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SubMulAction.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Module.Defs import Mathlib.Data.SetLike.Basic import Mathlib.Data.Setoid.Basic import Mathlib.GroupTheory.GroupAction.Defs import Mathlib.GroupTheory...
Defs.lean
/- Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel -/ import Mathlib.Data.ENNReal.Real import Mathlib.Tactic.Bound.Attribute import Mathlib.Topology...
Gronwall.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.SpecialFunctions.ExpDeriv /-! # Grönwall's inequality The main technical result of this file is the Grönwall-like inequality `norm_le_gron...
finfield.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 div tupl...
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, Mario Carneiro, Johannes Hölzl, Damiano Testa, Yuyang Zhao -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Defs import Mathlib.Data.Ordering.Basic imp...
Trace.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.Data.Matrix.Basis import Mathlib.Data.Matrix.Block import Mathlib.Data.Matrix.RowCol import Mathlib.Data.Matr...
ssrmatching.v
From Corelib Require Export ssrmatching.
Free.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.Module.Presentation.Basic import Mathlib.LinearAlgebra.Finsupp.VectorSpace import Mathlib.LinearAlgebra.FreeModule.Basic import Mathlib.Logic.UnivLE /-...
Erase.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, Jeremy Avigad, Minchao Wu, Mario Carneiro -/ import Mathlib.Data.Finset.Defs import Mathlib.Data.Multiset.Filter /-! # Erasing an element from a finite set ...
fieldext.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 tupl...
Imo1959Q2.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.Data.Real.Sqrt /-! # IMO 1959 Q2 For what real values of $x$ is $\sqrt{x+\sqrt{2x-1}} + \sqrt{x-\sqrt{2x-1}} = A,$ given (a) $A=\sqrt{2}$, (b) $A...
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, Bryan Gin-ge Chen -/ import Mathlib.Logic.Relation import Mathlib.Order.CompleteLattice.Basic import Mathlib.Order.GaloisConnection.Defs /-! # Equivalence relati...
Elementwise.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Kyle Miller -/ import Mathlib.CategoryTheory.ConcreteCategory.Basic import Mathlib.Util.AddRelatedDecl import Batteries.Tactic.Lint /-! # Tools to reformulate category-th...
HomologicalComplex.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.Double import Mathlib.Algebra.Homology.HomologicalComplexLimits import Mathlib.CategoryTheory.Generator.Basic /-! # Generators of the category ...
Residual.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.NumberTheory.Transcendental.Liouville.Basic import Mathlib.Topology.Baire.Lemmas import Mathlib.Topology.Baire.LocallyCompactRegular import Mathlib.T...
Basic.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Group.Invertible.Defs import Mathlib.Algebra.Module.Equiv.Defs import Mathlib.CategoryTheory.Preadditive.Basic ...
EquivalencePseudoabelian.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive import Mathlib.AlgebraicTopology.DoldKan.Compatibility import Mathlib.CategoryTheory.Idempotents.SimplicialObject i...
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, Yury Kudryashov, Neil Strickland -/ import Mathlib.Algebra.Ring.InjSurj import Mathlib.Algebra.Group.Units.Hom import Mathlib.Algebra...
AlternatingFaceMapComplex.lean
/- Copyright (c) 2021 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Adam Topaz, Johan Commelin -/ import Mathlib.Algebra.Homology.Additive import Mathlib.AlgebraicTopology.MooreComplex import Mathlib.Algebra.BigOperators.Fin import Mathlib.Catego...
SuccPred.lean
/- Copyright (c) 2022 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import Mathlib.Order.Fin.Basic import Mathlib.Order.SuccPred.Basic /-! # Successors and predecessors of `Fin n` In this file, we show that `Fin n` is both a `SuccOr...
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 -/ import Mathlib.Data.Set.UnionLift import Mathlib.Topology.ContinuousMap.Defs import Mathlib.Topology.Homeomorph.Defs import Mathlib.Topology.Separation.Hausdorff ...
Lattice.lean
/- Copyright (c) 2024 Judith Ludwig, Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Judith Ludwig, Christian Merten -/ import Mathlib.LinearAlgebra.Dimension.Localization import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathlib.LinearAlgeb...
QuasiIso.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.Algebra.Homology.ShortComplex.Homology /-! # Quasi-isomorphisms of short complexes This file introduces the typeclass `QuasiIso φ` for a morphism `φ : S₁ ⟶ S₂...
