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ULift.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.GroupWithZero.ULift import Mathlib.Algebra.Ring.ULift import Mathlib.Algebra.Module.Equiv.Defs import Mathlib.Data.ULift /-! # `ULift` instances f...
Cardinality.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Data.Complex.Basic import Mathlib.Data.Real.Cardinality /-! # The cardinality of the complex numbers This file shows that the...
InnerProduct.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.BumpFunction.Basic import Mathlib.Analysis.InnerProductSpace.Calculus import Mathlib.Analysis.SpecialFunctions...
PartOrd.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.Order.Antisymmetrization import Mathlib.Order.Category.Preord import Mathlib.CategoryTheory.Adjunction.Basic /-! # Category of partial orders This de...
Halting.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.Computability.PartrecCode import Mathlib.Data.Set.Subsingleton /-! # Computability theory and the halting problem A universal partial recursive funct...
LocalRing.lean
/- Copyright (c) 2025 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan -/ import Mathlib.RingTheory.AdicCompletion.Basic import Mathlib.RingTheory.LocalRing.Defs /-! # Basic Properties of Complete Local Ring In this file we prove that a ring t...
Basic.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.Algebra.Group.PUnit import Mathlib.Algebra.Group.TypeTags.Hom import Mathlib.Algebra.Group.ULift import Mathlib.CategoryTheory.Elementwise import Mathlib.C...
Rank.lean
/- Copyright (c) 2025 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.GroupTheory.Finiteness import Mathlib.SetTheory.Cardinal.Finite /-! # Rank of a group This file defines the rank of a group, namely the minimum siz...
Init.lean
/- Copyright (c) 2023 Miyahara Kō. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Miyahara Kō -/ import Mathlib.Init import Aesop /-! # Measurability Rule Set This module defines the `Measurable` Aesop rule set which is used by the `measurability` tactic. Aesop rule...
TensorProduct.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.RingTheory.Spectrum.Prime.Topology import Mathlib.RingTheory.SurjectiveOnStalks /-! # Lemmas regarding the prime spectrum of tensor products ## Main resul...
Perm.lean
/- Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Data.Fintype.Perm import Mathlib.SetTheory.Cardinal.Finite /-! # Properties of `Equiv.Perm` on `Finite` types -/ assert_not_exists Fi...
MulP.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.RingTheory.WittVector.IsPoly /-! ## Multiplication by `n` in the ring of Witt vectors In this file we show that multiplication by `n` in the ring of ...
PureCoherence.lean
/- Copyright (c) 2024 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence import Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes /-! # Coherence tactic for monoidal categories We pro...
Unused.lean
/- Copyright (c) 2024 Lean FRO. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Cli import Batteries.Data.List.Basic import ImportGraph.Imports import LongestPole.Rectangles import Mathlib.Util.FormatTable /-! # `lake exe unused` A tool for libr...
Monotonicity.lean
import Mathlib.Tactic.Monotonicity.Basic import Mathlib.Tactic.Monotonicity.Lemmas
MeasurableSpace.lean
/- Copyright (c) 2025 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.Analysis.Normed.Lp.PiLp import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic /-! # Measurable space structure on `WithLp` If `X` is a measurab...
FilteredColimits.lean
/- Copyright (c) 2021 Justus Springer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Justus Springer -/ import Mathlib.Algebra.Category.Ring.Basic import Mathlib.Algebra.Category.Grp.FilteredColimits import Mathlib.Algebra.Ring.ULift /-! # The forgetful functor from ...
Fintype.lean
/- Copyright (c) 2022 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Alex J. Best -/ import Mathlib.Data.Finsupp.Single import Mathlib.Data.Fintype.BigOperators /-! # Finiteness and infiniteness of `Finsupp` Some lemmas on the combination o...
Noetherian.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.Ideal.Quotient.Operations import Mathlib.RingTheory.Noetherian.Basic /-! # Noetherian quotient rings and quotient modules -/ instance Ideal.Quot...
OpenImmersion.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.Geometry.RingedSpace.OpenImmersion import Mathlib.AlgebraicGeometry.Scheme import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.Categor...
all_fingroup.v
From mathcomp Require Export action. From mathcomp Require Export automorphism. From mathcomp Require Export fingroup. From mathcomp Require Export gproduct. From mathcomp Require Export morphism. From mathcomp Require Export perm. From mathcomp Require Export presentation. From mathcomp Require Export quotient.
