filename
stringlengths
5
42
content
stringlengths
15
319k
all_order.v
Require Export order.
Basic.lean
/- Copyright (c) 2025 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.NumberTheory.Cyclotomic.Rat import Mathlib.NumberTheory.NumberField.Units.Basic /-! # Basic results on integral ideals of a number field We study resul...
Constructions.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, Patrick Massot -/ import Mathlib.Algebra.Group.TypeTags.Basic import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Finset.Piecewise import Mathlib.Or...
fingroup.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 div path...
lakefile.lean
import Lake open Lake DSL /-! ## Mathlib dependencies on upstream projects -/ require "leanprover-community" / "batteries" @ git "main" require "leanprover-community" / "Qq" @ git "master" require "leanprover-community" / "aesop" @ git "master" require "leanprover-community" / "proofwidgets" @ git "v0.0.71" -- Proof...
Bezout.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.PrincipalIdealDomain /-! # Bézout rings A Bézout ring (Bezout ring) is a ring whose finitely generated ideals are principal. Notable examples i...
Encodable.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.Data.DFinsupp.Defs import Mathlib.Logic.Encodable.Pi /-! # `Encodable` and `Countable` instances for `Π₀ i, α i` In this file we provide instances f...
Coord.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.Analysis.Calculus.AddTorsor.AffineMap import Mathlib.Analysis.Normed.Affine.AddTorsorBases /-! # Barycentric coordinates are smooth -/ variable {ι 𝕜 E P :...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
Coinvariants.lean
/- Copyright (c) 2025 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.RepresentationTheory.Rep /-! # Coinvariants of a group representation Given a commutativ...
div.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (******************************************************************************) (* Th...
Rename.lean
/- Copyright (c) 2021 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner -/ import Lean.Elab.Tactic.ElabTerm import Mathlib.Init /-! # The `rename'` tactic The `rename'` tactic renames one or several hypotheses. -/ namespace Mathlib.Tactic o...
ToApp.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne -/ import Mathlib.CategoryTheory.Category.Cat import Mathlib.Util.AddRelatedDecl /-! # The `to_app` attribute Adding `@[to_app]` to a lemma named `F` of shape `∀ .., η = θ`,...
path.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (******************************************************************************) (* ...
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...
IsSheafOneHypercover.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Sites.OneHypercover /-! # Characterization of sheaves using 1-hypercovers In this file, given a Grothendieck topology `J` on a category `C`, we ...
DivMod.lean
/- Copyright (c) 2023 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Mario Carneiro -/ import Mathlib.Tactic.NormNum.Basic import Mathlib.Tactic.NormNum.Ineq /-! # `norm_num` extension for integer div/mod and divides This file adds support f...
SeminormFromBounded.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import Mathlib.Analysis.Normed.Unbundled.RingSeminorm /-! # seminormFromBounded In this file, we prove [BGR, Proposition 1.2.1/2][bos...
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...
FinTopCat.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.CategoryTheory.FintypeCat import Mathlib.Topology.Category.TopCat.Basic /-! # Category of finite topological spaces Definition of the category of...
WithAbs.lean
/- Copyright (c) 2024 Salvatore Mercuri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Salvatore Mercuri -/ import Mathlib.Analysis.Normed.Ring.Basic /-! # WithAbs `WithAbs v` is a type synonym for a semiring `R` which depends on an absolute value. The point of this...
CompactOpen.lean
/- Copyright (c) 2018 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton -/ import Mathlib.Topology.Hom.ContinuousEval import Mathlib.Topology.ContinuousMap.Basic import Mathlib.Topology.Separation.Regular /-! # The compact-open topology In this ...
FactorSet.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.Data.Finsupp.Multiset import Mathlib.RingTheory.UniqueFactorizationDomain.Basic import Mathlib.Tactic.Ring /-! # Set o...
WittPolynomial.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Robert Y. Lewis -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Algebra.MvPolynomial.Variables import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Alg...
DiscreteUniformity.lean
/- Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Antoine Chambert-Loir, María Inés de Frutos Fernández -/ import Mathlib.Topology.UniformSpace.Basic /-! # Discre...
Basic.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Data.PFunctor.Univariate.M /-! # Quotients of Polynomial Functors We assume the following: * `P`: a polynomial functor * `W`: its W-type * `M`: its M...
