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Encoding.lean
/- Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pim Spelier, Daan van Gent -/ import Mathlib.Data.Fintype.Basic import Mathlib.Data.Num.Lemmas import Mathlib.Data.Option.Basic import Mathlib.SetTheory.Cardinal.Basic impo...
classfun.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...
Sort.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.List.Sort import Mathlib.Data.Multiset.Range import Mathlib.Util.Qq /-! # Construct a sorted list from a multiset. -/ variable {α β : Type*} na...
Chain.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas import Mathlib.Order.Interval.Set.OrdConnectedLinear /-! # Chains of roots Given roots `α` and `β`, the `α`-chain th...
EffectiveEpimorphic.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.Sites.Sieves import Mathlib.CategoryTheory.EffectiveEpi.Basic /-! # Effective epimorphic sieves We define the notion of effective epimorphic (...
BitVec.lean
/- Copyright (c) 2020 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Harun Khan, Alex Keizer -/ import Mathlib.Algebra.Ring.InjSurj import Mathlib.Algebra.Ring.Equiv import Mathlib.Data.ZMod.Defs import Mathlib.Data.Int.Cast.Lemmas /-! # Basi...
Prod.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.CliffordAlgebra.Grading import Mathlib.LinearAlgebra.TensorProduct.Graded.Internal import Mathlib.LinearAlgebra.QuadraticForm.Prod /-! # Cliff...
Sign.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.Data.Sign.Defs deprecated_module (since := "2025-05-11")
Opposites.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Thomas Read, Andrew Yang -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.Yoneda import Mathlib.CategoryTheory.Opposites /-! # Opposite adju...
Range.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro -/ import Mathlib.Data.Finset.Insert import Mathlib.Data.Multiset.Range import Mathlib.Order.Interval.Set.Defs /-! ...
SuccOrder.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.Order.LatticeIntervals import Mathlib.Order.SuccPred.Basic /-! # Successors in intervals If `j` is an element of a partially ordered set equipped with a succes...
polydiv.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ssralg poly. (**********************...
ConstructibleSet.lean
/- Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Andrew Yang -/ import Mathlib.Order.SuccPred.WithBot import Mathlib.RingTheory.Spectrum.Prime.Topology /-! # Constructible sets in the prime spectrum This fi...
GoingUp.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Yongle Hu -/ import Mathlib.RingTheory.Ideal.Over import Mathlib.RingTheory.Localization.AtPrime.Basic import Mathlib.RingTheory.Localization.Integral /-! # Ideals over/unde...
Header.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Tactic.Linter.Header import Lake import Mathlib.Tactic.Linter.Header import /- -/ Mathlib.Tactic -- the `TextBased` linter does not flag this `broadImpo...
Basic.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.Algebra.CharP.Basic import Mathlib.Algebra.CharP.Lemmas import Mathlib.Algebra.Ring.Regular import Mathlib.Data.Fintype.Units import Mathlib.GroupTheory....
Partition.lean
/- Copyright (c) 2019 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston, Bryan Gin-ge Chen, Patrick Massot, Wen Yang, Johan Commelin -/ import Mathlib.Data.Set.Finite.Range import Mathlib.Order.Partition.Finpartition /-! # Equivalenc...
DeriveFintype.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Tactic.ProxyType import Mathlib.Data.Fintype.Basic import Mathlib.Data.Fintype.Sigma import Mathlib.Data.Fintype.Sum /-! # The `Fintype` derive handler Thi...
ParseCommand.lean
/- Copyright (c) 2024 Matthew Robert Ballard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Matthew Robert Ballard, Damiano Testa -/ import Lean.Elab.Command import Mathlib.Init /-! # `#parse` -- a command to parse text and log outputs -/ namespace Mathlib.GuardExc...
Lemmas.lean
/- Copyright (c) 2020 Kenji Nakagawa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio -/ import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.Algebra.Squarefree.Basic import Mathlib.RingTheory.ChainOfDivisors i...
AffineScheme.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.AlgebraicGeometry.Cover.Open import Mathlib.AlgebraicGeometry.GammaSpecAdjunction import Mathlib.AlgebraicGeometry.Restrict import Mathlib.CategoryTheory.Lim...
Filtration.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.MeasureTheory.Constructions.Cylinders import Mathlib.MeasureTheory.Function.ConditionalExpectation.Real import Mathlib.MeasureTheory.Measurable...
