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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...
Limits.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.Pullbacks import Mathlib.AlgebraicGeometry.AffineScheme /-! # (Co)Limits of Schemes We construct various limits and colimits in the categ...
Periodic.lean
/- Copyright (c) 2021 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson -/ import Mathlib.Algebra.Field.Opposite import Mathlib.Algebra.Module.Opposite import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Algebra.Ring.Periodic...
IntervalAverage.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.MeasureTheory.Integral.IntervalIntegral.Basic import Mathlib.MeasureTheory.Integral.Average /-! # Integral average over an interval In this file we...
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, Mario Carneiro -/ import Mathlib.Data.Countable.Basic import Mathlib.Data.Fin.VecNotation import Mathlib.Order.Disjointed import Mathlib.MeasureTheory.OuterMeasure.Defs...
ssrnotations.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) (******************************************************************************) (* - Reserved notation for various arithmetic and algebraic operations: ...
Tarjan.lean
/- Copyright (c) 2025 Vasilii Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasilii Nesterov -/ import Mathlib.Tactic.Order.Graph.Basic /-! # Tarjan's Algorithm This file implements Tarjan's algorithm for finding the strongly connected components (SCCs) of...
hall.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
Trace.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.Tactic.ElabTerm import Lean.Meta.Eval /-! # Defines the `trace` tactic. -/ open Lean Meta Elab Tactic /-- Evaluates a term to ...
LocallyUniformLimit.lean
/- Copyright (c) 2022 Vincent Beffara. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vincent Beffara -/ import Mathlib.Analysis.Complex.RemovableSingularity import Mathlib.Analysis.Calculus.UniformLimitsDeriv import Mathlib.Analysis.NormedSpace.FunctionSeries /-! # L...
Kernel.lean
/- Copyright (c) 2024 Jujian. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Jujian Zhang -/ import Mathlib.RingTheory.TwoSidedIdeal.Basic import Mathlib.RingTheory.TwoSidedIdeal.Lattice /-! # Kernel of a ring homomorphism as a two-sided ideal In thi...
countalg.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 ss...
test_intro_rw.v
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Lemma test_dup1 : forall n : nat, odd n. Proof. move=> /[dup] m n; suff: odd n by []. Abort. Lemma test_dup2 : let n := 1 in False. Proof. move=> /[dup] m n; have : m = n :=...
Hom.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.Hom.Instances import Mathlib.Algebra.GroupWithZero.Action.End import Mathlib.Algebra.GroupWithZero.Action.Hom import Mathlib.Algebra.Module.End...
Basic.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.Analysis.Calculus.Deriv.Add /-! # Local extrema of differentiable functions ## Main definitions In a real normed space `E` we define `posTangentCo...
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...
maximal.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 choice. From mathcomp Require Import div fintype finfun bigop finset prime binomial. Fro...
Order.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Order.Field.Rat import Mathlib.Data.Rat.Cast.CharZero import Mathlib.Tactic.Positivity.Core /-! # Casts of rational numbers in...
SuperpolynomialDecay.lean
/- Copyright (c) 2021 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Devon Tuma -/ import Mathlib.Algebra.Polynomial.Eval.Defs import Mathlib.Analysis.Asymptotics.Lemmas /-! # Super-Polynomial Function Decay This file defines a predicate `Asymptotics.Supe...
Defs.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.RingTheory.NonUnitalSubsemiring.Defs /-! # Bundled subsemirings We define bundled subsemirings and some standard constructions: `subtype` and `incl...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
Syntax.lean
/- Copyright (c) 2021 Aaron Anderson, Jesse Michael Han, Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn -/ import Mathlib.Data.Set.Prod import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.ModelTheory...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
House.lean
/- Copyright (c) 2024 Michail Karatarakis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michail Karatarakis -/ import Mathlib.NumberTheory.SiegelsLemma import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic import Mathlib.NumberTheory.NumberField.EquivReind...
Fintype.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.Data.ZMod.Basic import Mathlib.Tactic.NormNum /-! # Some facts about finite rings -/ open Finset ZMod section Ring variable {R : Type*} [Ring R] [Fint...
InsertIdx.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 Mathlib.Data.List.Basic /-! # insertIdx Proves various lemmas about `List.insertIdx`....
Trifunctor.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.Bifunctor import Mathlib.CategoryTheory.Functor.CurryingThree import Mathlib.CategoryTheory.Products.Associator /-! # Lifting of tri...
