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test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
BundledFun.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Topology.UniformSpace.Ultra.Basic /-! # Pseudometrics as bundled functions This file defines a pseudometri...
DerivativeTest.lean
/- Copyright (c) 2024 Bjørn Kjos-Hanssen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bjørn Kjos-Hanssen, Patrick Massot, Floris van Doorn, Jireh Loreaux, Eric Wieser -/ import Mathlib.Topology.Order.OrderClosedExtr import Mathlib.Analysis.Calculus.Deriv.MeanValue i...
GradedObject.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Joël Riou -/ import Mathlib.CategoryTheory.ConcreteCategory.Basic import Mathlib.CategoryTheory.Shift.Basic import Mathlib.Data.Set.Subsingleton import Mathlib.Algebra.Grou...
Pi.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot -/ import Mathlib.Algebra.Group.Action.Pi import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.GroupWithZero.Defs import Mathlib.Algebra.Gro...
Lemmas.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 -/ import Mathlib.Algebra.Group.Indicator import Mathlib.Data.ENNReal.Basic import Mathlib.Data.Finset.Lattice.Fold /-! # Some lemmas on extended non-n...
Mathlib.lean
import Std import Batteries import Mathlib.Algebra.AddConstMap.Basic import Mathlib.Algebra.AddConstMap.Equiv import Mathlib.Algebra.AddTorsor.Basic import Mathlib.Algebra.AddTorsor.Defs import Mathlib.Algebra.Algebra.Basic import Mathlib.Algebra.Algebra.Bilinear import Mathlib.Algebra.Algebra.Defs import Mathlib.Algeb...
Opposite.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.Data.Opposite import Mathlib.Data.Set.Operations /-! # The opposite of a set The opposite of a set `s` is simply the set obtained by taking the opposit...
Shrink.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Countable.Small import Mathlib.Data.Fintype.EquivFin /-! # Fintype instance for `Shrink` -/ universe u v variable {α : Type u} [Fintype α] noncompu...
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...
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...
Product.lean
/- Copyright (c) 2021 Praneeth Kolichala. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Praneeth Kolichala -/ import Mathlib.Topology.Constructions import Mathlib.Topology.Homotopy.Path /-! # Product of homotopies In this file, we introduce definitions for the produ...
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...
Indicator.lean
/- Copyright (c) 2024 PFR contributors. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: PFR contributors -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Topology.Piecewise import Mathlib.Topology.Clopen /-! # Continuity of indicator functions -/ open Set o...
Imo1963Q5.lean
/- Copyright (c) 2024 Rida Hamadani. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rida Hamadani -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex /-! # IMO 1963 Q5 Prove that `cos (π / 7) - cos (2 * π / 7) + cos (3 * π / 7) = 1 / 2`. The main idea ...
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...
Init.lean
/- Copyright (c) 2023 Arend Mellendijk. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arend Mellendijk -/ import Mathlib.Init import Aesop /-! # arith_mult Rule Set This module defines the `IsMultiplicative` Aesop rule set which is used by the `arith_mult` tactic. ...
Hint.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 Batteries.Linter.UnreachableTactic import Batteries.Control.Nondet.Basic /-! # The `hint` tactic. The `hint` tactic tries the kit...
EpiMono.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.ObjectProperty.ClosedUnderIsomorphisms import Mathlib.Algebra.Homology.ShortComplex.ShortExact /-! # Properties of objects that are closed under ...
DeprecatedSyntaxLinter.lean
import Mathlib.Tactic.Cases import Mathlib.Tactic.Linter.DeprecatedSyntaxLinter set_option linter.style.refine true /-- warning: The `refine'` tactic is discouraged: please strongly consider using `refine` or `apply` instead. Note: This linter can be disabled with `set_option linter.style.refine false` --- warning: T...
Metric.lean
/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Vincent Beffara, Rida Hamadani -/ import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected import Mathlib.Data.ENat.Lattice /-! # Graph metric This module defines th...
Extensive.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.CategoryTheory.Limits.Shapes.StrictInitial import Mathlib.CategoryTheory.Limits.Types.Shapes impo...
Basic.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Algebra.Algebra.Field import Mathlib.Algebra.BigOperators.Balance import Mathlib.Algebra.Order.BigOperators.Expect import Mathlib.Algebra.Order.Star....
Basic.lean
/- Copyright (c) 2019 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Kim Morrison, Yuyang Zhao -/ import Mathlib.Data.Nat.Basic import Mathlib.Logic.Equiv.Defs import Mathlib.Tactic.Convert import Mathlib....
