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Basic.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Basic /-! # Ordered normed spaces In this file, we define classes for fields and groups that are both normed ...
Notation.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Simon Hudon, Yury Kudryashov -/ import Mathlib.Data.Nat.Notation /-! # Definition and notation for positive natural numbers -/ /-- `ℕ+` is the type of positive natur...
orderedzmod.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
TermReduce.lean
import Mathlib.Util.TermReduce -- On command line, tests format functions with => rather than ↦ without this. set_option linter.style.setOption false set_option pp.unicode.fun true /-- info: (fun x ↦ x) true : Bool -/ #guard_msgs in #check (fun x => x) true /-- info: true : Bool -/ #guard_msgs in #check beta% (fun x ...
EqualizerSheafCondition.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Sites.IsSheafFor import Mathlib.CategoryTheory.Limits.Types.Shapes import Mathlib.Tactic.ApplyFun /-! # The equalizer diagram sheaf conditi...
InnerProduct.lean
/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang -/ import Mathlib.Analysis.Calculus.Conformal.NormedSpace import Mathlib.Analysis.InnerProductSpace.ConformalLinearMap /-! # Conformal maps between inner product spaces A ...
Subsingleton.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Order.Filter.CountablyGenerated import Mathlib.Order.Filter.Prod import Mathlib.Order.Filter.Ultrafilter.Defs /-! # Subsingleton filters We say that...
CardinalInter.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Order.Filter.Tendsto import Mathlib.Order.Filter.Finite import Mathlib.Order.Filter.CountableInter import Mathlib.SetTheory.Cardinal.Regular import Mathlib...
IsIso.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.Morphisms.OpenImmersion /-! # Being an isomorphism is local at the target -/ open CategoryTheory MorphismProperty namespace AlgebraicG...
Units.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl -/ import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Algebra.Order.Monoid.Units /-! # The units of an ordered com...
SigmaComparison.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.Topology.Category.CompHausLike.Limits /-! # The sigma-comparison map This file defines the map `CompHausLike.sigmaComparison` associated to a pre...
BigZariski.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Adam Topaz -/ import Mathlib.AlgebraicGeometry.Sites.MorphismProperty import Mathlib.CategoryTheory.Sites.Canonical /-! # The big Zariski site of schemes In this file, we define...
Deriv.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, Sébastien Gouëzel, Rémy Degenne -/ import Mathlib.Analysis.SpecialFunctions.Pow.Continuity import Mathlib.Analysis.Special...
ssrmatching.v
From Corelib Require Export ssrmatching.
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.MeasureTheory.Group.AEStabilizer import Mathlib.Dynamics.Ergodic.Ergodic /-! # Ergodic group actions A group action of `G` on a space `α` with meas...
Boundary.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.BooleanAlgebra.Basic import Mathlib.Tactic.Common /-! # Co-Heyting boundary The boundary of an element of a co-Heyting algebra is the intersection ...
Unbundled.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Yuyang Zhao -/ import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs import Mathlib.Tactic.Linter.Deprecate...
Lagrange.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Wrenna Robson -/ import Mathlib.Algebra.BigOperators.Group.Finset.Pi import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.LinearAlgebra.Vandermonde import Mathlib.RingT...
Requests.lean
/- Copyright (c) 2023 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino -/ import Batteries.Data.String.Matcher import Cache.Hashing namespace Cache.Requests open System (FilePath) /-- Structure to hold repository information with priori...
MonoidWithZero.lean
/- Copyright (c) 2019 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.GroupWithZero.Hom import Mathlib.GroupTheory.MonoidLocalization.Basic import Mathlib.RingTheory.OreLocalization.Basic import Mathlib.Alge...
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 -/ import Mathlib.Algebra.Group.Irreducible.Defs import Mathlib.Algebra.GroupWithZero.Divisibility /-! # Prime elements In this file we define the pred...
Pow.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.Calculus.FDeriv.Pow /-! # Derivative of `(f x) ^ n`, `n : ℕ` In this file we prove that the Fréchet derivative of `fun x => f x ^ n`, ...
DeriveEncodable.lean
/- Copyright (c) 2024 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Lean.Meta.Transform import Lean.Meta.Inductive import Lean.Elab.Deriving.Basic import Lean.Elab.Deriving.Util import Mathlib.Logic.Encodable.Basic import Mathlib.Dat...
Basic.lean
/- Copyright (c) 2024 Ali Ramsey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ali Ramsey, Kevin Buzzard -/ import Mathlib.RingTheory.Coalgebra.Basic import Mathlib.RingTheory.TensorProduct.Basic /-! # Bialgebras In this file we define `Bialgebra`s. ## Main defini...
