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HasConicalLimits.lean
/- Copyright (c) 2025 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Eugster, Dagur Asgeirsson, Emily Riehl -/ import Mathlib.CategoryTheory.Enriched.Ordinary.Basic import Mathlib.CategoryTheory.Limits.Final /-! # Existence of conical limits This fil...
CubingACube.lean
/- Copyright (c) 2019 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Algebra.Order.Interval.Set.Group import Mathlib.Data.Real.Basic import Mathlib.Data.Set.Finite.Lemmas import Mathlib.Order.Interval.Set.Disjoint /...
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...
DegLex.lean
/- Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.RingTheory.MvPolynomial.MonomialOrder import Mathlib.Data.Finsupp.MonomialOrder.DegLex /-! # Some lemmas about the deglex monomial order...
DenselyOrdered.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Order.Interval.Finset.Basic /-! # Linear locally finite orders are densely ordered iff they are trivial ## Main results * `LocallyFiniteOrder.dense...
Curry.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Data.Fintype.Sort import Mathlib.LinearAlgebra.Multilinear.Basic /-! # Currying of multilinear maps We register isomorphisms corresponding to cu...
VectorField.lean
/- Copyright (c) 2024 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.Symmetric /-! # Vector fields in vector spaces We study functions of the form `V : E → E` on a vector space, thinking ...
Fold.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Sean Leather -/ import Mathlib.Algebra.Group.Opposite import Mathlib.Algebra.FreeMonoid.Basic import Mathlib.Control.Traversable.Instances import Mathlib.Control.Traversable....
ExtendFrom.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Anatole Dedecker -/ import Mathlib.Topology.Separation.Regular /-! # Extending a function from a subset The main definition of this file is `extendFrom A f` where `...
ValuedCSP.lean
import Mathlib.Algebra.Order.AbsoluteValue.Basic import Mathlib.Algebra.Order.Ring.Rat import Mathlib.Combinatorics.Optimization.ValuedCSP import Mathlib.Data.Fin.Tuple.Curry import Mathlib.Data.Fin.VecNotation import Mathlib.Tactic.Positivity /-! # VCSP examples This file shows two simple examples of General-Valued ...
Subobject.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.Subobject.Limits import Mathlib.CategoryTheory.Abelian.Basic /-! # Equivalence between subobjects and quotients in an abelian category -...
Pointwise.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Star.Basic import Mathlib.Data.Set.Finite.Basic import Mathlib.Data.Set.Lattice.Image import Mathlib.Algebra.Group.Pointwise.Set.Basic /-! # Poi...
ssrmatching.v
From Corelib Require Export ssrmatching.
CircleMap.lean
/- Copyright (c) 2025 Fabrizio Barroero. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Fabrizio Barroero, Christopher Hoskin -/ import Mathlib.Analysis.SpecialFunctions.Complex.Log import Mathlib.Order.Interval.Set.Defs /-! # circleMap This file def...
Log.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Complex.Arg import Mathlib.Analysis.SpecialFunctions.Log.Basic...
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...
Substructures.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Gabin Kolly -/ import Mathlib.Data.Fintype.Order import Mathlib.Order.Closure import Mathlib.ModelTheory.Semantics import Mathlib.ModelTheory.Encoding /-! # First-Orde...
Sum.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Faithful /-! # Sum instances for additive and multiplicative actions This file defines instances for additive and multiplicative act...
Ext.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kim Morrison -/ import Mathlib.Algebra.Group.Finsupp import Mathlib.Algebra.Group.Submonoid.Basic import Mathlib.Algebra.Group.TypeTags.Hom /-! # Extensionality for ma...
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.CategoryTheory.Limits.Shapes.Pullback.Square import Mathlib.CategoryTheory.Limits.Yoneda import Mathlib.CategoryTheory.Limits.Preserves.Ulift /-! # Preservation...
GCD.lean
/- Copyright (c) 2018 Guy Leroy. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.GroupWithZero.Semiconj import Mathlib.Algebra.Group.Commute.Units import Mathlib.Data.Set.Operati...
Real.lean
/- ! This file was ported from Lean 3 source file `test/real.lean` ! leanprover-community/mathlib commit d7943885503965d07ccaeb390d65fbc3f45962e6 ! Please do not edit these lines, except to modify the commit id ! if you have ported upstream changes. -/ import Mathlib.Data.Real.Basic private axiom test_sorry : ∀ {α}, α...
ScottContinuity.lean
/- Copyright (c) 2022 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Order.Bounds.Basic /-! # Scott continuity A function `f : α → β` between preorders is Scott continuous (referring to Dana Scott) if it distri...
Regular.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.Tactic.StacksAttribute import Mathlib.Topology.Compactness.Lindelof import Mathlib.Topology.Separation.Hausdorff import Mathlib.Topolog...