Datatypes.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Evgenia Karunus, Kyle Miller -/ import Mathlib.Init import Lean.Util.Trace /-! # Explode command: datatypes This file contains datatypes used by the `#explode` comman...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
OfArity.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.Logic.Function.FromTypes /-! # Function types of a given arity This provides `Function.OfArity`, such that `OfArity α β 2 = α → α → β`. Note that it...
Lemmas.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.GroupWithZero.Divisibility import Mathlib.Algebra.Ring.Rat import Mathlib.Algebra.Ring.Int.Parity import Mathlib.Data.PNat.Defs...
Monoid.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Hom.Basic import Mathlib.Algebra.Order.Group.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Orde...
separable.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...
Module.lean
/- Copyright (c) 2023 Apurva Nakade. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Apurva Nakade -/ import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.RingTheory.Finiteness.Basic /-! # Modules over nonnegative elements This file defines instances and pro...
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. ...
fingraph.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. From mathcomp Require Import seq path fintype. (******************************************...
Opposites.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Floris van Doorn -/ import Mathlib.CategoryTheory.Limits.Filtered import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts import Mathlib.CategoryTheory.Limits.Shapes.Ker...
CompactConvergence.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash, Yury Kudryashov -/ import Mathlib.Topology.CompactOpen import Mathlib.Topology.Compactness.CompactlyCoherentSpace import Mathlib.Topology.Maps.Proper.Basic import Mathlib.Top...
Sum.lean
/- Copyright (c) 2024 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.Matroid.Map import Mathlib.Logic.Embedding.Set /-! # Sums of matroids The *sum* `M` of a collection `M₁, M₂, ..` of matroids is a matroid on the dis...
GaugeRescale.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.Analysis.Convex.Gauge import Mathlib.Analysis.Normed.Module.Convex /-! # "Gauge rescale" homeomorphism between convex sets Given two convex von Neum...
finset.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 div seq. From mathcomp Require Import choice fintype finf...
Abelian.lean
/- Copyright (c) 2022 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Abelian.Subobject import Mathlib.CategoryTheory.Limits.EssentiallySmall import Mathlib.CategoryTheory.Preadditive.Injective.Basic import M...
Core.lean
/- Copyright (c) 2020 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Algebra.Field.Basic import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Data.Tree.Basic import Mathlib.Logic.Basic import Mathlib.Tactic.NormNum.Co...
Explicit.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Riccardo Brasca, Filippo A. E. Nuccio -/ import Mathlib.Condensed.Module import Mathlib.Condensed.Equivalence /-! # The explicit sheaf condition for condensed sets...
Quotient.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Riccardo Brasca -/ import Mathlib.Analysis.Normed.Module.Basic import Mathlib.Analysis.Normed.Group.Hom import Mathlib.RingTheory.Ideal.Quotient.Operations import Mathl...
Construction.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullbac...
Basic.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.HomologicalComplex import Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel /-! # Basic definitions for factorizations lemmas We define th...
Semicontinuous.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Algebra.GroupWithZero.Indicator import Mathlib.Topology.Piecewise import Mathlib.Topology.Instances.ENNReal.Lemmas /-! # Semicontinuous maps A ...
fingraph.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. From mathcomp Require Import seq path fintype. (******************************************...
OrderedMonoid.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Order.Group.Multiset import Mathlib.Algebra.Order.Monoid.Canonical.Defs /-! # Multisets as ordered monoids The `IsOrderedCancelAddMono...
WeaklyInitial.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers import Mathlib.CategoryTheory.Limits.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.Terminal /-! ...
Fibered.lean
/- Copyright (c) 2024 Paul Lezeau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul Lezeau, Calle Sönne -/ import Mathlib.CategoryTheory.FiberedCategory.Cartesian /-! # Fibered categories This file defines what it means for a functor `p : 𝒳 ⥤ 𝒮` to be (pre)fib...
Defs.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Group.Defs import Batteries.Data.List.Basic /-! # Levenshtein distances We define the Levenshtein edit distance `levenshtein C xy ys` between two...
Finite.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.Algebra.Group.TypeTags.Basic import Mathlib.Data.Finite.Defs import Mathlib.Data.Fintype.Card /-! # `Finite`, `Infinite` and `Fintype` are preserved b...
renameBvar.lean
import Mathlib.Tactic.RenameBVar import Lean set_option linter.unusedVariables false axiom test_sorry {α : Sort _} : α /- This test is somewhat flaky since it depends on the pretty printer. -/ /-- trace: ℕ : Sort u_1 P : ℕ → ℕ → Prop h : ∀ (n : ℕ), ∃ m, P n m ⊢ ∀ (l : ℕ), ∃ m, P l m --- trace: ℕ : Sort u_1 P : ℕ → ℕ ...
