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Lex.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.Order.RelClasses import Mathlib.Data.List.Basic /-! # Lexicographic ordering of lists. The lexicographic order on `List α` is defined by `L < M` iff ...
Cover.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Floris van Doorn, Bhavik Mehta -/ import Mathlib.Order.Antisymmetrization import Mathlib.Order.Hom.WithTopBot import Mathlib.Ord...
Quotient.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.Shift.CommShift import Mathlib.CategoryTheory.Shift.Induced import Mathlib.CategoryTheory.Quotient /-! # The shift on a quotient category Let `C...
ValuationRing.lean
/- Copyright (c) 2022 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.RingTheory.Bezout import Mathlib.RingTheory.LocalRing.Basic import Mathlib.RingTheory.Localization.FractionRing import Mathlib.RingTheory.Localization.Integer ...
CompareExp.lean
/- Copyright (c) 2020 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Eric Wieser -/ import Mathlib.Data.ENNReal.Holder import Mathlib.MeasureTheory.Function.LpSeminorm.Basic import Mathlib.MeasureTheory.Integral.MeanInequalities /-! # Compa...
CovBySMul.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.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Pointwise.Finset.Scalar import Mathlib.Data.Real.Basic import Mathlib.Tactic.Positivi...
Bimodule.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.RingTheory.TensorProduct.Basic /-! # Bimodules One frequently encounters situations in which several sets of scalars act on a single space, subject to comp...
AEMeasurableOrder.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.Constructions.BorelSpace.Order /-! # Measurability criterion for ennreal-valued functions Consider a function `f : α → ℝ≥0∞`. If ...
LiftToFinset.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.Limits.Constructions.Filtered import Mathlib.CategoryTheory.Preadditive.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! ...
Support.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.Algebra.Notation.Prod import Mathlib.Data.Set.Image /-! # Support of a function In this file we define `Fu...
Floor.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kevin Kappelmann -/ import Mathlib.Algebra.Order.Floor.Defs import Mathlib.Algebra.Order.Floor.Ring import Mathlib.Algebra.Order.Floor.Semiring deprecated_module (sinc...
CompleteField.lean
/- Copyright (c) 2024 Alex J. Best. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best -/ import Mathlib.Algebra.Order.CompleteField import Mathlib.Data.Real.Sqrt /-! # The reals are a conditionally complete linearly ordered field -/ /-- The reals are a cond...
Basic.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Order.Atoms import Mathlib.Order.OrderIsoNat import Mathlib.Order.RelIso.Set import Mathlib.Order.SupClosed import Mathlib.Order.SupIndep import Mathlib.Orde...
AlgebraicClosure.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.Algebra import Mathlib.Data.Multiset.Fintype import Mathlib.FieldTheory.IsAlgClosed.Basic import Mathlib.FieldTheory.SplittingField.Construction /...
Lattice.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.Algebra.Module.Submodule.Lattice import Mathlib.RingTheory.Ideal.Defs import Mathlib.Tactic.Ring /-! # The lattice of ideals in a ...
Proper.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patience Ablett, Kevin Buzzard, Harald Carlens, Wayne Ng Kwing King, Michael Schlößer, Justus Springer, Andrew Yang, Jujian Zhang -/ import Mathlib.AlgebraicGeometry.ProjectiveSpectrum....
Defs.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ -- Some proofs and docs came from mathlib3 `src/algebra/commute.lean` (c) Neil Strickland import Mathlib.Algebra.Group.Defs import Mathlib.Order.Defs.Unbundled /-...
Bordism.lean
/- Copyright (c) 2024 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Mathlib.Geometry.Manifold.Instances.Real /-! ## (Unoriented) bordism theory This file defines the beginnings of unoriented bordism theory. We define sing...
FreeAbelianGroup.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.Module.NatInt import Mathlib.GroupTheory.Abelianization.Defs import Mathlib.GroupTheory.FreeGroup.Basic /-! # Free abelian groups The free abelian grou...
Comonadicity.lean
/- Copyright (c) 2024 Jack McKoen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jack McKoen -/ import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Shapes.Reflexive import Mathlib.CategoryTheory.Monad.Equalizer import ...
gfunctor.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 fintype. From mathcomp Require Import bigop finset fingroup morphism automorphism. From math...
CompMul.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Calculus.FDeriv.Equiv import Mathlib.Analysis.Calculus.Deriv.Mul /-! # Derivative of `x ↦ f (cx)` In this file we prove that the derivativ...