SingleObj.lean
/- Copyright (c) 2023 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.Combinatorics.Quiver.Cast import Mathlib.Combinatorics.Quiver.Symmetric /-! # Single-object quiver Single object quiver with a given arrows type. ...
Hull.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Yaël Dillies -/ import Mathlib.Analysis.Convex.Basic import Mathlib.Order.Closure /-! # Convex hull This file defines the convex hull of a set `s` in a module. `con...
WideEqualizers.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.Limits.Shapes.Equalizers /-! # Wide equalizers and wide coequalizers This file defines wide...
ZeroCons.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Multiset.Defs import Mathlib.Order.BoundedOrder.Basic /-! # Definition of `0` and `::ₘ` This file defines constructors for multisets: * ...
IsCardinalFiltered.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Filtered.Basic import Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers import Mathlib.CategoryTheory.Comma.CardinalArrow import Mathlib.SetTheo...
UnionInter.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.List.Perm.Lattice import Mathlib.Data.Multiset.Filter import Mathlib.Order.MinMax import Mathlib.Logic.Pairwise /-! # Distributive lattice...
Basic.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.Control.Basic import Mathlib.Data.Nat.Basic import Mathlib.Data.Option.Basic im...
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...
ENNRealLog.lean
/- Copyright (c) 2024 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.Analysis.SpecialFunctions.Pow.NNReal import Mathlib.Data.EReal.Basic /-! # Extended Nonnegative Real...
intdiv.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
Count.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.List.Nodup import Mathlib.Data.Multiset.ZeroCons /-! # Counting multiplicity in a multiset -/ -- No algebra should be required assert_no...
Complexity.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.ModelTheory.Equivalence /-! # Quantifier Complexity This file defines quantifier complexity of first-order formulas, and constructs prenex normal for...
AEStronglyMeasurable.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic /-! # Strongly measurable and finitely strongly measurable functions A function `f` is...
Basic.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Algebra.Module.LinearMap /-! # Algebraic operations on `SeparationQuotient` In this file we define algebraic operations (multiplication, a...
Cardinality.lean
/- Copyright (c) 2022 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Polynomial.Cardinal import Mathlib.Algebra.Polynomial.Roots import Mathlib.RingTheory.Algebraic.Defs /-! # Cardinality of algebraic extensions Th...
ArithmeticFunction.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.BigOperators.Ring.Finset import Mathlib.Algebra.Module.BigOperators import Mathlib.NumberTheory.Divisors import Mathlib.Data.Nat.Squarefree imp...
BorelCantelli.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Yury Kudryashov -/ import Mathlib.MeasureTheory.OuterMeasure.AE /-! # Borel-Cantelli lemma, part 1 In this file we show one implication of the **Borel-Cantelli lemma**:...
Comma.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.Terminal import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic import Mathl...
DedekindDomain.lean
/- Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pierre-Alexandre Bazin -/ import Mathlib.Algebra.Module.Torsion import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas /-! # Modules over a Dedekind domain Over a Dedekind dom...
HasseDeriv.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Derivative import Mathlib.Data.Nat.Choose.Cast import Mathlib.Data.Nat.Choose.Vanderm...
Basic.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic import Mathlib.CategoryTheory.Limits.Shapes.Equivalence import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal...
ConjAct.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.GroupWithZero.Basic import Mathlib.GroupTheory.GroupAction.ConjAct /-! # Conjugation action of a group with zero on itself -/ assert_not_exists Rin...
TakeWhile.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.Order.Basic import Mathlib.Data.Nat.Basic import Mathlib.Tactic.Set /-! ### Li...
Unique.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.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital import Mathlib.Topology.ContinuousMap.StoneWeierstrass import Mathlib.Analysis.InnerProductS...
Hom.lean
/- Copyright (c) 2025 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.Group.Hom.Instances /-! # Zero-related `•` instances on group-like morphisms -/ variable {M N A B...
cyclic.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 bigo...
Operations.lean
/- Copyright (c) 2022 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov, Yakov Pechersky, Jireh Loreaux -/ import Mathlib.Algebra.Group.Prod impor...
ConvergentsEquiv.lean
/- Copyright (c) 2020 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence import Mathlib.Algebra.ContinuedFractions.TerminatedStable import Mathlib.Tactic.FieldSimp import ...
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...
Eval.lean
/- Copyright (c) 2024 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.Macro /-! # The `eval%` term elaborator This file provides the `eval% x` term elaborator, which evaluates the constant `x` at compile-time ...