Completion.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.Topology.Algebra.GroupCompletion import Mathlib.Topology.Algebra.Ring.Real import Mathlib.Topology.MetricSpace.Algebra import Mathlib.Topology.Me...
Set.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.Logic.Equiv.Set import Mathlib.Order.Hom.Basic import Mathlib.Order.Interval.Set.Defs import Mathlib.Order.WellFounded import Mathlib.Tactic.MinImports...
Antidiagonal.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.Data.Finset.NatAntidiagonal import Mathlib.Data.Finsupp.Multiset import Mathlib.Data.Multiset.Antidiagonal /-! # The `Finsupp` counte...
BigOperators.lean
/- Copyright (c) 2024 Joachim Breitner, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner, Yaël Dillies -/ import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Data.ENat.Lattice /-! # Sum of suprema in `ENat` -/ assert_not...
Take.lean
/- Copyright (c) 2024 Quang Dao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Quang Dao -/ import Mathlib.Data.Fin.Tuple.Basic /-! # Take operations on tuples We define the `take` operation on `n`-tuples, which restricts a tuple to its first `m` elements. * `Fin.t...
rat.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 prime fintype fi...
Defs.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.Group.Subgroup.Defs import Mathlib.GroupTheory.GroupAction.SubMulAction import Mathlib.Algeb...
Basic.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johan Commelin -/ import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic /-! # Minimal polynomials This file defines the minimal polynomial of an element `x` of an `A...
Module.lean
/- Copyright (c) 2020 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Yury Kudryashov, Frédéric Dupuis -/ import Mathlib.Topology.Algebra.InfiniteSum.Constructions import Mathlib.Topology.Algebra.Module.Equiv /-! # Infinite sums in top...
End.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Faithful import Mathlib.Algebra.Order.Group.End import Mathlib.Order.RelIso.Basic /-! # Tautological action by relation automorphisms...
CondDistrib.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.Unique import Mathlib.Probability.Notation /-! # Regular conditional probability distribution We define the regular con...
Comap.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.MvPolynomial.Rename /-! # `comap` operation on `MvPolynomial` This file defines the `comap` function on `MvPolynomial`. `MvPolynomial.comap`...
Operations.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.Algebra.Operations import Mathlib.Algebra.Module.BigOperators import Mathlib.Data.Fintype.Lattice import Mathlib.RingTheory.Coprime.Lemmas import Mathlib...
Basic.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, Aaron Anderson -/ import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Algebra.GCDMonoid.Nat import Ma...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
Localization.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Module.LocalizedModule.Submodule import Mathlib.LinearAlgebra.Dimension.DivisionRing import Mathlib.RingTheory.IsTensorProduct import Mathlib.RingThe...
GiryMonad.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.MeasureTheory.Integral.Lebesgue.Countable /-! # The Giry monad Let X be a measurable space. The collection of all measures on X again forms a measura...
toAdditive.lean
import Mathlib.Algebra.Group.Defs import Mathlib.Lean.Exception import Mathlib.Tactic.ReduceModChar.Ext import Qq.MetaM open Qq Lean Meta Elab Command ToAdditive set_option autoImplicit true -- work in a namespace so that it doesn't matter if names clash namespace Test -- [note] use the below options for diagnostics:...
vec_notation.lean
/- Manually ported from https://github.com/leanprover-community/mathlib/blob/fee91d74414e681a8b72cb7160e6b5ef0ec2cc0b/test/vec_notation.lean -/ import Mathlib.Data.Fin.VecNotation open Lean open Lean.Meta open Qq set_option linter.style.setOption false in set_option pp.unicode.fun false /-- info: ![1, 1 + 1, 1 + 1 +...
Actions.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Group.Submonoid.DistribMulAction import Mathlib.GroupTheory.Subgroup.Center /-! # Actions by `Subgroup`s These are just copies of the definitions a...
Ideals.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Topology.Algebra.Algebra import Mathlib.Topology.ContinuousMap.Compact import Mathlib.Topology.UrysohnsLemma import Mathlib.Analysis.RCLike.Basic import ...
PerpBisector.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Joseph Myers -/ import Mathlib.Analysis.InnerProductSpace.Orthogonal import Mathlib.Analysis.Normed.Group.AddTorsor /-! # Perpendicular bisector of a segment We def...
KleisliCat.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.CategoryTheory.Category.Basic /-! # The Kleisli construction on the Type category Define the Kleisli category for (control) monads. `CategoryTheory/Monad/...
interval_inference.v
(* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice. From mathcomp Require Import order ssralg ssrnum ssrint interval. (**md********************************************************...
FunctorToTypes.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.FunctorCategory.Basic import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Types.Limits impo...
