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cyclotomic.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 div choice fintype tuple finfun bigop prime. From mat...
ProbabilityMeasure.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.MeasureTheory.Measure.FiniteMeasure import Mathlib.MeasureTheory.Integral.Average import Mathlib.MeasureTheory.Measure.Prod /-! # Probability measures Th...
UnorderedInterval.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou -/ import Mathlib.Data.Set.Order import Mathlib.Order.Bounds.Basic import Mathlib.Order.Interval.Set.Image import Mathlib.Order.Interval.Set.LinearOrder import Mathlib.Tac...
SignedDist.lean
/- Copyright (c) 2025 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Geometry.Euclidean.Projection import Mathlib.LinearAlgebra.AffineSpace.ContinuousAffineEquiv import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional imp...
Ackermann.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Computability.PartrecCode import Mathlib.Tactic.Ring import Mathlib.Tactic.Linarith /-! # Ackermann function In this file, we...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
Regular.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.Order.GaloisConnection.Basic /-! # Heyting regular elements This file defines Heyting regular elements, elements of a Heyting algebra that are their own ...
Group.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.GroupWithZero.Action.Basic import Mathlib.Algebra.Ring.Action.Basic import Mathlib.Algebra.Ring.Equiv /-! # If a group acts multiplicatively on a semiri...
PiNat.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.Algebra.MetricSpace.Lipschitz import Mathlib.Topology.MetricSpace.HausdorffDistance /-! # Topological study of spaces `Π (n : ℕ), E n` ...
ssrmatching.v
From Corelib Require Export ssrmatching.
OrzechProperty.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.Algebra.Module.TransferInstance import Mathlib.RingTheory.Finiteness.Cardinality /-! # Orzech property of rings In this file we define the following property of rin...
DropRight.lean
/- Copyright (c) 2022 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Data.List.Induction import Mathlib.Data.List.TakeWhile /-! # Dropping or taking from lists on the right Taking or removing element from the tail e...
OfCompactT2.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.Separation.Regular import Mathlib.Topology.UniformSpace.Defs /-! # Compact separated uniform spaces ## Main statement * `u...
mxalgebra.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 b...
Basic.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Jakob von Raumer -/ import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Algebra.Group.Action.Units import Mathlib.Algebra.Module.End import Mathlib.CategoryTheory.Endomo...
AnalyticManifold.lean
/- Copyright (c) 2023 Michael Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Lee, Geoffrey Irving -/ import Mathlib.Analysis.Analytic.Constructions import Mathlib.Geometry.Manifold.IsManifold.Basic /-! # Analytic manifolds (possibly with boundary or corne...
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, Alexander Bentkamp -/ import Mathlib.LinearAlgebra.Basis.Defs import Mathlib.LinearAlgebra.LinearIndependent.Basic import Mathlib.LinearAlgebra.Span.Bas...
numdomain.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...
Prime.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, Mario Carneiro -/ import Mathlib.Tactic.NormNum.Basic import Mathlib.Data.Nat.Prime.Basic /-! # `norm_num` extensions on natural numbers This...
Convex.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis -/ import Mathlib.Analysis.Convex.Uniform import Mathlib.Analysis.InnerProductSpace.Basic /-! # Convexity properties of inner product...
EvenFunction.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.Algebra.Group.Action.Pi import Mathlib.Algebra.NoZeroSMulDivisors.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Even and odd func...
MorphismProperty.lean
/- Copyright (c) 2024 Christian Merten, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Andrew Yang -/ import Mathlib.AlgebraicGeometry.OpenImmersion import Mathlib.CategoryTheory.MorphismProperty.Limits /-! # Covers of schemes This file...
all_order.v
Require Export order.
Basic.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.BigOperators.Group.Finset.Sigma import Mathlib.Algebra.BigOperators.Pi import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Algebra.Group.Submo...
Finsupp.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.Equiv.Defs import Mathlib.Algebra.Group.Pi.Lemmas import Mathlib.Data.Finset.Max import Mathlib.Data.Finsupp.Single import ...
FinitePresentation.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.AlgebraicGeometry.Morphisms.QuasiSeparated import Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties import Mathlib.AlgebraicGeometry.Morphisms....
Coproduct.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.EffectiveEpi.Basic import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback import Mathlib.Tactic.ApplyFun /-! # Effective ...
Shift.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.ObjectProperty.ClosedUnderIsomorphisms import Mathlib.CategoryTheory.Shift.Basic /-! # Properties of objects on categories equipped with shift G...