TangentCone.lean
/- Copyright (c) 2025 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.TangentCone import Mathlib.Analysis.RCLike.Basic import Mathlib.Topology.Instances.RealVectorSpace /-! # Relationships between...
Finite.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.Measure.Restrict /-! # Classes for finite measures We introduce the following typeclasses for measures: * `IsFiniteMea...
Basic.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.Algebra.Group.PUnit import Mathlib.Algebra.Group.Subgroup.Ker import Mathlib.Algebra.Group.Submonoid.Membership import Mathlib.GroupTheory.Congruence...
Basic.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.AlternatingConst import Mathlib.AlgebraicTopology.SingularSet /-! # Singular homology In this file, we define the singular chain complex a...
Int.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Algebra.Group.Int.Defs import Mathlib.Algebra.Order.Monoid.Defs /-! # The integers form a linear ordered group This file contains the instance necessar...
ExteriorPower.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.LinearAlgebra.ExteriorPower.Basic import Mathlib.Algebra.Category.ModuleCat.Basic /-! # The exterior powers as functors on the category of modules In this file...
Sups.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Finset.NAry import Mathlib.Data.Finset.Slice import Mathlib.Data.Set.Sups /-! # Set family operations This file defines a few binary operations on `...
TensorProduct.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro, Eric Wieser -/ import Mathlib.LinearAlgebra.TensorProduct.Tower import Mathlib.Algebra.DirectSum.Module /-! # Tensor products of direct sums This file shows that...
Meta.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.Init import Lean.Elab.Term import Lean.Elab.Tactic.Basic import Lean.Meta.Tactic.Assert import Lean.Meta.Tactic.Clear import Batteries.CodeAction -- to...
HeronsFormula.lean
/- Copyright (c) 2021 Matt Kempster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Matt Kempster -/ import Mathlib.Geometry.Euclidean.Triangle /-! # Freek № 57: Heron's Formula This file proves Theorem 57 from the [100 Theorems List](https://www.cs.ru.nl/~freek/100/...
Field.lean
/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yaël Dillies, Patrick Stevens -/ import Mathlib.Algebra.CharZero.Defs import Mathlib.Data.Nat.Cast.Basic import Mathlib.Tactic.Common import Mathlib.Algebra.Field.Defs ...
Defs.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 -/ import Mathlib.Data.Nat.Notation /-! # Definition of `Stream'` and functions on streams A stream `Stream' α` is an infinite sequence of elements of `α`. O...
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, Benjamin Davidson -/ import Mathlib.Order.Monotone.Odd import Mathlib.Analysis.Calculus.LogDeriv import Mathlib.Analysis.Spe...
Multiplication.lean
/- Copyright (c) 2024 Theodore Hwa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kim Morrison, Violeta Hernández Palacios, Junyan Xu, Theodore Hwa -/ import Mathlib.Logic.Hydra import Mathlib.SetTheory.Surreal.Basic import Mathlib.Tactic.Linter.Deprec...
Deriv.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.Analysis.Calculus.Deriv.Inverse import Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv /-! # Inverse function theorem, 1D case In this file...
Defs.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro -/ import Mathlib.RingTheory.Ideal.Quotient.Basic import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic /-! # Residue Field of local rings ## Mai...
algC.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 ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
algebraics_fundamentals.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 ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
ring_quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
cyclic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype bigo...
Bounds.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Analysis.Calculus.ContDiff.Operations import Mathlib.Data.Finset.Sym import Mathlib.Data.Nat.Choose.Cast import Mathlib.Data.Na...
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...
finmodule.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...
Fin.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, Alexander Bentkamp -/ import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.Pi /-! # Bases indexed by `Fin` -/ assert_not_exists Ordin...
ssreflect.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Export ssreflect. Global Set SsrOldRewriteGoalsOrder. Global Set Asymmetric Patterns. Global Set Bullet Behavior "None". #[deprecated(sinc...
Basic.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.Algebra.Group.Submonoid.Membership import Mathlib.Algebra.Group.Subsemigroup.Membership import Mathlib.Algebra.Group.Subsemigroup.Operations import Mathl...