List.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Data.Finset.Powerset import Mathlib.Data.Fintype.Defs import Mathlib.Data.List.Permutation /-! # Fintype instance for nodup lists The subtype of `...
Int.lean
/- Copyright (c) 2018 Louis Carlin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Louis Carlin, Mario Carneiro -/ import Mathlib.Algebra.Group.Nat.Defs import Mathlib.Algebra.EuclideanDomain.Defs import Mathlib.Algebra.Order.Group.Unbundled.Int import Mathlib.Algebra....
Bounds.lean
/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.FieldTheory.Finite.Basic import Mathlib.NumberTheory.DirichletCharacter.Basic /-! # Bounds for values of Diri...
MersennePrimes.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.NumberTheory.LucasLehmer /-! # Explicit Mersenne primes We run some Lucas-Lehmer tests to prove the first Mersenne primes are prime. See the discussion ...
AlternatingConst.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.Algebra.Homology.ShortComplex.HomologicalComplex import Mathlib.Algebra.Module.BigOperators import Mathlib.AlgebraicTopology.ExtraDegeneracy /-! # The alter...
Relator.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Logic.Function.Defs /-! # Relator for functions, pairs, sums, and lists. -/ namespace Relator universe u₁ u₂ v₁ v₂ /- TODO(johoelzl): * should we i...
GroupCompletion.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Topology.Algebra.UniformMulAction import Mathlib.Topology.UniformSpace.Completion import Mathlib.Topology.Algebra.Group.Pointwise /-! ...
Slice.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Category.Basic import Mathlib.Tactic.Conv /-! # The `slice` tactic Applies a tactic to an interval of terms from a term obtained by repeat...
factors.lean
import Mathlib.Tactic.Simproc.Factors example : Nat.primeFactorsList 0 = [] := by simp only [Nat.primeFactorsList_ofNat] example : Nat.primeFactorsList 1 = [] := by simp only [Nat.primeFactorsList_ofNat] example : Nat.primeFactorsList 2 = [2] := by simp only [Nat.primeFactorsList_ofNat] example : Nat.primeFactorsList ...
Proper.lean
/- Copyright (c) 2024 Yaël Dillies, Kalle Kytölä, Kin Yau James Wong. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Kalle Kytölä, Kin Yau James Wong -/ import Mathlib.Probability.Kernel.Composition.CompNotation /-! # Proper kernels This file defines pr...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
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...
ReduceOption.lean
/- Copyright (c) 2020 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky, Anthony DeRossi -/ import Mathlib.Data.List.Basic /-! # Properties of `List.reduceOption` In this file we prove basic lemmas about `List.reduceOption`. -/ namespac...
Defs.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jens Wagemaker, Yaël Dillies -/ import Mathlib.Algebra.Group.Units.Defs import Mathlib.Logic.Basic /-! # Irreducible elements in a monoid This file defines irreducibl...
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...
Removal.lean
/- Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Combinatorics.SimpleGraph.DegreeSum import Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma import Mathlib.Combinatorics.Simp...
AddContent.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Peter Pfaffelhuber -/ import Mathlib.MeasureTheory.SetSemiring import Mathlib.MeasureTheory.OuterMeasure.Induced /-! # Additive Contents An additive content `m` on a set ...
Circle.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic import Mathlib.Analysis.Normed.Field.UnitBall /-! # The circle This file defines `circle` to be the m...
eval_elab.lean
import Mathlib.Tactic.Eval import Mathlib.Data.Finset.Powerset import Mathlib.Data.Finset.Sort import Mathlib.Util.Qq #guard_expr eval% 2^10 =ₛ 1024 #guard_expr (eval% 2^10 : Int) =ₛ (1024 : Int) #guard_expr (eval% Multiset.powerset ({1, 2, 3} : Multiset ℕ)) = {0, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, ...
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...
Algebra.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.Algebra.Pi import Mathlib.Algebra.GroupWithZero.Indicator import Mathlib.LinearAlgebra.Pi import Mathlib.Topology.LocallyConstant.Basic /-! # ...
FBinop.lean
import Mathlib.Tactic.FBinop import Mathlib.Data.Set.Prod import Mathlib.Data.Finset.Prod import Mathlib.Data.SetLike.Basic private axiom test_sorry : ∀ {α}, α universe u v w set_option autoImplicit true namespace FBinopTests /-- Notation type class for the set product `×ˢ`. -/ class SProd' (α : Type u) (β : Type v)...
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...
