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Basic.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.Group.Basic import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.Units.Defs import Mathlib.Algebra.Regular.Defs /-! # Regular ...
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. ...
Restrict.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.PerfectPairing.Basic import Mathlib.LinearAlgebra.Matrix.Basis import Mathlib.LinearAlgebra.Matrix.BaseChange /-! # Restriction to submodules ...
Uniform.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.Analysis.Convex.StrictConvexSpace /-! # Uniformly convex spaces This file defines uniformly convex spaces, which are real normed vector spaces in which f...
NatAntidiagonal.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.Algebra.BigOperators.Fin import Mathlib.Algebra.Group.Fin.Tuple import Mathlib.Data.Finset.NatAntidiagonal import Mathlib.Order.Fin.Tuple /-! # Collections ...
Basic.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.Algebra.GroupWithZero.Units.Lemmas import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Ring.Cast import Mathlib.Data.Fi...
Init.lean
/- Copyright (c) 2023 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.Init import Aesop /-! # Rule sets related to topological (pre)sheaves This module defines the `Restrict` Aesop rule set. Aesop rule sets only become vis...
algnum.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...
CharacteristicFunction.lean
/- Copyright (c) 2024 Jakob Stiefel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Stiefel, Rémy Degenne, Thomas Zhu -/ import Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar import Mathlib.Analysis.Fourier.FourierTransform import Mathlib.Analysis.InnerPr...
PowTransition.lean
/- Copyright (c) 2025 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan, Jiedong Jiang -/ import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.RingTheory.Ideal.Quotient.Defs import Mathlib.Algebra.Algebra.Operations import Mathlib.RingTheo...
Disintegration.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.MeasureTheory.Measure.Haar.Basic import Mathlib.Analysis.Normed.Module.FiniteDimension import Mathlib.MeasureTheory.Measure.Haar.Unique /-! # Pu...
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.Localization.HasLocalization import Mathlib.CategoryTheory.Center.Localization import Mathlib.CategoryTheory.Center.Linear import Mathlib.Category...
Lp.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.SimpleFuncDenseLp import Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas /-! # Finitely strongly measurable functions in `...
Export.lean
/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Init import Lean.CoreM import Lean.Util.FoldConsts /-! A rudimentary export format, adapted from <https://github.com/leanprover-community/lean/...
Basic.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Johannes Hölzl, Mario Carneiro, Patrick Massot -/ import Mathlib.Data.Set.Sigma import Mathlib.Order.Filter.Defs import Mathlib.Order.Filter.Map import Mathlib.Order....
CommRing.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro -/ import Mathlib.Algebra.MvPolynomial.Variables /-! # Multivariate polynomials over a ring Many results about polynomials hold when th...
right_actions.lean
import Mathlib.Algebra.GroupWithZero.Action.Opposite open MulOpposite renaming op → mop open AddOpposite renaming op → aop variable {α β : Type*} [SMul α β] [SMul αᵐᵒᵖ β] [VAdd α β] [VAdd αᵃᵒᵖ β] {a a₁ a₂ a₃ a₄ : α} {b : β} section delaborators section without_scope /-- info: a • b : β -/ #guard_msgs in #check a •...
Contrapose.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Tactic.Basic import Mathlib.Tactic.Contrapose example (p q : Prop) (h : ¬q → ¬p) : p → q := by contrapose guard_target = ¬q → ¬p exact h example...
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.Order.Ring.InjSurj import Mathlib.Algebra.Ring.Subsemiring.Defs import Mathlib.Order.Interval.Set.Defs import Mathlib.Tactic.FastInstance /-! # ...
Pi.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.RingTheory.Smooth.Pi import Mathlib.RingTheory.Unramified.Pi import Mathlib.RingTheory.Etale.Basic /-! # Formal-étaleness of finite products of rings ## M...
Basic.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yury Kudryashov -/ import Mathlib.Algebra.Algebra.Equiv import Mathlib.Algebra.Algebra.NonUnitalSubalgebra import Mathlib.RingTheory.SimpleRing.Basic /-! # Subalgebras over Comm...
Style.lean
/- Copyright (c) 2024 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Lean.Elab.Command import Lean.Server.InfoUtils -- Import this linter explicitly to ensure that -- this file has a valid copyright header and module docstr...
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...
Basic.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.LinearMap.Defs import Mathlib.Algebra.NoZ...
Module.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.Algebra.Category.ModuleCat.Abelian import Mathlib.Algebra.Category.ModuleCat.Adjunctions import Mathlib.Algebra.Category.ModuleCat.Colimits import ...
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. (******************************************...
