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ShiftedHom.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.Shift.CommShift import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor /-! Shifted morphisms Given a category `C` endowed with a shift by an ...
Center.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Group.Submonoid.Operations import Mathlib.GroupTheory.Subsemigroup.Center /-! # Centers of monoids ## Main definitions * `Submonoid.center`: the c...
Content.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 -/ import Mathlib.MeasureTheory.Measure.MeasureSpace import Mathlib.MeasureTheory.Measure.Regular import Mathlib.Topology.Sets.Compacts /-! # Contents In this file...
RingQuot.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.Algebra.Hom import Mathlib.RingTheory.Congruence.Basic import Mathlib.RingTheory.Ideal.Quotient.Defs import Mathlib.RingTheory.Ideal.Span /-! # Qu...
all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
Init.lean
/- Copyright (c) 2024 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geoffrey Irving -/ import Mathlib.Init import Aesop.Frontend.Command /-! # Bound Rule Set This module defines the `Bound` Aesop rule set which is used by the `bound` tactic. Aesop ...
SuccessIfFailWithMsg.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Simon Hudon, Sébastien Gouëzel, Kim Morrison, Thomas Murrills -/ import Lean.Elab.Eval import Lean.Elab.Tactic.BuiltinTactic import Mathlib.Init import Lean.Meta.Tactic...
Mates.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Emily Riehl -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.Functor.TwoSquare import Mathlib.CategoryTheory.HomCongr import Mathlib.Tactic....
Products.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang -/ import Mathlib.Topology.Category.TopCat.EpiMono import Mathlib.Topology.Category.TopCat.Limits.Basic import Mathlib.CategoryT...
BigOperators.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.BigOperators.Group.Finset.Basic import Mathlib.Algebra.Group.Pointwise.Finset.Basic /-! # Pointwise big operators on finsets...
TruncLE.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.Embedding.TruncGE /-! # The canonical truncation Given an embedding `e : Embedding c c'` of complex shapes which satisfies `e.IsTruncLE` and `...
Subsingleton.lean
/- Copyright (c) 2025 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kim Morrison, Eric Wieser, Junyan Xu, Andrew Yang -/ import Mathlib.LinearAlgebra.Dimension.Basic /-! # Dimension of trivial modules -/ variable (R M : Type*) [Semiring R]...
Ultra.lean
/- Copyright (c) 2024 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiedong Jiang -/ import Mathlib.Analysis.Normed.Field.Ultra import Mathlib.Analysis.Normed.Module.Basic /-! # Normed algebra preserves ultrametricity This file contains the proof tha...
Basic.lean
/- Copyright (c) 2021 Ashwin Iyengar. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Johan Commelin, Ashwin Iyengar, Patrick Massot -/ import Mathlib.Algebra.Group.Subgroup.Basic import Mathlib.Topology.Algebra.OpenSubgroup import Mathlib.Topology.Algebr...
Pi.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.CharP.Defs import Mathlib.Algebra.Ring.Pi /-! # Characteristic of semirings of functions -/ universe u v namespace CharP instance pi (ι : Type u) [h...
countalg.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ss...
GCongr.lean
/- Copyright (c) 2023 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Batteries.Lean.Position import Mathlib.Tactic.Widget.SelectPanelUtils import Mathlib.Tactic.GCongr /-! # GCongr widget This file defines a `gcongr?` tactic t...
Basic.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.RingTheory.SimpleRing.Defs import Mathlib.Algebra.Ring.Opposite import Mathlib.RingTheory.TwoSidedIdeal.Kernel /-! # Basic Properties of Simple rings A ...
ssrint.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 fintype finfun b...
div.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. (******************************************************************************) (* Th...
Basic.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.LinearAlgebra.LinearIndependent.Defs import Mathlib.SetTheory.Ordinal.Basic import Mathlib.Topology.Category.Profinite.Product import Mathlib.Topol...
StrongEpi.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Balanced import Mathlib.CategoryTheory.LiftingProperties.Basic /-! # Strong epimorphisms In this file, we define strong epimorphisms. A ...
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. (******************************************************...
Lemmas.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.LinearAlgebra.Dimension.DivisionRing import Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition import Mathlib.LinearAlgebra.FiniteDimensional.Basic...
hall.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 choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
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...
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...