PWO.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.Order.Preorder.Finsupp import Mathlib.Order.WellFoundedSet /-! # Partial well ordering on finsupps This file contains the fact that finitely supported fu...
eqtype.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. (********************************************************************...
TensorProduct.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.LinearAlgebra.BilinearForm.Hom import Mathlib.LinearAlgebra.Dual.Lemmas import Mathlib.LinearAlgebra.TensorProduct.Tower import Mathlib.RingTheory.TensorProd...
PerfectNumbers.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.NumberTheory.ArithmeticFunction import Mathlib.NumberTheory.LucasLehmer import Mathlib.Tactic.NormNum.Prime /-! # Perfect Numbers This file proves Th...
Bernoulli.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kevin Buzzard -/ import Mathlib.Algebra.BigOperators.Field import Mathlib.RingTheory.PowerSeries.Inverse import Mathlib.RingTheory.PowerSeries.WellKnown /-! # Bernoull...
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. (**********************...
Prod.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.MeasureTheory.MeasurableSpace.Embedding import Mathlib.MeasureTheory.PiSystem /-! # The product sigma algebra This file talks about the measurabi...
Units.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.Action.Units import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.GroupWithZero.Units.Basic /-! # Multiplicative actions wi...
Elements.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.Elements import Mathlib.CategoryTheory.Limits.Types.Limits import Mathlib.CategoryTheory.Limits.Creates import Mathlib.CategoryTheory.Limi...
TopComparison.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.Condensed.Light.Basic import Mathlib.Condensed.TopComparison /-! # The functor from topological spaces to light condensed sets We define the fun...
IsConnected.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Jakob von Raumer -/ import Mathlib.Data.List.Chain import Mathlib.CategoryTheory.PUnit import Mathlib.CategoryTheory.Groupoid import Mathlib.CategoryTheory.Category.ULift ...
Prod.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot, Eric Wieser -/ import Mathlib.Algebra.GroupWithZero.Action.Prod import Mathlib.Algebra.Module.Defs /-! # Prod instances for module and multiplicative actions...
HurwitzZetaValues.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.NumberTheory.ZetaValues import Mathlib.NumberTheory.LSeries.RiemannZeta /-! # Special values of Hurwitz and Riemann zeta functions This file gives t...
Curry.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.Alternating.Basic import Mathlib.LinearAlgebra.Multilinear.Curry /-! # Currying alternating forms In this file we define `AlternatingMap.curr...
ZModChar.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Data.Int.Range import Mathlib.Data.ZMod.Basic import Mathlib.NumberTheory.MulChar.Basic /-! # Quadratic characters on ℤ/nℤ This file defines some quadr...
SimpIntro.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 Lean.Elab.Tactic.Simp import Mathlib.Init /-! # `simp_intro` tactic -/ namespace Mathlib.Tactic open Lean Meta Elab Tactic /-- Main loop of the `simp_intro`...
test_order_conv.v
From mathcomp Require Import all_boot all_order. Import Order.Theory. Section dual_of_dual. Context (disp : Order.disp_t). Let eq_dual_dual_preorderType (T : preorderType disp) : Order.Preorder.on T = Order.Preorder.on T^d^d := erefl. Let eq_dual_dual_porderType (T : porderType disp) : Order.POrder.on T = Order....
Language.lean
/- Copyright (c) 2020 Fox Thomson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fox Thomson, Martin Dvorak -/ import Mathlib.Algebra.Order.Kleene import Mathlib.Algebra.Ring.Hom.Defs import Mathlib.Data.Set.Lattice import Mathlib.Tactic.DeriveFintype /-! # Languages...
Basic.lean
/- Copyright (c) 2019 Neil Strickland. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Neil Strickland, Yury Kudryashov -/ import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.Semiconj.Basic /-! # Additional lemmas about commuting pairs of elements in...
intdiv.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 div choice fintype...
RCLike.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.RCLike.Lemmas import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex /-! # Measurability of the basic `RCLike` functions -/ nonco...
ContinuousFunctions.lean
/- Copyright (c) 2020 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace import Mathlib.MeasureTheory.Function.LpSpace.Basic import Mathlib.MeasureTheory.Measure.O...
Instances.lean
/- Copyright (c) 2024. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: euprunin -/ import Mathlib.Algebra.Ring.Defs import Mathlib.RingTheory.NonUnitalSubring.Defs import Mathlib.RingTheory.TwoSidedIdeal.Basic /-! # Additional instances for two sided ideals. -/ instanc...
Quandle.lean
/- Copyright (c) 2020 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Algebra.Group.End import Mathlib.Data.ZMod.Defs import Mathlib.Tactic.Ring /-! # Racks and Quandles This file defines racks and quandles, algebraic structu...