ClearExclamation.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 Mathlib.Init import Lean.Elab.Tactic.ElabTerm /-! # `clear!` tactic -/ namespace Mathlib.Tactic open Lean Meta Elab.Tactic /-- A variant of `clear` which clears...
Simplex.lean
/- Copyright (c) 2025 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic /-! # Simplices in torsors over normed spaces. This file defines p...
order.v
(* (c) Copyright 2006-2019 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 path fintype tup...
all_fingroup.v
From mathcomp Require Export action. From mathcomp Require Export automorphism. From mathcomp Require Export fingroup. From mathcomp Require Export gproduct. From mathcomp Require Export morphism. From mathcomp Require Export perm. From mathcomp Require Export presentation. From mathcomp Require Export quotient.
FunctionField.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree import Mathlib.NumberTheory.ClassNumber.Finite import Mathlib.NumberTheory.FunctionField /-! # Class number...
Bilinear.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.RingTheory.Finiteness.Defs import Mathlib.Algebra.Module.Submodule.Bilinear /-! # Finitely generated submodules and bilinear maps -/ open Function (...
Module.lean
/- Copyright (c) 2025 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan -/ import Mathlib.RingTheory.KrullDimension.NonZeroDivisors import Mathlib.RingTheory.Spectrum.Prime.Module /-! # Krull Dimension of Module In this file we define `Module.s...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
EnoughInjectives.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.Algebra.Category.Grp.EnoughInjectives import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings import Mathlib.Algebra.Ring.Shrink /-! # Category of $R$-mod...
LeftHomotopy.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.AlgebraicTopology.ModelCategory.Cylinder import Mathlib.CategoryTheory.Localization.Quotient /-! # Left homotopies in model categories We introduce the types `...
Prod.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Finset.Lattice.Fold import Mathlib.Data.Finset.Prod /-! # Lattice operations on finsets of products This file is concerned with folding binary l...
Reduced.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash, Scott Carnahan -/ import Mathlib.LinearAlgebra.RootSystem.IsValuedIn /-! # Reduced root pairings This file contains basic definitions and results related to reduced root pa...
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, Floris van Doorn -/ import Mathlib.Data.Countable.Small import Mathlib.Data.Fintype.BigOperators import Mathlib.Data.Fintype.Powerset import Mathlib.Dat...
Min.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.Torsion import Mathlib.Data.ENat.Lattice import Mathlib.Data.ZMod.QuotientGroup /-! # Minimum order of an element This file defines the min...
Embedding.lean
/- Copyright (c) 2025 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.Fin.Tuple.Basic import Mathlib.Order.Fin.Basic /-! # Constructions of embeddings of `Fin n` into a type * `Fin.Embedding.cons` : f...
Topology.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.SetTheory.Ordinal.Enum import Mathlib.Tactic.TFAE import Mathlib.Topology.Order.Monotone /-! ### Topology of ordinals We prov...
Lists.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Sigma.Basic import Mathlib.Algebra.Order.Ring.Nat /-! # A computable model of ZFA without infinity In this file we define finite hereditary list...
PolynomialGaloisGroup.lean
/- Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Lutz -/ import Mathlib.FieldTheory.Galois.Basic /-! # Galois Groups of Polynomials In this file, we introduce the Galois group of a polynomial...
NNReal.lean
/- Copyright (c) 2025 Yoh Tanimioto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ import Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real /-! # Riesz–Markov–Kakutani representation theorem for `ℝ≥0` This file proves the Riesz-Markov-Kakutan...
MetrizableSpace.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov, Aaron Liu -/ import Mathlib.Topology.MetricSpace.HausdorffDistance import Mathlib.Topology.Metrizable.Basic import Mathlib.Topology.Separation.GD...
RingHom.lean
/- Copyright (c) 2015 Nathaniel Thomas. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.GroupWithZero.Action.End import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Ring.Hom....
ExpDecay.lean
/- Copyright (c) 2022 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.MeasureTheory.Integral.Asymptotics import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic import Mathlib.MeasureTheory.Integral.IntegralEqImprope...
Pretriangulated.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.HomotopyCategory.MappingCone import Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift import Mathlib.CategoryTheory.Triangulated.Functor...
FixedDetMatrices.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup import Mathlib.Data.Int.Interval /-! # Matrices with fixed determinant This file defines the type of matrice...