Basic.lean
/- Copyright (c) 2021 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.Normed.Module.Basic import Mathlib.MeasureTheory.Function.SimpleFuncDense /-! # Strongly measurable and finitely strongly meas...
Balanced.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Robin Carlier -/ import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic import Mathlib.CategoryTheory.Balanced import Mathlib.CategoryTheory.Functor.EpiMono /-! # Balanc...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
ssrnum.v
From mathcomp Require Export orderedzmod. From mathcomp Require Export numdomain. From mathcomp Require Export numfield. Module Num. Export orderedzmod.Num. Export numdomain.Num. Export numfield.Num. Module Theory. Export orderedzmod.Num.Theory. Export numdomain.Num.Theory. Export numfield.Num.Theory. End Theory. Mo...
Root.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.Order.Floor.Div import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Data.Nat.Factorization.Defs /-! # Roots of natural numbers, rounded up and do...
CommDiag.lean
/- Copyright (c) 2022 Wojciech Nawrocki. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wojciech Nawrocki -/ import ProofWidgets.Component.PenroseDiagram import ProofWidgets.Presentation.Expr import Mathlib.CategoryTheory.Category.Basic /-! This module defines tactic/...
Conformal.lean
/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang, Stefan Kebekus -/ import Mathlib.Analysis.Calculus.Conformal.NormedSpace import Mathlib.Analysis.Calculus.Deriv.Basic import Mathlib.Analysis.Calculus.FDeriv.Equiv import M...
Basic.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Semiquot import Mathlib.Data.Nat.Size import Batteries.Data.Rat.Basic import Mathlib.Data.PNat.Defs import Mathlib.Data.Rat.Init import Mathlib.Al...
Multiset.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.Data.DFinsupp.BigOperators import Mathlib.Data.DFinsupp.Order /-! # Equivalence between `Multiset` and `ℕ`-valued finitely supported functions This defines...
SumProd.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.Module.Equiv.Defs import Mathlib.Algebra.Module.Pi import Mathlib.Algebra.Module.Prod import Mathlib.Data.Finsupp.SMul /-! # Finsupps and sum/...
Count.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 Batteries.Data.List.Perm import Mathlib.Tactic.Common /-! # Counting in lists This fi...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
Basic.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.LinearAlgebra.LinearIndependent.Basic import Mathlib.Data.Set.Card /...
Action.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Data.ENNReal.Operations /-! # Scalar multiplication on `ℝ≥0∞`. This file defines basic scalar actions on extended nonnegative reals,...
Basic.lean
/- Copyright (c) 2019 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yury Kudryashov, Sébastien Gouëzel, Chris Hughes, Antoine Chambert-Loir -/ import Mathlib.Data.Fin.Rev import Mathlib.Data.Nat.Find import Mathlib.Order.Fin.Basic ...
BorelCantelli.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Probability.Martingale.BorelCantelli import Mathlib.Probability.ConditionalExpectation import Mathlib.Probability.Independence.Basic /-! # The second Borel...
NatAntidiagonal.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Data.List.Nodup /-! # Antidiagonals in ℕ × ℕ as lists This file defines the antidiagonals of ℕ × ℕ as lists: the `n`-th antidiagonal is the list of p...
Induced.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.ENNReal.Action import Mathlib.MeasureTheory.MeasurableSpace.Constructions import Mathlib.MeasureTheory.OuterMeasure.Caratheodory ...
FilteredColimitCommutesProduct.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.FunctorCategory.Filtered import Mathlib.CategoryTheory.Limits.Types.Filtered import Mathlib.CategoryTheory.Limits.Types.Shapes impo...
pgroup.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 prime fingroup morphism. From mat...
Ring.lean
/- Copyright (c) 2022 Alex J. Best, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best, Yaël Dillies -/ import Mathlib.Algebra.Order.Hom.MonoidWithZero import Mathlib.Algebra.Ring.Equiv /-! # Ordered ring homomorphisms Homomorphisms between ord...
ComposableArrows.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.Group.Nat.Defs import Mathlib.CategoryTheory.Category.Preorder import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.Functor.Const import M...
Rat.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.Rat import Mathlib.Topology.Algebra.ConstMulAction import Mathlib.Topology.Algebra.Monoid.Defs /-! # Topological (sub)algebras over `Rat` ...
extraspecial.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 choice fintype bigop finset prime binomial. From mathc...