Cyclotomic105.lean
/- Copyright (c) 2021 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.RingTheory.Polynomial.Cyclotomic.Basic import Mathlib.Tactic.NormNum.Prime /-! # Not all coefficients of cyclotomic polynomials are -1, 0, or 1 We ...
Duality.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.GroupTheory.FiniteAbelian.Duality import Mathlib.NumberTheory.MulChar.Basic /-! # Duality for multiplicative characters Let `M` be a finite commutative...
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.
IntegrableExpMul.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.L1Space.Integrable import Mathlib.MeasureTheory.Order.Group.Lattice /-! # Domain of the moment generating function For `X` a real ...
MulAntidiagonal.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Floris van Doorn -/ import Mathlib.Order.WellFoundedSet /-! # Multiplication antidiagonal -/ namespace Set variable {α : Type*} section Mul variable [Mul α] {s s₁...
BigOperators.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.BigOperators.Group.Finset.Piecewise import Mathlib.Algebra.Group.Pointwise.Set.Basic import Mathlib.Data.Fintype.Card /-! # Results about pointwise ...
bigop.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div fintype tuple ...
AList.lean
/- Copyright (c) 2018 Sean Leather. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sean Leather, Mario Carneiro -/ import Mathlib.Data.List.Sigma /-! # Association Lists This file defines association lists. An association list is a list where every element consists o...
Determinant.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.Ring /-! # Deter...
matrix.lean
/- manually ported from https://github.com/leanprover-community/mathlib/blob/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b/test/matrix.lean -/ import Mathlib.Data.Matrix.Notation import Mathlib.GroupTheory.Perm.Fin import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Qq set_option linter.style.commandStart false o...
QuadraticReciprocity.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.NumberTheory.Zsqrtd.GaussianInt import Mathlib.NumberTheory.LegendreSymbol.Basic /-! # Facts about the gaussian integers relying on quadratic reciprocity....
Series.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Yaël Dillies -/ import Mathlib.Analysis.SpecialFunctions.Exponential import Mathlib.Data.Complex.Trigonometric /-! # Trigonometric functions as sums of infinite series In t...
generic_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 ssrnat choice. From mathcomp Require Import seq fintype. (*****...
Order.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.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Module.Defs import Mathlib.Algebra.Order.Pi import Mathlib.Algebra...
Inverse.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic import Mathlib.Topology.Order.ProjIcc /-!...
BooleanRing.lean
/- Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bryan Gin-ge Chen, Yaël Dillies -/ import Mathlib.Algebra.Group.Idempotent import Mathlib.Algebra.Ring.Equiv import Mathlib.Algebra.Ring.PUnit import Mathlib.Order.Hom.BoundedLattic...
Goursat.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.GroupTheory.Goursat import Mathlib.LinearAlgebra.Prod import Mathlib.LinearAlgebra.Quotient.Basic /-! # Goursat's lemma for submodules Let `M, N` be ...
LogMeromorphic.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.Meromorphic.FactorizedRational import Mathlib.Analysis.NormedSpace.Connected import Mathlib.Analysis.SpecialFunctions.Integrability.Basic impo...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
Yoneda.lean
import Mathlib.CategoryTheory.Monoidal.Mon_ deprecated_module (since := "2025-05-11")
Zero.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.Category.Grp.Basic import Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects /-! # The category of (commutative) (additive) groups has a zero object...
Bind.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.Multiset.Basic /-! # Bind operation for multisets This file defines a few basic operations on `Multiset`, notably the mona...
pgroup.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset prime fingroup morphism. From mat...
ArithMult.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.NumberTheory.ArithmeticFunction open ArithmeticFunction variable {R : Type*} [Field R] set_option linter.unusedVariables false example : IsMu...
Rename.lean
import Mathlib.Tactic.Rename example (a : Nat) (b : Int) : Int × Nat := by rename' a => c, b => d exact (d, c) example (a : Nat) (b : Int) : Int × Nat := by rename' a => b, b => a exact (a, b)
OrderClosedExtr.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 -/ import Mathlib.Topology.Order.OrderClosed import Mathlib.Topology.Order.LocalExtr /-! # Local maxima from monotonicity and antitonicity In ...
Prime.lean
/- Copyright (c) 2020 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Nat.Prime.Defs import Mathlib.Data.Num.ZNum import Mathlib.Tactic.Ring /-! # Primality for binary natural numbers This file defines versions of ...
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...