PreservesHomology.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.ShortComplex.QuasiIso import Mathlib.CategoryTheory.Limits.Preserves.Finite import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels /-! ...
burnside_app.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...
ExtractGoal.lean
import Mathlib.Tactic.ExtractGoal import Mathlib.Order.Basic import Mathlib.Data.Nat.Basic set_option linter.style.setOption false set_option pp.unicode.fun true set_option autoImplicit true set_option linter.unusedVariables false -- the example in the documentation for the tactic. /-- info: theorem _example.extracte...
IntegerCompl.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Analysis.Complex.UpperHalfPlane.Basic /-! # Integer Complement We define the complement of the integers in the complex plane and give some basic lem...
IsometryEquiv.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Eric Wieser -/ import Mathlib.LinearAlgebra.QuadraticForm.Basic import Mathlib.LinearAlgebra.QuadraticForm.Isometry /-! # Isometric equivalences with respect to quadratic fo...
TotallyUnimodular.lean
/- Copyright (c) 2024 Martin Dvorak. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Dvorak, Vladimir Kolmogorov, Ivan Sergeev, Bhavik Mehta -/ import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.Data.Matrix.ColumnRowPartitioned import Mathlib.Da...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
NonZeroDivisors.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.RingTheory.Ideal.MinimalPrime.Localization import Mathlib.RingTheory.KrullDimension.Basic import Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors import Mathl...
RootPairingCat.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.LinearAlgebra.RootSystem.Hom import Mathlib.CategoryTheory.Category.Basic /-! # The category of root pairings This file defines the category of root p...
ContentIdeal.lean
/- Copyright (c) 2025 Fabrizio Barroero. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fabrizio Barroero -/ import Mathlib.Order.CompletePartialOrder import Mathlib.RingTheory.Ideal.Quotient.Operations import Mathlib.RingTheory.Polynomial.Content /-! # The content i...
MulExpNegMulSq.lean
/- Copyright (c) 2024 Jakob Stiefel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Stiefel -/ import Mathlib.Analysis.SpecialFunctions.ExpDeriv import Mathlib.Analysis.SpecialFunctions.Log.Basic import Mathlib.Topology.ContinuousMap.Bounded.Normed /-! # Definit...
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, Jeremy Avigad -/ import Mathlib.Order.SetNotation import Mathlib.Tactic.Continuity import Mathlib.Tactic.FunProp import Mathlib.Tactic.MkIffOfInductiveP...
MellinTransform.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals import Mathlib.Analysis.Calculus.ParametricIntegral import Mathlib.MeasureTheory.Measure.Haar.NormedSpace ...
DirectSumIsInternal.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Kevin Buzzard -/ import Mathlib.Algebra.DirectSum.Module import Mathlib.Algebra.Group.ConjFinite import Mathlib.Data.Fintype.Lattice import Mathlib.Tactic.FinCases /-! # Not...
IntegralCharFun.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.SpecialFunctions.Integrals.Basic import Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc import Mathlib.MeasureTheory.Measure.CharacteristicFu...
GabrielPopescu.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.Algebra.Category.ModuleCat.Injective import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected import Mathlib.CategoryTheory.Abelian.Grothendiec...
Adjunctions.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johan Commelin -/ import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic import Mathlib.CategoryTheory.Monoidal.Types.Basic import Mathlib.LinearAlgebra.DirectSum.Finsupp...
LocallyInjective.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.Sites.LeftExact import Mathlib.CategoryTheory.Sites.PreservesSheafification import Mathlib.CategoryTheory.Sites.Subsheaf import Mathlib.CategoryTh...
WellApproximable.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Dynamics.Ergodic.AddCircle import Mathlib.MeasureTheory.Covering.LiminfLimsup /-! # Well-approximable numbers and Gallagher's ergodic theorem Gallagher's e...
Basic.lean
/- Copyright (c) 2020 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Algebra.Order.Group.Multiset import Mathlib.Data.Setoid.Basic import Mathlib.Data.Vector.Basic import Mathlib.Logic.Nontrivial.Basic import Mathlib.Tactic.Ap...
Defs.lean
/- Copyright (c) 2020 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import Mathlib.Analysis.SpecialFunctions.Pow.NNReal import Mathlib.MeasureTheory.Function.EssSup import Mathlib.MeasureTheory.Function.StronglyMeasurab...
RCLike.lean
/- Copyright (c) 2019 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.Analysis.Calculus.ContDiff.Defs import Mathlib.Analysis.Calculus.MeanValue /-! # Higher differentiability over `ℝ` or `ℂ` -/ ...