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. (**************************************************...
Fold.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 /-! # The fold operation for a commutative associative operation over a multiset. -/ namespace Multiset variable {α β : Type*} ...
falgebra.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype div...
VertexOperator.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.Vertex.HVertexOperator import Mathlib.Data.Int.Interval /-! # Vertex operators In this file we introduce vertex operators as linear maps to La...
ConjAct.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Group.Subgroup.ZPowers.Basic import Mathlib.Data.Fintype.Card import Mathlib.GroupTheory.GroupAction.Defs import Mathlib.GroupTheory.Subgroup.Centr...
Inhabit.lean
/- Copyright (c) 2022 Joshua Clune. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joshua Clune -/ import Lean.Elab.Tactic.ElabTerm import Mathlib.Tactic.TypeStar /-! Defines the `inhabit α` tactic, which tries to construct an `Inhabited α` instance, constructively or...
Hom.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 -/ import Mathlib.CategoryTheory.Products.Basic import Mathlib.CategoryTheory.Types /-! The hom functor, sending `(X, Y)` to the type `X ⟶ Y`. -/ universe v u...
GelfandDuality.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.Analysis.CStarAlgebra.Spectrum import Mathlib.Analysis.CStarAlgebra.ContinuousMap import Mathlib.Analysis.Normed.Group.Quotient import Mathlib.Analysis.N...
ModularLattice.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Yaël Dillies -/ import Mathlib.Data.Set.Monotone import Mathlib.Order.Cover import Mathlib.Order.LatticeIntervals import Mathlib.Order.GaloisConnection.Defs /-! # Modu...
PerfectPairing.lean
/- Copyright (c) 2025 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.LinearAlgebra.BilinearMap import Mathlib.Topology.Algebra.Module.LinearMap /-! # Continuous perfect pairings This file defines ...
Tower.lean
/- Copyright (c) 2022 Yuyang Zhao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuyang Zhao -/ import Mathlib.Algebra.Algebra.Subalgebra.Tower import Mathlib.Algebra.MvPolynomial.Eval /-! # Algebra towers for multivariate polynomial This file proves some basic resu...
hall.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 choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
Bilinear.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.LinearAlgebra.BilinearMap import Mathlib.LinearAlgebra.Basis.Defs /-! # Lemmas about bilinear maps with a basis over each argument -/ open Module namespac...
MeanValue.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.MeasureTheory.Integral.CircleAverage /-! # The Mean Value Property of Complex Differentiable Functions ...
Opposite.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Group.Equiv.Opposite import Mathlib.Algebra.GroupWithZero.Opposite import Mathlib.Algebra.Ring.Hom.Defs import Mathlib.Data.Int.Cast.Basic /-! # Ring st...
PUnit.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Group.PUnit import Mathlib.Algebra.Ring.Defs /-! # `PUnit` is a commutative ring This file collects facts about algebraic structures on the one-element...
Basic.lean
/- Copyright (c) 2023 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Limits.Shapes.Products /-! # Effective epimorphisms We define the notion of effective epimorphism and effective epimorphic family of morphisms...
Basic.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.RegularMono import Mathlib.CategoryTheory.Shift.Opposite import Mathlib.CategoryTheory.Shift.Pullback /-! # The shift on the opposi...
IsClosedRestrict.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Peter Pfaffelhuber -/ import Mathlib.Topology.Homeomorph.Lemmas /-! # Restriction of a closed compact set in a product space to a set of coordinates We show that the imag...
MonomialOrder.lean
/- Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Data.Finsupp.Lex import Mathlib.Data.Finsupp.WellFounded import Mathlib.Data.List.TFAE /-! # Monomial orders ## Monomial orders A *mon...
Diffeomorph.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Yury Kudryashov -/ import Mathlib.Geometry.Manifold.ContMDiffMap import Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential /-! # Diffeomorphisms This file implem...
Basic.lean
/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Lean.Elab.Tactic.Simp import Lean.Elab.App import Mathlib.Tactic.Simps.NotationClass import Mathlib.Lean.Expr.Basic /-! # Simps attribute This file defin...