Indicator.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Support import Mathlib.Algebra.GroupWithZero.Basic import Mathlib.Algebra.Notation.I...
Monoidal.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.Closed.FunctorCategory.Basic import Mathlib.CategoryTheory.Localization.Monoidal import Mathlib.CategoryTheory.Sites.Localization import Mathlib....
Synonym.lean
/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Nat.Cast.Defs import Mathlib.Order.Synonym /-! # Cast of natural numbers (additional theorems) This file proves additional properties about the ...
Ergodic.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Dynamics.Ergodic.MeasurePreserving import Mathlib.MeasureTheory.Measure.Typeclasses.Probability /-! # Ergodic maps and measures Let `f : α → α` be measure ...
Basic.lean
/- Copyright (c) 2023 Winston Yin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Winston Yin -/ import Mathlib.Geometry.Manifold.MFDeriv.Tangent /-! # Integral curves of vector fields on a manifold Let `M` be a manifold and `v : (x : M) → TangentSpace I x` be a vect...
sesquilinear.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup. From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector. (************************************************...
integral_char.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...
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, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Logic.Equiv.Defs /-! # Multiplicative and additive equivs In this file we defin...
PrettyPrinting.lean
/- Copyright (c) 2024 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Functor.Basic /-! # Tests that terms used in category theory pretty-print as expected -/ section open Opposite /-- info: Opposite.op_u...
Star.lean
/- Copyright (c) 2023 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux, Yaël Dillies -/ import Mathlib.Algebra.GroupWithZero.Commute import Mathlib.Algebra.Order.Monoid.Submonoid import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Algebra.Or...
propose.lean
import Mathlib.Tactic.Propose import Mathlib.Tactic.GuardHypNums import Mathlib.Algebra.Ring.Associated import Mathlib.Data.Set.Subsingleton import Batteries.Data.List.Lemmas -- For debugging, you may find these options useful: -- set_option trace.Tactic.propose true -- set_option trace.Meta.Tactic.solveByElim true se...
HeineCantor.lean
/- Copyright (c) 2020 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Yury Kudryashov -/ import Mathlib.Topology.Algebra.Support import Mathlib.Topology.UniformSpace.Compact import Mathlib.Topology.UniformSpace.Equicontinuity /-! # Compa...
Eqns.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Init import Lean.Meta.Eqns import Batteries.Lean.NameMapAttribute import Lean.Elab.Exception import Lean.Elab.InfoTree.Main /-! # The `@[eqns]` attribute T...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
UnsetOption.lean
/- Copyright (c) 2022 Alex J. Best. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best -/ import Mathlib.Init import Lean.Parser.Term import Lean.Parser.Do import Lean.Elab.Command /-! # The `unset_option` command This file defines an `unset_option` user com...
Bases.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Dagur Asgeirsson -/ import Mathlib.Topology.Bases import Mathlib.Topology.Compactness.Compact /-! # Topological bases in compact sets and compact spaces -/ open Set Topolog...
Pi.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yury Kudryashov -/ import Mathlib.Algebra.Algebra.Equiv import Mathlib.Algebra.Algebra.Opposite import Mathlib.Algebra.Algebra.Prod /-! # The R-algebra structure on families of ...
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. (**********************...
CommShift.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Shift.Basic /-! # Functors which commute with shifts Let `C` and `D` be two categories equipped with shifts by an additive monoid `A`. In this ...
IsAdjoinRoot.lean
/- Copyright (c) 2022 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed import Mathlib.RingTheory.PowerBasis /-! # A predicate on adjoining root...
Monoidal.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.CategoryTheory.Monoidal.Transport import Mathlib.Algebra.Category.AlgCat.Basic import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic import Mathlib.RingTh...
AdeleRing.lean
/- Copyright (c) 2024 Salvatore Mercuri, María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Salvatore Mercuri, María Inés de Frutos-Fernández -/ import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic import Mathlib.NumberTheory.Num...
Basic.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne -/ import Mathlib.MeasureTheory.Group.MeasurableEquiv import Mathlib.MeasureTheory.Integral.Bochner.L1 import Mathlib.Mea...
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...
KummerDedekind.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.KummerDedekind import Mathlib.NumberTheory.NumberField.Basic import Mathlib.RingTheory.Ideal.Norm.AbsNorm import Mathlib.RingTheory.Ideal.In...
Equipartition.lean
/- Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Data.Set.Equitable import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Order.Partition.Fi...