DoubleUnderscore.lean
import Mathlib.Tactic.Linter.Style set_option linter.style.nameCheck true variable (n : Nat) -- this notation generates the declaration `«term__,»` that has a double underscore, -- but is allowed by `linter.style.nameCheck`. notation "_" n "," => Nat.succ n /-- info: `«term__,» : Lean.Name -/ #guard_msgs in #check `...
algC.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 ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
archimedean.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop or...
Defs.lean
/- Copyright (c) 2018 Ellen Arlt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang -/ import Mathlib.Algebra.Module.Pi /-! # Matrices This file defines basic properties of matrices up to...
Units.lean
/- Copyright (c) 2025 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Group.Units.Basic import Mathlib.Algebra.Order.Monoid.Unbundled.Basic /-! # Lemmas for units in an ordered monoid -/ variable {M : Type*} [Monoid M] [...
Strict.lean
/- Copyright (c) 2022 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.Bicategory.Basic /-! # Strict bicategories A bicategory is called `Strict` if the left unitors, the ri...
SmoothFunctions.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri -/ import Mathlib.Geometry.Manifold.Algebra.Structures /-! # Algebraic structures over `C^n` functions In this file, we define instances of algebraic structures ov...
MinMax.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.Unbundled.Basic /-! # Lemmas about `min` and `max` in an ordered monoid. -/ op...
finalg.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 finset f...
algebraics_fundamentals.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 ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
CrossProduct.lean
/- Copyright (c) 2021 Martin Dvorak. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Dvorak, Kyle Miller, Eric Wieser -/ import Mathlib.Algebra.Lie.Basic import Mathlib.Data.Matrix.Notation import Mathlib.LinearAlgebra.BilinearMap import Mathlib.LinearAlgebra.Lin...
Fin.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.Order.Fin.Basic import Mathlib.Order.Interval.Set.UnorderedInterval /-! # (Pre)images of set intervals under `Fin` operations In this file we prove...
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.
choice.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (**************************************************...
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, Jeremy Avigad -/ import Mathlib.Data.Set.Insert import Mathlib.Order.SetNotation import Mathlib.Order.BooleanAlgebra.Set import Mathlib.Order.Bounds.Defs /-! # Definit...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Bryan Gin-ge Chen -/ import Mathlib.Order.BooleanAlgebra.Defs /-! # Basic properties of Boolean algebras This file provides some basic definitions, functions as well ...
Fin.lean
/- Copyright (c) 2023 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.BigOperators.Finsupp.Basic import Mathlib.Data.Finsupp.Fin /-! # `Finsupp.sum` and `Finsupp.prod` over `...
all_field.v
From mathcomp Require Export algC. From mathcomp Require Export algebraics_fundamentals. From mathcomp Require Export algnum. From mathcomp Require Export closed_field. From mathcomp Require Export cyclotomic. From mathcomp Require Export falgebra. From mathcomp Require Export fieldext. From mathcomp Require Export fin...
Functor.lean
/- Copyright (c) 2018 Michael Jendrusch. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Jendrusch, Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Monoidal.Category import Mathlib.CategoryTheory.Adjunction.FullyFaithful import Mathlib.CategoryTheory...
G2.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.Base import Mathlib.LinearAlgebra.RootSystem.Chain import Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas /-! # Properties of the `�...
Note.lean
/- Copyright (c) 2025 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Init import Batteries.Util.LibraryNote /-! # Documentation concerning the continuous functional calculus A library note giving advice on developing and...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
Disjoint.lean
/- Copyright (c) 2019 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yury Kudryashov -/ import Mathlib.Data.Set.Lattice.Image import Mathlib.Order.Interval.Set.LinearOrder /-! # Extra lemmas about intervals This file contains lemma...
Operations.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Antoine Chambert-Loir -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.RingTheory.Ideal.Maps import Mathlib.Algebra.Ring.Action.Submonoid /-! # More operation...
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...
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...
Basic.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.Algebra.Group.TransferInstance import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers import Mathlib.CategoryTheory.Limit...
IsolatedZeros.lean
/- Copyright (c) 2022 Vincent Beffara. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vincent Beffara, Stefan Kebekus -/ import Mathlib.Analysis.Analytic.Constructions import Mathlib.Analysis.Calculus.DSlope import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathl...