Spectrum.lean
/- Copyright (c) 2021 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Algebra.Spectrum.Quasispectrum import Mathlib.FieldTheory.IsAlgClosed.Spectrum import Mathlib.Analysis.Complex.Liouville import Mathlib.Analysis....
IntegralRepresentation.lean
/- Copyright (c) 2025 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals /-! # Integral representations of `rpow` This file contains an integral representation of the `rpow` f...
normed.lean
import Mathlib.Analysis.Complex.Basic -- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/defeq.20of.20.60NormedAddCommGroup.20.E2.84.82.60/near/422248635 example : (NonUnitalNormedRing.toNormedAddCommGroup : NormedAddCommGroup ℂ) = Complex.instNormedAddCommGroup := by with_reducible_a...
Independent.lean
/- Copyright (c) 2021 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.Analysis.Convex.Combination import Mathlib.Analysis.Convex.Extreme /-! # Convex independence This file defines convex indepen...
RCLike.lean
/- Copyright (c) 2021 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Analysis.RCLike.Basic import Mathlib.Analysis.NormedSpace.Real import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic /-! # Normed spaces over R or C Thi...
test_guard.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Inductive tree := Node { children : seq tree }. Inductive ptree (T : Type) := singleton of T | branch of list (ptree T). (* has *) Fixpoint tree_has (T : Type) (p : pred T) (t : ptree T) : bool :...
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
nilpotent.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import fintype div bigop prime finset fingroup morphism. Fro...
Basic.lean
/- Copyright (c) 2025 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete import Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Oplax import Mathlib.CategoryTheory.Bicategory.End impor...
Datatypes.lean
/- Copyright (c) 2020 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Tactic.Linarith.Lemmas import Mathlib.Tactic.NormNum.Basic import Mathlib.Util.SynthesizeUsing /-! # Datatypes for `linarith` Some of the data stru...
FTaylorSeries.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.FDeriv.Add import Mathlib.Analysis.Calculus.FDeriv.Equiv import Mathlib.Analysis.Calculus.FormalMultilinearSeries import Mathli...
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...
RootPositive.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.LinearAlgebra.RootSystem.IsValuedIn import Mathlib.LinearAlgebra.RootSystem.WeylGroup /-! # Invariant and root-positive bilinear forms on root pairing...
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...
Basic.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Logic.Small.Defs import Mathlib.Logic.Equiv.Set /-! # Instances and theorems for `Small`. In particular we prove `small_of_injective` and `small_of_surje...
matrix.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 finfun f...
Sinc.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds import Mathlib.Analysis.Calculus.DSlope /-! # Sinc function This file contains the definition of the sinc ...
Noetherian.lean
/- Copyright (c) 2023 Fangming Li. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fangming Li -/ import Mathlib.RingTheory.GradedAlgebra.Basic import Mathlib.RingTheory.Noetherian.Basic /-! # The properties of a graded Noetherian ring. This file proves that the 0-th ...
Quotient.lean
/- Copyright (c) 2020 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn -/ import Mathlib.CategoryTheory.NatIso import Mathlib.CategoryTheory.EqToHom /-! # Quotient category Constructs the quotient of a category by an arbitrary family of relations...
Biproducts.lean
/- Copyright (c) 2019 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.Limits.Shapes.FiniteProducts import Mathlib.CategoryTheory.Limits.Shapes.Kernels /-! # Biproducts and binary biproducts ...
center.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset fingroup morphism perm. From math...
orderedzmod.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
UniversalEnveloping.lean
/- Copyright (c) 2020 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Algebra.RingQuot import Mathlib.LinearAlgebra.TensorAlgebra.Basic /-! # Universal enveloping algebra Given a commu...
HomotopyGroup.lean
/- Copyright (c) 2021 Roberto Alvarez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Roberto Alvarez -/ import Mathlib.Algebra.Group.Ext import Mathlib.Algebra.Group.TransferInstance import Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup import Mathlib....
Tower.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Anne Baanen -/ import Mathlib.Algebra.Algebra.Equiv import Mathlib.LinearAlgebra.Span.Basic /-! # Towers of algebras In this file we prove basic facts about towers of algebras....
ssrbool.v
From mathcomp Require Import ssreflect ssrfun. From Corelib Require Export ssrbool. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (**********************) (* not yet backported *) (**********************) Lemma homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT] [aP : pred ...