CatCospanTransform.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.CatCommSq /-! # Morphisms of categorical cospans. Given `F : A ⥤ B`, `G : C ⥤ B`, `F' : A' ⥤ B'` and `G' : C' ⥤ B'`, this files defines ...
test_rat.v
From mathcomp Require Import all_boot all_order all_algebra. Local Open Scope ring_scope. Goal 2%:Q + 2%:Q = 4%:Q. Proof. reflexivity. Qed. Goal - 2%:Q = -1 * 2%:Q. Proof. reflexivity. Qed. Goal 2%:Q ^+ 2 = 4%:Q. Proof. reflexivity. Qed. Goal (-1)^-1 = -1 :> rat. Proof. reflexivity. Qed. Local Open Scope rat_scop...
Qify.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Mario Carneiro, Robert Y. Lewis -/ import Mathlib.Algebra.Order.Ring.Cast import Mathlib.Data.Int.Cast.Lemmas import Mathlib.Data.NNRat.Defs import Mathlib.Tactic.Basic impor...
Iso.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tim Baumann, Stephen Morgan, Kim Morrison, Floris van Doorn -/ import Mathlib.Tactic.CategoryTheory.Reassoc /-! # Isomorphisms This file defines isomorphisms between objects of a categ...
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.Data.EReal.Basic import Mathlib.Topology.Order.T5 /-! # The reals are equipped with their order topology This file contains results r...
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 seq div. From mathcomp Require Import choice fintype prim...
AharoniKorman.lean
/- Copyright (c) 2024 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Algebra.Order.Field.Basic import Mathlib.Algebra.Order.Field.Rat import Mathlib.Data.Setoid.Partition import Mathlib.Order.Filter.AtTopBot.Basic import Mat...
WellFounded.lean
/- Copyright (c) 2020 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro -/ import Mathlib.Data.Set.Function import Mathlib.Order.Bounds.Defs /-! # Well-founded relations A relation is well-founded if it can be used for induct...
InverseTriangleSum.lean
/- Copyright (c) 2020. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jalex Stark, Yury Kudryashov -/ import Mathlib.Algebra.BigOperators.Group.Finset.Powerset import Mathlib.Data.Real.Basic import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Positivity.Basic import ...
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 ...
Equicontinuity.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.UniformSpace.UniformConvergenceTopology /-! # Equicontinuity of a family of functions Let `X` be a topological space and `α` a `UniformS...
FieldSimp.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, David Renshaw -/ import Mathlib.Tactic.FieldSimp.Discharger /-! # `field_simp` tactic Tactic to clear denominators in algebraic expressions, based on `simp` wi...
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.MonomialOrder import Mathlib.Data.Finsupp.WellFounded import Mathlib.Data.List.TFAE import M...
OmegaCompletePartialOrder.lean
/- Copyright (c) 2020 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Ira Fesefeldt -/ import Mathlib.Control.Monad.Basic import Mathlib.Dynamics.FixedPoints.Basic import Mathlib.Order.CompleteLattice.Basic import Mathlib.Order.Iterate import M...
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...
LinearFunctor.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor import Mathlib.CategoryTheory.Linear.Basic import Mathlib.Algebra.Module.LinearMap.Rat /-! # Linear Functors A...
ValuationTopology.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Algebra.Order.Group.Units import Mathlib.Topology.Algebra.Nonarchimedean.Bases import Mathlib.Topology.Algebra.UniformFilterBasis import Mathlib.RingTh...
Div.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Shing Tak Lam, Mario Carneiro -/ import Mathlib.Data.List.Palindrome import Mathlib.Data.Nat.Digits.Lemmas /-! # Divisibility tests for natural numbers in terms of digits....
SetIntegral.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap import Mathlib.MeasureTheory.Integral.Bochner.FundThmCalculus import Mathlib.MeasureT...
all_algebra.v
(* N.B. interval_inference is not exported here. To enjoys the automation it provides, you need to explictly "Import interval_inference". *) From mathcomp Require Export ssralg. From mathcomp Require Export ssrnum. From mathcomp Require Export finalg. From mathcomp Require Export countalg. From mathcomp Require Export...
LocallyFiniteOrder.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.Group.Subgroup.Ker import Mathlib.Algebra.Order.Group.Units import Mathlib.Algebra.Order.Hom.MonoidWithZero import Mathlib.Algebra.Order.Hom.TypeTags...
CantorScheme.lean
/- Copyright (c) 2023 Felix Weilacher. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Felix Weilacher -/ import Mathlib.Topology.MetricSpace.PiNat /-! # (Topological) Schemes and their induced maps In topology, and especially descriptive set theory, one often constru...
Invertible.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Ring.Parity import Mathlib.Algebra.GroupWithZero.Invertible import Mathlib.Algebr...
Algebra.lean
/- Copyright (c) 2025 Michal Staromiejski. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michal Staromiejski -/ import Mathlib.RingTheory.Artinian.Ring import Mathlib.RingTheory.IntegralClosure.Algebra.Defs import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic /...