Lattice.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Kyle Miller -/ import Mathlib.Data.Finite.Sigma import Mathlib.Data.Set.Finite.Powerset import Mathlib.Data.Set.Finite.Range /-! # Finiteness of unions...
Basic.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, Kevin Buzzard, Yury Kudryashov -/ import Mathlib.Algebra.Module.Equiv.Basic import Mathlib.GroupTheory.QuotientGroup.Basic import Mathlib.LinearAlgebra....
depRewrite.lean
import Mathlib.Tactic.DepRewrite /-! ## Basic tests for `rewrite!`. -/ private axiom test_sorry : ∀ {α}, α /-- Turn a term into a sort for testing. -/ private axiom P.{u} {α : Sort u} : α → Prop /-- Non-deprecated copy of `Fin.ofNat` for testing. -/ private def finOfNat (n : Nat) (a : Nat) : Fin (n + 1) := ⟨a % (...
Uniform.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker, Devon Tuma, Kexing Ying -/ import Mathlib.Probability.Notation import Mathlib.Probability.Density import Mathlib.Probability.ConditionalProbability import Mathlib.Probabili...
Finsupp.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Aaron Anderson -/ import Mathlib.Data.Finsupp.Defs /-! # Pointwise order on finitely supported functions This file lifts order structures on `M` to `ι →₀ M`. -/ asse...
Ideal.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Topology.Algebra.Ring.Basic import Mathlib.Topology.Algebra.Group.Quotient import Mathlib.RingTheory.Ideal.Quotient.Defs /-! # Ideals and quotients of...
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: ...
Integer.lean
/- Copyright (c) 2025 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.GCDMonoid.Finset import Mathlib.Algebra.GCDMonoid.Nat import Mathlib.Data.Matrix.Mul import Mathlib.Data.Ra...
CompactOpenCovered.lean
/- Copyright (c) 2025 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.Topology.Spectral.Prespectral /-! # Compact open covered sets In this file we define the notion of a compact-open covered set with respect to a f...
Oka.lean
/- Copyright (c) 2025 Anthony Fernandes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anthony Fernandes, Marc Robin -/ import Mathlib.RingTheory.Ideal.Colon /-! # Oka predicates This file introduces the notion of Oka predicates and standard results about them. ## ...
SmallDegree.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.Polynomial.Degree.Operations import Mathlib.Data.Nat.WithBot /-! # Results on polynomials of specifi...
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, Jeremy Avigad, Yury Kudryashov -/ import Mathlib.Order.Filter.Map import Mathlib.Order.ZornAtoms /-! # Ultrafilters An ultrafilter is a minimal (maximal in the set or...
Fin.lean
/- Copyright (c) 2022 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Ring.Equiv import Mathlib.Data.Fin.Tuple.Basic /-! # Rings and `Fin` This file collects some basic results involving rings and the `Fin` type ## M...
PID.lean
/- Copyright (c) 2025 Jingting Wang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jingting Wang -/ import Mathlib.RingTheory.KrullDimension.Zero import Mathlib.RingTheory.PrincipalIdealDomain /-! # The Krull dimension of a principal ideal domain In this file, we pr...
Basic.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yury Kudryashov -/ import Mathlib.Logic.Function.Basic import Mathlib.Tactic.MkIffOfInductiveProp /-! # Additional lemmas about sum types Most of the former contents ...
Functorial.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion import Mathlib.AlgebraicGeometry.PullbackCarrier /-! # Functorial constructions of ideal sheaves We define the ...
path.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. (******************************************************************************) (* ...
SMulAntidiagonal.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Algebra.Group.Pointwise.Set.Scalar import Mathlib.Data.Set.SMulAntidiagonal /-! # Antidiagonal for scalar multiplication as a `Finset`. Given partial...
Measure.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.Normed.Affine.AddTorsorBases import Mathlib.Analysis.Normed.Module.Convex import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar /-! # Convex...
BubbleSortInduction.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Data.Fin.Tuple.Sort import Mathlib.Order.WellFounded import Mathlib.Order.PiLex import Mathlib.Data.Finite.Prod /-! # "Bubble sort" induction We implem...
Operations.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Filippo A. E. Nuccio -/ import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.RingTheory.FractionalIdeal.Basic import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basi...
Lemmas.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.RingTheory.Localization.Away.Basic import Mathlib.RingTheory.Localization.Submodule /-! # More lemmas on localization away This file contains lem...
Basic.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Category.Basic import Mathlib.CategoryTheory.Functor.Basic import Mathlib.CategoryTheory.Iso import Mathlib.Order.Basic /-! # Properties of objec...