Finset.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.Algebra.BigOperators.Group.Finset.Basic import Mathlib.Algebra.GroupWithZero.Units.Basic import Mathlib.Algebra.Notation.Support import Mathlib.Data.Se...
BallAction.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Heather Macbeth -/ import Mathlib.Analysis.Normed.Field.UnitBall import Mathlib.Analysis.Normed.Module.Basic import Mathlib.LinearAlgebra.Basis.VectorSpace /-! # Mul...
OrdContinuous.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Johannes Hölzl -/ import Mathlib.Order.ConditionallyCompleteLattice.Basic import Mathlib.Order.RelIso.Basic /-! # Order continuity We say that a function is *left o...
NatPowAssoc.lean
/- Copyright (c) 2023 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Prod import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Data.Nat.Cast.Basic /-! # Typeclasses for...
TruncGE.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.Embedding.HomEquiv import Mathlib.Algebra.Homology.Embedding.IsSupported import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex /-! # ...
mxrepresentation.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...
Extension.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Algebra.Lie.Ideal /-! # Extensions of Lie algebras This file defines extensions of Lie algebras, given by short exact sequences of Lie algebra homomor...
AB.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.Algebra.Category.ModuleCat.AB import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf import Mathlib.CategoryTheory.Sites.Coherent.Extensive...
GRewrite.lean
/- Copyright (c) 2023 Sebastian Zimmer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Zimmer, Mario Carneiro, Heather Macbeth, Jovan Gerbscheid -/ import Mathlib.Data.Int.ModEq import Mathlib.Tactic.GRewrite import Mathlib.Tactic.GCongr import Mathlib.Tactic...
ShortExact.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.Algebra.Homology.ShortComplex.Exact import Mathlib.CategoryTheory.Preadditive.Injective.Basic /-! # Short exact short complexes A short complex `S : ShortCompl...
Finset.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.Card import Mathlib.Algebra.Order.BigOperators.Group.Multiset import Mathlib.Algebra.Order.Group.Nat import Mathlib.Data.Multiset.OrderedM...
Caratheodory.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.Analysis.Convex.Combination import Mathlib.LinearAlgebra.AffineSpace.Independent import Mathlib.Tactic.FieldSimp /-! # Carathéodory's conv...
SchurComplement.lean
/- Copyright (c) 2022 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, Eric Wieser, Jeremy Avigad, Johan Commelin -/ import Mathlib.Data.Matrix.Invertible import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.Linear...
Cone.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kim Morrison, Artie Khovanov -/ import Mathlib.Algebra.Order.Monoid.Submonoid import Mathlib.Algebra.Order.Group.Unbundled.Basic /-! # Construct ordered groups from gr...
Basic.lean
/- Copyright (c) 2021 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.CategoryTheory.NatIso /-! # Bicategories In this file we define typeclass for bicategories. A bicategory `B` consists of * objects `a : B`, * 1-morphisms ...
Sequences.lean
/- Copyright (c) 2018 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Patrick Massot, Yury Kudryashov -/ import Mathlib.Topology.Sequences import Mathlib.Topology.MetricSpace.Bounded /-! # Sequential compacts in metric spaces In t...
LowDegree.lean
/- Copyright (c) 2023 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston, Joël Riou -/ import Mathlib.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic import Mathlib.Represent...
Pointed.lean
/- Copyright (c) 2023 Apurva Nakade. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Apurva Nakade -/ import Mathlib.Algebra.Order.Nonneg.Module import Mathlib.Geometry.Convex.Cone.Basic /-! # Pointed cones A *pointed cone* is defined to be a submodule of a module whe...
Quotient.lean
/- Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, Jujian Zhang -/ import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.LinearAlgebra.TensorProduct.Tower import Mathlib.RingTheory.Ideal.Maps import M...
Basic.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.Analysis.SpecialFunctions.Log.NegMulLog import Mathlib.Analysis.SpecialFunctions.NonIntegrable import Mathlib.Analysis.SpecialFunctions.Pow.Deriv...
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.CategoryTheory.Comma.Arrow import Mathlib.Order.CompleteBooleanAlgebra /-! # Properties of morphisms We provide the basic framework for talking about prope...
Subgroup.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.Subgroup.Pointwise import Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise /-! # Subgroups in a group with zero -/ assert_not_exists Ring o...
Quotient.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, Yury Kudryashov -/ import Mathlib.GroupTheory.GroupAction.Quotient import Mathlib.GroupTheory.QuotientGroup.Defs import Mathlib.Topology...