice ssrnat seq. From mathcomp Require Import fintype tuple fi...
test_order_conv.v
From mathcomp Require Import all_boot all_order. Import Order.Theory. Section dual_of_dual. Context (disp : Order.disp_t). Let eq_dual_dual_preorderType (T : preorderType disp) : Order.Preorder.on T = Order.Preorder.on T^d^d := erefl. Let eq_dual_dual_porderType (T : porderType disp) : Order.POrder.on T = Order....
ControlledClosure.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Analysis.Normed.Group.Hom import Mathlib.Analysis.SpecificLimits.Normed /-! # Extending a backward bound on a normed group homomorphism from a dense s...
fieldext.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 div. From mathcomp Require Import choice fintype tupl...
eqtype.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. (********************************************************************...
Lemmas.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Control.Applicative import Mathlib.Control.Traversable.Basic /-! # Traversing collections This file proves basic properties of traversable and applicative ...
CauchyIntegral.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.Analytic.Uniqueness import Mathlib.Analysis.Calculus.DiffContOnCl import Mathlib.Analysis.Calculus.DSlope import Mathlib.Analysis.Calculus.F...
Sqrt.lean
/- Copyright (c) 2020 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn, Yury Kudryashov -/ import Mathlib.Topology.Instances.NNReal.Lemmas import Mathlib.Topology.Order.MonotoneContinuity /-! # Square root of a real numbe...
FiberPartition.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.LocallyConstant.Basic import Mathlib.Logic.Function.FiberPartition /-! This file provides some API surrounding `Function.Fiber` (see `Mat...
GCongr.lean
/- Copyright (c) 2023 Mario Carneiro, Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Heather Macbeth -/ import Mathlib.Tactic.GCongr.CoreAttrs import Mathlib.Tactic.Hint /-! # Setup for the `gcongr` tactic The core implementation of t...
ComplexMGF.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.Calculus.ParametricIntegral import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.MeasureTheory.Measure.CharacteristicFunction import Math...
Ext.lean
/- Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bryan Gin-ge Chen, Yury Kudryashov -/ import Mathlib.Algebra.Group.Hom.Defs /-! # Extensionality lemmas for monoid and group structures In this file we prove extensionality lemmas...
WeakSpace.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.Analysis.NormedSpace.HahnBanach.Separation import Mathlib.LinearAlgebra.Dual.Defs import Mathlib.Topology.Algebra.Module.WeakDual /-! # Closures of conv...
Connected.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.Topology.Separation.Basic import Mathlib.Topology.Connected.TotallyDisconnected /-! # Interaction of separation properties with connec...
ssrnum.v
From mathcomp Require Export orderedzmod. From mathcomp Require Export numdomain. From mathcomp Require Export numfield. Module Num. Export orderedzmod.Num. Export numdomain.Num. Export numfield.Num. Module Theory. Export orderedzmod.Num.Theory. Export numdomain.Num.Theory. Export numfield.Num.Theory. End Theory. Mo...
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) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Group.Action.Units import Mathlib.Algebra.Group.Invertible.Basic import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Logic.Embedding.Basic /-! # ...
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********************************************************...
seq.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. (******************************************************...
bigop.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 fintype tuple ...
Lemmas.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear import Mathlib.LinearAlgebra.RootSystem.Reduced import Mathlib.LinearAlgebra.RootSystem.Irreducible import ...
Supported.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.Module.Submodule.Range import Mathlib.LinearAlgebra.Finsupp.LSum import Mathlib.LinearAlgebra.Span.Defs /-! # `Finsupp`s supported on a given ...
Connected.lean
/- Copyright (c) 2025 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic import Mathlib.CategoryTheory.Limits.Connected import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommS...
Rolle.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Anatole Dedecker -/ import Mathlib.Analysis.Calculus.LocalExtr.Basic import Mathlib.Topology.Order.Rolle /-! # Rolle's Theorem In this file we prove Rolle's Theorem...
LucasPrimality.lean
/- Copyright (c) 2020 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey -/ import Mathlib.Algebra.Field.ZMod import Mathlib.RingTheory.IntegralDomain /-! # The Lucas test for primes This file implements the Lucas test for primes (not to be c...
Decomposition.lean
/- Copyright (c) 2025 Matteo Cipollina. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Matteo Cipollina -/ import Mathlib.Algebra.Order.Group.Nat import Mathlib.Combinatorics.Quiver.Path import Mathlib.Tactic.Cases /-! # Path Decomposition and Boundary Crossing This...
FunctionsBoundedAtInfty.lean
/- Copyright (c) 2022 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, David Loeffler -/ import Mathlib.Algebra.Module.Submodule.Basic import Mathlib.Analysis.Complex.UpperHalfPlane.Topology import Mathlib.Order.Filter.ZeroAndBoundedAtFilt...
finset.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 div seq. From mathcomp Require Import choice fintype finf...