StarProjection.lean
/- Copyright (c) 2025 Monica Omar. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Monica Omar -/ import Mathlib.Algebra.Star.SelfAdjoint import Mathlib.Algebra.Group.Idempotent import Mathlib.Algebra.Ring.Idempotent /-! # Star projections This file defines star proje...
AbelRuffini.lean
/- Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Lutz -/ import Mathlib.GroupTheory.Solvable import Mathlib.FieldTheory.PolynomialGaloisGroup import Mathlib.RingTheory.RootsOfUnity.Basic /-...
Vanishing.lean
/- Copyright (c) 2024 Mitchell Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Lee, Junyan Xu -/ import Mathlib.LinearAlgebra.TensorProduct.RightExactness import Mathlib.LinearAlgebra.TensorProduct.Finiteness import Mathlib.LinearAlgebra.DirectSum.Finsupp ...
Continuity.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, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Topology.Algebra.Ring.Real import Mathlib.Topology.Metrizable.Uniformity impor...
Reflection.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.Projection.Basic /-! # Reflection A linear isometry equivalence `K.reflection : E ≃ₗᵢ[𝕜] ...
WellOrderInductionData.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.Category.Preorder import Mathlib.CategoryTheory.Functor.Category import Mathlib.CategoryTheory.Types import Mathlib.Order.SuccPred.Limit /-! # L...
IsSplittingField.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.RingTheory.Adjoin.Field import Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra /-! # Splitting fields This file introduces the notion of a splitting...
EnoughInjectives.lean
/- Copyright (c) 2023 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Junyan Xu -/ import Mathlib.Algebra.Module.CharacterModule import Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup import Mathlib.Algebra.Category.Grp.EpiMono import ...
Archimedean.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.GroupTheory.ArchimedeanDensely import Mathlib.RingTheory.Valuation.ValuationRing /-! # Ring of integers under a given valuation in an multiplicative...
Pullbacks.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.AffineScheme import Mathlib.AlgebraicGeometry.Gluing import Mathlib.CategoryTheory.Limits.Opposites import Mathlib.CategoryTheory.Limits.Sh...
Separable.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.Polynomial.Expand import Mathlib.Algebra.Polynomial.Splits import Mathlib.Algebra.Squarefree.Basic import Mathlib.FieldTheory.IntermediateField.Basic imp...
ssrint.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import fintype finfun b...
RadonNikodym.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.Dynamics.Ergodic.MeasurePreserving import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym import Mathlib.Topology.Order.CountableSeparating ...
ValuedCSP.lean
/- Copyright (c) 2023 Martin Dvorak. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Dvorak -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.Order.BigOperators.Group.Multiset import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Matrix.Notation...
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...
Units.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.Divisibility.Basic import Mathlib.Algeb...
HasKan.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.CategoryTheory.Limits.Shapes.Terminal import Mathlib.CategoryTheory.Bicategory.Kan.IsKan /-! # Existence of Kan extensions and Kan lifts in bicategories We...
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...
FunctorCategory.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.CategoryTheory.Abelian.Basic import Mathlib.CategoryTheory.Preadditive.FunctorCategory import Mathlib.CategoryTheory.Limits.FunctorCategory.Finite import M...
Datatypes.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.Datatypes import Mathlib.Tactic.CategoryTheory.BicategoricalComp /-! # Expressions for bicategories This file converts lean...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
Basic.lean
/- Copyright (c) 2022 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer, Kevin Klinge, Andrew Yang -/ import Mathlib.Algebra.Group.Submonoid.DistribMulAction import Mathlib.GroupTheory.OreLocalization.Basic import Mathlib.Algebra.GroupWi...
Extend.lean
/- Copyright (c) 2020 Ruben Van de Velde. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ruben Van de Velde -/ import Mathlib.Algebra.Algebra.RestrictScalars import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic import Mathlib.Analysis.RCLike.Basic /-! # Extending a ...
Coherence.lean
/- Copyright (c) 2022. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Yuma Mizuno, Oleksandr Manzyuk -/ import Mathlib.CategoryTheory.Monoidal.Free.Coherence import Mathlib.Lean.Meta import Mathlib.Tactic.CategoryTheory.BicategoryCoherence import Mathlib....
Lemmas.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.Bool.Set import Mathlib.Data.Nat.Set import Mathlib.Order.CompleteLattice.Basic /-! # Theory of complete lattices This file contains results on ...