FindSyntax.lean
import Mathlib.Tactic.FindSyntax infix:65 " #find_syntax_add " => Nat.add /-- info: Found 2 uses among over 600 syntax declarations In `MathlibTest.FindSyntax`: «term_#find_syntax_add_»: '#find_syntax_add' In `Mathlib.Tactic.FindSyntax`: Mathlib.FindSyntax.«command#find_syntax_Approx»: '#find_syntax _ approx' ...
BalancedCoreHull.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.LocallyConvex.Basic /-! # Balanced Core and Balanced Hull ## Main definitions * `balancedCore`: The largest balanced subset of a set `s`. * `bala...
Coseparator.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.GrothendieckCategory.EnoughInjectives import Mathlib.CategoryTheory.Generator.Abelian /-! # Grothendieck categories have a cosepa...
ApplyFun.lean
/- Copyright (c) 2019 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Keeley Hoek, Patrick Massot, Kim Morrison -/ import Mathlib.Lean.Expr.Basic import Mathlib.Order.Monotone.Basic import Mathlib.Order.Hom.Basic /-! # The `apply_fun` tactic. Apply a f...
ReflQuiver.lean
/- Copyright (c) 2024 Mario Carneiro and Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Emily Riehl -/ import Mathlib.Data.Set.Function import Mathlib.CategoryTheory.Category.Cat /-! # Reflexive Quivers This module defines reflexive quive...
ClearExclamation.lean
import Mathlib.Tactic.ClearExclamation set_option linter.unusedVariables false -- Most basic test example (delete_this : Nat) (_delete_this_dep : delete_this = delete_this) : Nat := by clear! delete_this fail_if_success assumption exact 0 -- Confirms clear! deletes class instances example [delete_this : Inhabi...
Imo1982Q1.lean
/- Copyright (c) 2024 Alex Brodbelt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex Brodbelt, Violeta Hernández -/ import Mathlib.Tactic.NormNum import Mathlib.Tactic.Linarith import Mathlib.Data.PNat.Basic /-! # IMO 1982 Q1 The function `f` is defined for all ...
binomial.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import div fintype tuple ...
ring_quotient.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. From mathcomp Require Import seq ssralg generic_q...
HasPullback.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne -/ import Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone /-! # HasPullback `HasPullback f g`...
Tutte.lean
/- Copyright (c) 2024 Pim Otte. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pim Otte -/ import Mathlib.Combinatorics.SimpleGraph.Matching import Mathlib.Combinatorics.SimpleGraph.Metric import Mathlib.Combinatorics.SimpleGraph.Operations import Mathlib.Combinatoric...
Strict.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.Analysis.Convex.Basic import Mathlib.Topology.Algebra.Group.Pointwise import Mathlib.Topology.Order.Basic /-! # Strictly convex sets This file defines st...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
Projective.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Kim Morrison -/ import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic import Mathlib.CategoryTheory.Preadditive.Projective.Basic import Mathlib.Algebra.Category.Grp.EpiM...
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...
Basic.lean
/- Copyright (c) 2020 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Bhavik Mehta, Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Monad.Limits import Mathlib.Topology.Compactification.StoneCech import Mathlib.Topology.UrysohnsLemma import Mat...
alt.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype tupl...
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...
Monad.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.Prod import Mathlib.Data.Set.Finite.Lattice import Mathlib.Data.Set.Functor /-! # Finiteness of the Set monad...
Basic.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.Localization.AtPrime.Basic import Mathlib.RingTheory.Localization.BaseChange import Mathlib.RingTheory.Localization.Submodule import Mathlib.RingT...
Equiv.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.Algebra.Group.Equiv.Defs import Mathlib.Algebra.GroupWithZero.Hom /-! # Isomorphisms of monoids with zero -/ assert_not_exists Ring namespace MulEquivCl...
TypeTags.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Simon Hudon, Yury Kudryashov -/ import Mathlib.Order.Notation /-! # Order-related type synonyms In this file we define `WithBot`, `WithTop`, `ENat`, and `PNat`. The d...
Replace.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino -/ import Mathlib.Tactic.Replace set_option linter.unusedVariables false private axiom test_sorry : ∀ {α}, α /-- Test the `:=` syntax works -/ example {A B : Type} (h...
IntegralConvolution.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.MeasureTheory.Group.Convolution import Mathlib.MeasureTheory.Integral.Prod /-! # Bochner integrals of convolutions This file contains results about the B...
all_order.v
Require Export order.