Shapiro.lean
/- Copyright (c) 2025 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.CategoryTheory.Preadditive.Projective.Resolution import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic import Mathlib.Representat...
Synonym.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.GroupWithZero.Defs import Mathlib.Algebra.Order.Group.Synonym /-! # Group with zero structure on the order type synonyms Transfer algebraic i...
SchroederBernstein.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Data.Set.Piecewise import Mathlib.Order.FixedPoints import Mathlib.Order.Zorn /-! # Schröder-Bernstein theorem, well-ordering of cardi...
WellFounded.lean
/- Copyright (c) 2022 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Data.DFinsupp.Lex import Mathlib.Order.Antisymmetrization import Mathlib.Order.GameAdd import Mathlib.SetTheory.Cardinal.Order import Mathlib.Tactic.AdaptationNo...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
Finset.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Data.Finset.Max import Mathlib.Data.Set.Finite.Lattice import Mathlib.Order.ConditionallyCompleteLattice.Indexed /-! # Conditionally complete la...
Order.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Sigma.Lex import Mathlib.Util.Notation3 import Mathlib.Data.Sigma.Basic import Mathlib.Order.Lattice import Mathlib.Order.BoundedOrder.Basic /-! # Or...
Comp.lean
/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao -/ import Mathlib.Analysis.Calculus.Deriv.Basic import Mathlib.Analysis.Calculus.FDeriv.Comp import Mathlib.Analysis.Calcu...
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. ...
Groebner.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.MonomialOrder import Mathlib.Data.Finsupp.WellFounded import Mathlib.Data.List.TFAE import M...
NhdsKer.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Yury Kudryashov -/ import Mathlib.Topology.NhdsSet import Mathlib.Topology.Inseparable /-! # Neighborhoods kernel of a set In `Mathlib/Topology/Defs/Filter.lean`, `nhdsKe...
CommMon_.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Braided.Basic import Mathlib.CategoryTheory.Monoidal.Mon_ /-! # The category of commutative monoids in a braided monoidal category...
OrderClosed.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov -/ import Mathlib.Topology.Order.LeftRight import Mathlib.Topology.Separation.Hausdorff /-! # Order-closed topologies In this file we ...
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...
AbelianImages.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.Images import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels /-! # Preservation of coimage-image comparisons If a functo...
Ring.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.Canonical import Mathlib.Algebra.Order.Nonneg.Basic import Mathlib.Algebra.Order.Nonneg.Lattice import Mathlib.Algebra....
Basic.lean
/- Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Analysis.Convex.Hull import Mathlib.LinearAlgebra.AffineSpace.Independent /-! # Simplicial complexes In this file, we define ...
Real.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Topology.MetricSpace.Bounded import Mathlib.Topology.Order.Bornology /-! # The reals are equipped with their order bornology This fil...
Rify.lean
/- Copyright (c) 2023 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Mario Carneiro, Robert Y. Lewis, Patrick Massot -/ import Mathlib.Data.Rat.Cast.Order import Mathlib.Data.Real.Basic import Mathlib.Tactic.Qify /-! # `rify` tactic The `...
Tauto.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, David Renshaw -/ import Mathlib.Tactic.Tauto import Mathlib.Tactic.SplitIfs import Mathlib.Data.Part set_option autoImplicit true section tauto₀ variable (p q r : Prop) var...
poly.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 bigop fi...
Yoneda.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.CategoryTheory.Limits.Preserves.Finite import Mathlib.CategoryTheory.Limits.Opposites import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Product...
Pi.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Notation.Pi.Basic import Mathlib.Data.Set.BooleanAlgebra import Mathlib.Data.Set.Piecewise import Mathlib.Order.Interval.Set.Basic import Mat...
Result.lean
/- Copyright (c) 2022 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.GroupWithZero.Invertible import Mathlib.Data.Sigma.Basic import Mathlib.Algebra.Ring.Nat import Mathlib.Data....
Finite.lean
/- Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Patrick Massot -/ -- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl. import Mathlib.Algebra.Group.Subgroup.Finite imp...
DenseEmbedding.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot -/ import Mathlib.Topology.Bases import Mathlib.Topology.Separation.Regular /-! # Dense embeddings This file defines three properties of f...
Connected.lean
/- Copyright (c) 2024 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Filtered.Basic import Mathlib.CategoryTheory.IsConnected /-! # Filtered categories are connected -/ universe v u namespace CategoryTheo...