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...
sesquilinear.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup. From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector. (************************************************...
PartialFractions.lean
/- Copyright (c) 2023 Sidharth Hariharan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Sidharth Hariharan -/ import Mathlib.Algebra.Polynomial.Div import Mathlib.Logic.Function.Basic import Mathlib.RingTheory.Coprime.Lemmas import Mathlib.RingTheory.Lo...
NetEntropy.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 -/ import Mathlib.Dynamics.TopologicalEntropy.CoverEntropy /-! # Topological entropy via nets We implement Bowen-Dinaburg's definitions of the topolog...
EverywherePos.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Group.Measure import Mathlib.Tactic.Group import Mathlib.Topology.UrysohnsLemma /-! # Everywhere positive sets in measure spaces ...
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...
Linarith.lean
/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Tactic.Linarith.Frontend import Mathlib.Tactic.NormNum import Mathlib.Tactic.Hint /-! We register `linarith` with the `hint` tactic. -/ register_hi...
interval.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 div fintype bigo...
CountHeartbeats.lean
import Mathlib.Util.CountHeartbeats import Mathlib.Util.SleepHeartbeats /-- info: Used approximately 0 heartbeats, which is less than the current maximum of 200000. -/ #guard_msgs in #count_heartbeats approximately in example (a : Nat) : a = a := rfl /-- info: Used approximately 0 heartbeats, which is less than the m...
nilpotent.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import fintype div bigop prime finset fingroup morphism. Fro...
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...
SetInterval.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.Algebra.Order.Ring.Int import Mathlib.Data.Nat.Cast.Order.Basic import Mathlib.Order.Interval.Set.OrdConnected import Mathlib.Order.Nat import Mathli...
Infix.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.TakeDrop import Mathlib.Data.List.Induction /-! # Prefixes, suffixes, infixes This file proves properties about * `List.isPrefix`: `l₁` is ...
Arrow.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.Comma.Basic /-! # The category of arrows The category of arrows, with morphisms commutative squares. We set this up as a specialization ...
CocompactMap.lean
/- Copyright (c) 2024 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Topology.ContinuousMap.CocompactMap import Mathlib.Topology.MetricSpace.Bounded /-! # Cocompact maps in normed g...
Indexed.lean
/- Copyright (c) 2018 Sébastian Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastian Gouëzel -/ import Mathlib.Order.ConditionallyCompleteLattice.Basic /-! # Indexed sup / inf in conditionally complete lattices This file proves lemmas about `iSup` and `i...
Shrink.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Group.Shrink import Mathlib.Algebra.Ring.TransferInstance /-! # Transfer ring structures from `α` to `Shrink α` -/ noncomputable section namespa...
Defs.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Analytic.Within import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries /-! # Higher d...
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. (******************************************************...
FiniteType.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.FiniteStability import Mathlib.RingTheory.Localization.InvSubmonoid import Mathlib.RingTheory.RingHom.Finite /-! # The meta properties of finite...
Basic.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.Group.Nat.Units import Mathlib.Algebra.GroupWithZero.Divisibility import Mathlib.Algebra.GroupWi...
commutator.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 fintype. From mathcomp Require Import bigop finset binomial fingroup morphism. From mathcomp...
Prod.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Yaël Dillies -/ import Mathlib.Algebra.Group.Prod import Mathlib.Algebra.GroupWithZero.Hom import Mathlib.Algebra.GroupWithZero.Units.Basic import Mathlib.Algebra.GroupWithZe...
CentroidHom.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Christopher Hoskin -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Group.Action.Pi import Mathlib.Algebra.Module.Hom import Mathlib.GroupTheory.GroupAction.Ri...
Basic.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Patrick Massot, Floris van Doorn -/ import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps import Mathlib.Topology.FiberBundl...
WellOrderContinuous.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.Limits.IsLimit import Mathlib.CategoryTheory.Limits.Shapes.Preorder.PrincipalSeg import Mathlib.CategoryTheory.Limits.Final import Mathlib.Categor...
Init.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Yaël Dillies -/ import Mathlib.Data.Nat.Notation import Mathlib.Tactic.Lemma import Mathlib.Tactic.TypeStar import Batteries.Classes.RatCast /-! # Basi...
WithLp.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ import Mathlib.Analysis.Calculus.FDeriv.Prod import Mathlib.Analysis.Calculus.FDeriv.Equiv import Mathlib.Analysis.Normed.Lp.PiLp /-! # Derivatives ...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
Pi.lean
/- Copyright (c) 2023 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.Analysis.Calculus.FDeriv.Add import Mathlib.Analysis.Calculus.FDeriv.Const /-! # Derivatives on pi-types. -/ variable {𝕜 ι : Ty...