Bounds.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable /-! # Asymptotic bounds for Jacobi theta functions The goal of this file is to establish some tech...
HSpaces.lean
/- Copyright (c) 2022 Filippo A. E. Nuccio Mortarino Majno di Capriglio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Filippo A. E. Nuccio, Junyan Xu -/ import Mathlib.Topology.CompactOpen import Mathlib.Topology.Homotopy.Basic import Mathlib.Topology.Path /-! # H-s...
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...
UniformFilterBasis.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Topology.Algebra.FilterBasis import Mathlib.Topology.Algebra.IsUniformGroup.Defs /-! # Uniform properties of neighborhood bases in topological algebra...
Use.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Gabriel Ebner, Kyle Miller -/ import Mathlib.Tactic.WithoutCDot import Lean.Meta.Tactic.Util import Lean.Elab.Tactic.Basic /-! # The `use` tactic The `use` and `use!`...
MoveAdd.lean
import Mathlib.Tactic.MoveAdd import Mathlib.Algebra.Ring.Nat import Mathlib.Data.Nat.Basic universe u variable {R : Type u} section add section semigroup variable [AddCommSemigroup R] {a b c d e f g h : R} example (h : a + b + c = d) : b + (a + c) = d := by move_add [← a] assumption example : let k := c + (a ...
Equicontinuity.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.Algebra.UniformConvergence import Mathlib.Topology.UniformSpace.Equicontinuity /-! # Algebra-related equicontinuity criterions -/ open ...
FactorisationProperties.lean
/- Copyright (c) 2024 Colin Jones. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Colin Jones -/ import Mathlib.Algebra.Ring.GeomSum import Mathlib.NumberTheory.Divisors import Mathlib.Tactic.FinCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.NormNum.Prime ...
Basic.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.Field.IsField import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Nat.Choose.Sum import Mathlib.LinearAlgebra.Finsupp.L...
SDiff.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.Lattice.Lemmas /-! # Difference of finite sets ## Main declarations * `Finset.instS...
Complex.lean
/- Copyright (c) 2025 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.SpectralNorm import Mathlib.NumberTheory.Padics.PadicNumbers import Mathlib.Topology.Algebra....
LintStyle.lean
import Mathlib.Tactic.Linter.Style import Mathlib.Order.SetNotation /-! Tests for all the style linters. -/ /-! Tests for the `setOption` linter -/ section setOption set_option linter.style.setOption true -- All types of options are supported: boolean, numeric and string-valued. -- On the top level, i.e. as commands...
Liouville.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.Analysis.Complex.CauchyIntegral import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathlib.Analysis.Normed.Module.Completion /-! # Liouville's ...
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...
bigop.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 fintype tuple ...
Shadow.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies -/ import Mathlib.Data.Finset.Grade import Mathlib.Data.Finset.Sups import Mathlib.Logic.Function.Iterate /-! # Shadows This file defines shad...
Module.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Frédéric Dupuis -/ import Mathlib.Algebra.Star.SelfAdjoint import Mathlib.Algebra.Module.Basic import Mathlib.Algebra.Module.Equiv.Defs import Mathlib.Algebra.Module.LinearMa...
PresheafedSpace.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.Adjunction.FullyFaithful import Mathlib.CategoryTheory.Elementwise import Mathlib.Topology.Sheaves.Presheaf /-! # Presheafed spaces Introd...
Vieta.lean
/- Copyright (c) 2020 Hanting Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Hanting Zhang -/ import Mathlib.Algebra.Polynomial.Splits import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs /-! # Vieta's Formula The main result is `Multiset.prod_X_add_C_eq_sum_...
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 -/ import Mathlib.Order.Max import Mathlib.Order.ULift import Mathlib.Tactic.Push import Mathlib.Tactic.Finiteness.Attr import Mathlib.Util.AssertExists /-! # ⊤ and ⊥, ...
HomologicalComplex.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.Algebra.Homology.Additive import Mathlib.CategoryTheory.Idempotents.Karoubi /-! # Idempotent completeness and homological complexes This file contains simplifi...
Finite.lean
/- Copyright (c) 2025 Floris van Doorn and Hannah Scholz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Hannah Scholz -/ import Mathlib.Topology.CWComplex.Classical.Basic /-! # Finiteness notions on CW complexes In this file we define what it mean...
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...
ZPow.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.Deriv.Pow import Mathlib.Analysis.Calculus.Deriv.Inv import Mathlib.Analysis.Calculus.Deriv.Shift /-! # Deriv...
ENat.lean
/- Copyright (c) 2022 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.ENat.Basic import Mathlib.Topology.Instances.Discrete import Mathlib.Order.Interval.Set.WithBotTop import Mathlib.Order.Filter.Pointwise import Mathli...