Hydra.lean
/- Copyright (c) 2022 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Data.Finsupp.Lex import Mathlib.Data.Finsupp.Multiset import Mathlib.Order.GameAdd /-! # Termination of a hydra game This file deals with the following version...
Basic.lean
/- Copyright (c) 2023 Ashvni Narayanan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ashvni Narayanan, Moritz Firsching, Michael Stoll -/ import Mathlib.Algebra.Group.EvenFunction import Mathlib.Data.ZMod.Units import Mathlib.NumberTheory.MulChar.Basic /-! # Dirichl...
Associator.lean
/- Copyright (c) 2025 Bernhard Reinke. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bernhard Reinke -/ import Mathlib.Algebra.Ring.Basic import Mathlib.Tactic.Abel /-! # Associator in a ring If `R` is a non-associative ring, then `(x * y) * z - x * (y * z)` is cal...
Definability.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.ModelTheory.Definability import Mathlib.RingTheory.MvPolynomial.FreeCommRing import Mathlib.RingTheory.Nullstellensatz import Mathlib.ModelTheory.Algebra....
TopologicalSimplex.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Adam Topaz -/ import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.AlgebraicTopology.SimplexCategory.Basic import Mathlib.Topology.Category.TopCat.Basic import Ma...
Reassoc.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Robin Carlier -/ import Mathlib.CategoryTheory.Functor.Basic import Mathlib.Lean.Meta.Simp import Mathlib.Tactic.Simps.Basic import Mathlib.Util.AddRelatedDecl /-! # The `...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
fraction.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 div seq. From mathcomp Require Import ssrAC choice tuple ...
PEquiv.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.Data.Option.Basic import Batteries.Tactic.Congr import Mathlib.Data.Set.Basic import Mathlib.Tactic.Contrapose /-! # Partial Equivalences In this file, ...
Imo2021Q1.lean
/- Copyright (c) 2021 Mantas Bakšys. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mantas Bakšys -/ import Mathlib.Order.Interval.Finset.Nat import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith /-! # IMO 2021 Q1 Let `n ≥ 100` be an integer. Ivan writes...
Locus.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.Etale.Kaehler import Mathlib.RingTheory.Spectrum.Prime.FreeLocus import Mathlib.RingTheory.Support /-! # Smooth locus of an algebra Most results...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
ContinuousOn.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.Constructions /-! # Neighborhoods and continuity relative to a subset This file develops API on the relative versions * `nhdsWithin` ...
Three.lean
/- Copyright (c) 2024 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca, Sanyam Gupta, Omar Haddad, David Lowry-Duda, Lorenzo Luccioli, Pietro Monticone, Alexis Saurin, Florent Schaffhauser -/ import Mathlib.NumberTheory.FLT.Basic import...
Lint.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 -/ import Batteries.Tactic.Lint import Mathlib.Tactic.DeclarationNames /-! # Linters for Mathlib In this file we define additional linters for mathlib, which conce...
Nat.lean
/- Copyright (c) 2024 Arend Mellendijk. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arend Mellendijk -/ import Mathlib.Algebra.Order.Antidiag.Pi import Mathlib.NumberTheory.ArithmeticFunction import Mathlib.Tactic.IntervalCases /-! # Sets of tuples with a fixed pro...
perm.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 tup...
ExistsAndEq.lean
import Mathlib.Tactic.Simproc.ExistsAndEq universe u variable (α : Type u) (p q : α → Prop) example (a : α) (hp : p a) (hq : q a) : ∃ b : α, (p b ∧ b = a) ∧ q b := by simp only [existsAndEq] guard_target = (p a ∧ True) ∧ q a exact ⟨⟨hp, trivial⟩, hq⟩ example (a : α) : ∃ b : α, b = a := by simp only [existsAn...
Basic.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.BigOperators.Group.Finset.Basic import Mathlib.Algebra.Group.Submonoid.Operations import Mathlib.GroupTheory.Congruence.Hom import Mathli...
Final.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Jakob von Raumer -/ import Mathlib.CategoryTheory.Category.Cat.AsSmall import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic import Mathlib.CategoryTheory.IsConnected i...
HomCongr.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.Iso /-! # Conjugate morphisms by isomorphisms We define `CategoryTheory.Iso.homCongr : (X ≅ X₁) → (Y ≅ Y₁) → (X ⟶ Y) ≃ (X₁ ⟶ Y₁)`, c...