ShortExact.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.HomotopyCategory.HomologicalFunctor import Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence import Mathlib.Algebra.Homology.HomologySeque...
Perfection.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.Frobenius import Mathlib.Algebra.CharP.Pi import Mathlib.Algebra.CharP.Quotient import Mathlib.Algebra.CharP.Subring import Mathlib.Analysis.Specia...
Basic.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Kim Morrison -/ import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.NatIso import Mathlib.CategoryTheory.Products.Basic /-! # Categories of indexed families...
inertia.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...
TProd.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Data.List.Nodup import Mathlib.Data.Set.Prod /-! # Finite products of types This file defines the product of types over a list. For `l : List ι` ...
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...
Defs.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kim Morrison -/ import Mathlib.Algebra.Notation.Support import Mathlib.Data.Set.Finite.Basic /-! # Type of functions with finite support For any type `α` and any type...
rat.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 prime fintype fi...
Imo2001Q6.lean
/- Copyright (c) 2021 Sara Díaz Real. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sara Díaz Real -/ import Mathlib.Algebra.Ring.Associated import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination /-! # IMO 2001 Q6 Let $a$, $b$, $c$, $d$ be integers wi...
Prod.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, Eric Wieser -/ import Mathlib.Algebra.Group.Action.Faithful import Mathlib.Algebra.Group.Action.Hom import Mathlib.Algebra.Group.Prod /-! # Prod instances fo...
KrullDimension.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Fangming Li -/ import Mathlib.Order.KrullDimension import Mathlib.Topology.Homeomorph.Lemmas import Mathlib.Topology.Sets.Closeds /-! # The Krull dimension of a topologica...
Common.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ -- First import Aesop, Qq, and Plausible import Aesop import Qq import Plausible -- Tools for analysing imports, like `#find_home`, `#minimize_imports`, ... import Impo...
Associator.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stephen Morgan, Kim Morrison -/ import Mathlib.CategoryTheory.Products.Basic /-! The associator functor `((C × D) × E) ⥤ (C × (D × E))` and its inverse form an equivalence. -/ univers...
Disjoint.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot -/ import Mathlib.Order.Filter.AtTopBot.Defs import Mathlib.Order.Interval.Set.Disjoint /-! # Disjointness of `Filter.at...
ExtractLets.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.Lean.Expr.Basic import Mathlib.Tactic.Basic import Batteries.Tactic.Lint.Misc import Mathlib.Tactic.Linter.DeprecatedModule deprecated_module "The extract_l...
Images.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.ModuleCat.Abelian import Mathlib.CategoryTheory.Limits.Shapes.Images /-! # The category of R-modules has images. Note that we don't need...
Basic.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Gabriel Ebner -/ import Mathlib.Data.Int.Cast.Defs import Mathlib.Algebra.Group.Basic import Mathlib.Data.Nat.Basic /-! # Cast of integers (additional theorems) This ...
RiemannZeta.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.NumberTheory.LSeries.HurwitzZeta import Mathlib.Analysis.PSeriesComplex /-! # Definition of the Riemann zeta function ## Main definitions: * `rieman...
Defs.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Order.BoundedOrder.Basic import Mathlib.Order.Monotone.Basic import Mathlib.Tactic.Monotonicity.Attr import Mathlib.Util.AssertExists /-! # Galois con...
ModifyLast.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 Batteries.Data.List.Basic import Batteries.Tactic.Alias import Mathlib.Tactic.TypeStar ...
Prj.lean
/- Copyright (c) 2020 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Control.Functor.Multivariate import Mathlib.Data.QPF.Multivariate.Basic /-! Projection functors are QPFs. The `n`-ary projection functors on `i` is an `n`-a...
Gershgorin.lean
/- Copyright (c) 2023 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.LinearAlgebra.Eigenspace.Basic import Mathlib.LinearAlgebra.Determinant /-! # Gershgorin's circle theorem Th...
Opens.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.Order.Hom.CompleteLattice import Mathlib.Topology.Compactness.Bases import Mathlib.Topology.ContinuousMap.Basic impor...
Hom.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.Order /-! # Properties of C⋆-algebra homomorphisms Here we collect properties of C⋆-algebra homomor...
RBMap.lean
/- Copyright (c) 2019 mathlib community. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Wojciech Nawrocki -/ import Batteries.Data.RBMap.Basic import Mathlib.Data.Tree.Basic /-! # Binary tree and RBMaps In this file we define `Tree.ofRBNode`. This def...
ReplaceRec.lean
/- Copyright (c) 2019 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Simon Hudon, Kim Morrison, Keeley Hoek, Robert Y. Lewis, Floris van Doorn, Edward Ayers -/ import Lean.Expr import Mathlib.Util.MemoFix /-! # ReplaceRec We define a ...