Polynomial.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Degree.Lemmas import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib....
Sqrt.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.Ring.Abs import Mathlib.Algebra.Order.Ring.Unbundled.Rat import Mathlib.Data.Rat.Lemmas import Mathlib.Data.Int.Sqrt /-!...
Resolution.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Joël Riou -/ import Mathlib.Algebra.Homology.QuasiIso import Mathlib.Algebra.Homology.SingleHomology import Mathlib.CategoryTheory.Preadditive.Projective.Preserves /-! # P...
Delaborators.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Init import Mathlib.Util.PPOptions import Lean.PrettyPrinter.Delaborator.Builtins /-! # Pi type notation Provides the `Π x : α, β x` notation as an alterna...
UniversallyClosed.lean
/- Copyright (c) 2023 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Etienne Marion -/ import Mathlib.Topology.Maps.Proper.Basic import Mathlib.Topology.Compactification.StoneCech /-! # A map is proper iff it is continuous and unive...
Equiv.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Topology.Algebra.Module.LinearMapPiProd /-! # Continuous linear...
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...
DershowitzManna.lean
/- Copyright (c) 2024 Haitian Wang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Haitian Wang, Malvin Gattinger -/ import Mathlib.Algebra.Order.Sub.Unbundled.Basic import Mathlib.Data.Multiset.OrderedMonoid /-! # Dershowitz-Manna ordering In this file we define the...
Complex.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.Complex.Basic import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic /-! # Equip `ℂ` with the Borel sigma-algebra -/ noncomputable s...
Init.lean
/- Copyright (c) 2023 Jannis Limperg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jannis Limperg -/ import Mathlib.Init import Aesop /-! # Category Theory Rule Set This module defines the `CategoryTheory` Aesop rule set which is used by the `aesop_cat` tactic. Ae...
Basic.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.Tactic.Monotonicity.Attr import Mathlib.Tactic.SetLike import Mathlib.Data.Set.Basic /-! # Typeclass for types with a set-like extensionality property The ...
Quotient.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Eric Wieser -/ import Mathlib.GroupTheory.OrderOfElement import Mathlib.RingTheory.Ideal.Maps import Mathlib.RingTheory.Ideal.Nonunits import Mathlib.RingTheory.Ideal.Quotient.De...
Basic.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Algebra.Subalgebra.Tower import Mathlib.Algebra.Field.IsField import Mathlib.Algebra.Field.Subfield.Basic import Mathlib.Algebra.Polynomial.AlgebraMa...
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...
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...
JacobiSymbol.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll, Thomas Zhu, Mario Carneiro -/ import Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity /-! # The Jacobi Symbol We define the Jacobi symbol and prove its main pro...
Support.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Exact import Mathlib.RingTheory.Ideal.Colon import Mathlib.RingTheory.Localization.Finiteness import Mathlib.RingTheory.Nakayama import Mathlib.RingT...
UnitTrinomial.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Algebra.Polynomial.UnitTrinomial import Mathlib.Analysis.Complex.Polynomial.Basic /-! # Irreducibility of unit trinomials ## TODO Develop more the...
Ring.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.Algebra.Order.Ring.Defs import Mathlib.Order.Filter.AtTopBot.Group /-! # Convergence to ±infinity in ordered rings -/ variable {α β : Type*} names...
Equalizers.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.Limits.Indization.FilteredColimits import Mathlib.CategoryTheory.Limits.FullSubcategory import Mathlib.CategoryTheory.Limits.Indization.Pa...
Congr.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.FDeriv.Basic /-! # The Fréchet derivative: congruence properties Lemmas about congruence properti...
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, Jeremy Avigad, Yury Kudryashov -/ import Mathlib.Order.Filter.Ultrafilter.Defs import Mathlib.Order.Filter.Cofinite import Mathlib.Order.ZornAtoms /-! # Ultrafilters ...
Presheaf.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.Generator.Basic import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic /-! # Generators in the category of presheaves In this file, we show...
AddTorsor.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Yury Kudryashov -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Analysis.Normed.Module.Basic import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.LinearA...
FreeAlgebra.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.FreeAlgebra import Mathlib.LinearAlgebra.Basis.Cardinality import Mathlib.LinearAlgebra.Dimension.StrongRankCondition import Mathlib.LinearAlgebra.Di...
Pi.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot -/ import Mathlib.Algebra.Notation.Lemmas import Mathlib.Algebra.Order.Monoid.Canonical.Defs import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Algebra.Ring...
GradedModule.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.RingTheory.GradedAlgebra.Basic import Mathlib.Algebra.GradedMulAction import Mathlib.Algebra.DirectSum.Decomposition import Mathlib.Algebra.Module.BigOpera...