Disjoint.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.Insert /-! # Disjoint finite sets ## Main declarations * `Disjoint`: defined via th...
Basic.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.Algebra.Module.LinearMapPiProd import Mathlib.LinearAlgebra.Multilinear.Basic import Mathlib.Algebra.BigOperators.Fin /-! # Continuous ...
Cardinality.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.Algebra.Module.Card import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.SetTheory.Cardinal.Continuum import Mathlib.SetTheory.Cardinal.C...
Induction.lean
/- Copyright (c) 2014 Parikshit Khanna. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro -/ import Mathlib.Data.List.Basic /-! ### Induction principles for lists -/ variable {α : Type*...
FDRep.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.Algebra.Category.FGModuleCat.Limits import Mathlib.CategoryTheory.Monoidal.Rigid.Braided import Mathlib.CategoryTheory.Preadditive.Schur import Mathlib.Rep...
meta.lean
import Lean.Elab.Tactic.ElabTerm import Lean.Elab.Tactic.Rfl import Mathlib.Lean.Expr.Basic import Mathlib.Lean.Meta.Basic import Mathlib.Tactic.Relation.Rfl /-! # Tests for mathlib extensions to `Lean.Expr` and `Lean.Meta` -/ namespace Tests open Lean Meta private axiom test_sorry : ∀ {α}, α set_option linter.styl...
Gal.lean
/- Copyright (c) 2022 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots import Mathlib.FieldTheory.PolynomialGaloisGroup /-! # Galois group of cyclotomic extensions In this file, we ...
Regulator.lean
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Algebra.Module.ZLattice.Covolume import Mathlib.LinearAlgebra.Matrix.Determinant.Misc import Mathlib.NumberTheory.NumberField.Units.DirichletTheorem /-!...
Invariant.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.Basic deprecated_module (since := "2025-05-24")
Hairer.lean
/- Copyright (c) 2023 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Sébastien Gouëzel, Patrick Massot, Ruben Van de Velde, Floris van Doorn, Junyan Xu -/ import Mathlib.Algebra.MvPolynomial.Funext import Mathlib.Analysis.Analytic.Poly...
Midpoint.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Module.Basic import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv /-! # Midpoint of a segment ## Main definitions * `midpoint R x y`: midp...
sylow.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 div. From mathcomp Require Import fintype prime bigop finset fingroup morphism. From mat...
Order.lean
/- Copyright (c) 2021 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Algebra.Module.Submodule.Order import Mathlib.Algebra.Ring.Subsemiring.Order /-! # Order instances on s...
LiminfLimsup.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, Yaël Dillies -/ import Mathlib.Order.Filter.CountableInter import Mathlib.Order.LiminfLimsup import Mathlib.Topology.Order.Monotone /-...
Pi.lean
/- Copyright (c) 2024 Madison Crim. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Madison Crim -/ import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.BigOperators.Pi import Mathlib.Algebra.Divisibility.Prod import Mathlib.Algebra.Group.Submonoid.BigOperators impo...
FiniteAdeleRing.lean
/- Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import Mathlib.RingTheory.DedekindDomain.AdicValuation import Mathlib.RingTheory.DedekindDomain.Factorization import Mathlib.Topology....
polyXY.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 choice ssrnat seq. From mathcomp Require Import fintype tuple fi...
FiniteDimension.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Anatole Dedecker -/ import Mathlib.Analysis.LocallyConvex.BalancedCoreHull import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathlib.LinearAlgebra.FreeM...
QuasiMeasurePreserving.lean
/- Copyright (c) 2025 Oliver Butterley. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Butterley, Lua Viana Reis -/ import Mathlib.Dynamics.BirkhoffSum.Average import Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving /-! # Birkhoff sum and average for quasi ...
cyclotomic.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 div choice fintype tuple finfun bigop prime. From mat...
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: ...
CurryingThree.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.Functor.Currying import Mathlib.CategoryTheory.Functor.Trifunctor import Mathlib.CategoryTheory.Products.Associator /-! # Currying of functors i...
SuccPred.lean
/- Copyright (c) 2025 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Interval.Finset.Defs import Mathlib.Order.Interval.Set.SuccPred /-! # Finset intervals in a successor-predecessor order This file proves relations ...
Defs.lean
/- Copyright (c) 2021 Stuart Presnell. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stuart Presnell -/ import Batteries.Data.List.Count import Mathlib.Data.Finsupp.Multiset import Mathlib.Data.Finsupp.Order import Mathlib.Data.Nat.PrimeFin import Mathlib.NumberTheory...
Antilipschitz.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.UniformSpace.CompleteSeparated import Mathlib.Topology.EMetricSpace.Lipschitz import Mathlib.Topology.MetricSpace.Basic import Mathlib.Topol...