Basic.lean
/- Copyright (c) 2015 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Pow import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Algebra.Ring.Parity import Mathlib.Tactic.Bound...
Basic.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.RingTheory.Ideal.IsPrimary import Mathlib.Order.Minimal /-! # Minimal primes We provide various results concerning the minimal primes above an ideal ## M...
vector.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop fi...
Floor.lean
/- Copyright (c) 2024 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Order.Floor.Semiring import Mathlib.Data.NNRat.Order import Mathlib.Data.Rat.Floor /-! # Floor Function for Non-negative Rational Numbers ## Summar...
Fin.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Yury Kudryashov -/ import Mathlib.Data.Finset.Fin import Mathlib.Order.Interval.Finset.Nat import Mathlib.Order.Interval.Set.Fin /-! # Finite intervals in `Fin n` This fi...
preorder.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...
FreeRing.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Johan Commelin -/ import Mathlib.Algebra.FreeMonoid.Basic import Mathlib.GroupTheory.FreeAbelianGroup /-! # Free rings The theory of the free ring over a type. ## Main definit...
Have.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Edward Ayers, Mario Carneiro -/ import Mathlib.Init import Lean.Elab.Binders import Lean.Elab.SyntheticMVars import Lean.Meta.Tactic.Assert /-! # Extending `have`, `le...
CountablyGenerated.lean
/- Copyright (c) 2023 Felix Weilacher. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Felix Weilacher, Yury Kudryashov, Rémy Degenne -/ import Mathlib.MeasureTheory.MeasurableSpace.Embedding import Mathlib.Data.Set.MemPartition import Mathlib.Order.Filter.CountableSepa...
Ascoli.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.CompactConvergence import Mathlib.Topology.UniformSpace.Equicontinuity import Mathlib.Topology.UniformSpace.Equiv /-! # Asco...
Homeomorph.lean
/- Copyright (c) 2025 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Junyan Xu -/ import Mathlib.FieldTheory.PurelyInseparable.Basic import Mathlib.RingTheory.Flat.Basic import Mathlib.RingTheory.Spectrum.Prime.Topology /-! # Purely...
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...
Support.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker -/ import Mathlib.Algebra.MonoidAlgebra.Support import Mathlib.Algebra.Polynomial.Degree.Operations /-! # Degree and support o...
archimedean.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop or...
Nim.lean
/- Copyright (c) 2020 Fox Thomson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fox Thomson, Markus Himmel -/ import Mathlib.SetTheory.Game.Birthday import Mathlib.SetTheory.Game.Impartial import Mathlib.SetTheory.Nimber.Basic import Mathlib.Tactic.Linter.DeprecatedM...
Exponential.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.Normed.Algebra.Exponential /-! # The exponential map from selfadjoint to unitary In this file, we establish various properties related to the m...
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.
BoundedOperation.lean
/- Copyright (c) 2024 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Topology.MetricSpace.ProperSpace.Real import Mathlib.Analysis.Normed.Ring.Lemmas /-! # Bounded operations This...
Basis.lean
/- Copyright (c) 2021 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.LinearAlgebra.Basis.Defs import Mathlib.LinearAlgebra.Multilinear.Basic /-! # Multilinear maps in relation to bases. This file proves lemmas about the ac...
ChineseRemainder.lean
/- Copyright (c) 2023 Shogo Saito. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shogo Saito. Adapted for mathlib by Hunter Monroe -/ import Mathlib.Algebra.BigOperators.Ring.List import Mathlib.Data.Nat.ModEq import Mathlib.Data.Nat.GCD.BigOperators /-! # Chinese Re...
Field.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.EuclideanDomain.Defs import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.GroupWithZero.Units.Basic /-! # Instances for Euclid...
Complex.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, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Complex.Log /-! # Power funct...
Field.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kim Morrison -/ import Mathlib.Algebra.Field.Subfield.Defs import Mathlib.Algebra.GroupWithZero.Divisibility import Mathlib.Algebra.Order.Group.Pointwise.Interval impor...
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, Floris van Doorn, Yury Kudryashov, Neil Strickland -/ import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.Hom.Instances import Mathl...
Basic.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.CategoryTheory.Monoidal.Functor /-! # The free monoidal category over a type Given a type `C`, the free monoidal category over `C` has as objects forma...