IsoIoo.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.Order.Monotone.Odd import Mathlib.Algebra.Order.Field.Basic import Mathlib.Tactic.FieldSimp /-! # Order isomorphism between a linear ordered field a...
Balanced.lean
/- Copyright (c) 2022 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.EpiMono /-! # Balanced categories A category is called balanced if any morphism that is both monic and epic is an isomorphism. Balanced...
fraction.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq. From mathcomp Require Import ssrAC choice tuple ...
Basic.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.InformationTheory.KullbackLeibler.KLFun import Mathlib.MeasureTheory.Measure.Decomposition.IntegralRNDeriv /-! # Kullback-Leibler diverg...
Sigma.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.DFinsupp.Module import Mathlib.Data.Fintype.Quotient /-! # `DFinsupp` on `Sigma` types ## Main definitions * `DFinsupp.sigmaCurry`: turn ...
Expr.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.Init import Qq /-! # Helpers to invoke functions involving algebra at tactic time This file provides instances on `x y : Q($α)` such that `x + y = q($x + $...
all_ssreflect.v
Attributes deprecated(since="mathcomp 2.5.0", note="Use 'all_boot' and/or 'all_order' instead."). From mathcomp Require Export all_boot. From mathcomp Require Export preorder. From mathcomp Require Export order.
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...
IntegralEqImproper.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Bhavik Mehta -/ import Mathlib.Analysis.Calculus.Deriv.Support import Mathlib.Analysis.SpecialFunctions.Pow.Deriv import Mathlib.MeasureTheory.Function.JacobianOneD...
Prod.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot -/ import Mathlib.Data.Finset.Prod import Mathlib.Order.Filter.AtTopBot.Basic import Mathlib.Order.Filter.Prod /-! # `Fi...
Jacobson.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.RingTheory.Jacobson.Ring import Mathlib.RingTheory.Spectrum.Prime.Noetherian import Mathlib.Topology.JacobsonSpace /-! # The prime spectrum of a jacobson ri...
InjSurj.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.Group.Defs import Mathlib.Logic.Function.Basic import Mathlib.Tactic.Spread /-! # Lifting algebraic data classes along injective/surjective ma...
Abelian.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits import Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits import Mathlib.Algebra.Category.ModuleCat.Abelian import M...
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. (***********...
Embedding.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.Algebra.Group.Action.Basic import Mathlib.Algebra.Group.Action.Pi import Mathlib.Algebra.Group.Opposite /-! # Group actions on embeddings This file provide...
Konig.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.CategoryTheory.Filtered.Basic import Mathlib.Topology.Category.TopCat.Limits.Basic /-! # Topological Kőnig's lemma A topological version of Kőnig's lemma i...
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 -/ import Mathlib.Topology.Constructions.SumProd /-! # Topological monoids - definitions In this file we define two mixin typeclasses: - `ContinuousMul M` says that t...
ProperSpace.lean
/- Copyright (c) 2024 Jou Glasheen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jou Glasheen, Kevin Buzzard -/ import Mathlib.Analysis.Normed.Field.ProperSpace import Mathlib.NumberTheory.Padics.RingHoms /-! # Properness of the p-adic numbers In this file, we pro...
Determinant.lean
/- Copyright (c) 2022 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Data.Complex.Module import Mathlib.LinearAlgebra.Determinant /-! # Determinants of maps in the complex numbers as a vector space over `ℝ` This file provi...
Closeds.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.Topology.Sets.Opens import Mathlib.Topology.Clopen /-! # Closed sets We define a few types of closed sets in a topological space. ...
Convergence.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.Data.EReal.Basic import Mathlib.NumberTheory.LSeries.Basic /-! # Convergence of L-series We define `LSeries.abscissaOfAbsConv f` (as an `EReal`) to be ...
CofilteredSystem.lean
/- Copyright (c) 2022 Kyle Miller, Adam Topaz, Rémi Bottinelli, Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Adam Topaz, Rémi Bottinelli, Junyan Xu -/ import Mathlib.Topology.Category.TopCat.Limits.Konig /-! # Cofiltered systems This file de...
Basic.lean
/- Copyright (c) 2024 Yudai Yamazaki. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yudai Yamazaki -/ import Mathlib.GroupTheory.GroupExtension.Defs import Mathlib.GroupTheory.SemidirectProduct import Mathlib.GroupTheory.QuotientGroup.Basic import Mathlib.Tactic.Grou...
Resolution.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Kim Morrison, Jakob von Raumer, Joël Riou -/ import Mathlib.CategoryTheory.Preadditive.Projective.Resolution import Mathlib.Algebra.Homology.HomotopyCategory import Mathli...