IsLocalization.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Jujian Zhang -/ import Mathlib.Algebra.Algebra.Bilinear import Mathlib.Algebra.Module.LocalizedModule.Basic /-! # Equivalence between `IsLocalizedModule` and `IsLocalizatio...
dfinsupp_notation.lean
import Mathlib.Algebra.Group.Int.Defs import Mathlib.Data.DFinsupp.Notation example : (fun₀ | 1 => 3 : Π₀ i, Fin (i + 10)) 1 = 3 := by simp example : (fun₀ | 1 | 2 | 3 => 3 | 3 => 4 : Π₀ i, Fin (i + 10)) 1 = 3 := by simp example : (fun₀ | 1 | 2 | 3 => 3 | 3 => 4 : Π₀ i, Fin (i + 10)) 2 = 3 := by simp example : (fun...
Currying.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.Products.Basic /-! # Curry and uncurry, as functors. We define `curry : ((C × D) ⥤ E) ⥤ (C ⥤ (D ⥤ E)...
Dvr.lean
/- Copyright (c) 2020 Kenji Nakagawa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio, Yongle Hu -/ import Mathlib.RingTheory.DiscreteValuationRing.TFAE import Mathlib.RingTheory.LocalProperties.IntegrallyClosed /-! # D...
Torsion.lean
/- Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pierre-Alexandre Bazin -/ import Mathlib.Algebra.DirectSum.Module import Mathlib.Algebra.Module.ZMod import Mathlib.GroupTheory.Torsion import Mathlib.LinearAlgebra.Isomorphism...
Basic.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Andrew Yang -/ import Mathlib.RingTheory.Derivation.ToSquareZero import Mathlib.RingTheory.Ideal.Cotangent import Mathlib.RingTheory.IsTensorProduct import Mathlib....
Exponential.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ import Mathlib.Analysis.Normed.Algebra.Exponential import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathlib.Data.Complex.Exponential import Ma...
Partition.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.Combinatorics.Enumerative.Composition import Mathlib.Tactic.ApplyFun /-! # Partitions A partition of a natural number `n` is a way of writing `n` as a su...
RegularTopology.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves /-! # Description of the covering sieves of the regular topology This file characterises the coverin...
AttachCells.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.MorphismProperty.Limits /-! # Attaching cells Given a family of morphisms `g a : A a ⟶ B a` and a morphism `f : X₁ ⟶ X₂`, we introduce a structu...
Embedding.lean
/- Copyright (c) 2025 Weiyi Wang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Weiyi Wang -/ import Mathlib.Data.Real.Archimedean import Mathlib.Data.Real.Basic import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Algebra.Order.Group.Pointwise.CompleteLatti...
galois.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 tupl...
Basic.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, Mario Carneiro -/ import Mathlib.Data.Sum.Basic import Mathlib.Logic.Equiv.Option import Mathlib.Logic.Equiv.Sum import Mathlib.Logic.Function.Conjugate impor...
Birkhoff.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Filippo A. E. Nuccio, Sam van Gool -/ import Mathlib.Data.Fintype.Order import Mathlib.Order.Interval.Finset.Basic import Mathlib.Order.Irreducible import Mathlib.Order.Upp...
MorphismProperty.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.Limits.Comma import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic import Mathlib.CategoryTheory.Limits.FullSubcategory impo...
Positivity.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.Complex.TaylorSeries /-! # Nonnegativity of values of holomorphic functions We show that if `f` is holomorphic on an open disk `B(c,r)` and al...
H1.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.Category.Grp.Basic /-! The cohomology of a sheaf of groups in degree 1 In this file, we shall define the cohomology in degree 1 of a sheaf of groups (T...
LocallyConstant.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.Condensed.Discrete.Basic import Mathlib.Condensed.TopComparison import Mathlib.Topology.Category.CompHausLike.SigmaComparison import Mathlib.Topolo...
MahlerBasis.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Giulio Caflisch, David Loeffler -/ import Mathlib.Algebra.Group.ForwardDiff import Mathlib.Analysis.Normed.Group.Ultra import Mathlib.NumberTheory.Padics.ProperSpace import Mathlib.Rin...
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...
Constructions.lean
/- Copyright (c) 2015 Joseph Hua. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Hua -/ import Mathlib.Data.W.Basic /-! # Examples of W-types We take the view of W types as inductive types. Given `α : Type` and `β : α → Type`, the W type determined by this dat...
Pi.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Notation.Pi.Defs import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE import Mathlib.Data.Finset.Latti...