EpiMono.lean
/- Copyright (c) 2022 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.EquivalenceGroupAddGroup import Mathlib.CategoryTheory.ConcreteCategory.EpiMono import Mathlib.CategoryTheory.Limits.Constructions.Epi...
Basic.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Chris Hughes, Floris van Doorn, Yaël Dillies -/ import Mathlib.Data.Nat.Basic import Mathlib.Tactic.Common import Mathlib.Tactic.Monotonicity.Attr /-! # Factorial and ...
Imo2011Q5.lean
/- Copyright (c) 2021 Alain Verberkmoes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alain Verberkmoes -/ import Mathlib.Algebra.Order.Group.Int import Mathlib.Algebra.Order.Group.Unbundled.Basic import Mathlib.Algebra.Ring.Divisibility.Basic import Mathlib.Algebra....
SelectPanelUtils.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 Lean.Meta.ExprLens import ProofWidgets.Component.MakeEditLink import ProofWidgets.Component.OfRpcMethod -- needed in all files using this one. import Mathlib.T...
mxpoly.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 div fintype tupl...
MoebiusAction.lean
/- Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu -/ import Mathlib.Analysis.Complex.UpperHalfPlane.Basic import Mathlib.Data.Fintype.Parity import M...
Open.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.Topology.ContinuousMap.Basic /-! # Continuous open maps This file defines bundled continuous open maps. We use the `DFunLike` design, so each type of mo...
Flat.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.RingTheory.Flat.Localization import Mathlib.RingTheory.LocalProperties.Basic import Mathlib.RingTheory.Ideal.GoingDown /-! # Flat ring homomorphis...
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...
RowCol.lean
/- Copyright (c) 2019 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Eric Wieser -/ import Mathlib.Data.Matrix.ConjTranspose /-! # Row and column matrices This file provides results about row and column matrices. ## Main definitions * `Mat...
center.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 fingroup morphism perm. From math...
DeprecatedModuleTest.lean
import MathlibTest.DeprecatedModule /-- warning: We can also give more details about the deprecation 'MathlibTest.DeprecatedModule' has been deprecated: please replace this import by import Mathlib.Tactic.Linter.DocPrime import Mathlib.Tactic.Linter.DocString Note: This linter can be disabled with `set_option linte...
PiLex.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.Algebra.Group.Pi.Basic import Mathlib.Algebra.Order.Group.Synonym import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Order.PiLex /-! # Lexicographic ...
EngelSubalgebra.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Lie.Engel import Mathlib.Algebra.Lie.Normalizer import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Algebra.Lie.Subalgebra import Mathlib.D...
UnbundledHom.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.CategoryTheory.ConcreteCategory.BundledHom /-! # Category instances for structures that use unbundled homs This file provides basic infrastructure ...
SeminormLatticeNotDistrib.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.Analysis.Seminorm /-! # The lattice of seminorms is not distributive We provide an example of three seminorms over the ℝ-vector space...
Sort.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Algebra.Group.End import Mathlib.Data.Finset.Sort import Mathlib.Data.Fintype.Sum import Mathlib.Data.Prod.Lex import Mathlib.Order.Interval.Finset.Fin /-! ...
ssrmatching.v
From Corelib Require Export ssrmatching.
Finsupp.lean
/- Copyright (c) 2023 Antoine Chambert-Loir and María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández, Eric Wieser, Bhavik Mehta, Yaël Dillies -/ import Mathlib.Algebra.Order.Antidiag.Pi i...
Module.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov, Kim Morrison -/ import Mathlib.Algebra.Module.BigOperators import Mathlib.Algebra.Module.Submodule.Basic import Mathlib.Algebra.MonoidAlgebra.Lift impo...
Subobject.lean
/- Copyright (c) 2021 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.EpiMono import Mathlib.Algebra.Category.ModuleCat.Kernels import Mathlib.CategoryTheory.Subobject.WellPowered import Mathlib.C...
test_rat.v
From mathcomp Require Import all_boot all_order all_algebra. Local Open Scope ring_scope. Goal 2%:Q + 2%:Q = 4%:Q. Proof. reflexivity. Qed. Goal - 2%:Q = -1 * 2%:Q. Proof. reflexivity. Qed. Goal 2%:Q ^+ 2 = 4%:Q. Proof. reflexivity. Qed. Goal (-1)^-1 = -1 :> rat. Proof. reflexivity. Qed. Local Open Scope rat_scop...
abelian.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import choice div fintype finfun bigop finset prime. From ma...
Spectrum.lean
/- Copyright (c) 2021 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Algebra.Spectrum.Quasispectrum import Mathlib.FieldTheory.IsAlgClosed.Basic /-! # Spectrum mapping theorem This file develops proves the spectr...