Killing.lean
/- Copyright (c) 2024 Frédéric Marbach. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Marbach -/ import Mathlib.Algebra.Lie.Derivation.AdjointAction import Mathlib.Algebra.Lie.Killing import Mathlib.LinearAlgebra.BilinearForm.Orthogonal /-! # Derivations of ...
numfield.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...
Two.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.CharP.Lemmas import Mathlib.GroupTheory.OrderOfElement /-! # Lemmas about rings of characteristic two This file contains results about `CharP R 2`,...
Shatter.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.Combinatorics.SetFamily.Compression.Down import Mathlib.Data.Fintype.Powerset import Mathlib.Order.Interval.Finset.Nat import Mathlib.Algebra.BigOperators....
ENat.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.Hom.Ring import Mathlib.Data.ENat.Basic import Mathlib.SetTheory.Cardinal.Basic /-! # Conversion between `Cardinal` and `ℕ∞` In this ...
Probability.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.Typeclasses.Finite /-! # Classes for probability measures We introduce the following typeclasses for measures: ...
CyclotomicCharacter.lean
/- Copyright (c) 2023 Hanneke Wiersema. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Hanneke Wiersema, Andrew Yang -/ import Mathlib.Algebra.Ring.Aut import Mathlib.NumberTheory.Padics.RingHoms import Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity ...
BigOperators.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.Basic import Mathlib.RingTheory.Ideal.Defs /-! # Big operators for ideals This contains some results on...
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. (**************************************************...
all_order.v
Require Export order.
recover.lean
import Mathlib.Tactic.Recover set_option linter.unusedTactic false /-- problematic tactic for testing recovery -/ elab "this" "is" "a" "problem" : tactic => Lean.Elab.Tactic.setGoals [] /- The main test -/ example : 1 = 1 := by recover this is a problem rfl /- Tests that recover does no harm -/ example : 3 < ...
EckmannHilton.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kenny Lau, Robert Y. Lewis -/ import Mathlib.Algebra.Group.Defs /-! # Eckmann-Hilton argument The Eckmann-Hilton argument says that if a type carries two monoid structures...
Chain.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.Data.Set.Pairwise.Basic import Mathlib.Data.SetLike.Basic import Mathlib.Order.Directed import Mathlib.Order.Hom.Set /-! # Chains and flags This file...
Monomial.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.Polynomial.Degree.Definitions import Mathlib.Algebra.Polynomial.Monomial import Mathlib.Data.Nat.Succ...
IsOpenComapC.lean
/- Copyright (c) 2021 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.RingTheory.Polynomial.Basic import Mathlib.RingTheory.Spectrum.Prime.Topology /-! The morphism `Spec R[x] --> Spec R` induced by the natural inclusion `...
polydiv.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ssralg poly. (**********************...
Algebra.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.Algebra.Defs import Mathlib.Algebra.Order.Module.OrderedSMul /-! # Ordered algebras An ordered algebra is an ordered semiring, which is an algebr...
Defs.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs /-! # Integral closure as a characteristic predicate ## Main definitions Let `R` be a `CommRing` and let `A` be an ...
perm.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 tup...
Operations.lean
/- Copyright (c) 2019 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard -/ import Mathlib.Data.EReal.Basic /-! # Addition, negation, subtraction and multiplication on extended real numbers Addition and multiplication in `EReal` are problemat...
Elements.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic import Mathlib.CategoryTheory.Category.Cat /-! # The category of elements This file defines the category of el...
Basic.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 -/ import Mathlib.Tactic.Attr.Register import Mathlib.Tactic.AdaptationNote import Mathlib.Tactic.Basic import Batteries.Logic import Batteries.Tactic.T...
Different.lean
/- Copyright (c) 2023 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.NumberTheory.KummerDedekind import Mathlib.NumberTheory.RamificationInertia.Unramified import Mathlib.RingTheory.Finiteness.Quotient import Mathlib.RingTheor...
gproduct.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype bigo...
Quotient.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.Tactic.Common /-! # Algebraic quotients This file defines notation for algebraic quotients, e.g. quotient groups `G ⧸ H`, quotient modules `M ⧸ N` and idea...
Square.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.CommSq import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square /-! # Relation between pullback/pushout squares and kernel/cokernel sequence...
Ultra.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.Analysis.Normed.Ring.Ultra import Mathlib.Data.Nat.Choose.Sum /-! ## Conditions to have an ultrametric no...