OldObtain.lean
/- Copyright (c) 2024 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Lean.Elab.Command -- Import this linter explicitly to ensure that -- this file has a valid copyright header and module docstring. import Mathlib.Tactic.Li...
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...
FinallySmall.lean
/- Copyright (c) 2023 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.Logic.Small.Set import Mathlib.CategoryTheory.Filtered.Final /-! # Finally small categories A category given by `(J : Type u) [Category.{v} J]` is `w`-...
tuple.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. From mathcomp Require Import seq choice fintype path. S...
Defs.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Combinatorics.Additive.FreimanHom /-! # Corners This file defines corners, namely triples of the form `(x, y), (x, y + d), (x + d, y)`, and the property ...
Pi.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.Algebra.Algebra.Spectrum.Quasispectrum import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Algebra.Prod import Mathlib.Algebra.Group.Pi.Units ...
Basic.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.CollectFacts /-! # Graphs for the `order` tactic This module defines the `Graph` structure and basic operations on it. The `order` t...
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...
Basic.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison, Adam Topaz -/ import Mathlib.AlgebraicTopology.SimplicialObject.Basic import Mathlib.CategoryTheory.Limits.Types.Colimits import Mathlib.CategoryTheory.Yone...
polyXY.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 seq. From mathcomp Require Import fintype tuple fi...
LiftingProperty.lean
/- Copyright (c) 2024 Jack McKoen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jack McKoen, Joël Riou -/ import Mathlib.CategoryTheory.MorphismProperty.Limits import Mathlib.CategoryTheory.MorphismProperty.Retract import Mathlib.CategoryTheory.LiftingProperties.Limi...
Algebra.lean
/- Copyright (c) 2021 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Eugster, Eric Wieser -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.FreeAlgebra import Mathlib.RingTheory.Localization.FractionRing import Mathlib.RingTheory.SimpleRing.B...
Basic.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Johan Commelin, Patrick Massot -/ import Mathlib.Algebra.Order.Hom.Monoid import Mathlib.Algebra.Order.Ring.Basic import Mathlib.RingTheory.Ideal.Maps import Mathlib.Tac...
Basic.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jens Wagemaker -/ import Mathlib.Algebra.Ring.Associated import Mathlib.Algebra.Ring.Regular /-! # Monoids with normalization functions, `gcd`, and `lcm` This file de...
Down.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Lattice.Fold /-! # Down-compressions This file defines down-compression. Down-compressing `𝒜 : Finset (Fins...
GrowsPolynomially.lean
/- Copyright (c) 2023 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent import Mathlib.Analysis.SpecialFunctions.Pow.Real import Mathlib.Algebra.Order.ToIntervalMod import Mathli...
Field.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.RingTheory.SimpleRing.Basic import Mathlib.Algebra.Algebra.Defs import Mathlib.Data.Rat.Cast.Defs /-! # Facts about `algebraMap` when the coeff...
Barrelled.lean
/- Copyright (c) 2023 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Topology.Semicontinuous import Mathlib.Topology.Baire.Lemmas /-! # Barrelled spaces and the Ba...
Induction.lean
/- Copyright (c) 2021 Stuart Presnell. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stuart Presnell -/ import Mathlib.Data.Nat.Factorization.Defs /-! # Induction principles involving factorizations -/ open Nat Finset List Finsupp namespace Nat variable {a b m n p ...
Monotonicity.lean
/- Copyright (c) 2019 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Data.List.Defs import Mathlib.Tactic.Monotonicity import Mathlib.Tactic.NormNum private axiom test_sorry : ∀ {α}, α o...
Small.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.Comma.StructuredArrow.Basic import Mathlib.CategoryTheory.EssentiallySmall import Mathlib.Logic.Small.Set /-! # Small sets in the categor...
Equivalence.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tim Baumann, Stephen Morgan, Kim Morrison, Floris van Doorn -/ import Mathlib.CategoryTheory.Functor.FullyFaithful import Mathlib.CategoryTheory.ObjectProperty.FullSubcategory import Mat...
SumTwoSquares.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Michael Stoll -/ import Mathlib.Data.Nat.Squarefree import Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity import Mathlib.NumberTheory.Padics.PadicVal.Basic /-! # Sums of...
SpanRank.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wanyi He, Jiedong Jiang, Xuchun Li, Christian Merten, Jingting Wang, Andrew Yang -/ import Mathlib.Data.Set.Card import Mathlib.Data.ENat.Lattice import Mathlib.RingTheory.Finiteness.Defs...