RealDeriv.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yourong Zang -/ import Mathlib.Analysis.Calculus.ContDiff.Operations import Mathlib.Analysis.Calculus.Deriv.Linear import Mathlib.Analysis.Complex.Basic /-! # Re...
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...
ComplexShapeSigns.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.ComplexShape import Mathlib.Algebra.Ring.NegOnePow import Mathlib.CategoryTheory.GradedObject.Trifunctor /-! Signs in constructions on homologi...
Basic.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Jujian Zhang, Yunzhou Xie -/ import Mathlib.Algebra.Central.Defs /-! # Central Algebras In this file, we prove some basic results about central algebras over a commutat...
PolarCoord.lean
/- Copyright (c) 2025 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Analysis.SpecialFunctions.PolarCoord import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic /-! # Polar coordinate change of variables for the...
Intersecting.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.Data.Fintype.Card import Mathlib.Order.UpperLower.Basic /-! # Intersecting families This file defines intersecting families and proves their basic proper...
Prime.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro -/ import Mathlib.RingTheory.Ideal.Lattice /-! # Prime ideals This file contains the definition of `Ideal.IsPrime` for prime ideals. ## TODO Sup...
Basic.lean
/- Copyright (c) 2021 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Unbundled.Pow import Mathlib.Algebra.Order.ZeroLEOne import Mathlib...
Colimits.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 import Mathlib.Algebra.Category.ModuleCat.Colimits /-! # Colimits in categories of presheaves of modules In this file, it i...
ExternalProduct.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.Monoidal.ExternalProduct.Basic deprecated_module (since := "2025-06-19")
Contractible.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.Convex.Star import Mathlib.Topology.Homotopy.Contractible /-! # A convex set is contractible In this file we prove that a (star) convex se...
mxalgebra.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype finfun b...
Basic.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.ModelTheory.Syntax import Mathlib.ModelTheory.Semantics import Mathlib.Algebra.Ring.Equiv /-! # First Order Language of Rings This file defines the firs...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
BigOperators.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura -/ import Batteries.Data.Nat.Gcd import Mathlib.Algebra.BigOperators.Group.Finset.Defs /-! # Lemmas about coprimality with big products. These lemmas ...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
Ramification.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.NumberTheory.NumberField.InfinitePlace.Basic /-! # Ramification of infinite places of a number field This file studies the ramification of infinite places ...
VitaliFamily.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Measure.AbsolutelyContinuous /-! # Vitali families On a metric space `X` with a measure `μ`, consider for each `x : X` a family o...
BernoulliPolynomials.lean
/- Copyright (c) 2021 Ashvni Narayanan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ashvni Narayanan, David Loeffler -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Derivative import Mathlib.Data.Nat.Choose.Cast import Mathlib.Numbe...
Basic.lean
/- Copyright (c) 2021 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs /-! # Basic lemmas about the general linear group $GL(n, R)$ This file lists various basic lemmas about ...
IntervalCases.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Mario Carneiro -/ import Mathlib.Tactic.NormNum import Mathlib.Tactic.FinCases import Mathlib.Control.Basic /-! # Case bash on variables in finite intervals This file pro...
Centralizer.lean
/- Copyright (c) 2020 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Algebra.Group.Action.End import Mathlib.GroupTheory.Subgroup.Center import Mathlib.GroupTheory.Submonoid.Centralizer /-! # Centralizers of subgroups -/ ass...
Perm.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.BigOperators.Group.List.Defs import Mathlib.Algebra.Group.End import Mathlib.Algebra.Group.Nat.Defs import Mathlib.Data.Fintype.EquivFin import...
Constructions.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.Algebra.Category.Ring.Instances import Mathlib.Algebra.Category.Ring.Limits import Mathlib.Algebra.Category.Ring.Colimits import Mathlib.Tactic.Algebraize im...
Esakia.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Hom.Bounded import Mathlib.Topology.Order.Hom.Basic /-! # Esakia morphisms This file defines pseudo-epimorphisms and Esakia morphisms. We use the ...
EffectiveEpi.lean
/- Copyright (c) 2023 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Boris Bolvig Kjær, Jon Eugster, Sina Hazratpour, Nima Rasekh -/ import Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular import Mathlib.Topology.Category.CompHaus...