filename stringlengths 5 42 | content stringlengths 15 319k |
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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... |
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