SchwartzSpace.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.Calculus.ContDiff.Bounds import Mathlib.Analysis.Calculus.IteratedDeriv.Defs import Mathlib.Analysis.Calculus.LineDeriv.Basic import Mathlib.Analysi...
Defs.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash, Johan Commelin -/ import Mathlib.Algebra.Lie.Solvable /-! # Semisimple Lie algebras In this file we define simple and semisimple Lie algebras, together with related concept...
Basic.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.Monoidal.FunctorCategory import Mathlib.CategoryTheory.Limits.HasLimits /-! # `lim : (J ⥤ C) ⥤ C` is lax monoidal when `C` is a monoidal ca...
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...
reduce_mod_char.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.Tactic.ReduceModChar /-! # Tests for `reduce_mod_char` tactic -/ open Polynomial -- Numerals: example : (5 : ZMod 4) = 1 := by reduce_mod_char -- Negatio...
Finite.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.Group.Action.Basic import Mathlib.Algebra.Group.Pointwise.Set.Scalar import Mathlib.Data.Set.Finite.Basic /-! # Finiteness lemmas for pointwise op...
HermitianFunctionalCalculus.lean
/- Copyright (c) 2024 Jon Bannon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Bannon, Jireh Loreaux -/ import Mathlib.LinearAlgebra.Matrix.Spectrum import Mathlib.LinearAlgebra.Eigenspace.Matrix import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus....
Duplicate.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky, Chris Hughes -/ import Mathlib.Data.List.Nodup /-! # List duplicates ## Main definitions * `List.Duplicate x l : Prop` is an inductive property that holds when `x`...
NonUnitalHom.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.Algebra.Hom import Mathlib.Algebra.GroupWithZero.Action.Prod /-! # Morphisms of non-unital algebras This file defines morphisms between two types, ...
ValuationSubring.lean
/- Copyright (c) 2022 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Junyan Xu, Jack McKoen -/ import Mathlib.RingTheory.Valuation.ValuationRing import Mathlib.RingTheory.Localization.AsSubring import Mathlib.Algebra.Algebra.Subalgebra.Tower imp...
CartesianClosed.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.Closed.Types import Mathlib.CategoryTheory.Sites.CartesianClosed import Mathlib.Condensed.Basic import Mathlib.CategoryTheory.Sites....
eqtype.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. (********************************************************************...
Pi.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Polynomial.AlgebraMap /-! # Algebraic functions This file defines algebraic functions as the image of the `algebraMap R[X] (R → S)`. -/ asse...
Operations.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker -/ import Mathlib.Algebra.GroupWithZero.Regular import Mathlib.Algebra.Polynomial.Coeff import Mathlib.Algebra.Polynomial.Degre...
trig.lean
import Mathlib open Real grind_pattern cos_sq_add_sin_sq => cos x grind_pattern cos_sq_add_sin_sq => sin x -- Whenever `grind` sees `cos` or `sin`, it adds `(cos x)^2 + (sin x)^2 = 1` to the blackboard. -- That's a polynomial, so it is sent to the Grobner basis module. -- And we can prove equalities modulo that rela...
Isometric.lean
/- Copyright (c) 2025 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric /-! #...
Exponent.lean
/- Copyright (c) 2025 Michal Staromiejski. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michal Staromiejski -/ import Mathlib.FieldTheory.PurelyInseparable.Basic /-! # The exponent of purely inseparable extensions This file defines the exponent of a purely insepar...
Basic.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Data.Prod.Basic import Mathlib.Logic.Function.Basic import Mathlib.Logic.Nontrivial.Defs import Mathlib.Logic.Unique import Mathlib.Order.Defs.Li...
CharP.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.CharP.Defs import Mathlib.Data.Matrix.Diagonal /-! # Matrices in prime characteristic In this file we prove that matrices over a ring of char...
Schwarz.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.Analysis.Complex.AbsMax import Mathlib.Analysis.Complex.RemovableSingularity /-! # Schwarz lemma In this file we prove several versions of the Schw...
Widesubcategory.lean
/- Copyright (c) 2024 Sina Hazratpour. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sina Hazratpour -/ import Mathlib.CategoryTheory.Functor.FullyFaithful import Mathlib.CategoryTheory.MorphismProperty.Composition /-! # Wide subcategories A wide subcategory of a ca...
Basic.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.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Basic import Mathlib.RingTheory.MvPowerSer...
Defs.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau -/ import Mathlib.Data.Set.Finite.Basic import Mathlib.Algebra.Group.InjSurj import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Pi.Basic import M...
Duality.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.GroupTheory.FiniteAbelian.Basic import Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity /-! # Duality for finite abelian groups Let `G` be a finite a...