TopCatAdjunction.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.TopComparison import Mathlib.Topology.Category.Sequential import Mathlib.Topology.Category.LightProfinite.Sequence /-! # The adjun...
Irreducible.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.Polynomial.Eval.Coeff import Mathlib.Algebra.Polynomial.Eval.Degree import Mathlib.Algebra.Prime.Defs...
Small.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.Logic.Small.Basic import Mathlib.Data.Countable.Defs /-! # All countable types are small. That is, any countable type is equivalent to a type in any univ...
Translations.lean
/- Copyright (c) 2019 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.Basic import Mathlib.Algebra.GroupWithZero.Basic /-! # Basic Translation Lemmas Between Functions Defined for Continued...
Embedding.lean
/- Copyright (c) 2021 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import Mathlib.Logic.Embedding.Set /-! # Equivalences on embeddings This file shows some advanced equivalences on embeddings, useful for constructing larger embeddi...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
Basic.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Kexing Ying, Eric Wieser -/ import Mathlib.Data.Finset.Sym import Mathlib.LinearAlgebra.BilinearMap import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathlib.Linea...
Pigeonhole.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn -/ import Mathlib.Data.Set.Finite.Lattice import Mathlib.SetTheory.Cardinal.Regular /-! # Infinite pigeonhole principle This file proves variants of ...
Propose.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Lean.Meta.Tactic.TryThis import Lean.Meta.Tactic.SolveByElim import Mathlib.Lean.Expr.Basic import Mathlib.Lean.Meta import Mathlib.Lean.Meta.Basic import Batterie...
TransferInstance.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.TransferInstance import Mathlib.Algebra.Group.InjSurj im...
ZeroAndBoundedAtFilter.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.Asymptotics.Lemmas import Mathlib.Algebra.Algebra.Pi /-! # Zero and Bounded at ...
Basic.lean
/- Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller -/ import Mathlib.Combinatorics.Hall.Finite import Mathlib.CategoryTheory.CofilteredSystem import Mathlib.Data.Rel /...
BoundedContinuousFunctionChar.lean
/- Copyright (c) 2025 Jakob Stiefel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Stiefel -/ import Mathlib.Algebra.MonoidAlgebra.Basic import Mathlib.Analysis.Complex.Circle import Mathlib.Analysis.InnerProductSpace.Basic import Mathlib.Topology.ContinuousMap....
FinsetOps.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.Multiset.Dedup import Mathlib.Data.List.Infix /-! # Preparations for defining operations on `Finset`. The operations here ignore multiplicities,...
Imo1988Q6.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.Data.Nat.Prime.Defs import Mathlib.Data.Rat.Defs import Mathlib.Order.WellFounded import Mathlib.Tactic.Linarith import Mathlib.Tactic.Ring import Math...
Finite.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.Subpresheaf.OfSection /-! # Subpresheaves that are generated by finitely many sections Given `F : Cᵒᵖ ⥤ Type w`, `G : Subpresheaf F`, objects `X...
Sort.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Batteries.Data.List.Pairwise import Batteries.Data.List.Perm import Mathlib.Data.List.OfFn import Mathlib.Data.List.Nodup import Mathlib.Data.List.TakeWhile impo...
jordanholder.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 big...
Basic.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Functor.Category import Mathlib.CategoryTheory.Products.Basic /-! # Joins of category Given categories `C, D`, this file constructs a ca...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
Exterior.lean
import Mathlib.Topology.NhdsKer deprecated_module (since := "2025-07-09")
fun_prop.lean
/- Copyright (c) 2024 Tomáš Skřivan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tomáš Skřivan -/ import Mathlib.MeasureTheory.MeasurableSpace.Basic import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap import Mathlib.MeasureTheory.Constructions....
Roots.lean
/- Copyright (c) 2020 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.RingTheory.Polynomial.Cyclotomic.Basic import Mathlib.RingTheory.RootsOfUnity.Minpoly /-! # Roots of cyclotomic polynomials. We gather results abou...
Minpoly.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio -/ import Mathlib.FieldTheory.IntermediateField.Adjoin.Basic import Mathlib.RingTheory.Valuat...
Scheme.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Andrew Yang -/ import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf import Mathlib.AlgebraicGeometry.GammaSpecAdjunction import Mathlib.RingTheory.GradedAlgeb...
Rank.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Lie.EngelSubalgebra import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Algebra.Module.LinearMap.Polynomial import Mathlib.LinearAlgebra.Ei...
CoeSort.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Johannes Hölzl, Reid Barton, Kim Morrison, Patrick Massot, Kyle Miller, Minchao Wu, Yury Kudryashov, Floris van Doorn -/ import Mathlib.Data.Set.Defs /-! # Coercing sets...