OrderOfElement.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Julian Kuelshammer -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.Group.Commute.Basic import Mathlib.Algebra.Group.Pointwise.Set.Finite import Mathlib.Alge...
Injective.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Kim Morrison -/ import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic import Mathlib.CategoryTheory.Preadditive.Injective.Basic import Mathlib.Algebra.Category.Grp.EpiMo...
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.
Pi.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.Data.Fintype.Pi import Mathlib.Algebra.BigOperators.Group.Finset.Defs /-! # Products over `univ.pi` -/ assert_not_exists MonoidWithZero MulAction O...
norm_cast.lean
/- Tests for norm_cast -/ import Mathlib.Tactic.Ring import Mathlib.Data.Complex.Basic import Mathlib.Data.ENNReal.Inv -- set_option trace.Tactic.norm_cast true -- set_option trace.Meta.Tactic.simp true set_option autoImplicit true set_option linter.unusedVariables false variable (an bn cn dn : ℕ) (az bz cz dz : ℤ) ...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
StructureSheaf.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison -/ import Mathlib.Algebra.Category.Ring.Colimits import Mathlib.Algebra.Category.Ring.Instances import Mathlib.Algebra.Category.Ring.Limits import Mathlib.Al...
Mon_.lean
/- Copyright (c) 2025 Markus Himmel, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Andrew Yang -/ import Mathlib.Algebra.Category.MonCat.Limits import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic import Mathlib.CategoryTheory.Monoidal.Mo...
Base.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.Chain import Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas import Mathlib.LinearAlgebra.RootSystem.IsValuedIn /-! # Bases for root...
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...
Unitary.lean
/- Copyright (c) 2022 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam, Frédéric Dupuis -/ import Mathlib.Algebra.Group.Submonoid.Operations import Mathlib.Algebra.Star.SelfAdjoint import Mathlib.Algebra.Algebra.Spectrum.Basic import Mathli...
ResidueField.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.Geometry.RingedSpace.LocallyRingedSpace import Mathlib.RingTheory.LocalRing.ResidueField.Basic /-! # Residue fields of points Any point `x` of a...
Maps.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.MeasureTheory.MeasurableSpace.Embedding import Mathlib.Order.Restriction /-! # Auxiliary maps for Ionescu-Tulcea theorem This file contains auxiliary...
SInteger.lean
/- Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.RingTheory.DedekindDomain.AdicValuation /-! # `S`-integers and `S`-units of fraction fields of Dedekind domains Let `K` be the fi...
Dioph.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.Fin.Fin2 import Mathlib.Data.PFun import Mathlib.Data.Vector3 import Mathlib.NumberTheory.PellMatiyasevic /-! # Diophantine functions and Matiyas...
character.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 choice ssrnat seq. From mathcomp Require Import path div fintype...
Defs.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.Nat.Cast.Defs /-! # Cast of integers This file defines the *canonical* homomorphism from the integers into an additive group with...
SelmerGroup.lean
/- Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.Algebra.Group.Equiv.TypeTags import Mathlib.Data.ZMod.QuotientGroup import Mathlib.RingTheory.DedekindDomain.AdicValuation import M...
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...
NormalizedFactors.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.GCDMonoid.Basic import Mathlib.Data.Multiset.OrderedMonoid import Mathlib.RingTheory.UniqueFactorizationDomain....
presentation.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. From mathcomp Require Import fintype finset fingroup morphism. (**********************...
Completion.lean
/- Copyright (c) 2024 Mitchell Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Lee -/ import Mathlib.Topology.Algebra.Nonarchimedean.Basic import Mathlib.Topology.Algebra.GroupCompletion import Mathlib.Topology.Algebra.UniformRing /-! # The completion of ...
Summable.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Algebra.Ring.Action.Rat import Mathlib.RingTheory.HahnSeries.Multiplication import Mathlib.Data.Rat.Cast.Lemmas /-! # Summable families of Hahn Series...
Monad.lean
/- Copyright (c) 2020 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Devon Tuma -/ import Mathlib.Probability.ProbabilityMassFunction.Basic /-! # Monad Operations for Probability Mass Functions This file constructs two operations on `PMF` ...
finfun.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple. ...
Basic.lean
/- Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.Algebra.Polynomial.Bivariate import Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange /-! # Weierstrass equations and the non...