Finite.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Preserves.Basic import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts /-! # Preservation of finite (co)limits. These functors ar...
Ring.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.Algebra.Order.Group.Unbundled.Abs import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Algebra.Order.Sub.Basic import Mathlib.Data.Nat.Cast.Order.Basic...
Basic.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Kexing Ying -/ import Mathlib.Probability.Notation import Mathlib.Probability.Process.Stopping /-! # Martingales A family of functions `f : ι → Ω → E` is a martingale wit...
InfiniteSum.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Analysis.Normed.Group.InfiniteSum import Mathlib.Topology.Algebra.InfiniteSum.Real import Mathlib.Analysis.Normed.Ring.Lemmas /-! # Multiplying tw...
Equivalence.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.DenseSubsite.InducedTopology import Mathlib.CategoryTheory.Sites.LocallyBijective import Mathlib.CategoryTheory.Sites.Preserve...
Basic.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Felix Weilacher -/ import Mathlib.MeasureTheory.Constructions.BorelSpace.Metric import Mathlib.MeasureTheory.Constructions.BorelSpace.Order import Mathlib.Topolog...
Basic.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.Analytic.ConvergenceRadius import Mathlib.Topology.Algebra.InfiniteSum.Module /-! # Analytic functions A function is ...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
Arsinh.lean
/- Copyright (c) 2020 James Arthur. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: James Arthur, Chris Hughes, Shing Tak Lam -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv import Mathlib.Analysis.SpecialFunctions.Log.Basic /-! # Inverse of the sinh fu...
LpOrder.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.Normed.Order.Lattice import Mathlib.MeasureTheory.Function.ConvergenceInMeasure import Mathlib.MeasureTheory.Function.LpSpace.Basic /-! # Order r...
NoZeroDivisors.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.Data.Finsupp.WellFounded import Mathlib.RingTheory.MvPowerSeries.LexOrder import Mathlib.RingTheory.MvPowerSeries.Order /-! # ZeroDivis...
Alexandrov.lean
/- Copyright (c) 2025 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Justin Curry, Adam Topaz -/ import Mathlib.Combinatorics.Quiver.ReflQuiver import Mathlib.Order.CompletePartialOrder import Mathlib.Topology.Order.UpperLowerSetTopology import Mathlib.Topo...
CompactlyGenerated.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.Topology.Compactness.CompactlyGeneratedSpace import Mathlib.CategoryTheory.Elementwise /-! # Compactly generated topological spaces This file def...
Walk.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.DeleteEdges /-! # Walk In a simple graph, a *walk* is a finite sequence of adjacent vertices, and can be thought of equally well...
Real.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.Complex import Qq /-! # P...
Lemmas.lean
/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Data.Nat.Bitwise import Mathlib.Data.Nat.Cast.Order.Basic import Math...
Ring.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Junyan Xu, Jujian Zhang -/ import Mathlib.Algebra.Field.Equiv import Mathlib.RingTheory.Artinian.Module import Mathlib.RingTheory.Localization.Defs import Mathlib.RingTheor...
gseries.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 bigop finset fingroup morphism. From mathcomp...
RetractArgument.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.MorphismProperty.Factorization import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty /-! # The retract argument Let `W₁` and `W₂` be cl...
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.Defs import Mathlib.Algebra.Field.Subfield.Defs import Mathlib.Algebra.GroupWithZero.Units.Lemmas import Mathlib.Algebra.Ring.Subring.Basic ...
Equivalence.lean
/- Copyright (c) 2023 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Nikolas Kuhn, Dagur Asgeirsson -/ import Mathlib.Topology.Category.Profinite.EffectiveEpi import Mathlib.Topology.Category.Stonean.EffectiveEpi import Mathlib.Condensed.Basic i...
Rayleigh.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Frédéric Dupuis -/ import Mathlib.Analysis.InnerProductSpace.Calculus import Mathlib.Analysis.InnerProductSpace.Dual import Mathlib.Analysis.InnerProductSpace.Adjoint...
EmbeddingReal.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Data.Real.Cardinality import Mathlib.MeasureTheory.Constructions.Polish.Basic /-! # A Polish Borel space is measurably equivalent to a set of reals -/ op...
BoundedContinuousFunction.lean
/- Copyright (c) 2023 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.MeasureTheory.Integral.Bochner.Basic import Mathlib.Topology.ContinuousMap.Bounded.Normed import Mathlib.Topology.Algebra.Order.LiminfLimsup /-! # Integra...