Defs.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, Matthew Robert Ballard -/ import Mathlib.RingTheory.Multiplicity import Mathlib.Data.Nat.Factors /-! # `p`-adic Valuation This file defines the `p`-adic valuation o...
CompTypeclasses.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.Logic.Function.CompTypeclasses import Mathlib.Algebra.Group.Hom.Defs /-! # Propositional typeclasses on several monoid homs This file...
Divisibility.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, Floris van Doorn, Amelia Livingston, Yury Kudryashov, Neil Strickland, Aaron Anderson -/ import Mathlib.Algebra.GroupWithZero.Units.Basic import Mathli...
Bifunctor.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stephen Morgan, Kim Morrison -/ import Mathlib.CategoryTheory.Products.Basic /-! # Lemmas about functors out of product categories. -/ open CategoryTheory namespace CategoryTheory.Bi...
MeasurablyGenerated.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.MeasureTheory.MeasurableSpace.Constructions import Mathlib.Order.Filter.AtTopBot.CompleteLattice import Mathlib.Order.Filter.AtTopBot.C...
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...
UnitsOfNormedAlgebra.lean
/- Copyright (c) 2021 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Heather Macbeth, Winston Yin -/ import Mathlib.Geometry.Manifold.Algebra.LieGroup /-! # Units of a normed algebra We construct the Lie group structure on the grou...
Topology.lean
/- Copyright (c) 2023 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.Multilinear.Bounded import Mathlib.Topology.Algebra.Module.UniformConvergence import Mathlib.Topology.Algebra.SeparationQuoti...
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...
Congruence.lean
/- Copyright (c) 2024 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid, Newell Jensen -/ import Mathlib.Topology.MetricSpace.Pseudo.Defs /-! # Congruences This file defines `Congruent`, i.e., the equivalence between indexed families o...
ToReal.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.Data.Real.Sqrt import Mathlib.NumberTheory.Zsqrtd.Basic /-! # Image of `Zsqrtd` in `ℝ` This file defines `Zsqrtd.toReal` and related lemmas. It is in a sep...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
PartitionOfUnity.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.PartitionOfUnity import Mathlib.Analysis.Convex.Combination /-! # Partition of unity and convex sets In this file we prove the following l...
Subsemiring.lean
/- Copyright (c) 2024 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Star.NonUnitalSubsemiring import Mathlib.Algebra.Ring.Subsemiring.Basic /-! # Star subrings A *-subring is a subring of a *-ring whic...
ContinuousMaps.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.Topology.ContinuousMap.Compact import Mathlib.Topology.MetricSpace.Ultra.Basic /-! # Ultrametric structure on continuous maps -/ /-- Continuous maps...
Pointwise.lean
/- Copyright (c) 2021 Alex J. Best. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best, Yaël Dillies -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Group.Pointwise.Set.Scalar import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra....
MonoCoprod.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.ConcreteCategory.Basic import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Shapes.RegularMon...
Basic.lean
/- Copyright (c) 2019 Robert A. Spencer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert A. Spencer, Markus Himmel -/ import Mathlib.Algebra.Category.Grp.Preadditive import Mathlib.Algebra.Module.Equiv.Basic import Mathlib.Algebra.Module.PUnit import Mathlib.Cate...
IsPrimePow.lean
/- Copyright (c) 2022 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Order.Nat import Mathlib.Data.Nat.Prime.Basic /-! # Prime powers This file deals with prime powers: numbers which a...
NatAntidiagonal.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.Data.Finset.NatAntidiagonal import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Big operators for `NatAntidiagonal` This file contains theor...
Lemmas.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Mathlib.Data.Ordering.Basic import Mathlib.Order.Defs.Unbundled /-! # Some `Ordering` lemmas -/ universe u namespace Ordering @[simp] theorem ite...
BigOperators.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yury Kudryashov, Yaël Dillies -/ import Mathlib.Algebra.BigOperators.GroupWithZero.Action import Mathlib.Algebra.Module.Defs import Mathlib.Data.Fintype.BigOperators /-! #...
Computation.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Nat.Find import Mathlib.Data.Stream.Init import Mathlib.Tactic.Common /-! # Coinductive formalization of unbounded computations. This fil...
Inv.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.Finset.Basic import Mathlib.Data.Fintype.Defs /-! # Computable inverses for injective/surjective functions on finite types ## Main results * `F...
Basic.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.Algebra.Field.Subfield.Defs import Mathlib.Algebra.Order.Group.Pointwise.Interval import Mathlib.Analysis.Normed.Ring.Basic /-! # Norm...